Between Leibniz, Newton, and Kant: Philosophy and Science in the Eighteenth Century (Boston Studies in the Philosophy and History of Science, 341) [2 ed.] 3031343395, 9783031343391

Table of contents :
Preface to the 2nd Edition
Introduction
Contents
Part I: Seismic Vibrations in Metaphysics
Chapter 1: Disciplinary Transformations in the Age of Newton: The Case of Metaphysics
1.1 Introduction
1.2 Speculative Philosophy in the Peripatetic Tradition
1.3 Newton and Leibniz
1.4 Locke and Berkeley
1.5 Metaphysics in the Public Domain in Mid-century Britain and Germany
1.6 Hume
1.7 Metaphysics and the Physicians: William Cullen
1.8 The Kantian Turn
References
Part II: Metaphysics and the Analytical Method
Chapter 2: Leibniz’ Concept of Possible Worlds and the Analysis of Motion in Eighteenth-Century Physics
2.1 The Year 1686
2.2 Individual Substance and World
2.3 Causality and Finality in Leibniz’ Physics
2.4 1732: The Birth-Certificate of Maupertuis’ Ideas
2.5 The Least Action Quantity Principle
2.6 The Essay on Cosmology
2.7 A Final View to Euler
2.8 A Priority Problem and Its Recent Discussion
2.9 Resume
References
Chapter 3: The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s Philosophy
3.1 Abstraction
3.2 Restoration
3.3 Properties
3.4 Simplicity
3.5 Winds
3.6 Essences
3.7 Impenetrability
3.8 Necessity
3.9 Springs and Other Gaps
3.10 Well-Known Facts About Forces
3.11 Attraction as a Last Recourse
3.12 Fluids
3.13 Fluids as Systems: D’Alembert’s Principle
3.14 The Privilege of Destruction
3.15 Broken Branches
References
Chapter 4: “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate on the Physical Significance of Mathematical Objects
4.1 Introduction
4.2 The Ambivalent Reception of Newton’s Mathematical Physics
4.3 Du Châtelet on the Metaphysics of Mathematical Objects
4.3.1 Mathematical Objects and Metaphysical Idealism
4.3.2 The Metaphysics and Epistemology of Magnitude
4.3.3 The Power of Abstraction
4.3.4 Abstraction and Fictions
4.4 Du Châtelet’s Defense of Inferences from Mathematics to Material Nature
4.4.1 Mathematical Fictions and Approximate Truth
4.4.2 From Mathematical to Physical Continuity
4.5 Conclusion
References
Chapter 5: Order of Nature and Orders of Science
5.1 Preliminaries: Three Points of Departure and One Aim
5.1.1 ‘Semantical Ladenness’ of Mathematics
5.1.2 Euclideanism
5.1.3 Orders of Science
5.1.4 Understanding the Change of Concepts of Science
5.2 Mechanical Euclideanism: The Case of Newton’s Principia
5.2.1 Mechanical Euclideanism
5.2.2 Axiomatic Structure and Empiristic Methodology
5.2.3 Newton’s Euclideanism
5.3 Newtonian and Analytical Perspectives: Euler’s Program of Rational Mechanics
5.3.1 ‘Synthetical’ Beginnings of Analytical Mechanics
5.3.2 ‘Newtonian’ Axiomatisation Without Newtonian Ontology
5.3.3 ‘Inflation of Principles’ and Metatheoretical ‘Sliding of the Center of Gravity’
5.3.4 Analytical Principles of Mechanics
5.4 The Edge of Certainty: Lagrange’s Analytical Mechanics
5.4.1 Changing Principles and Concepts
5.4.2 No Geometry, No Methodology, No (Explicit) Scientific Metaphysics: The New Meaning of ‘Analytical’
5.4.3 Loss of Evidence: ‘Rubber Euclideanism’
5.5 Kant and Eighteenth-Century Rational Mechanics: Two Projections
5.5.1 The ‘Synthetical’ Projection: Metaphysical Foundations
5.5.2 The ‘Analytical’ Projection: Critique of Judgement
5.6 Conclusion
References
Part III: Avenues of Newtonianism
Chapter 6: Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique, and How They Contributed to Popularising Newton’s Physics
6.1 Newton’s Physics Disseminated by a Cartesian Textbook
6.2 Jacques Rohault and His Traité de Physique
6.3 Rohault’s Traité Translated and Annotated by Samuel Clarke
6.3.1 Hoadley’s Account
6.3.2 Whiston’s Account
6.3.3 A Document Unparalleled in the History of Physics
6.4 The Structure of Rohault’s Traité
6.4.1 Matter, Inertia, and Conservation of the Quantity of Motion
6.4.2 Vacuum and Elements
6.4.3 Rules of Collision
6.4.4 Attractive and Repulsive Forces
6.4.5 Light and Colour
6.4.6 Planetary Motion and Free Fall
6.5 Charles Morgan’s Annotations
References
Chapter 7: Kant on Extension and Force: Critical Appropriations of Leibniz and Newton
7.1 Newton, Locke, Descartes, and Leibniz on Extension
7.1.1 Newton, Locke, and Descartes on Extension as a Primitive
7.1.2 Leibniz on Extension
7.2 Kant’s Objections to Extension as Primitive
7.2.1 Kant’s Rejection of Leibniz’s Criticisms of Extension as a Primitive
7.2.2 Kant’s Arguments Against Atomism
7.3 Force and Causality
7.3.1 Leibniz on Force
7.3.2 Kant on Force
7.4 Brief Methodological Conclusion
References
Chapter 8: Scotland’s Philosophico-Chemical Physics
8.1 Joseph Black and Thomas Reid in the 1760s
8.2 John Anderson and John Robison, Circa 1780
8.3 Conclusion
References
Part IV: Can Matter Think?
Chapter 9: Materialistic Theories of Mind and Brain
9.1 Introduction
9.2 Can Matter Think?
9.3 The Question of the Soul
9.4 The Workings of the Brain
9.5 Conclusion
Afterword 2022
References
Chapter 10: Kant’s Second Paralogism in Context: The Critique of Pure Reason on Whether Matter Can Think
10.1 The Paralogism: Its Formal Structure
10.2 The Context: Kant and His Opponents
10.3 Conclusion
Postscript (2022): Materialism and Anti-materialism in the Eighteenth Century
References
Part V: Metaphysics and Natural History
Chapter 11: Kant’s Universal Natural History and Analogical Reasoning in Cosmology
11.1 Introduction
11.2 Kant’s Analogical Method in the Universal Natural History
11.3 Analogical Reasoning: Some Historical Context
11.4 Kant’s Theory of Analogy
11.5 Kant’s Cosmological Analogy
11.6 Conclusion
References
Chapter 12: Natural or Artificial Systems? The Eighteenth-Century Controversy on Classification of Animals and Plants and Its Philosophical Contexts
12.1 Eighteenth-Century Classification as a Double-Faced Enterprise
12.2 Are Systems as Such Unnatural?
12.3 Method and Form I – Is the Tree of Porphyry Natural?
12.4 Method and Form II – Method Versus System
12.5 Biological Content I – Resemblance of Structure
12.6 Biological Content II – Growing Tensions
12.6.1 Natural Groups
12.6.2 Buffon’s Species Concept
12.6.3 From Structure to Organisation
12.7 Prospects: A Meaningless Nature
References
Part VI: Looking Back and Ahead
Chapter 13: Beyond Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786
13.1 Introduction
13.2 Background Distinctions
13.3 The Shape of Mechanics After 1730
13.4 Sufficient Foundations, 1760–1830
13.5 Insufficient Foundations: Laws
13.6 Insufficient Foundations: Matter
13.7 Some Morals
References
Appendices
Appendix I: Newton’s Scholia from David Gregory’s Estate on the Propositions IV Through IX Book III of His Principia
The Sources for Our Edition
About the English Translation
Abbreviations Used
Newton’s Scholia
Newton’s Excerpts from Macrobius’ Commentary on Clcero’s Dream of Sclplo
Newton’s Excerpts from Macrobius’ Commentary on Cicero’s Dream
Remarks on Newton’s Scholia
References
Appendix II: The Concepts of Immanuel Kant’s Natural Philosophy (1747–1780): A Database Rendering Their Explicit and Implicit Networks
Networks of Concepts and Their Representation
Kant’s Natural Philosophy
Explicit and Implicit Networks Among Concepts
The Form of Representation
Aspects of Kant’s Theory of Matter as Rendered in the Database
The Databases
“Begriffe”
Rendering Networks of Concepts
Context I – The Location of Concepts in Kant
Context II – The Location of Concepts in Contemporary Science
Grouping According to Fields of Knowledge
The Additional Databases

Citation preview

Boston Studies in the Philosophy and History of Science  341

Wolfgang Lefèvre   Editor

Between Leibniz, Newton, and Kant Philosophy and Science in the Eighteenth Century Second Edition

Boston Studies in the Philosophy and History of Science Founding Editor Robert S. Cohen

Volume 341

Series Editors Jürgen Renn, Max Planck Institute for the History of Science, Berlin, Germany Lydia Patton, Virginia Tech, Ona, WV, USA Associate Editor Peter McLaughlin, Department of Philosophy, Universität Heidelberg, Heidelberg, Baden-Württemberg, Germany Managing Editor Lindy Divarci, c/o Divarci, Max Planck Institute for the History of Science, Berlin, Berlin, Germany Editorial Board Members Kostas Gavroglu, University of Athens, Athens, Greece Thomas F. Glick, Department of History, Boston University, Boston, USA John Heilbron, University of California, Berkeley, UK Diana Kormos-Buchwald, Dept. of Humanities and Social Sciences, California Institute of Technology, Pasadena, CA, USA Agustí Nieto-Galan, Dept. de Filosofia, Edifici B, Universitat Autonoma de Barcelona, Bellaterra (Cerdanyola del V.), Spain Nuccio Ordine, Campus di Arcavacata - Dip. di Filologia, Universitá della Calabria, RENDE, Cosenza, Italy Ana Simões, Fac of Sciences, Unit for the Histo, Universidade de Lisboa, Lisboa, Portugal John J. Stachel, Boston University, Brookline, MA, USA Baichun Zhang, Inst for the History of Natural Sciences, Chinese Academy of Science, Beijing, China

The series Boston Studies in the Philosophy and History of Science was conceived in the broadest framework of interdisciplinary and international concerns. Natural scientists, mathematicians, social scientists and philosophers have contributed to the series, as have historians and sociologists of science, linguists, psychologists, physicians, and literary critics. The series has been able to include works by authors from many other countries around the world. The editors believe that the history and philosophy of science should itself be scientific, self-consciously critical, humane as well as rational, sceptical and undogmatic while also receptive to discussion of first principles. One of the aims of Boston Studies, therefore, is to develop collaboration among scientists, historians and philosophers. Boston Studies in the Philosophy and History of Science looks into and reflects on interactions between epistemological and historical dimensions in an effort to understand the scientific enterprise from every viewpoint.

Wolfgang Lefèvre Editor

Between Leibniz, Newton, and Kant Philosophy and Science in the Eighteenth Century Second Edition

Editor Wolfgang Lefèvre Wissenschaftsgeschichte Max Planck Institute for the History of Science Berlin, Berlin, Germany

ISSN 0068-0346     ISSN 2214-7942 (electronic) Boston Studies in the Philosophy and History of Science ISBN 978-3-031-34339-1    ISBN 978-3-031-34340-7 (eBook) https://doi.org/10.1007/978-3-031-34340-7 1st edition: © Springer Science+Business Media Dordrecht 2001 2nd edition: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface to the 2nd Edition

More than 20 years have passed since the publication of the first edition of the volume Between Leibniz, Newton, and Kant. When the question of a second edition arose, it was therefore obvious from the outset for both the publisher and the editor to think of a revised and extended new edition. All the authors of the first edition that I was able to reach were immediately ready to go through their chapter again, to update, revise, improve, or supplement it where necessary  – especially with regard to the literature on their topic that has been published since 2001. Fortunately, I was also able to win three new authors, whose chapters are a welcome enrichment, especially since they fit optimally into the original structure of the volume and add new and essential aspects to the respective parts. Aaron Wells’ chapter on the “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate on the Physical Significance of Mathematical Objects adds to Part II  – Metaphysics and the Analytical Method  – an essential facet. Stephen Howard’s chapter on Kant’s Universal Natural History and Analogical Reasoning in Cosmology gives Part V – Metaphysics and Natural History – the weight it deserves. Finally, the critical review of the limits of natural theory/natural philosophy of the eighteenth century, which Marius Stan’s chapter Beyond Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786 demonstrates as a prerequisite for an adequate historical and philosophical understanding of this epoch, offers an important addition and counterpoint to the critical opening chapter by Alan Gabbey. I would like to thank all the authors, both those of the original first edition and those who contributed new chapters to the second edition, for the good cooperation, which made the task of the editor easy and stimulating for me. Special thanks to Svetlana Kleiner, editorial assistant at Springer Nature, who suggested a second extended edition and who together with her team supported me competently and were friendly whenever necessary. Berlin, Germany October 2022

Wolfgang Lefèvre

v

Introduction

This volume deals with philosophy and the sciences in the age between Leibniz, Newton, and Kant. Hence, the subject matter under consideration is neither the development of metaphysics during this period in all its purity, nor, at the empirical end, the transformations that physics underwent from Newton to Lagrange or those in botany from Ray to Jussieu. This volume centers rather on the interactions among these two spheres of change and on how they were generated by the given conditions of history. The choice of this theme was prompted in the main by three convictions: first, this was a unique period in that the agenda, methods, and even basic concepts of seventeenth and eighteenth-century philosophy (probably including practical philosophy no less than theoretical) were strongly permeated and given a new shape by the emerging world of modern science. Second, in the process, the conceptual frameworks emerging from philosophy were absorbed by the sciences (even by the least philosophical) and began to serve as their bedrock in a process whose intensity has remained unsurpassed ever since. Third, the concomitant changes in the relationships between philosophy and the sciences during the eighteenth century were not only indicative of developments that took place within these two fields of human activity. Rather, these changes began in their own right to serve as an important factor of those transformations in eighteenth-century philosophy as well as the sciences. This is a much-neglected point in contemporary studies. The age between Leibniz, Newton, and Kant has always been of special interest to historians of philosophy as well as to historians of science, and it comes without surprise that their views of that age often differ, not only in the details but also in broad outline. For many historians of philosophy, this period is marked by the dissolution of metaphysics and the emergence of fresh attempts to supply an epistemological, instead of metaphysical, foundation for the sciences. For historians of science, a dominant feature of the age may appear to be the sharing of well-­ established theories and attitudes on a wealth of singular items by a large community of scientists, who were, however, unable to reach agreement on any one overarching theory devised in the interest of integrating these scattered elements of knowledge. However, though by modern standards these latter theories prove to be little more than untenable speculations, they cannot be taken simply to be wild vii

viii

Introduction

speculations which had to await more progressive scientific methods. Rather, they indicate a characteristic contradiction that permeated the modern sciences before the nineteenth century: While their methodically gained and accumulated empirical knowledge had successfully undermined speculative global theories of the Aristotelian tradition, the sciences were yet unable to provide a sufficiently broad basis for less speculative overarching theories. Despite their different perspectives, both the historian of philosophy and the historian of science realize principally that the philosophy of early modern age cannot be adequately appreciated in isolation from what was happening in the sciences, and vice versa. It is, in fact, a truism that philosophy and the sciences were closely linked during this period, and it is also well known that the beginnings of a dissolution of this linkage must be dated exactly to this period; what is needed is a more precise determination of the structure and dynamics of this linkage, covering the age between Bacon and Hegel. Without belittling the achievements of the fifteenth and sixteenth centuries, one can state that modern sciences (classic and Baconian) took shape in the seventeenth century, urged on by individuals like Kepler, Galileo, Harvey, Boyle, Huygens, Newton, Leibniz, Homberg, or Ray. At the same time, new branches of mathematics (algebra, analytic geometry, differential calculus), new metaphysical systems (Descartes, Spinoza, Leibniz), and new general methodologies (new deductive as well as inductive strategies) were established. True, these beginnings referred to, picked up, revivified, reshaped, and carried on, in a variety of ways, doctrines and theories coming from Antiquity through the Renaissance. But they also consisted in more than new combinations of old elements. Only when this is realized is it possible to fully appreciate the new mathematical achievements or the philosophical developments that set in with Descartes and others. Especially the interrelations between the sciences, mathematics, metaphysics, and methodological strategies emerged as a completely new quality in the seventeenth century. All of these fields of knowledge entered into an intimate interdependence without, however, merging into a homogeneous whole, thus maintaining a dynamical relationship that, one way or another, was a hallmark of the period. Let us begin with mutual dependence. First, it was the rule rather than the exception that a single individual contributed to developments in more than one of these fields of knowledge, and sometimes even to all of them. That is why figures like Descartes, Newton, or Leibniz do not comply with our division of learned women and men into either philosophers, or mathematicians, or scientists. Moreover, the mathematics of, say, Descartes strongly affected his philosophy and his various scientific investigations, and vice versa. Second, there are many cases in which the interdependence of developments amounted to a process of mutual interaction in which innovations in one field provided new initial conditions or even new means and tools for investigations in another field. Thus processes of co-evolution among different fields of knowledge ensued. The co-evolution of mechanics and mathematics in early modern times is something of a standard case. Of course, it is also possible to study the role played by mathematics and the sciences in the elaboration and proliferation of new methodical strategies and metaphysics. Also, the significance

Introduction

ix

of metaphysics for mathematics and the sciences went far beyond its foundational role. Third, even in all of those cases where the actor focussed in a straightforward manner on a topic within the competence of a single field, applied the means and methods typical of the field, and stood squarely its tradition, one should not overlook the possibility of tacit responses towards challenges arising from new developments in other fields. All these interdependencies confirm the well-known principle: it is impossible to understand what is going on in any one field when one studies them in isolation from each other. Nevertheless, these fields also led lives of their own. Developments in any one branch cannot be deduced from or reduced to those of another: mechanics, for instance, was decidedly more than applied metaphysics, and the latter no mere underpinning to mechanics. Today, there are numerous studies in philosophy, history, and sociology of science that attempt to achieve scholarly distinction by boldly sweeping across traditional distinctions, like between science and philosophy, science and religion, science and folk-knowledge, etc. When viewed with such elevated spirits, it may indeed arise that all seems like a homogeneous whole and any distinctions among the fields arbitrary and old-fashioned. However, such approaches are often more successful in dissolving a problem than in solving it. There is indeed a difference between rethinking previously accepted bifurcations and dichotomies like those in the field of eighteenth-century philosophy and science and the formal creation of new historical units in a process of lumping. And also, there is the more promising alternative of interpreting the integrity of fields as dependent on their mutual relations, i.e., as different and distinguishable parts which, through their interaction, constitute a unifying network. The element of independence in philosophy, mathematics, and the individual sciences becomes particularly prominent when these fields are looked upon as social enterprises in the pursuit and accumulation of knowledge. Although not scientific disciplines in the modern sense of the term, and though they underwent permanent change, each of these fields constituted a distinct collective practice of learning and investigation that was held together by particular modes of training, communication, and transmission; particular constraints, traditions, and resources; and, last but not least, by a particular social embeddedness. Thus each of these fields cohered by virtue of distinct collective activities, driving forces, and rules. Without this element of partial autonomy, it is impossible to understand the sources of change in the relationship between philosophy and the sciences in the eighteenth century on which this volume focusses. The fact that philosophy, mathematics, and the sciences formed such a unity of parts which, in turn, also led lives of their own is perhaps even the most important novelty that developed in early modern times (especially the seventeenth century) and which gave this period its unique setting. Building on the sweeping changes in the fifteenth and sixteenth centuries, the seventeenth century posed a challenge to the peripatetic tradition in philosophy that believed in the hierarchical arrangement of the whole corpus of knowledge. In this tradition, unification was endeavored by distinguishing between “proper” and “improper” knowledge assigning the former – physics, for instance,  – a subordinate rank within philosophy and expelling the

x

Introduction

latter – mechanics, for instance – from its sacred halls. Though peripatetic philosophy continued to prevail in terms of quantity during the seventeenth century (and at various locations also in the eighteenth), the spell was broken by this new attitude. Whatever their status at the universities, physics (natural philosophy), mathematics, and mechanics overcame their former isolation and, now of equal legitimacy, unfolded a productive interplay in a growing industry of new investigations. It was also this fruitful interaction between natural philosophy, mathematics, and mechanics that provided the underpinning for a new class of attempts at integration of all pieces of knowledge into a consistent whole. This gave birth to the philosophical systems of Descartes and Leibniz. Along with these (but not confined to them), new kinds of metaphysics were devised, for it was still believed that metaphysics provided some foundational basis that was needed to enable physics to be established and treated in an intelligible manner. Never did these new philosophical systems accomplish an all-embracing unification of scientific knowledge nor any agreement about the metaphysical principles on which they were built. Yet, the belief in the feasibility of such an undertaking remained unbroken throughout the camps of the Cartesians, Leibnizians, and Newtonians. Moreover, irrespective of the controversies about the appropriate principles of unification, all camps shared explicitly or implicitly the conviction that those principles were of both ontological and methodological denotation. The interrelation between philosophy and science in the early modern age seems, thus, to be historically unique in several aspects: The great peripatetic syntheses of all kinds of knowledge, still a formidable antagonist to the new philosophical systems of the seventeenth century, dwindled in importance in the course of the eighteenth century, while attempts at synthesizing the totality of scientific knowledge were of serious philosophical import throughout this period. (Only in the nineteenth century did such undertakings become increasingly dilettantish, owing to the explosion of knowledge.) These attempts shared with the peripatetic tradition the claim to successfully integrate all knowledge, but the decisive difference was that these claims now were made with respect to the knowledge produced by the partly autonomous sciences of early modern times rather than subordinate branches of a hierarchically organized all-encompassing philosophy. In the course of the eighteenth century, however, and especially in its second half, ontologically based systems of this kind increasingly met with indifference, skepticism, or criticism. And as a concomitant, numerous of those philosophical presuppositions that had served as guiding principles in the different fields of knowledge since the seventeenth century lost their weight and finally faded away. Obviously, the balance between philosophy, mathematics, and sciences set up in the age of Newton and Leibniz was no longer stable and was in want of renewed adjustment in the age of Kant. What had happened? What was the source of this upsetting? Had philosophy simply decreased in importance? And if so, for what reasons? Or did developments in some of the sciences lead to some fundamental change in the interrelations between philosophy, mathematics and science? And if so, can we identify and describe the pertinent sources? Those were the questions from which the first ideas of this volume arose.

Introduction

xi

Thus, this volume deals with the changes in the interrelations between philosophy and the different branches of science in the age between Leibniz, Newton, and Kant. Considering how the manifold developments in all of these fields of knowledge may have played their role in these processes, inclusive of the material and social conditions in the background, a sample of ten essays hardly can achieve more than a modest outline of the work actually needed to construct a comprehensive view. This volume will have served its purpose if the essays, together, lead to some conviction that the interrelations sketched above may provide a key towards a deeper understanding of the historical developments of the period and, towards this end, stimulate further investigations in this field. Emphasis is in order that the contributors to this volume share no common understanding of how to distinguish between eighteenth-century philosophy and science, and of course there is indeed agreement that modern distinctions must not be imputed to the past. Going by this volume, the problem centers probably on the correct reconstruction of the eighteenth-century use of “physics” or philosophia naturalis. Did, then, the historical actors treat physics like a branch of philosophy, and is any attempt to detect a difference between philosophy and physics on this account a failure? Yet it is also known that eighteenth-century physics was modern science in an early stage of development (in contrast, for instance, to Aristotelian physics). Does it, then, matter whether the historical actors called physics by the name of philosophia naturalis? Furthermore, is there a difference between modern theoretical physics and philosophia naturalis as opposed to historia naturalis (the latter being an inventory of descriptive knowledge devoid of explanations proper)? If, however, philosophia naturalis was a branch of philosophy, would this not straightforwardly bring about some interdependence, for instance, with metaphysics? On this condition, the relationship between philosophia naturalis and metaphysics, though surely not identical with that between science and philosophy, may stand in some analogy to the latter. This is, approximately, the position taken by a large portion of this volume’s contributions. Presently, at any rate, the question as to when and how to distinguish between eighteenth-century philosophy and science needs continual rephrasing to do justice to each step in the process of work rather than being answered in advance. The volume is divided into six parts. Part I, entitled “Seismic Vibrations in Metaphysics,” subjects metaphysics to scrutiny with Alan Gabbey’s “Disciplinary Transformations in the Age of Newton: The Case of Metaphysics.” It is important to fully realize the entangled state of metaphysics at the end of the seventeenth century when looking for transformations in eighteenth-century metaphysics which are symptomatic of changes in the relationship between philosophy and science. The subdividing of philosophy, and in particular of speculative philosophy, in the peripatetic tradition was still predominant. The links between metaphysics, physics, and mathematics, however, which were postulated by leading figures of seventeenth-­ century philosophy and science, conformed to, but also challenged implicitly, the peripatetic framework. Showing the variance in attitudes among Leibniz, Newton, and Locke on how to draw a line of division between metaphysics and physics with regard to a sample of topics, this essay draws attention to the divergent starting

xii

Introduction

points of British and German metaphysical conceptions in the course of the eighteenth century. Tracing a trajectory of such conceptions in Britain  – Berkeley, Hume, Cullen – and contrasting it with the position of Kant in Germany, this essay records the trembling or perhaps even crumbling of metaphysics caused by the growing tensions between philosophy and science. In the end, this state of affairs led to a remarkably indifferent attitude toward metaphysics (Cullen) and, alternatively, to a radical critique of its epistemological foundations (Kant). Part II is entitled “Metaphysics and the Analytical Method” and focusses on how the beginnings of analytical mechanics in the second third of the eighteenth century affected the metaphysical foundations of mechanics. In his essay “Leibniz’ Concept of Possible Worlds and the Analysis of Motion in Eighteenth-Century Physics,” Hartmut Hecht investigates the role Leibniz’ famous theorem of God’s choice between possible worlds played for his metaphysical foundations of physics and especially for the introduction of an “optimization principle” into his theory of scientific explanation. Taking this principle as related, and in some aspects equivalent, to the so-called analytical principles that Euler, d’Alembert, and Maupertuis introduced into mechanics two generations later, the essay shows that a different set of conditions began to prevail in the eighteenth century. This was epitomized by the dwindling role played by universal metaphysical assumptions for the introduction of such principles in this century’s mechanics. In his essay “The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s Philosophy,” François De Gandt treats this fade-away of metaphysical foundations of mechanics from a different point of view. D’Alembert based in an unmistakably Cartesian manner scientific truth on the intact chain of scientific knowledge that links the fundamental cognition of the most abstract properties of natural beings at the top to a series of descending levels of knowledge about entities with increasingly compound and complex properties. But he did not hide the numerous gaps and lacunae existing in this chain which had to be filled in by underived propositions. This is even true of the famous d’Alembert principle, that was, indeed, regarded by its author only as a methodical means that facilitates the “geometers” the appropriate use of the proper principles of composition of motion and of equilibrium. Moreover, as this essay substantiates, the fundamental course of ascending by abstraction of properties and descending by restoring them step by step, on which the Cartesian chain of scientific knowledge rests, was taken by d’Alembert to be a methodical “strategy” rather than a procedure that secures the ontological foundations of physics. The analytical method itself occupies the foreground in Helmut Pulte’s essay “Order of Nature and Orders of Science.” In the beginning, it is shown that “Mechanical Euclideanism” dominated seventeenth-century foundations of physics, i.e., principles were treated like axioms and laws of nature (axiomata sive leges naturae). With hindsight, it becomes obvious that such an Euclideanism could be maintained only as long as the tensions generated by this lumping of ontology and methodology did not exceed a certain degree. But these tensions were raised beyond limits by the introduction of analytical mechanics. And this explains to a large extent why Euler’s program of rational mechanics abandoned ontological

Introduction

xiii

foundations in favor of an advancement of Newton’s axiomatization by appropriate mathematical techniques. New analytical principles like the least action principle were prompted in the beginning by certain concrete problems and only later proved applicable to a wider range of phenomena. And when this application, in turn, proved useful for improving the deductive organization of his rational mechanics, Euler elevated these principles to formal axioms rather than laws of nature. Finally, in Lagrange’s analytical mechanics, we encounter a rational system that is held together by logical coherence rather than “material truth.” Part III is entitled “Avenues of Newtonianism” and documents changes in the interrelation between philosophy and science through three case studies that indicate the wide spectrum of transformations in eighteenth-century Newtonianism. In his essay “Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique, and How They Contributed to Popularising Newton’s Physics,” Volkmar Schüller investigates one of the most peculiar episodes in the history of science: A Cartesian textbook on physics, Rohault’s Traité of 1671, happened to become the chief vehicle for the dissemination of Newton’s physics among his British countrymen in the first half of the eighteenth century. After having provided the essentials about the individuals involved and an introduction to the general condition of teaching and learning physics at that time, the particular circumstances of the translation and annotation of Rohault’s textbook by Samuel Clarke are reported. In a point-by-point analysis, Schüller investigates how exactly Clarke’s annotations were opposed to the text’s main body and in which manner they rendered Newton’s position. Probably the most striking feature is, however, that these Newtonian annotations do agree with the Cartesian main text in that they treat ontological issues like physical ones that can be settled by experience and vice versa. This attests to an interestingly innocent back-and-forth of Newtonianism between metaphysics and physics. Eric Watkin’s essay “Kant on Extension and Force: Critical Appropriations of Leibniz and Newton” presents a very different case of Newtonianism (if no exception is taken to listing Kant among the Newtonians). This essay gives a historical reconstruction of Kant’s dynamical concept of extension that sided with Leibniz in rejecting the predominant notion of extension as a primitive term maintained by Cartesians as well as Newtonians. However, though following Leibniz in basing extension on forces, Kant rejected his monadological ontology, that is, especially the notion of substance as a simple term as well as the teleological interpretation of forces. This was how Kant attempted to build a metaphysics that was suitable for the founding of Newtonian physics. In this highly reflective (non-innocent) attempt to conjoin metaphysics and physics, the roles of metaphysics and physics appear tacitly altered. In the seventeenth century, metaphysics was supposed to provide fundamental prerequisites that were essential for establishing physics in an intelligible manner. Now metaphysics had to be revised to accommodate the requirements of a thoroughly established physics. Thus, Kant’s grounding of Newtonian physics by metaphysics seemed to be controlled more by the physics of the day, and less by metaphysics. The third essay of this part, David Wilson’s “Scotland’s Philosophico-Chemical Physics,” focusses on the natural philosophy of the Scottish Newtonians John

xiv

Introduction

Anderson and John Robison. It begins with an investigation of the conceptual framework of this natural philosophy provided by Joseph Black’s research on heat and Thomas Reid’s famous Inquiry from 1764 who, for their part, built on Newton’s theory of matter and short-range forces as indicated in Query 31 of his Opticks (Black) but also on the Rules of Reasoning of the second edition of his Principia (Black and Reid). The issue of whether hidden entities like minute particles, matter of heat, or short-range forces were or were not permitted by these rules (Black and Reid, respectively) reveals aspects of the often-neglected tensions generated by Newtonian physics’ self-understanding as an experiential science. This understanding was latently at variance not only with the axiomatic basic structure of this physics but also with its ontological assumptions. By uncovering how Anderson and Robison, in their courses on chemistry and physics in the years around 1780, handled these tensions, a brand of Newtonianism becomes visible (and is portrayed in this essay) that is remarkable mainly for two of its features: first, it was sufficiently elastic to accommodate various syncretistic combinations of scientific assumptions and theories of heterogeneous and mildly incompatible character; second, the adoption or rejection of certain scientific theories seemed almost independent of the epistemological beliefs of these Newtonians. Part IV is entitled “Can Matter Think?” and approaches the interrelations between philosophy and the sciences in the eighteenth century within a rather different field of knowledge, namely, psychology. Psychology is of particular interest in this respect since it was at the time in dispute whether this field belonged to metaphysics or medicine. In her essay “Materialistic Theories of Mind and Brain,” Ann Thomson focusses on two related, albeit independent, questions which were discussed by eighteenth-century materialists in Britain and France when dealing with the mind-body problem: How was it possible to conceive of matter as able to sense, feel, and think? And how did the brain function? With respect to the first question, any attempt to distinguish between philosophical and scientific positions seems indeed pointless. And yet, as shown by this essay, the materialistic denial of the existence of an immaterial soul had an important general impact on the sciences (especially physiology and anatomy) concerning the notion of matter. Reversely, developments in the life sciences of the eighteenth century and the then emerging notion of organized matter allowed a far more subtle handling of the issue of thinking matter than before. Furthermore, physiological and anatomical inspection of nerve and brain function from Thomas Willis in the seventeenth century to La Mettrie in the eighteenth provided an underpinning for a materialistic approach that was considerably removed from the eclectic philosophy of these physicians. For the rational psychology in the Leibnizian metaphysics tradition predominant in eighteenth-century Germany, the idea that only simple substances possessed consciousness and thought appeared to be the ultimate refutation of the thesis that matter could think. By listing rational psychology’s proof of the simplicity of the soul among the paralogisms, Kant called a cornerstone of the idealistic stance into question. In his essay “Kant’s Second Paralogism in Context: The Critique of Pure Reason on Whether Matter Can Think,” Falk Wunderlich investigates how Kant, in dealing with this issue, employs his critical philosophy. In a characteristic shift,

Introduction

xv

Kant centered his attention on the possibility of proving or refuting the proposition that matter could think, and demonstrated that neither alternative could be achieved by a mere analysis of the notion of a thought. He also denied the possibility of proving any substantial difference between the soul and the substratum (noumenon) of matter (matter in itself). This indeed established a new kind of relationship between philosophy and science: Kant’s critical philosophy does not claim a foundational role as the ontological part of science; rather, it seems to protect science against such pretentious philosophical claims. Part V is entitled “Metaphysics and Natural History” and tries to compensate for, or if you like to draw attention to, a shortcoming that is characteristic of most of the studies about the relationship of philosophy and the sciences in early modern times (but, unfortunately, is also shown by this volume): It is mainly the relation between philosophy and physics that dominates the stage while the Baconian sciences and the culture of natural history are almost reduced to the role of supernumeraries. As claimed by the title, Wolfgang Lefèvre’s essay “Natural or Artificial Systems? The Eighteenth-Century Controversy on Classification of Animals and Plants and Its Philosophical Contexts” investigates the interplay between philosophy and science in the field of biological classification. Generally, the results conform to a pattern that is also supported by most other essays of this volume: metaphysical assumptions, like the “chain of being” in the present article, had an important intrinsic function for the sciences at the turn of the eighteenth century, but then this function diminished gradually, and what was ultimately left was, at best, a few useful heuristic ideas; or worse, these ideas began to impede further developments in the sciences before they were abandoned altogether. Yet it would be an undue simplification to reduce the sources of this pattern to a joint change in mentalities. Rather, this essay underlines once more that specific developments in each of the different fields of knowledge brought into being new interrelations between philosophy and the sciences. Hence, the importance of continuing to broaden our knowledge about disciplinary fields that hitherto were somewhat neglected by historians of science and philosophy. The volume supplements two appendices that might be welcome by both historians of science as well as historians of philosophy. Appendix I contains a new edition of Newton’s scholia on propositions IV through IX of book III of his Principia that he prepared for a later edition but ultimately did not publish. After these scholia were discovered in the estate of David Gregory (1659–1708) in the first half of the nineteenth century and after their first analysis in the 1960s by McGuire and Rattansi, the complete Latin text was edited for the first time by Casini in 1984. This edition, however, hardly stands up to modern philological standards. The new edition by Volkmar Schüller presented here is supplemented by the first translation into English, and also by an abundance of historical, philological, and analytical annotations and references. Appendix II introduces a database on Kant’s scientific concepts that has been newly published in Germany. The database is intended not only for Kant scholars, but particularly for historians who are keenly aware of the fact that the philosophy of early modern times cannot be adequately appreciated without a solid

xvi

Introduction

understanding of the contemporary condition of the sciences and vice versa. There are two reasons for appending this brief description here. First, this description is thought to compensate for a shortcoming: since the database had to be composed in German (because it builds on the original wording of Kant’s writings), it may easily escape the attention of even those among the English-speaking scholars with an intimate knowledge of Kant’s natural philosophy, or more generally of those well-­ versed in the history of science in the eighteenth century. Second, I think the time has come to foster more strongly use of the electronic medium in the humanities. Finally, I wish to express my gratitude to the authors of this volume who willingly committed themselves to all that kind of labor that is involved not only in writing a paper but also in commenting on drafts of other papers included in this volume, and in accepting similar comments by co-contributors. Much of this was facilitated and speeded up by a meeting of the contributors and extensive discussion of the issues that took place at the Max Planck Institute for History of Science in Berlin in July 1999. I am thankful to Jürgen Renn, Director of Department I of the Institute, who made this meeting possible and gave substantial support to the editing process. Also, I wish to thank my colleague and friend Peter Beurton for linguistic help during the editing process. Berlin, Germany July 31, 2000

Wolfgang Lefèvre

Contents

Part I Seismic Vibrations in Metaphysics 1

Disciplinary Transformations in the Age of Newton: The Case of Metaphysics ������������������������������������������������������������������������    3 Alan Gabbey

Part II Metaphysics and the Analytical Method 2

 Leibniz’ Concept of Possible Worlds and the Analysis of Motion in Eighteenth-­Century Physics����������������������������������������������   29 Hartmut Hecht

3

The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s Philosophy������������������������������������������������������   53 François De Gandt

4

“In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate on the Physical Significance of Mathematical Objects ������������������������������������������������������������������������   69 Aaron Wells

5

 Order of Nature and Orders of Science ������������������������������������������������   99 Helmut Pulte

Part III Avenues of Newtonianism 6

Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique, and How They Contributed to Popularising Newton’s Physics��������������������������������������������������������������������������������������  139 Volkmar Schüller

xvii

xviii

Contents

7

Kant on Extension and Force: Critical Appropriations of Leibniz and Newton����������������������������������������������������������������������������  157 Eric Watkins

8

Scotland’s Philosophico-Chemical Physics��������������������������������������������  177 David B. Wilson

Part IV Can Matter Think? 9

 Materialistic Theories of Mind and Brain ��������������������������������������������  197 Ann Thomson

10 Kant’s  Second Paralogism in Context: The Critique of Pure Reason on Whether Matter Can Think������������������������������������  227 Falk Wunderlich Part V Metaphysics and Natural History 11 K  ant’s Universal Natural History and Analogical Reasoning in Cosmology��������������������������������������������������������������������������������������������  247 Stephen Howard 12 Natural  or Artificial Systems? The Eighteenth-Century Controversy on Classification of Animals and Plants and Its Philosophical Contexts����������������������������������������������������������������  271 Wolfgang Lefèvre Part VI Looking Back and Ahead 13 Beyond  Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786�������������������������������������������������������������������������������������������������  295 Marius Stan Appendices��������������������������������������������������������������������������������������������������������  311

Part I

Seismic Vibrations in Metaphysics

Chapter 1

Disciplinary Transformations in the Age of Newton: The Case of Metaphysics Alan Gabbey

Abstract  The chapter emphasizes the complexity of the relations between philosophy and science in the eighteenth century, as they must be seen against the background that, in the early modern period, as in the preceding centuries, philosophy generally included physics or natural philosophy, mathematics, and metaphysics. Showing the variance in attitudes among Leibniz, Newton, and Locke on how to draw a line of division between metaphysics and physics with regard to a sample of topics, this chapter draws attention to the divergent starting points of British and German metaphysical conceptions in the course of the eighteenth century. Tracing a trajectory of such conceptions in Britain – Berkeley, Hume, Cullen – and contrasting it with the position of Kant in Germany, this essay records the trembling or perhaps even crumbling of metaphysics caused by the growing tensions between metaphysics/philosophy and natural philosophy/science. In the end, this state of affairs led to a remarkably indifferent attitude toward metaphysics (Cullen) and, alternatively, to a radical critique of its epistemological foundations (Kant).

1.1 Introduction The thematic core of this volume is “Philosophy and Science in the Eighteenth Century.” As the editor explained in his invitation to the contributors, the title refers to the interrelations and distinctions between philosophy and science, as signposted principally in the work of Leibniz, Newton, and Kant. I should be surprised if anyone’s reply to the invitation included a request that someone explain the meaning of “philosophy” and “science” in this context. We knew that we would be exploring changes in the distinctions and relations between matters broadly philosophical and matters broadly scientifical. Yet I for one began to worry about what the thematic A. Gabbey (*) Barnard College, Columbia University, New York, NY, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_1

3

4

A. Gabbey

core referred to. More precisely, and less skittishly, I offered an article that would arise from an assumed worry about the referents of the volume’s thematic core. In the early modern period, as in the preceding centuries, philosophy generally included physics or natural philosophy, mathematics, and metaphysics, for some simply another name for philosophy, for others the philosophical subject par excellence. So when we contemplate the relations between “philosophy” and “science” in the eighteenth century, we confront a lattice of shifting contrasts and identities whose complexity makes it problematic how those relations should be disentangled and understood.

1.2 Speculative Philosophy in the Peripatetic Tradition At the risk of over-generalisation, the Peripatetic tradition – Protestant in Germany, Holland and Britain, Catholic in France, Spain and Italy – was the framework within which nearly all late sixteenth- and seventeenth-century philosophers, and many in the eighteenth century, were educated and within or in reaction to which many of them pursued their philosophical or scientific careers. In that tradition, philosophy typically comprises two broad divisions: speculative and practical philosophy. Speculative philosophy divides into three principal sciences (scientiae): metaphysics or first philosophy, natural philosophy or physics, and the mathematical sciences; to which are added the middle sciences (scientiae mediae), which include theoretical mechanics, optics, and astronomy. Science (scientia), properly speaking, results from demonstration with respect to “the why,” and is knowledge (cognitio) of necessary things through their proximate causes. Loosely speaking, scientia can be knowledge, in some accepted sense, of virtually anything; or a habitus, an intellectual state attained or disposition enjoyed by the possessor of scientific knowledge; it can be qualified adjectivally or be the science of something (political science, the science of medicine, etc.).1 Natural philosophy is the science of “natural body in so far as it is natural,” the science of the causes of change and rest in the natural world, the artificial domain being the concern of the mechanical arts, one of the divisions of practical philosophy, the others being active or moral philosophy (ethics, home economics, and politics). Some writers included logic as a branch of philosophy, though it was more commonly seen as an art.2 In its widest acceptation, metaphysics is the science of being qua being, in abstraction from particular beings,

 Goclenius, Lexicon philosophicum, 1010. See ibid., 623–625, 1012; Heereboord, Meletemata, Collegium logicum, Positionum logicarum disputatio quarta, de Qualitate, 6; Keckermann, Opera, cols. 871–875, Lib. I, Cap. VI (De explicatione qualitatum), Exemplum primae speciei qualitatis nempe Habitus. See also Lohr, Metaphysics and Natural Philosophy. 2  For Toletus’s division into speculative, practical and factive philosophy, on which the above division is based, see Wallace 1988, 209–13. For the disciplinary divisions and sub-divisions common in Germany, see Freedman 1985, 65–105. On the three-way division of moral philosophy, see Kraye 1988, 303–06. 1

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

5

though there were those later in the period who argued that metaphysics in this sense should be banished from the circle of the sciences. For others metaphysics is the science of beings in abstraction from physical bodies, that is, God, angels, and separated souls or minds, though there were those who argued that to treat of God, angels, and souls is not the business of metaphysics. For others it is the universal science of concepts that apply transcendentally to beings in general.3 For Francis Bacon, in a self-confessed departure from Peripatetic tradition, metaphysics and physics are the two sub-divisions of natural philosophy qua investigation of causes (as distinct from the production of effects): physics deals with efficient and material causes, metaphysics with formal and final causes (Bacon, Advancement, II 7.3 3). There were varying links perceived between the three scientiae of speculative philosophy. Physics without mathematics would be ineffective (the programmatic Descartes, Huygens, Leibniz, Newton, Kant); physics must be grounded in and was inseparable from metaphysics under some description (Descartes, Leibniz, Newton possibly, Kant); physics and metaphysics were divisions within natural philosophy qua inquisition into causes (Bacon); physics without metaphysics was the right way forward (Hobbes, Huygens, practitioners of “the experimental philosophy,” d’Alembert). Another classification of philosophy, which also had its origins in antiquity, was that of the Stoics, or of the Hellenistic philosophers in general, who divided philosophy into physics, ethics, and logic. This division was influential in the seventeenth and eighteenth centuries, notably in Locke, as we shall see, and Kant discusses it with approval at the beginning of his Groundwork of the Metaphysics of Morals (1785). Accompanying all of these positions on links within speculative philosophy were differing views on whether the referent of the term “science,” in the context of natural philosophy, could still be taken to be knowledge of necessary causal relations, as it had been in the Peripatetic tradition, or whether scientia in the Peripatetic sense should be recognized as an impossibility and replaced by an attainable, experimentally grounded body of knowledge informed by hypothesis and probable theory. Of the three sciences of Peripatetic speculative philosophy, it is metaphysics that shows most taxonomic change in the late seventeenth century and eighteenth centuries. The content, scope and methodologies of mathematics and the mathematical sciences changed enormously from the days of Viète to the age of Euler, yet it would be fair to say that throughout that period mathematics retained its disciplinary identity as the science of quantity, measure, and number, as it had been generally understood within the Peripatetic tradition. During the same period the taxonomic identity of natural philosophy changed little, for all its revolutionary advances and despite the decline of the Peripatetic conception of natural philosophy as a demonstrative science. Eighteenth-century dictionaries continued to define natural philosophy as  For a splendid general survey of the complexities of metaphysics in the sixteenth and early-seventeenth centuries, see Lohr, Metaphysics (1988). For a useful summary of differing conceptions of metaphysics in vogue in the early eighteenth century, at least on the Continent, see the article on metaphysica in Chauvin, Lexicon. Chauvin himself argues that the study of God, angels, and souls does not belong to metaphysics. 3

6

A. Gabbey

the science of natural bodies, of their powers, natures and interactions, and the range of topics deemed to fall within natural philosophy underwent no substantial change from the Peripatetic manuals of Descartes’s college days to Newton’s late years and well beyond. The case of metaphysics was significantly different, as I will try to show by considering its fortunes in Britain, with comparative though I fear less systematic glances at the situation in Germany. To focus the argument, I will cite mostly texts that are explicitly about metaphysics, or in which the author employs the term “metaphysics” (or a cognate) in an instructive way.

1.3 Newton and Leibniz I begin with the contrast between Newton and Leibniz, which I think we can choose as the representative terminus a quo in the parallel histories of metaphysics in Britain and Germany. Leibniz’s understanding of the nature of metaphysics remained constant throughout his intellectual life. In corollaries attached to the early Dissertatio de arte combinatoria (1666), he notes the necessity for a “discipline concerning created beings in general, but nowadays that is usually included in Metaphysics,” and he explains that Metaphysics, to begin at the top, deals with being and with the affections of being, which are not beings themselves, and “neither quality nor quantity nor relation is a being: it is their treatment in a designated act [in actu signato] that belongs to metaphysics.

Accordingly, since number is […] something of greatest universality, it rightly belongs to metaphysics, if you take metaphysics to be the science of those properties that are common to all classes of beings. For to speak accurately, mathematics [mathesis] (adopting this term now) is not one discipline but small parts taken out of different disciplines and dealing with the quantity of the objects belonging to each of them.

For the same reasons, the study of composite parts and of situs, the mutual disposition of composite parts of the whole, also belongs to metaphysics (Leibniz, GP, IV 41n, 35–36; PL, 75–77 – translation slightly modified). Thirteen years later, writing to Johann-Friedrich von Braunschweig-Lüneburg in the Fall of 1679, Leibniz was describing his Catholic Demonstrations. This ecumenical project was to be grounded in the true philosophy. We needed a new logic to deal with probability, we needed deeper insights into physics to deal with objections to the creation, the Flood, and the resurrection of the body, we needed a true politics. And “we must also push metaphysics further than has been done so far, in order to have true notions of God and the soul, of [the] person, of substance and accidents” (Leibniz, PL, 260 – translation slightly modified). Leibniz’s intentions were to unfold in Primae veritates (early to mid-1680s)4 and, despite its theological cast, in the Discours de Métaphysique (1686). These texts show that the topical  In Leibniz, C, 518–23; PL, 267–71.

4

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

7

extension of metaphysics includes causality, especially body-soul interactions, order in God’s actions in the world, the nature of miracles, the concept of substance, substantial forms, the praedicatum-inest-subjecto doctrine, the communication between substances, new solidly-grounded metaphysical foundations for physics and for the doctrine of motion and of mechanics, final causes in physics, the problem of definition, doctrines of ideas, the nature of spirits. In De primae philosophiae Emendatione, et de Notione Substantiae (Acta eruditorum, March 1694), in which Leibniz announced publicly the creation of the metaphysically-grounded science of dynamics, we find even a proto-Kantian description of metaphysics as “this primary and architectonic discipline” (Leibniz, GP, IV 468; PL, 432).5 Finally, Leibniz’s response to Locke’s chapter on “Trifling Propositions” (see below)  – “Des propositions frivoles”  – is a defence of Metaphysics in its real colours. Leibniz agrees that standard-issue metaphysical manuals teach only words, but note the terms in which he expresses his agreement: It is indeed an abuse of the name of Science to say, for example, that Metaphysics is the science of Being in general, which explains its principles and the affections that derive from it; that the principles of Being are Essence and Existence; and that affections are either primitive, namely the one, the true, the good, or derivative, namely the same and the different, the simple and the composite, etc., and in speaking of each of these terms, to give only vague notions and distinctions between terms.6

But there are Scholastics and Scholastics. If you read the better sort of Peripatetic author, such as Suarez, you will find solid discussions of real metaphysical issues, such as the continuum, the infinite, contingency, the principle of individuation, God and His management of creatures, spirits, the soul and its faculties, substances in general, the will, even issues in moral philosophy and the principles of justice. In sum, “it has to be admitted that there is still gold in this dross, but that only enlightened persons will profit from it […].”7 And as for true Metaphysics, we are just about beginning to establish it, and we are finding important truths about substances in general that are founded in reason and confirmed by experience. I hope also that I have increased a little our general knowledge of minds and the soul.8

 Loemker translates Leibniz’s title as “On the Correction of Metaphysics and the Concept of Substance.” 6  “De dire, par exemple, que la Metaphysique est la science de l’Estre en general, qui en explique les principes et les affections qui en emanent; que les principes de l’Estre sont l’Essence et l’Existence; et que les affections sont ou primitives, savoir l’un, le vrai, le bon, ou derivatives, savoir le même et divers, le simple et le composé etc., et en parlant de chacun de ces termes, ne donner que des notions vagues, et des distinctions des mots, c’est bien abuser du nom de Science” (Leibniz, GP, V 412). 7  “il faut avouer qu’il y a encor de l’or dans ces scories, mais il n’y a que des personnes eclairées qui en puissent profiter […]” (Leibniz, GP, V 412). 8  “[…] la Metaphysique reelle, nous commençons quasi à l’etablir, et nous trouvons des verités importantes fondées en raison et confirmées par l’experience, qui appartiennent aux substances en general. J’espere aussi d’avoir avancé un peu la connoissance generale de l’ame et des esprits” (Leibniz, GP, V 412). 5

8

A. Gabbey

And that, after all, that was the kind of metaphysics that Aristotle had sought for, the science on which the other sciences depend, from which they borrow their principles, and in which these principles are demonstrated (Leibniz, Nouveaux Essais, IV.8 – GP, V 411–13). The classification of knowledge was not one of Newton’s central concerns  – except for the status of rational and practical mechanics in relation to mathematics and natural philosophy. Yet the scattered evidence we have suggests that Newton’s notion of metaphysics was much narrower than that of Leibniz. There is a Lockean flavour in what he says about metaphysics (or alternatively, perhaps, there is a Newtonian flavour in what Locke says about metaphysics and the division of the sciences). In De gravitatione, written probably in the early 1680s, there is a section where Newton discusses the nature of body. Not knowing what its real nature is, he speculates that since we can move our bodies at will, so God, merely through the action of the divine will, could “prevent a body from penetrating any space defined by certain limits,” and for us such spaces would be indistinguishable from bodies. One lesson to draw from this possibility is “that the analogy between the Divine faculties and our own is greater than has formerly been perceived by Philosophers. That we were created in God’s image holy writ testifies.” Some might prefer the supposition that God entrusts the task of “solidifying” space to “the soul of the world,” but Newton does not see why God should not do it directly, without intermediary, thereby creating bodies on all fours with Cartesian res extensae. Then he comments, the usefulness of the idea of body that I have described is brought out by the fact that it clearly involves the chief truths of metaphysics, and thoroughly confirms and explains them. For we cannot postulate bodies of this kind without at the same time supposing that God exists, and has created bodies in empty space out of nothing, and that they are beings distinct from created minds, but able to [unite] with minds.

The Cartesian account of body fails this test. It leads to atheism; it makes unintelligible the mind-body distinction, unless we say that mind has no extension and therefore exists nowhere, in which case you might as well say it doesn’t exist at all, or at least admit that its union with body is impossible and utterly unintelligible. Furthermore, the Cartesian real distinction between body and mind implies that God does not contain extension eminenter and so cannot create it. Similarly, for the Peripatetic notion of body as substance-with-qualities, whose unintelligibility ensures in turn the unintelligibility of the distinction between mind and body as substances, or of their union (Newton, Scientific Papers, 105, 108–109: Latin; 139, 141, 142, 143: English). Newton continues this attack on Cartesian and Peripatetic notions of body and mind for another two or three pages. This section of De gravitatione shows that for Newton, in this text at least, metaphysics deals with God the Creator and His management of his creation, with doctrines of substance, the nature of mind and body, and of their interaction and union. Yet in the Principia (1687) we find a different perspective that is all the more telling because it is a public pronouncement made in dogmatic fashion, unlike the suppositions about the nature of body in De gravitatione, or the speculative rhetoric of the

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

9

Quaeries in the Opticks. The famous General Scholium contains a long passage on God and His nature. He is Lord over all, is eternal, infinite, absolutely perfect, omnipotent and omniscient, He is substantially omnipresent. We have no idea of His substance (or of the substance of anything else, for that matter), we know Him only through his attributes, and through the excellency of the natural order and through the final causes of things. He is the God of providence: “no variation in things arises from blind metaphysical necessity, which especially is always and everywhere the same.” Newton rounds off the passage with the remark: “And thus much concerning God, to reason about whom, at least from phenomena, is a concern of Natural Philosophy.”9 So the study of God qua Author of Nature, and I think by implication of souls and mind, is now part of natural philosophy, as Locke’s division of the sciences allows (below). Metaphysics seems to be restricted to such topics as freedom and necessity, causality, and (presumably) being qua being. In 1705 or thereabouts Newton wrote a number of manuscript drafts relating to Query 23 of the Latin Optice (1706), which became Query 31 of the second English edition (1717–1718). These drafts deal with the problems of how to correlate laws of motion, the passivity of bodies, the myriad phenomena of nature not explicable in mechanical terms and the forces that must underwrite them, the mysteries of divine and human volition. In one draft Newton writes that because of the essential passivity of bodies, they cannot move themselves; & without some other principle than the vis inertia there could be no motion in the world. (And what that Principle is & by (means of) [what] laws it acts on matter is a mystery or how it stands related to matter is difficult to explain.) And if there be another Principle of motion there must be other laws of motion depending on that Principle. And the first thing to be done in Philosophy is to find out all the general laws of motion (so far as they can be discovered) on which the frame of nature depends. (For the powers of nature are not in vain [two illegible words]. And in this search metaphysical arguments are very slippery. A man must argue from phenomena.) We find in ourselves a power of moving our bodies by our thoughts (but the laws of this power we do not know) & see the same power in other living creatures but how this is done & by what laws we do not know […]. (U.L.C. Add. 3970, f. 620r)10

The material in round brackets is deleted in the manuscript, but deletion does not necessarily imply rejection of deleted content. Bearing in mind the implications of the General Scholium, we can take it that in this passage Newton means by “metaphysical arguments” non-empirical inquiries into the hidden non-inertial powers, and associated laws of motion hitherto undiscovered, that activate the interacting realms of the spiritual and the corporeal. I think that allows us to identify the referent of “Metaphysicks” in a passage from Query 28 in the Opticks as printed (3rd and  Newton, Principia, II 763–64 (my translation). In an interleaf belonging to Newton’s own interleaved and annotated copy of the second edition (1713), caeca (blind) is omitted. More strikingly, in an interleaf belonging to Newton’s interleaved copy, and in the second edition itself, experimentalem replaces naturalem: “to discourse of God, at least from the phenomena, belongs to experimental philosophy.” 10  Quoted from McGuire, Force, 170–71. 9

10

A. Gabbey

4th English editions, 1721, 1730). Query 28 rejects the hypothesis that light is propagated through a universal fluid medium. The ancient atomists rejected such a medium, tacitly attributing Gravity to some other Cause than dense Matter. Later Philosophers banish the Consideration of such a Cause out of natural Philosophy, feigning Hypotheses for explaining all things mechanically, and referring other Causes to Metaphysicks: Whereas the main Business of natural Philosophy is to argue from Phaenomena without feigning Hypotheses, and to deduce Causes from Effects, till we come to the very first Cause, which certainly is not mechanical […]. (Newton, Opticks, 369)

Still, there is an ambiguity, or maybe a tension arising from an awareness of disciplinary unsettlement, in Newton’s overall position on the question of metaphysics. The problem can be stated simply: how much of the study of God belongs to natural philosophy, how much to metaphysics?

1.4 Locke and Berkeley John Locke stands out from the generality of those who were educated in the Peripatetic tradition. In the final pages of his Essay concerning Human Understanding (1689–1690) he presented a tripartite “Division of the Sciences”: All that can fall within the compass of Humane Understanding, being either, First, the Nature of Things, as they are in themselves, their Relations, and their manner of Operation: Or, Secondly, That which Man himself ought to do, as a rational and voluntary Agent, for the Attainment of any End, especially Happiness: Or, Thirdly, The ways and means, whereby the Knowledge of both the one and the other of these, are attained and communicated […].

So for Locke, following the Stoic (Hellenistic) classification of knowledge (as Leibniz was to note in the Nouveaux Essais), the categorisation of possible sciences is exhausted by Natural Philosophy, Ethics, and Logic, or the Doctrine of Signs. They are “the three great Provinces of the intellectual World,” and are wholly separate, distinct and different from each other (Locke, Essay, IV.21.1–5 720–21). But there has to be room within Lockean natural philosophy for metaphysics qua the science of God, spirits, and minds. His “more enlarged sense” of physics or natural philosophy, the First Division of the sciences, includes the Knowledge of Things, as they are in their own proper Beings, their Constitutions, Properties, and Operations, whereby I mean not only Matter, and Body, but Spirits also, which have their proper Natures, Constitutions, and Operations as well as bodies. (ibid. 720)

And Locke was no Epicurean or Hobbesian materialist. The irony is that he had no account to offer of the nature of the soul, or of the mind. In his analysis of personal identity as consciousness of the person, whether or not attached to the same man, Locke concludes by admitting that some readers will find some of his suppositions strange, and perhaps they are strange. But he may be forgiven, because of

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

11

this ignorance we are in of the Nature of that thinking thing, that is in us, and which we look on as our selves. Did we know what it was, or how it was tied to a certain System of fleeing Animal Spirits; or whether it could, or could not perform its Operations of Thinking and Memory out of a Body organized as ours is; and whether it has pleased God, that no one such spirit shall ever be united to any but one such Body, upon the right Constitution of whose Organs its Memory should depend, we might see the Absurdity of some of those Suppositions I have made. But taking, as we ordinarily now do, (in the dark concerning these Matters) the Soul of a Man, for an immaterial substance, independent from Matter, and indifferent alike to it all, there can from the Nature of things, be no Absurdity at all, to suppose, that the same Soul may, at different times be united to different Bodies, and with them make up, for that time, one Man. (Locke, Essay, II.27.27 347)

In fact, although Locke does not say so, a great deal of the Essay is concerned with metaphysics qua talk about substances, qualities, accidents, causality, mind and souls. But those topics now fall within natural philosophy, or in some cases logic. So what does he actually say about metaphysics? In the Essay, in the chapter “Of Trifling Propositions,” Locke makes it clear what he thinks of one sort of “metaphysick” which does not belong within his division of the sciences. The trifling propositions Locke denounces are analytic or tautologous propositions, whose truths depend solely on the definitions of the terms used. “Hence it comes to pass,” Locke writes, that one may often meet with very clear and coherent Discourses, that amount yet to nothing […] one may make Demonstrations and undoubted Propositions in Words, and yet thereby advance not one jot in the Knowledge of the Truth of Things; v.g. he that having learnt these following Words, with their ordinary mutually relative Acceptations annexed to them; v.g. Substance, Man, Animal, Form, Soul, Vegetative, Sensitive, Rational, may make several undoubted Propositions about the Soul, without knowing at all what the Soul really is; and of this sort, a Man may find an infinite number of Propositions, Reasonings, and Conclusions, in Books of Metaphysicks, School-Divinity, and some sort of natural Philosophy; and after all, know as little of GOD, Spirits, or Bodies, as he did before he set out. (Locke, Essay, IV.8.9 615)

For Locke, metaphysics is the name for a degenerate and dispensable aspect of Peripateticism. But one can discourse critically without resort to tautology, and in a spirit of sceptical inquiry, about substance, man, soul, and the limits of rational, thereby redrawing the boundaries of natural philosophy and logic. George Berkeley seems to have been happy with the traditional classification of knowledge into natural philosophy, first philosophy or metaphysics (which he sometimes uses interchangeably with philosophy), and mathematics. Berkelean idealism makes issues of disciplinary classification less pressing than they were for realists like Descartes, Leibniz, or Locke. Yet Berkeley took a dim view of a certain kind of metaphysics, and of certain paradoxical claims of the mathematicians, while insisting that natural and experimental philosophy suffered not at all from his philosophical doctrines. His dismissal of abstract ideas in the Treatise (1710, 1734) is a dismissal of a certain kind of metaphysics: The plainest things in the world, those we are most intimately acquainted with, and perfectly know, when they are considered in an abstract way, appear strangely difficult and incomprehensible. Time, place, and motion, taken in particular or concrete, are what everybody knows; but having passed through the hand of a metaphysician, they become too abstract and fine, to be apprehended by men of ordinary sense.

12

A. Gabbey

Furthermore, the doctrine of abstract ideas hath had no small share in rendering those sciences intricate and obscure, which are particularly conversant about spiritual things. Men have imagined they could frame abstract notions of the powers and acts of the mind, and consider them prescinded, as well from the mind or spirit itself, as from their respective objects and effects. Hence a great number of dark and ambiguous terms presumed to stand for abstract notions, have been introduced into metaphysics and morality, and from these have grown infinite distractions and disputes amongst the learned. (Berkeley, Principles of Human Knowledge, I.97 and 143, Works, 106f., 122)

Berkeley’s idealism therefore offers an antidote to metaphysical excess. In the Three Dialogues between Hylas and Philonous (1713, 1725, 1734) he lists the advantages of his philosophy for physics and mathematics, and indeed for all sciences, and asks rhetorically, supplying thereby an answer: Then in metaphysics; what difficulties concerning entity in abstract, substantial forms, hylarchic principles, plastic natures, substance and accident, principle of individuation, possibility of matter’s thinking, origin of ideas, the manner how two independent substances, so widely different as spirit and matter, should mutually operate on each other? What difficulties, I say, and endless disquisitions concerning these and innumerable other the like points, do we escape by supposing only spirits and ideas? (Berkeley, Hylas and Philonous Third Dialogue, 204)

This is not to dismiss metaphysics en bloc, but to rid it of semantically vacuous baggage. A memo to himself in “Notebook A” of his Philosophical Commentaries (1707–1708) reads: “Mem: To be eternally banishing Metaphisics &c & recalling Men to Common Sense” (Berkeley, Works, 324). We must be eternally vigilant: trafficking in abstract ideas and unintelligible notions about substance and the like is bad metaphysics, but there is a better kind of metaphysics that contemplates God and His activity, and the human mind and its actions. In De motu (1721) metaphysical abstractions in theories of motion are the target of Berkeley’s criticism, particularly forces or gravity obscurely conceived as natures that are not “objects of sense.” Quoting Leibniz on active primitive force, Berkeley comments that even the greatest men when they give way to abstractions are bound to pursue terms which have no certain significance and are mere shadows of scholastic things. Other passages in plenty from the writings of the younger men could be produced which give abundant proof that metaphysical abstractions have not in all quarters given place to mechanical science and experiment, but still make useless trouble for philosophers. (Berkeley, De motu art 8, 212)

Some have affirmed the existence in bodies of vital principles or active forces, obscure notions unsupported by any experimental or experiential evidence. But those who will have mind to be the principle of motion are advancing an opinion fortified by personal experience, and one approved by the suffrages of the most learned men in every age. (Berkeley, De motu art 31, 217)

Some, such as Descartes and Newton, have correctly recognised God as the source of all corporeal activity and as the cause of the existence of individual bodies in this or that state of motion or rest. However, Berkeley warns against disciplinary misunderstandings:

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

13

But to treat of the good and great God, creator and preserver of all things, and to show how all things depend on supreme and true being, although it is the most excellent part of human knowledge, is, however, rather the province of first philosophy or metaphysics and theology than of natural philosophy, which to-day is almost entirely confined to experiments and mechanics. And so natural philosophy either presupposes the knowledge of God or borrows it from some superior science. […] 35. The imperfect understanding of this situation has caused some to make the mistake of rejecting the mathematical principles of physics on the ground that they do not assign the efficient causes of things. It is not, however, the business of physics or mechanics to establish efficient causes, but only the rules of impulsions or attractions, and, in a word, the laws of motions, and from the established laws to assign the solution, not the efficient cause, of particular phenomena. (Berkeley, De motu art 34 and 35, 218)

In physics, as he explains at the end of De motu, sense and experience which reach only to apparent effects hold sway; in mechanics the abstract notions of mathematicians are admitted. In first philosophy or metaphysics we are concerned with incorporeal things, with causes, truth, and the existence of things. […] 72. Only by meditation and reasoning can truly active causes be rescued from the surrounding darkness and be to some extent known. To deal with them is the business of first philosophy or metaphysics. Allot to each science its own province; assign its bounds; accurately distinguish the principles and objects belonging to each. Thus it will be possible to treat them with greater ease and clarity. (Berkeley, De motu art 71 and 72, 227)

1.5 Metaphysics in the Public Domain in Mid-century Britain and Germany Before coming to Hume, let us see what readers in eighteenth-century Britain and Germany learned about the discipline of metaphysics from the encyclopaedist and the systematiser. Locke’s Essay, and Newton’s remark about God in the General Scholium of the Principia, were significant – perhaps decisive – factors in the emergence in Britain of new senses of “metaphysics.” Locke’s influence can be seen in John Harris’s widely-read Lexicon Technicum. In the preface to the first edition (1704), Harris chauvinistically criticises Etienne Chauvin’s Lexicon Philosophicum for being “too much filled with School Terms, to be usefully instructive; and is as defective in the Modern Improvements of Mathematical and Physical Learning, as it abounds with a Cant which was once mistaken for Science.” So he tells his readers that “in Logick, Metaphysicks, Ethicks, Grammar, Rhetorick, &c. I have been designedly short; giving usually the bare meaning only of the Words and Terms of Art […].” He was indeed short in the case of metaphysics, for which he provides no entry at all. The oversight is not too surprising, because in the article on “Physiology, Physicks, or Natural Philosophy, […] the Science of Natural Bodies, and their various Affections, Motions, and Operations,” we learn that “the Only True Philosophers” to have engaged in physics are the experimental and mechanical philosophers, whereas the Peripatetics merely gave names to things, rather than find their true reasons and causes, “so that their Physicks is a kind of Metaphysicks”

14

A. Gabbey

(Harris, Lexicon 1st ed., a2 recto and a4 verso).11 In the second edition of the Lexicon (1708, 1710), we learn further that Physicks, or Natural Philosophy, is the Speculative Knowledge of all Natural Bodies, (and Mr. Lock thinks, That God, Angels, Spirits &c, which usually are accounted as the Subject of Metaphysicks, should come into this Science) and of their proper Natures, Constitutions, Powers, and Operations. (Harris, Lexicon 2nd ed., I (no pagination), art. “Physicks”)

Though neither encyclopaedist nor systematiser, Thomas Johnson (d. 1737), Fellow of Magdalene College, Cambridge, merits a mention at this point. His Quaestiones philosophicae (3rd edition 1741), written for the use of Cambridge students, is a valuable indication of the bibliographical state of philosophy, and of the variety of currently debated questions, in mid-century British academia. The quaestiones fall within the main branches of science and philosophy. Johnson states each quaestio without comment, and follows it with a list of those texts (ancient and modern) whose authors are “in favour,” and with another list of those who are “against” (occasionally some are “undecided”). Johnson does not define “metaphysics,” but it emerges from his Chapter X, on “Quaestiones metaphysicae,” that for him metaphysics admits a long roster of topics that give rise to disputation: ideas and perception, mind and soul, thinking matter, God and His existence, causality, infinity and eternity, space, time, motion, liberty and necessity, divine foreknowledge, evil, personal identity, individuation, reason and faith (Johnson, Quaestiones Philosophicae, chap. X).12 Ephraim Chambers’ Cyclopaedia (seventh edition, 1751–1752) sets out what we can suppose the general educated public in mid-century Britain would have known about “metaphysics.” Chambers recognises the differences of opinion on its definition. Some take it to be “that part of science which considers spirits, and immaterial beings; which others choose to distinguish by the name of pneumatics.” For others, recalling the etymology of the term, metaphysics is “trans-natural, praeter-natural, or even post-natural philosophy.” Yet others, with more propriety, conceive metaphysics to be what some others call ontology, or ontosophy, i.e., the doctrine de ente, or of being, quatenus being. In the same view, some philosophers call this science by the name philosophia, or scientia generalis, as being the foundation, or, as it were, the stamen or root from whence all the other parts of philosophy arise, and wherein they all meet; its object being being in the abstract, or general, not restrained to this or that species of beings; not to spirit any more than body; so the doctrines of metaphysics are applicable to all beings whatever. (Chambers, Cyclopedia, II, article “Metaphysics.”)

It is likely that Chambers knew the work of Christian Wolff, the most influential systematiser of eighteenth-century German philosophy. Wolff took a broad view of the scope of metaphysics. For example, according to his Philosophia rationalis sive  Though the two Lexica were not intended to serve the same purpose, Chauvin’s Lexicon (1692, 1713), an encyclopaedia of Scholastic and Cartesian notions compiled post-Descartes, is much more useful than we should infer from Harris’s dismissive remarks. See Gilson, Index, v. 12  I am indebted to Justin Broackes for allowing me to see his translation of Chapter X of Johnson, Philosophical Questions. 11

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

15

Logica (1740), metaphysics is the science of being, of spirits, and of the world in general. Accordingly, it comprises Ontology or First Philosophy, General Cosmology, Psychology (Rational and Empirical), Pneumatics, and Natural Theology.13 Apparently less sweeping in his understanding of metaphysics was the most important historian of philosophy of the eighteenth-century, Wolff’s compatriot Jakob Brucker. We can infer from Tome IV (1744) of his Historia critica philosophiae (1742–1767) what he took to be the domain of metaphysics. Book II, Part II, deals in detail “De emendatione philosophiae in singulis eius partibus,” and the five parts in question are philosophia rationalis (logic and methodology), philosophia naturalis, metaphysica et pneumatologia, philosophia moralis, and philosophia civilis. To judge by the chapter “De metaphysicae et pneumatologiae mutationibus recentioribus,” metaphysics deals with God and his existence (which provokes Brucker into enormously long digressions on the atheists Vanini and Spinoza, and on Spinoza’s followers and critics), psychologia (the special name for doctrines de anima), and separated spirits and immaterial substances.14 That sense of metaphysics concords with the first of the senses listed by Chambers, yet one gets the impression that the general public understanding of what metaphysics is about was of a more monolithic and inclusive discipline in mid-eighteenth-century Germany than was the case in Britain.

1.6 Hume On the question of metaphysics in Hume’s thought, his Treatise of Human Nature (1739–1740) is perhaps more exploratory, and less incisive, than the Enquiries concerning Human Understanding (1748), but I think they express basically the same view. In the Treatise, there are sections on the infinite divisibility of space and time, on scepticism with regard to the senses, and on the immateriality of the soul, in each of which Hume employs the term “metaphysics” or “metaphysicians.” The context in which they appear suggests that he understands metaphysics to consist in the study of typically profound or abstruse issues, such as the nature of numbers and geometrical extension, the ontological status of the objects of thought, the relation of real existents to spatial location, individuation and personal identity (Hume, Treatise, 30, 32, 189–190, 235–36). The same holds for the corresponding sections of the Enquiries, except that personal identity and the immateriality of the soul are not discussed in the later work. At the beginning of the Treatise we have Hume’s optimistic conviction that success in the sciences will come only if we “march up directly to the capital or center  Wolff, Logica, 45. On the inclusion of empirical psychology, see Jean Ecole’s editorial comments in ibid. (Hildesheim 1983), xxx and lxxx–lxxxi. 14  Brucker, Historia critica, IV.2 664–721. On Brucker’s influential conception of the history of philosophy, see Schmidt-Biggemann, Jacob Brucker, Part II (“Die Konzeption der Philosophiegeschichte und deren Wirkung”). 13

16

A. Gabbey

of these sciences, to human nature itself; which being once masters of, we may every where else hope for an easy victory.” “There is no question of importance,” he explained, “whose decision is not compriz’d in the science of man; and there is none, which can be decided with any certainty, before we become acquainted with that science.” (Hume, Treatise, xvi). Yet it is human nature, more precisely “the operations of the understanding,” that will emerge in the Enquiries as the subject of “true metaphysics.” (Wright, Sceptical Realism, 124–25) At the beginning of the Enquiries, in the opening section on “the different species of philosophy,” Hume notes that the science of human nature – moral philosophy – can be treated in two ways. First, it is the science of man considered as born for action, in which “the most striking observations and instances from common life” furnish the materials out of which sound precepts for the good life will emerge, and in which vice and virtue are felt, not thought. Second, it is also the more difficult science of man the rational and speculative creature, more mindful of his understanding than of his actions, disdainful of those who speak of truth and falsehood, vice and virtue, beauty and deformity, without knowing the origin of these dichotomies. Not surprisingly, most people will always prefer the first kind of moral philosophy, being more useful and more in touch with ordinary life. On the other hand, the second kind, the abstruse philosophy, is out of place in ordinary life, its principles being beyond the comprehension of most people, and its influence on our conduct minimal. Thus posterity has not been kind to the abstract reasoners; fame has attended the easy philosophy of action. Mistakes are common in the deeper sort of philosophy, they are necessarily the mother of apparent contradiction and unusual conclusions. Less common in the other sort are the mistakes that lead away from common sense, the court of appeal that saves the philosopher from the winding paths of illusion (Hume, Enquiries, 6–7). A page or so later Hume remarks: Were the generality of mankind contented to prefer the easy philosophy to the abstract and profound, without throwing any blame or contempt on the latter, it might not be improper, perhaps, to comply with this general opinion, and allow every man to enjoy, without opposition, his own taste and sentiment. But as the matter is often carried farther, even to the absolute rejecting of all profound reasonings, or what is commonly called metaphysics, we shall now proceed to consider what can reasonably be pleaded in their behalf. (Hume, Enquiries, 9)

Hume’s defense of metaphysics – that is, the proper sort of metaphysics – begins by noting that “the easy and humane philosophy” depends on the findings of metaphysics, without which it “can never attain a sufficient degree of exactness in its sentiments, precepts, or reasonings.” Literature and art depend on a knowledge of human behaviour, of human passions and “the operations of the understanding.” In this way the abstruser kind of philosophy will improve the work of the artist, the politician, the lawyer and the military commander. And even if there were no such advantages, “the gratification of an innocent curiosity” ought not to be despised, since it is one of the few harmless pleasures we have. To produce light from obscurity is a delight, and a matter for rejoicing.

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

17

But obscurity is the inevitable source of error, so another objection, the justest and most plausible objection against a considerable part of metaphysics, [is] that they are not properly a science; but arise either from the fruitless efforts of human vanity, which would penetrate into subjects utterly inaccessible to the understanding, or from the craft of popular superstitions, which, being unable to defend themselves on fair ground, raise these intangling brambles to cover and protect their weakness. (Hume, Enquiries, 12)

Is that a reason to abandon metaphysics and leave the field to the enemy? Not at all. Despair has no place in the sciences, and past failures should challenge us to make new discoveries. How then should we proceed? The only method of freeing learning, at once, from these abstruse questions, is to enquire seriously into the nature of human understanding, and show, from an exact analysis of its powers and capacity, that it is by no means fitted for such remote and abstruse subjects. We must submit to this fatigue, in order to live at ease ever after: And must cultivate true metaphysics with some care, in order to destroy the false and adulterate. […] Accurate and just reasoning is the only catholic remedy, fitted for all persons and all dispositions; and is alone able to subvert that abstruse philosophy and metaphysical jargon, which, being mixed up with popular superstition, renders it in a manner impenetrable to careless reasoners, and gives it the air of science and wisdom.” (Hume, Enquiries, 12–13)

One positive outcome of this method will be the development of a “mental geography, or delineation of the distinct parts and powers of the mind,” which are much more difficult to analyse than the objects of natural philosophy. As for whether such a science is “uncertain and chimerical,” only a scepticism “subversive of all speculation, and even action” could undermine it on that score. The mind has many distinct and identifiable powers and faculties that lie within our understanding, so it is possible to make true or false claims about them. We respect the work of a Newton, who has discovered the forces and laws that govern the system of the planets, and others who have made comparable advances in other areas of natural philosophy. So “there is no reason to despair of equal success in our enquiries concerning the mental powers and economy, if prosecuted with equal capacity and caution.” (Hume, Enquiries, 13–15).

1.7 Metaphysics and the Physicians: William Cullen The impact of Hume’s view of metaphysics in eighteenth-century Britain can be seen in the work of William Cullen, Professor of the Theory of Medicine in the University of Edinburgh, and a friend of Hume and his physician. Some twenty years after Hume’s Enquiry, Cullen was delivering his lectures on the Institutions of Medicine (1766–1773), first published in 1772. In his lectures of 1770–1771 Cullen declared: “if by Metaphysics we understand as I think we should the Operations of the human Mind in thinking, that is, the History of the human Mind, then I say Metaphysics are unavoidable not only in Physick, but perhaps in every Science if a

18

A. Gabbey

man does deep.”15 Hume’s contemporaries and post-Cartesian predecessors clearly understood the close links between “physick” (including physiology) and the operations of the mind – the core of metaphysics proper. They knew that a satisfactory theory of mind was a requirement for understanding the relations between mental behaviour and physiological processes, and therefore for acquiring knowledge of the external world as mediated through the senses. In contrast to the Cartesian self-­ assurance of the previous century, that understanding was mingled with a sense of the mysteriousness of the relationship between the mental and the physiological.16 In his account of volition in the Enquiries Hume had noted that the immediate object of power in voluntary motion, is not the member itself which is moved, but certain muscles, and nerves, and animal spirits, and perhaps, something still more minute and more unknown, through which the motion is successively propagated, ere it reach the member itself whose motion is the immediate object of volition. Can there be a more certain proof, that the power, by which this whole operation is performed, so far from being directly and fully known by an inward sentiment of consciousness, is, to the last degree, mysterious and unintelligible? (Hume, Enquiries, VII.1 66)

Cullen’s lecturing style was to comment in class, often at length, on what appeared in their first published form as numerous numbered sections of the Institutions, but without the commentaries. Fortunately, this additional material exists in manuscript in Cullen’s Papers in the National Library of Scotland (Edinburgh), and a selection of them was collected and published by John Thompson in his 1827 edition of Cullen’s Works. They and Cullen’s work in general have been studied anew most recently by John Wright, to whom we are indebted for showing the importance of medical writers for our understanding of metaphysics and the philosophy of mind in mid-eighteenth-century Britain, and to whom I am indebted for providing the inspiration and starting point for this paper.17 Part I of Cullen’s Institutions of Medicine is on Physiology. His definition of “physiology,” or “animal economy,” is of particular interest (Art. IV): “The doctrine which explains the conditions of the body and of the mind necessary to life and health.” Commenting on this definition, he explains that physiology makes use of the teachings of natural philosophy, chemistry, and anatomy, and continues: I have added here a particular in my Physiology that is not common – ‘and of the mind’; and some persons may think that this is hardly done with propriety. However the condition of the mind may ultimately arise, we often do see conditions of mind arise, that we cannot trace to a corporeal cause; while, at the same time, they may produce very considerable effects upon the bodily state; so that it was necessary to say that Physiology referred to the conditions of the mind, as well as those of the corporeal part. So far from being able to neglect the mind, the most considerable functions are connected with particular operations,  Lectures on the institutes of medicine by Dr Cullen, 1770–71: National Library of Scotland, Ms 3535, fol. 25–26, quoted in Wright, Metaphysics and Physiology, 251. 16  For seventeenth- and eighteenth-century conceptions of and debates on the mind-body (soulbody, res extensa-res cogitans) problem and its contemporary physiological underpinnings as well as ideological context, see the chapter »Materialistic Theories of Mind and Brain« by Ann Thomson in the present volume. 17  Wright, Metaphysics and Physiology. See also his Matter, mind and active principles. 15

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

19

and a particular state of our immaterial part; and, indeed, I find that the conditions of the human mind must engage our attention more than they have done hitherto. Some, indeed, have thought that I have gone too far in introducing a great deal of metaphysics into my course; but unless the history of the operations of the human mind is to be considered as such, they are mistaken; and I resolve to go no further than I can point out these operations as referring to the state of the body. (Cullen, Works, I 5–6)

Cullen continues with an analysis of the mutual dependence of the will and the muscles, via the brain: most muscular movement is at the command of the will, most volitions are caused by sensations. Hence the fundamental importance of the nervous system, the topic of Section II of his Physiology. He gives a detailed general description of the nervous system, including in Art. XXXI and commentary a long consideration of mind and its relation to the body. In the living man there is an immaterial thinking substance or MIND constantly present; and every phenomenon of thinking is to be considered as an affection or faculty of the mind alone. But this immaterial and thinking part of man is so connected with the material and corporeal part of him, and particularly with the nervous system, that motions excited in this give occasion to thought; and thought, however occasioned, gives occasion to new motions in the nervous system.

Then he makes a nice methodological move that Hume and Locke would have approved. This mutual communication of influence we assume with confidence as a fact; but the mode of it we do not understand, nor pretend to explain; and therefore we are not bound to obviate the difficulties that attend any of the suppositions which have been made concerning it. (Cullen, Works, I 17–18)

In his commentary on the article, Cullen recognises an ambiguity in the phrase “of the mind alone,” and settles for “of the mind,” meaning that thought as such is caused by and is therefore ultimately dependent on an immaterial substance. He refers his students to “divines and metaphysicians,” who have demonstrated the proposition. Still, the causal relation between “the thinking part of man” and the body, especially the nervous system, is an established but inexplicable fact. There is not in nature, seemingly in the acknowledgement of all philosophers, a greater mystery than this mutual action of the soul and body upon one another; philosophers have at least talked about the matter, and there are three very celebrated systems with regard to it.

The three systems are the doctrine of physical influx, which he attributes to Aristotle, meaning I think the Scholastics; the system of occasional causes, which he attributes to Descartes, meaning I think the Cartesians; and lastly, “Leibnitz has proposed a third, which supposes the existence of a pre-established harmony.” (Cullen, Works, I 18–19)18 “You may consult these,” he says,

 For an excellent account of the tricky notion of physical influx, see O’Neill, Influxus Physicus. Cullen’s sources for the three systems of causality were probably Leibniz, or Wolff, or a standard Wolffian textbook such as Baumgarten’s Metaphysica (the prescribed reading in Kant’s metaphysics lectures). See for example Baumgarten’s Metaphysica (4th ed. 1757), Pars II (Cosmologia), Caput III (Perfectio Universi), Sect. II (Substantiarum mundanarum commercium), reprinted in 18

20

A. Gabbey but I do not say a word of them, because when I have considered them as well as I can, I cannot perceive that they have the least effect or influence in explaining any thing: they do not admit of any application, either in physic or any other part of science, that I see. With regard to the mode of this mutual influence, it will be allowed that as you adopt one or other of these hypotheses, it may affect religious belief, but it can have no effect in physic, so that it is not my province to consider them.” (Cullen, Works, I 18–19)

Is this the contemptuous dismissal that it seems? Perhaps not. Cullen is not pronouncing on the truth or falsity of the three systems, only on their explanatory relevance to the sciences, especially medicine. Furthermore, the fact that he mentions these doctrines at all in his Institutions of Medicine reflects the belief, shared by his medical contemporaries, that at least they do have a prima facie relevance to medical research and teaching. Still, Cullen’s remarks suggest a new demarcation between the metaphysical world and the world of empirical and experimental inquiry into animate and inanimate nature. In Britain at least, something had happened to metaphysics since the days of Descartes and Leibniz and the Cartesians, none of whom would have been pleased to learn that their theories of causal interaction explained nothing whatsoever. To see more closely what had happened to metaphysics, we may look at how Cullen continues his commentary on Art. XXXI, and on Arts. XXXII–XXXV. You might expect him now to draw the curtain over mind-body interactions and get on with the physiology of the nervous system. But he continues for another seven or eight pages on the problem, and includes critical accounts of the mind-body theories of physicians and medical writers: Robert Whytt, Boerhaave, Haller, Stahl, and Jerome David Gaub. “But I must say,” he explains, that the mutual influence being supposed and granted, physicians have differed very much with respect to the degree and extent of that influence, and therefore I am obliged to take some notice of these opinions, though they truly have not such influence as has been imagined, nor is it necessary to adopt either the one or other opinion upon the subject.

Is this a concession, made before medical students, to fellow-physicians, whose metaphysical doctrines belong nonetheless in the same bag as those of non-medical people like Leibniz and Descartes? Or is there still a difference between the metaphysical doctrines of the physicians and those of the philosophers that justifies a two-sentence dismissal of the one, and a five-page critical exposition of the other? A bit of both, no doubt, but I think there is something in the difference between the two kinds of metaphysics that clarifies Cullen’s attitude to them. The doctrines of influxus physicus, of occasionalism, and of the pre-established harmony, have this in common, that they are general doctrines of causality that apply to any causal interaction whatever. Cullen is aware of this, as would be anyone who learned these doctrines from a contemporary manual such as Baumgarten’s Metaphysica. That is what permits him to declare that “they do not admit of any application, either in

Kant’s Gesammelte Schriften, herausgegeben von der Preussischen Akademie der Wissenschaften, Bd. XVII (Berlin and Leipzig, 1926), 119–123.

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

21

physic or any other part of science.” Cullen is saying in effect that a metaphysical doctrine that purports to explain everything in general, explains nothing in particular. However, Cullen’s fellow physicians are not trying to explain everything within the domain of causal relations, just the relation between mind and the nervous system, and naturally they have differing theories about it. He tells his students that they don’t have to decide between these competing theories, but it is clear that Cullen himself has preferences. He rejects the system of the materialists, a narrow sect with few adherents, and sides with the generality of physicians, who are “sufficiently orthodox upon this point,” and who admit the existence of soul. The late Dr Whytt (1714–1766), Cullen’s predecessor in the Chair of the Institutes of Medicine, argued that physiological phenomena cannot be explained without “the supposition of a soul as a sentient principle.” But this dualism carries with it an unmistakable whiff of necessitarianism. The involuntary, non-rational actions of the mind on the body are “as certainly determined by an ungrateful sensation or stimulus affecting the organs, to exert its power in bringing about these motions, as a scale which, by mechanical laws, turns with the greatest weight.”19 Cullen shares these views, as do the majority of physicians. He cites Boerhaave to the effect that body and mind are distinct substances so united that there is a one-to-one correspondence between bodily states and states of thought. Haller too believes that soul and body act on each other by physical necessity. Stahl takes a quite different view, which Cullen rejects. The Stahlians believe correctly that the soul has power to move the body, but they mistakenly think that the soul is not necessarily determined by bodily states, but surveys the body from within, seeing what needs attending to, and excites or stops motions in the body accordingly. David Gaub’s position falls somewhere between that of Boerhaave and Stahl. Cullen declares himself “equally remote” from the materialists and the Stahlians, and “if I were to choose, I would take the opinion of Dr Gaubius.” (Cullen, Works, I 22) And yet, Cullen insists to his students that none of these systems is “necessary to the system of physics,” which suggests uncertainty, or a certain ambivalence, on the proper role of such theories in the business of medicine.

1.8 The Kantian Turn This survey of the fortunes of metaphysics in the writings of Leibniz, Newton, Berkeley, Hume and Cullen, indicates that metaphysics in Britain followed a radically different path from its parallel development in Germany, from Leibniz through Wolff and Baumgarten to Kant. I do not have the space to argue this wider claim in detail, but I began with an instructive contrast between Newton and Leibniz, and on the way mentioned Wolff and Brucker, so in closing I point to the end of the Critique

 Cullen is quoting from Whytt’s An Essay on the Vital and other Involuntary Motions of Animals (1751). 19

22

A. Gabbey

of Pure Reason, where Kant rounds off the “Transcendental Doctrine of Method” with two chapters, one on “The Architectonic of Pure Reason,” the other on “The History of Pure Reason.” Ordinary knowledge reaches the level of science only if it can be made to show systematic or architectonic unity. This is not the unity of a system like that of Wolff, even less the encyclopedic unity of taxonomists like Alsted that results from a historically contingent accretion of disciplinary areas, but the architectonic unity that arises in conformity with an idea whose purposes are imposed by reason a priori. Science can arise only architectonically, on account of the affinity [of its parts] and [their] derivation from a single supreme and internal purpose that makes the whole possible in the first place. For the schema of what we call science must contain the whole’s outline (monogramma) and the whole’s division into members in conformity with the idea – i.e., it must contain these a priori – and must distinguish this whole from all others securely and according to principles.” (Kant, Critique of Pure Reason, (A 833–34 / B 861–62) 756)

All rational knowledge comes from concepts (philosophical knowledge), or from the construction of concepts (mathematical knowledge). Now, the philosophy of pure reason either is the propadeutic (preparation), which investigates our power of reason with regard to all pure a priori cognition, and is called critique; or, second, it is the system of pure reason (science), i.e., the whole (true as well as seeming) philosophical cognition from pure reason in its systematic coherence, and is called metaphysics. This latter name, however, may also be given to the whole of pure philosophy, including critique, in order to encompass therein the investigation of all that can ever be cognized a priori, as well as the exposition of what makes up a system of pure philosophical cognitions of this a priori kind while differing from all empirical and likewise from the mathematical use of reason. (ibid., (A 841 / B 869) 761–62)

The Kantian sense of metaphysics as an architectonic system of pure reason was not an option in Britain, or even a possibility, once Locke, with the support of the public Newton, had shifted its viable content to other disciplines, retaining the name “metaphysics” for exercises in tautology. Berkeley’s contribution was not to dispense with metaphysics in one of its important traditional senses, but to make it easier for practitioners of the sciences, like Cullen, to dispense with the kind of metaphysics that Descartes and Leibniz insisted formed the groundwork of the science of nature. Hume restricted the topical extension of metaphysics, retaining for the title of “true metaphysics” the most abstruse and most difficult of all inquiries, the workings and powers of the human mind itself, investigated according to “the experimental method of reasoning,” as promised on the title-page of the Treatise. British physiologists and psychologists, like Cullen, maintained that Human spirit of inquiry, and carried into effect the associated experimental program. It is surely within that tradition that we can place the laconic remarks that Charles Darwin entered into one of his Notebooks on 16 August 1838: “Origin of man now proved. – Metaphysics must flourish. – He who understands baboon would do more toward metaphysics than Locke.”20

20

 Notebook M, 16 August 1838. Darwin, Notebooks, 539.

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

23

References Alsted, Johann-Heinrich. 1630. Encyclopedia. Septem tomis distincta, I.  Praecognita disciplinarum, libris quatuor. II.  Philologia, libris sex. III.  Philosophia theoretica, libris decem. IV. Philosophia practica, libris quatuor. V. Tres superiores facultates, libris tribus. VI. Artes mechanicae, libris tribus. VII. Farragines disciplinarum, libris quinque. Serie praeceptorum, regularum, & commentariorem perpetua. 4 vols. Herborn: Hulsius, 1630; Lyons: J. A. Huguetan filii et M. A. Ravaud, 1649. Bacon, Francis. 1973. The Advancement of Learning (1605), ed. G.W. Kitchin, introduction by Arthur Johnston. Everyman’s University Library, London: J.M. Dent & Sons Ltd. Berkeley, George. 1975. Philosophical Works, Including the Works on Vision, introduction and notes by M. R. Ayers. London: Dent; Totowa: Rowman and Littlefield. Brucker, Johann Jacob. 1975. Historia critica philosophiae a tempore resuscitatarum in occidente litterarum ad nostra tempora. 6 vols. (Leipzig. 1742–1767), Hildesheim: Olms. Chambers, Ephraim. 1751–1752. Cyclopaedia: or, An Universal Dictionary of Arts and Sciences; Containing the Definitions of the Terms, and Accounts of the Things Signify’d Thereby, in the Several Arts, Both Liberal and Mechanical, and the Several Sciences, Human and Divine. 7th ed. London: printed for W. Innys, 1751–1752. (1st ed., 1728.) Chauvin, Etienne. 1967. Lexicon philosophicum secundis curis Stephani Chauvini... novum opus in lucem prodeat. 2nd ed. Leeuwarden: Franciscus Halma, 1713. First ed. Lexicon rationale, sive Thesaurus philosophicus ordine alphabetico digestus. Rotterdam: Peter van der Slaart, 1692. Reprinted Düsseldorf: Stern. Cullen, William. 1827. The Works of William Cullen, M.D.  Professor of the Practice of Physic in the University of Edinburgh: Containing His Physiology, Nosology, and the First Lines of the Practice of Physic: With Numerous Extracts from His Manuscript Papers, and from His Treatise of the Materia Medica, ed. John Thompson. 2 vols. Edinburgh: Blackwood. Darwin, Charles. 1987. Charles Darwin’s Notebooks, 1836–1844: Geology, Transmutation of Species, Metaphysical Enquiries, transcribed & edited by Paul H.  Barrett, Peter J.  Gautrey, Sandra Herbert, David Kohn, and Sydney Smith. London: British Museum (Natural History); Ithaca: Cornell University Press. Freedman, Joseph S. 1985. Deutsche Schulphilosophie im Reformationszeitalter (1500–1650): ein Handbuch für den Hochschulunterricht. Arbeiten zur Klassifikation 4, Münster: Münsteraner Arbeitskreis für Semiotik. Gilson, Etienne. n.d. Index scolastico-cartésien (1912). New York: Burt Franklin. Goclenius, Rodolphus. 1980a. Lexicon philosophicum, quo tanquam clave philosophiae fores aperiuntur (1613). Hildesheim: Olms. ———. 1980b. Lexicon philosophicum Graecum (1615). Hildesheim: Olms. Harris, John. 1708–1710. Lexicon Technicum: or, An Universal English Dictionary of Arts and Sciences: Explaining Not Only the Terms of Art, But the Arts Themselves. 2 vols. London: Printed for Dan. Brown, Tim. Goodwin, Tho. Newborough [et  al.], 1704–1710 (2nd ed. 1708–1710). Heereboord, Adriaan. 1659. Meletemata philosophica. Editio altera Leiden. Hume, David. 1975. Enquiries Concerning Human Understanding and Concerning the Principles of Morals, ed. L. A. Selby-Bigge (based on posthumous edition of 1777). 3rd ed. (with text revised & notes by P. H. Nidditch) Oxford: Clarendon Press. ———. 1978. A Treatise of Human Nature, ed. L. A. Selby-Bigge. 2nd ed. (text revised and variant readings by P. H. Nidditch). Oxford: Clarendon Press. Johnson, Thomas. 1741. Quaestiones Philosophicae, in Justi Systematis Ordinem Dispositae. Auctoribus Adductis, et Singulis in proprias Hypotheses dispertitis. Editio Tertia, prioribus Auctior, & ad Usus Philosophicos Accommodatior. Ad calcem subjicitur Appendix de Legibus Disputandi. Operâ Tho. Johnson, A.M. Coll. Magd. Cantab. Soc. Cambridge: [Typis Academicis, excudebat Josephus Bentham] impensis Gul. Thurlbourn, 1741. (1st ed. 1732, 2nd ed. 1735)

24

A. Gabbey

———. 2002. Thomas Johnson’s Philosophical Questions, Translated from the Latin: An 18th-­ Centuy Guide to Disputes in Physics, Astronomy and the Other Natural Sciences, As Well As in Logic, Metaphysics and Ethics. Introduction, bibliography and notes by Justin Broackes. S.l., s.p. Kant, Immanuel. 1996. Critique of Pure Reason, Unified Edition (with All Variants from the 1781 and 1787 editions), trans. Werner S.  Pluhar, introduction by Patricia Kitcher. Indianapolis; Cambridge: Hackett Publishing Company. Keckermann, Bartholomew. 1614. Operum omnium quae extant tomus primus. Complectens Praecognita Philosophiae, Gymnasia, variáque Systema Logica, Systema Physicum, Astronomicum, Geographicum, Metaphysicae Compendium. Geneva: apud Petrum Aubertum. Kraye, Jill. 1988. Moral Philosophy. In The Cambridge History of Renaissance Philosophy, ed. Charles B. Schmitt et al., 303–386. Cambridge: Cambridge University Press. Leibniz, Gottfried Wilhelm. 1960–1961. Philosophische Schriften, ed. by C. I. Gerhardt. Vols. 1–7 (1875–1890), Hildesheim: Olms [GP]. ———. 1966. Opuscules et fragmnets inedits de Leibniz: extraits des manuscrits de la Bibliotheque royale de Hanovre, ed. Louis Couturat (1903). Hildesheim: Olms [C]. ———. 21969. Philosophical Papers and Letters, ed. and trans. by Leroy E. Loemker. Synthese Historical Library, vol. 2. Dordrecht: Reidel [PL]. Locke, John. 1979. An Essay Concerning Human Understanding, ed. Peter Nidditch (based on 4th edition of 1700). Oxford: Clarendon Press. Lohr, Charles. 1988. Metaphysics. In The Cambridge History of Renaissance Philosophy, ed. Charles B. Schmitt et al., 537–638. Cambridge: Cambridge University Press. ———. 2016. Metaphysics and Natural Philosophy as Sciences: The Catholic and Protestant Views in the Sixteenth and Seventeenth Centuries. In Philosophy in the Sixteenth and Seventeenth Centuries: Conversations with Aristotle, ed. C. Blackwell and S. Kusukawa, 280–295. London/ New York: Routledge. McGuire, J.E. 1968. Force, Active Principles, and Newton’s Invisible Realm. Ambix 15: 154–208. Micraelius, Johann. 1653. Lexicon philosophicum terminorum philosophis usitatorum ordine alphabetico. Jena: impensis Jeremiae Mamphrasii, Bibliop; Stetinensis: typis Casparis Freyschmidii. Nadler, Steven, ed. 1993. Causation in Early Modern Philosophy: Cartesianism, Occasionalism, and Preestablished Harmony. The Pennsylvania State University Press: University Park. Newton, Isaac. 1962. Unpublished Scientific Papers of Isaac Newton: A Selection from the Portsmouth Collection in the University Library, Cambridge, ed. A.R.  Hall and M.B.  Hall. Cambridge: Cambridge University Press, 1978. ———. 1972. Isaac Newton’s Philosophiae Naturalis Principia Mathematica, ed. A.  Koyré, I. B. Cohen, and Anne Whitman (based on 3rd edition 1726, with variant readings). 2 vols. Cambridge: Cambridge University Press. ———. 1979. Opticks, or A Treatise of the Reflections, Refractions, Inflections & Colours of Light, Based on the Fourth Edition London, 1730. Foreword by Albert Einstein; introduction by Edmund Whittaker; preface by I. Bernard Cohen; Analytical Table of Contents prepared by Duane H.D. Roller. New York: Dover Publications. (1st English ed. 1704, 1st Latin ed. 1706) O’Neill, Eileen. 1993. Influxus Physicus. In Causation in Early Modern Philosophy, ed. S. Nadler, 27–55. University Park: The Pennsylvania State University Press. Schmidt-Biggemann, Wilhelm and Theo Stammen, eds. 1998. Jacob Brucker (1696–1770), Philosoph und Historiker der europäischen Aufklärung. Colloquia Augustana (Institut für Europäischen Kulturgeschichte der Universität Augsburg), vol. 7. Berlin: Akadamie Verlag. Stewart, M.A., ed. 1990. Studies in the Philosophy of the Scottish Enlightenment, Oxford Studies in the History of Philosophy. Vol. 1. Oxford: Clarendon Press. Wallace, William A. 1988. Traditional Natural Philosophy. In The Cambridge History of Renaissance Philosophy, ed. Charles B.  Schmitt et  al., 201–235. Cambridge: Cambridge University Press.

1  Disciplinary Transformations in the Age of Newton: The Case of Metaphysics

25

Wolff, Christian. 1983. Philosophia rationalis sive Logica, methodo scientifica pertractata et ad usum scientiarum atque vitae aptata. Praemittitur discursus praeliminaris de Philosophia in genere. Editio tertia emendatior (1740). Gesammelte Werke II. Abt. Bd. 1.1. Hildesheim: Olms. Wright, John P. 1983. The Sceptical Realism of David Hume. Minneapolis: University of Minnesota Press. ———. 1985. Matter, Mind and Active Principles in Mid Eighteenth-Century British Physiology. Man and Nature (Edmonton) 4: 17–27. ———. 1990. Metaphysics and Physiology: Mind, Body, and the Animal Economy in Eighteenth-­ Century Scotland. In Studies in the Philosophy of the Scottish Enlightenment, ed. M.A. Stewart, 251–301. Oxford: Clarendon.

Part II

Metaphysics and the Analytical Method

Chapter 2

Leibniz’ Concept of Possible Worlds and the Analysis of Motion in Eighteenth-­Century Physics Hartmut Hecht

Abstract  The following text describes the development of the problem of the choice of the best of all possible worlds as a fruitful methodological means. It begins with Leibniz’metaphysical formulation and demonstrates that already Leibniz used it in order to solve scientific problems. As an example his derivation of the laws of geometric optics will be analyzed. The first step beyond Leibniz is given by the Principle of least action of Maupertuis. It is the first mathematical formulation of the possible world problem and draws the attention from metaphysics to natural philosophy. The survey ends with Euler’s endeavor to base the scientific research on two methods called by him direct and indirect method. Finally the controversy on the priority of the Principle of least action will be discussed. It took place in the middle of the eighteenth century at the Berlin academy of science and was reanimated in our days. It will be demonstrated that all the historical discussions, which focussed on the alleged Leibniz-letter could not solve the problem, whereas its analysis from the point of view of this paper sheds new light on it. It allows for a better understanding of the positions of Maupertuis and Euler in the historical controversy.

2.1 The Year 1686 The concept of a multitude of ‘possible worlds’ was first presented by Leibniz in a letter to Antoine Arnauld in 1686. This marked the beginning of a new period in the intellectual biography of Leibniz that would later result in his well-known metaphysics of individual substances. It was in the 1680s that these ideas began to I am grateful for the testimonies of collegiality of Herbert Breger (Hannover) and Helmut Pulte (Bochum) who critically read the paper. H. Hecht (*) Leibniz-Edition, Berlin-Brandenburgische Akademie der Wissenschaften, Potsdam, Germany © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_2

29

30

H. Hecht

surface in various of his papers, such as Meditationes de Cognitione, Veritate, et Ideis, published in 1684, but also in the manuscript De Synthesi et Analysi universali seu Arte inveniendi et iudicandi written in the same year. In these two papers Leibniz outlined the project for a new philosophy based on a methodology that he would ultimately shape into a logical discourse in his Generales inquisitiones de analysi notionum et veritatum (1686). Moreover, in the Brevis demonstratio erroris memorabilis Cartesii, he published at the same time one more crucial text that helped him pave the way towards a new science called ‘dynamics’. All these thoughts, essays and marginalia, the sketches and short notes, were given a systematic presentation and interconnection in a manuscript that he announced, with some understatement, as his “petit discours de métaphysique.” In fact, this Discourse on Metaphysics should to be considered the “birth certificate” of the metaphysical system, which later became known as the System of Pre-established Harmony or as Monadology. Leibniz sent a first “Sommaire” of this specimen to Arnauld, asking this outstanding theologian, logician, and philosopher for a critical reading and possible objections. Arnauld’s response initiated an intensive and productive exchange of letters that was beneficial to both of them. One of the highlights of this correspondence was that passage in which the term ‘possible world’ for the first time acquired its strong meaning in the argument of Leibniz. But, in order to make myself better understood, I will add that I think there is an infinity of possible ways in which to create the world, according to the different designs which God could form, and that each possible world depends on certain principal designs or purposes of God which are distinctive of it, that is, certain primary free decrees (conceived sub ratione possibilitatis) or certain laws of the general order of this possible universe with which they are in accord and whose concept they determine, as they do also the concepts of all the individual substances which must enter into this same universe. (Leibniz, Correspondence with Arnauld, 511)

Thus, the world was determined by its substances and the substances were determined by ‘their’ world. Both of them, world and substances were in accord with and determined by each other, but they did not depend on one another. Later, in the 1690s, Leibniz would denominate the individual substances as ‘monads’ and underscore this substance-world relation by his claim that monads are devoid of windows, since each monad is a mirror of one and the same real world.

2.2 Individual Substance and World Leibniz had introduced the concept of an ‘individual substance’ in § 13 of his Discourse on Metaphysics where he defined it as something that had to include everything that would ever happen to it. Julius Caesar, for example, was first dictator, and then he became master of the republic; later he would curtail the liberty of the Romans, and so on. Leibniz claimed that all these actions of the person Julius Caesar were contained in the concept of the individual ‘Julius Caesar’ which existed as a concept only when related to a particular world. Much of the correspondence

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

31

revolved around this particular point. Arnauld asked Leibniz to clarify his concept of an individual and chose as his case-study the creation of Adam by God. He wanted to learn from Leibniz whether or not Adam’s ensuing fate, including all that had happened and would happen to him and his offspring, was independent of God’s previous decrees. If so, insurmountable difficulties would arise according to Arnauld who argued: “[...] there is an infinity of human events which happen through particular ordinances of God, such, for example, as the Jewish and Christian religions, and especially the incarnation of the divine Word.” (Leibniz, Correspondence with Arnauld, 510). Thus, the problem was that it was beyond imagination to understand how all these events could have happened as a consequence of God’s free issuing of prior decrees that would simultaneously be of binding significance for the real Adam, i.e., how could these real-world events be interpreted as consequences following from the individual concept of the ‘possible Adam’? To solve this problem, Leibniz presented his concept of a multitude of possible worlds. He argued that the subject of God’s primary choice could not have been ‘Adam’ or any other particular concept, but a certain world itself as a whole selected from the set of all possible worlds. Leibniz stated that the choice of any individual substance, e.g., the possible Adam, always correlated to and was determined by a forgoing choice of a world. Moreover, it was not a choice that God would have committed himself to by mere chance; quite on the contrary, he invoked an additional principle for his selection that allowed him to choose and create one particular world, i.e., the best of all possible worlds. Leibniz posited the existence of one specific world within the infinity of all possible worlds that could be discerned and distinguished from the others owing to its unique properties. Furthermore, he presupposed that God would be unwilling to create any other world but this best one that could be discerned as a consequence of its specific quality, that is, its degree of perfection. Therefore, the conditio sine qua non for God’s choice had to be the application of a ranking procedure to the set of all possible worlds that led to the determination of the most perfect. Hence, it follows: If in the life of some person, moreover, or even in the universe as a whole, some event were to occur in a different way than it actually does, there would still be nothing to prevent us from saying that this would be another person or another possible universe which God has chosen. And it would in that case be truly another individual. (Leibniz, Correspondence with Arnauld, 514)

Consequently, there existed a unique and distinguished relationship between the best of all possible worlds and the identity of an individual. Clearly, Arnauld’s objection was refuted by Leibniz’ reasoning, for a real individual person was not determined by mere logical or empirical properties, but is correlated to a possible world and becomes a member of it. It is God who appoints this membership (Leibniz, Monadology, § 51), and the problem of choice requires that we accept the ontological status that Leibniz described in terms of contingency. He wrote in the above-mentioned letter to Arnauld: If we wished absolutely to reject such pure possibles [possibilities], we should destroy contingency and freedom, for if nothing is possible except what God has actually created,

32

H. Hecht whatever God has created would be necessary, and, in willing to create something, God could create only that thing alone, without any freedom of choice. (Leibniz, Correspondence with Arnauld, 516)

As this remark reveals, Leibniz’ new system provided a basis for the discussion and reinterpretation of those standing metaphysical problems like freedom, immortality of the soul, and grace. In addition, Leibniz discussed the problems involved in the foundation and understanding of natural laws. Obviously, the laws of nature could be treated similarly: they too were inherently contingent. Also, it followed immediately from the same set of arguments that no law of nature could be reduced merely to a logical scheme or empirical facts, but had to be endowed with a perspective of contingency flowing from God’s choice among possible worlds. In other words, the laws of nature called for a metaphysical foundation. At the end of the same letter Leibniz drew his conclusion: We must always explain nature mathematically and mechanically, provided we keep in mind that the principles themselves, or the laws of mechanics or of force, do not depend on mere mathematical extension but on certain metaphysical reasons. (Leibniz, Correspondence with Arnauld, 520)

Such a principle was, as Leibniz claimed in § 42 of his Theodicy, “[...] my principle of an infinitude of possible worlds [...]” (Leibniz, Theodicy 146). The bearing of this principle on the analysis of motion will now be discussed.

2.3 Causality and Finality in Leibniz’ Physics In Leibniz, the real existence of a world could not be comprehended through any principle that removed contingency. For each possible world has a claim to its right of existence; the creation of a world is unthinkable without a principle of choice, or in other words, in terms of optimisation. Also, as we saw above, the existence of a most perfect implied that the chosen world could be characterised by well-­ determined natural laws. These laws were determined not only by geometry, but also depended on metaphysical principles. Leibniz wrote in § 21 of his Discourse on Metaphysics: “If the mechanical laws depended upon geometry alone without metaphysics, the phenomena would be entirely different.”1 (Leibniz, Discours, 1563). This meant that in Leibniz’ scheme the laws of nature were the manifestations of God’s wisdom and choice. Additionally, the changes in the world were not arbitrary, but followed a general economy. Thus, the constitution of the laws was such that they could harbour God’s wisdom, and this wisdom was manifest in the ways the general laws of nature acted. This is why Leibniz believed the banishing of final causes from physics violated our understanding of nature. True, each singular phenomenon had to be explained mechanically, but this procedure did not imply  “Si les regles mecaniques dependoient de la seule Geometrie sans la Metaphysique les phenomenes seroient tout autres.” 1

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

33

that finality is automatically excluded. Leibniz said, “I hold, on the contrary, that it is exactly in this that the principle of all existences and of the laws of nature is to be sought, for God always aims at the best and the most perfect.” (Leibniz, Discourse on Metaphysics, 485). Finality was required for the comprehension and explanation of motion in general, i.e., for the explication of its subjects, causes, and fundamental features. In order to understand each singular motion, one had to rely on both, mechanical explanation and finality. Leibniz described motion as a change of situs, that is, a thing is in motion if it changes its situs. But, in addition, motion takes place only if there is something like a reason for the observed change. Furthermore, neither time nor motion can ever exist as a whole. This was so […] because a whole does not exist if it has no coexisting parts. Thus there is nothing real in motion itself except that momentaneous state which must consist of a force striving toward change. Whatever there is in corporeal nature besides the object of geometry, or extension, must be reduced to this force. (Leibniz, Specimen, 712)

So Leibniz thought that motion could not come into being without an acting force which guaranteed existence as well as individuality and identity of all beings. Such forces operated on the metaphysical level of thinking, and they were nothing but the activities of the monads, expressed in terms of perception and appetition. By “perception” was meant the transitory state of a monad that represented the momentary state of the whole world, whereas the “[...] action of the internal principle which brings about change or the passage from one perception to another can be called appetition [...]” (Leibniz, Monadology, 1046), as Leibniz notes in § 15 of his Monadology. Consequently, all activities in the world were governed by an internal principle revealing the wisdom and perfection of its creator. In particular, this metaphysics involved an affinity to ancient philosophy: All simple substances or created monads might be given the name of entelechies, for they have in them a certain perfection ἔχουσɩ τò  ἐντελέζ. There is in them a certain sufficiency ἀυτάρκεια which makes them the sources of their internal actions and, so to speak, incorporeal automata. (Leibniz, Monadology, 1047)

It is clear from this passage that in Leibniz’ scheme the optimisation principle was a metaphysical one. To demonstrate the applicability of these metaphysical reflections to physics, Leibniz introduced a highly complex notion of force. He distinguished between primitive and derivative forces, corresponding to the more general distinction in scientific discourse between the metaphysical and the physical. Primitive forces were those that operated only on the metaphysical level. They were the dynamical explications of what was called in metaphysics the activities of monads. These forces determined what was real about bodies as a source of sensual perceptions, but did not provide an empirical content. The phenomena are well-­ founded by primitive forces alone. Thus, for Leibniz, this meant that the phenomena did not exist without a metaphysical basis. The interpretation of phenomena as particular and empirical was based on derivative forces that specified the action of primitive forces. They did not add any new content, but allowed for quantification; derivative forces rendered the action of

34

H. Hecht

primitive forces in terms of quantities. Hence, the action of primitive forces became manifest only through the activity of derivative forces, and through this interplay we know of physical bodies, not only by reason, but also from observation. All physical terms were defined by this scheme, e.g., the mass of a body was the effect of a primitive force which, however, as a derivative force, was calculable as the product of volume and density. More precisely, this derivative force was a passive one. Leibniz, by distinguishing between passive and active forces in his reconstruction of the physical world, responded to an intensively debated problem of the day. He explained the interaction of forces of the Newtonian type in terms of derivative active forces that result from a restriction imposed on the primitive force by the mutual collision of bodies. In Leibniz’ scheme, a physical body and its motion was fully determined by these four ingredients of his force concept; and one of its most important outcomes, the conservation law of living force, built on it. The concept of living force enabled him to describe every corporeal individual as a carrier of a quantum of a living force that characterises its individual state of motion. Physical motion could be described dynamically as the exchange of such quanta of living forces that explained the interaction of all physical individuals and constituted a corporeal world. This Leibnizian physics comprised a theory of the unique real world. In other words, it was a physical, so to speak, dynamical model of the metaphysical world, or even more to the point: it was in symbolic agreement with the metaphysical world. This meant that in Leibniz, a physical explication was given in terms of the construction of a dynamical model that was regarded to be true because of its metaphysical basis. The above-mentioned general laws were, therefore, laws that controlled dynamical models, and one of them was the measure of the living force. Living forces had their real basis in metaphysics; nevertheless, it so became possible to demonstrate the emergence of each singular phenomenon without referring to primary forces. Thus, mechanical constructions on the basis of living forces freed the physicist from having to invoke metaphysical notions in physical theories. Physical explications had to be given in terms of causality, and had to obey the corresponding rules and laws of causality. However, didn’t this strategy ignore the important point mentioned above that God’s wisdom and perfection should be apparent in the general laws of nature? An answer to this question emerges when we account for the mathematically describable mechanism that was not governed by the law of conservation alone, but also by another law, called by Leibniz the conservation law of the total direction of motion. Leibniz thought, as he stressed in § 80 of his Monadology, that if Descartes had known this law of nature, “[...] he would have fallen upon my system of pre-established harmony.” (Leibniz, Monadology, 1058). Leibniz explained in more detail in his Specimen Dynamicum: Descartes rightly distinguished between velocity and direction and also saw that in the collision of bodies that state results which least changes the prior conditions. But he did not rightly estimate this minimum change, since he changes either the direction alone or the velocity alone, while the whole change must be determined by the joint effect of both together. (Leibniz Specimen, 718)

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

35

This passage attests to the systemic relevance of the two conservation principles in Leibniz’ physics. Clearly, Leibniz hoped that he would be able to derive every single physical phenomenon through these means. Today we know that this holds true only for certain problems in impact physics. It is, however, of interest to try to understand Leibniz’ reasons for attempting such universal explanation, and indeed they were permeated by a metaphysical component. For the very reason that all phenomena were well-founded in metaphysical entities in Leibniz’ scheme, a complete scientific representation of physical phenomena presupposed knowledge of these entities. Given that this knowledge was inaccessible, no dynamical demonstration would be possible. That is precisely what happened in geometrical optics. With respect to the laws of geometric optics Leibniz employed a methodological strategy that was to counteract the insufficiency of this situation. This strategy, which sheds light on the function of final causes in physics, is found in the remarkable text Tentamen Anagogicum. Leibniz opened the discussion by presenting two “kingdoms” that existed even in corporeal nature and [...] which interpenetrate without confusing or interfering with each other – the realm of power, according to which everything can be explained mechanically by efficient causes when we have sufficiently penetrated into its interior, and the realm of wisdom, according to which everything can be explained architectonically, so to speak, or by final causes when we understand its ways sufficiently. (Leibniz Tentamen, 780)

The implication was that we would be able to give a demonstration in terms of causality only if the nature of the things in question was known to us. But even if they were not, this undertaking was not in vain because we could also employ final causes to aid our understanding. In this latter case the demonstration had to take a mathematical point of view as its foundation, and then the calculations would yield a path described by a subject in motion. The supposed methodological strategy followed the well-known dictum: “Physics is subordinated to arithmetic by geometry, and to metaphysics it is subordinated by dynamics”2 (Leibniz, Mathematische Schriften, 104), according to which a physical explanation encompassed mathematical as well as metaphysical (dynamical) elements. Each in isolation yielded only an imperfect description of the phenomenon in question. But if its nature was not known well enough, i.e., if the metaphysically founded dynamical properties were only incompletely known, mathematics could help to “complete the puzzle” by applying a special kind of analysis. That is why the calculus encompassed two methods of analysis, the method de maximis et minimis quantitatibus, and another which Leibniz called the method de formis optimis, i.e., an analysis of forms. The first method provided the ordinary differential and the integral analysis, allowing for the determination of the maxima, minima, and other distinguished points of a curve, whereas, when using the second method, one did not intend to distinguish particular points of a curve, but rather to characterise the curve as a whole. We can observe the efficiency of the two methods in Leibniz’ discussion of optical laws.  “[...] Physica per Geometriam Arithmeticae, per Dynamicen Metaphysicae subordinatur.”

2

36

H. Hecht

Leibniz began his analysis by stressing that the ancients were already well-­ informed about the laws of catoptrics, and that Ptolemy and others were able to demonstrate the equality of the angles of incidence and reflection of a light beam falling on a plane mirror by using the hypothesis of the easiest path, a hypothesis later discussed by Fermat when he used it to demonstrate the law of refraction. Leibniz added that the ancients, nevertheless, were very careful in asserting this hypothesis of the easiest path when dealing with a concave mirror because in that case such an observation revealed that the path of reflection sometimes happens to be the longest. He thought that the reservations of the ancients in the case of the concave mirror was due to their method de maximis et minimis quantitatibus, and he was convinced that his own principle de formis optimis would supersede theirs. He noted that, in the absence of a minimum, “[...] it is necessary to hold to the most determined, which can be the simplest even when it is a maximum” (Leibniz Tentamen, 781). As we can learn from the analysis of the Tentamen Anagogicum, the property of the most determined is a proximity relation, or put in another way, it is a relation of order that rests on the a priori assumption of similarity and homogeneity. Under this condition the most determined or the optimum holds not only for the whole, but also for each part, and it would not even suffice for the whole without this. Clearly, Leibniz was speaking about the so-called isoperimetrical method here, a method that today is well-known under the name ‘method of variation’. But, in emphasising that his analysis could give us some insight into the wisdom of the created world, Leibniz had much more in mind than the demonstration of a new mathematical method. In a letter to De Volder, written during the same period, he states: This is an axiom that I use – no transition is made through a leap. I hold that this follows from the law of order and rests upon the same reason by which everyone knows that motion does not occur in a leap; that is, that a body can move from one place to another only through intervening positions. I admit that, once we have assumed that the Author of things has willed continuity of motion, this itself will exclude the possibility of leaps. But how can we prove that he has willed this, except through experience or by reason of order? For since all things happen by the perpetual production of God, or, as they say, by continuous creation, why could he not have transcreated a body, so to speak, form one place to another distant place, leaving behind a gap either in time or in space; producing a body at A, for example, and then forthwith at B, etc.? Experience teaches us that this does not happen, but the principle of order proves it too, according to which, the more we analyse things, the more they satisfy our intellect. This is not true of leaps, for here analysis leads to mysteries ἄῤῥηα. Thus I believe that the same thing applies not only in transitions from place to place but also in transitions from one form to another or from one state to another. (Leibniz, Correspondence with De Volder, 837–838)

Indeed, we find the same kind of argument in his reflections on space, time, and the states of monads, as revealed from a paper written in 1714: Space is the order of coexisting things, or the order of existence for things which are simultaneous. In each of two orders – that of time and that of space – we can judge relations of nearer to and farther from between its terms, according as more or less middle terms are required to understand the order between them. Thus two points are nearer if the maximally determined intervening forms arising from them produce a simpler configuration. Such an

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

37

interval of maximum determination, that is, the minimum and at once the most conformal figure made by the intervening terms is the simplest path from one to the other; in the case of points this is the straight line, which is shorter between nearer points. (Leibniz, Mathematical Foundations, 1083–84)

It was, therefore, according to the property of the most determined that space and time could be characterised not only as the order of coexisting things or of those things that were not simultaneous, but also as an optimal order. And this optimal order corresponded to the most perfect as the signature of the one real world. We know from the Theodicy that in such a world any part taken in isolation was no longer able to be as perfect as the whole itself, but it always had to be the most determined one. This meant that our real world was an ordered world and that all individuals in it could be distinguished from one another by this ordering. Furthermore, this meant that there were fundamental laws that described this order; among them was the law of continuity as a metaphysical consequence of the world’s perfectibility. And Leibniz concludes: Perhaps someone will deny that what I have said above applies to the laws of motion and will maintain that an entirely geometric demonstration can be given of them. I reserve the proof of the contrary for another discourse, where I shall show that they cannot be derived from their sources without assuming architectonic grounds. One of the most important of these, which I believe I am the first to have introduced into physics, is the law of continuity [...]. It serves not merely to test, however, but also as a very fruitful principle of discovery, as I plan to show some day. [...] Nothing seems to me to be more effectual in proving and admiring the sovereign wisdom of the Author of things as shown in the very principles of things themselves. (Leibniz, Tentamen, 788)

The mathematical analysis of the Tentamen Anagogicum made use of this fundamental principle. As a result of Leibniz’ discussion, the insight emerged that there was a unique path for the light beam which was the simplest throughout all experimental situations, i.e., independent of the form of the mirror surface. Leibniz obtained this result solely by investigating relations of order. However, ordered relationships corresponded to individuals that maintained their identity in the course of motion, as we have seen in the letter to De Volder quoted above. Regarding the problem of the image of the possible world, the implication was that a path calculated by means of isoperimetric principles corresponded to an identical and distinguished physical entity. Moreover, after calculating this, it was possible to claim that the determined path, due to its extreme properties, was more than merely a mathematical outcome. Indeed, the certainty arose that even when it was impossible to give a demonstration of a phenomenon by means of efficient causes because its nature was insufficiently known, physical knowledge was available. But, nevertheless, an equivalence between causal demonstration and mathematical demonstration is not a full description, and Leibniz never fails to emphasise the need of causal and final explication in physics. The shortest formulation of this point I found, was in a letter to Bayle, where Leibniz speaks of “[...] metaphysico-mathematical laws of nature [...]”3 (Leibniz, Briefwechsel, 72).  “[...] les loix metaphysico-mathematiques de la nature [...].”

3

38

H. Hecht

Final causes were, so to speak, the methodological link through which metaphysics and mathematics are intertwined; they showed that existence on the physical level of thinking required an underlying basis of acting monads that obeyed an internal principal of optimisation. Later, in the eighteenth century, the question of how to legitimise physical subjects through optimisation principles became a central issue of philosophy. Such a question is better dealt with in terms of the least action quantity principle of Maupertuis.

2.4 1732: The Birth-Certificate of Maupertuis’ Ideas In the history of philosophy and sciences Maupertuis is known to be the first Newtonian on the continent. This honourable pronouncement was due to a paper he read at the Paris Academy of Science in 1732 on the theme Sur les lois de l’attraction, and the topic to which he referred in the title of his lecture was the major subject of his thinking at the time. In the Discours sur les différentes figures des astres, the elaborated version of the paper, Maupertuis aimed to demonstrate that the metaphysical foundation of Cartesian physics was by no means superior to the Newtonian one, and he wrote: Attraction is as possible in nature of things as impact: The phenomena which prove attraction are just as frequent as those which prove impact: To say of a body striving towards another that its tendency isn’t caused by attraction but by a kind of invisible matter that pushes it, that is just like thinking of a partisan of attraction, who, seeing a body moving by impact, would interpret this movement as the effect of invisible attractive bodies rather than explaining it by impact.4 (Maupertuis, Discours, 132–133)

The best accepted traditional interpretation of Maupertuis takes this passage to be a careful and reserved vote for Newton.5 A more subtle analysis shows, however, that it never had been the aim of Maupertuis merely to legitimise Newtonian attraction,  “L’attraction n’étant pas moins possible dans la nature des choses que l’impulsion: les phénomenes qui prouvent l’attraction étant aussi fréquens que ceux qui prouvent l’impulsion: lorsqu’on voit un corps tendre vers un autre, dire que ce n’est point qu’il soit attiré, mais qu’il y a quelque matiere invisible qui le pousse, c’est à peu près raisonner comme feroit un partisan de l’attraction, qui voyant un corps poussé par un autre se mouvoir, diroit que ce n’est point par l’effet de l’impulsion qu’il se meut, mais parce que quelque corps invisible l’attire.” 5  See for instance David Beeson’s Maupertuis biography wherein the author gave a very detailed analysis of the text in question and its early influence on scientific discourse, thereby writing: “It is not overtly a Newtonian text, but effects a certain even-handedness in its treatment of the opposing camps. Maupertuis doubtless has two motives for acting in this way: one is the need for caution towards the Cartesian-dominated Academy of which he was a member and which had officially approved the work. [...] In addition there was a tactical consideration: we have seen that Maupertuis had previously told Bemoulli that he believed the conversion of opponents virtually impossible, and felt that it was only possible to convince bystanders to the dispute. What better way is there to win the support of the undecided than to present both sides of the debate as clearly as possible, and with the greatest possible appearance of fairness, to give the reader the impression of being free to choose between the two. “(Beeson, Maupertuis, 94) 4

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

39

but also to find a common methodological strategy that could make apprehensible both, Cartesian pressure-and-impact interaction and Newtonian long-range forces acting at a distance. Moreover, Maupertuis emphasised in the paper just quoted that it was not his intention to prove attraction. The sentence in question reads: “What we will say doesn’t prove the existence of attraction in nature; also, I won’t do anything to prove it.”6 (Maupertuis, Discours, 103). This statement must be seen against the background of a more general scepticism that arose from the doubt that human thinking was able to apprehend attraction as well as the impact of bodies through the postulation of primary or substantial qualities. Maupertuis argued that it is impossible to find the least causes of things and also that we could not penetrate the mystery of how primary qualities are able to reside inside bodies. And because of this, he concluded, it was absolutely impossible to demonstrate that pressure and impact were the unique and ultimate effects that things could exert upon one another. We only could show that, if God had built the world of extended and impenetrable particles, he would also had to make provision for the possibility of its motion. Moreover, these properties of matter, once stated, would imply the well-known laws of impact, provided that God had wanted motion to emerge from the collision of bodies. But if not, i.e., if God’s aim was directed more strongly at bringing about motion by attraction, then as a consequence, the Newtonian law of gravitation would result. That is why there was a specific quality that distinguished the 1/r2-law of gravitation from all of the other possible types of laws. The Newtonian law, namely, was the only one that allowed the gravitational interaction of material spheres, as far as their masses are concerned, to be placed in the centres of the spheres. Consequently, the gravitational interaction was independent of the surface of the body. And if, therefore, God intended to establish a system of the world wherein attraction has no preferred direction in space, Maupertuis argued, then he was forced to chose the 1/r2-law of gravitation as the only one possible. The outcome of these reflections is remarkable since (1) Maupertuis made a distinction between a law and a principle of motion, but (2) he interpreted the world even in this respect as one of God’s conscious choice. True, a similar reasoning was found in Leibniz. To repeat, in Leibniz’ scheme a complete scientific representation of physical phenomena presupposed knowledge of the nature of things just because of the foundation of all phenomena in metaphysical entities. But if such knowledge was only insufficiently available, no dynamical demonstration would be possible. Hence Leibniz countermoves in the Tentamen Anagogicum, where he, referring to God’s choice, demonstrated the function of final causes in physics. Yet there was a significant difference between these two scholars, right from the beginning. In the above-quoted early text of Maupertuis, the choice-argument had, in contrast to Leibniz, no systemic meaning. It appeared purely as a ad-hoc

 “Tout ce que nous venons de dire ne prouve pas qu’il y ait de l’attraction dans la Nature; je n’ai pas non plus entrepris de le prouver.” 6

40

H. Hecht

construction enabling him to demonstrate the equivalence of the principles in question by empirical means. Some years later Maupertuis reformulated his early empirically-minded view in terms of the following idea: “Concerning a priori demonstrations of such a kind of principle, it doesn’t appear that physics could provide them; they seem to belong to a superior kind of science.”7 (Maupertuis, Lois, 46). The reason for this metaphysical turn in 1740 must be sought in the context of his Lapland expedition. Maupertuis believed that the results of his measurements at the polar circle would furnish an irrefutable proof for the Newtonian theory; but then he learnt that an experimental demonstration alone neither convicted the scientific community nor altered public opinion. The first steps toward a new understanding of what he called ‘science supérieure’ can be observed in the Lettre sur la comète (1742). Addressed to Mme. Du Châtelet, and related to various points concerned with the appearance of a comet in 1742, Maupertuis discussed some metatheoretical themes. In particular he presented the following idea: It is true that there is universal coherence between all that exists in nature; in physics as well as in morals: Every event, being connected to a proceeding one and followed by another, is merely a link of a chain that forms the order and the succession of things: were it not located like it was, the chain would be another one and it would be part of another universe.8 (Maupertuis, Lettre, 211–212)

Reflecting on this passage, one observes a renewed proximity to Leibnizian ideas. In 1732 Maupertuis had handled the problem of God’s choice in a more strongly empirical perspective of thought. By now (8 years later) he was looking for a metaphysical solution to this problem stating that all things in the world were fully determined, and if there were only a single exception to this principle, this would no longer be the same world. As above, there is also here a fundamental difference to Leibniz. When Leibniz referred to the universe, he had in mind the whole world of material and immaterial things in one, and from the beginning on. This was the world which was his pretension to describe in terms of efficient causes and final causes. Maupertuis, in contrast, only had nature in mind. He accepted the Leibnizian point, but for God only, and while Leibniz developed a methodology to uncover the world as a whole world postulating an infinite process, Maupertuis saw a significant difference between God’s and man’s knowledge. He was sure that man’s skill never could lead to thorough knowledge, and that he could only describe parts of the world with sufficient certainty. He found the basic idea of promoting such a methodological strategy in 1744.

 “Quant aux démonstrations à priori de ces sortes de principe, il ne paroît pas que la Physique les puisse donner; elles semblent appartenir à quelque science supérieure.” 8  “Il est bien vrai qu’il y a une connexion universelle entre tout ce qui est dans la Nature, tant dans le physique que dans le moral: chaque événement lié à celui qui le précede, & à celui qui le suit, n’est qu’un des anneaux de la chaîne qui forme l’ordre & la succession des choses: s’il n’étoit pas placé comme il est, la chaîne seroit différente, & appartiendroit à un autre Univers.” 7

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

41

2.5 The Least Action Quantity Principle This idea can be illustrated by the Mémoire Maupertuis read in 1744 at the Paris Academy of Science on Accord de différentes lois de la nature qui avoient paru jusqu’ici incompatibles. This paper dealt with the optical laws, or more precisely, those of refraction. Following Mairan in his analysis of the historical discussion, Maupertuis stated: In the Mémoire on reflection and refraction presented by M. de Mayran, one may discern the history of the dispute between Fermat and Descartes as well as the obstacles and inabilities in which one is trapped up to the present when attempting to adjust the law of refraction to a metaphysical principle.9 (Maupertuis, Accord, 16)

What Maupertuis had in mind is that in the seventeenth century various contrasting derivations of these laws had already been put forward by Snellius, Descartes, Fermat, Newton and Leibniz. They all yielded the result that the ratio of the sines of the angles of incidence and refraction of a light beam that passes through two media of different optical densities is a constant depending on optical resistances, or in more modern terms, on the densities of the optical media. Nevertheless, the statement that the ratio of the optical densities in the refraction law was proportional to that of the corresponding velocities had not been generally accepted in his day, and this was precisely the point to which Maupertuis was referring. After stressing that there was a gap between mathematically describable laws and metaphysical principles, he tried to bridge this gap by his principle of least action quantity. The principle he referred to presupposed (1) that all motions that occur in nature could be described by a single quantity, the so-called action quantity, and (2) that the real path which a body follows going from one point to another is distinguished by a definite property of this quantity, which in all cases must be the minimum of all possible paths. On the basis of this outcome Maupertuis postulated the possibility of reconciling his earlier methodological attempts, because his principle stated that there is one and only one path that each body describes in nature (1744), and that this feature is a consequence of a special choice God had to make when creating nature (1732). Against this background he, then, claimed that, though exhaustive knowledge is only available to God, the new principle guarantees that a law that is compatible with it never could fail. Maupertuis chose the following example to give a demonstration of his new insights into the principles and laws of nature. He presupposed a physical system consisting of two optical media separated by the boundary layer CD. The starting point A lay in the medium with the light speed m whereas the endpoint B lay in the medium with the light speed n. The question was how to determine the path that the light beam followed combining A with B, and the Maupertuisian answer read: One has to give an approximate determination of the refraction point R by applying the  “On peut voir dans le Mémoire que M. de Mayran a donné sur la réflextion & la réfraction, l’histoire de la dispute entre Fermat & Descartes, & l’embarras & l’impuissance où l’on a été jusqu’ici pour accorder la loi de la réfraction avec le principe métaphysique.” 9

42

H. Hecht

least action quantity principle, i.e., by carrying out the variation of the path of light given by the equation

m • AR + n • RB = min .

The solution demanded that the ratio of the sines of the angles of incidence, and refraction of a light beam was the reciprocal of the ratio of the corresponding speeds. Interestingly, Fermat had found that the ratios in question must be proportional. In his interpretation the derivation is merely a mathematical tool. Maupertuis, in contrast, interpreted Fermat’s principle of least time through his own spectacles, by integrating the idea of final principles into his methodological equipment. Fermat had the correct idea, Maupertuis maintained, but he failed to make appropriate use of it. Instead of minimising the time he should have minimised the action quantity, and the reason for this misunderstanding was, in Maupertuis’ eyes, that Fermat had confounded the final principle with one of its consequences. He wrote: In the two cases of light reflection and propagation, when velocity remains constant, with reference to the least action quantity given at one and the same time, space and time intervals are the shortest possible. But these intervals exist only as a consequence of the least action quantity. This was the consequence that Fermat took to be a principle.10 (Maupertuis, Accord, 20)

It may be gathered from this passage that a physical law like that of the refraction of light could not be legitimised without final principles.

2.6 The Essay on Cosmology A few years later, when working on his Cosmology, Maupertuis began to generalise his conclusions. The laws in question that he demanded to be compatible with the action principle referred no longer to optical laws alone, but also covered the Cartesian quantity of motion and the Leibnizian vis-viva-conservation principle. Now Maupertuis took them to be a product of generalised experience. To such concepts, he proclaimed, consistency did not apply since they described the relationship between mere phenomena. Consequently, we read in his cosmology: Because we cannot entirely ignore the mutual influence of bodies of whatever nature, we will continue to use the word force, but we will measure it only in terms of its appearing effects.11 (Maupertuis, Cosmologie, 30f.)

 “Dans les deux cas de la réflexion & de la propagation, la vitesse de la lumiere demeurant la même, la plus petite quantité d’action donne en même tems le chemin le plus court, & le tems le plus prompt. Mais ce chemin le plus court & le plutôt parcouru n’est qu’une conséquence de la plus petite quantité d’action: & c’est cette conséquence que Fermat avoit prise pour le principe.” 11  “Cependant, comme nous ne pouvons pas dépouiller entiérement les corps d’une espece d’influence les uns sur les autres, de quelque nature qu’elle puisse être, nous conserverons, si l’on veut, le nom de force: mais nous ne la mesurerons que par ses effets apparens.” 10

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

43

The Cartesian quantity of motion as well as the Leibnizian quantity of living force were no more than the measures of a momentary phenomenal effect that Maupertuis saw to be brought about through causality. Such effects could not explain the existence of bodies nor the continuity of motion since they were reduced to a sequence of isolated points of succession. More to the truth (in Maupertuis’ eyes), causal explications were ad hoc constructions dependent on the phenomena rather than a device to explain them. A true understanding, in contrast, had to furnish the phenomena with a fundamentum in re, and even this Maupertuis believed he had accomplished when he formulated his Principe de la moindre quantité d’action that stated: “In any change which happens in nature, the action quantity, employed for this change, always is the least possible.”12 (Maupertuis, Cosmologie, xxii). Action itself was defined mathematically as the product of mass, velocity, and length of the path, while in metaphysics it was construed in terms of a particular type of force, being, strictly speaking, the only real one in nature because it could not be reduced to mere phenomena. Thus, we read in his Essai de Cosmology: “Perhaps it would have been better to name it force, but because I found this word was used by Leibniz and Wolff to express the same idea, I didn’t want to alter the term, which I had found to be adequate.”13 (Maupertuis, Cosmologie, xxxivf.). This type of force was neither identical with the one construed by Leibniz nor was it equivalent to the Newtonian version. By the technical term ‘action’ Maupertuis described an entity of natural philosophy that was not exhaustible by any of the given force concepts because they were all ignorant about the emergence of real effects. This was the difference between his action principle and the handling of the action concept in Leibniz and Wolff. Accordingly, he wrote in an unpublished paper: Also, one is by all means entitled to call by the name Action the product of the mass times the space times the velocity, and to name Force the product of the mass times the velocity; or times the square of velocity. For, in all these cases, we are equally ignorant of the manner in which the Action and the Force produce their effects.14 (Fonds Maupertuis, 6–7)

Presenting his principle, Maupertuis finally found the answer to his early question of how to understand the outcome of physical effects in terms of metaphysics when there are no means by which to derive them from primary qualities. The solution consisted in what he called the metaphysical meaning of his principle, which arose from recourse to final causes governing the activity of force [...] that is constantly renewed and so to speak created at any one instant with utmost economy. Thereby the universe gives manifestation of its independence and of the necessity of  “[...] lorsqu’il arrive quelque changement dans la Nature, la quantité d’action employée pour ce changement est toujours la plus petite qu’il foit possible [...].” 13  “Il auroit peut-être mieux valu l’appeller force mais ayant trouvé ce mot établi par Leybnitz et par Wolff pour exprimer la même idée, et trouvant qu’il y répond bien, je n’ai pas voulu changer les termes.” 14  “Et l’on est tout au moins aussi en droit d’appeller Action le produit de la Masse par l’Espace et par la vitesse qu’on l’est nommer Force, le produit de la Masse par la vitesse; ou par le quarré de la vitesse. Parce que dans tous ces cas nous sommes dans la même ignorance sur la manière dont l’action et la Force produisent leurs Effets.” 12

44

H. Hecht the presence of its creator, and demonstrates his wisdom and omnipotence. This is the force called by us action; and precisely from this principle we derived all laws of motion, both of solid and elastic bodies.15 (Maupertuis, Cosmologie, xxvf.)

The message is clear: Maupertuis asserted that he was able to derive from his principle of the least action quantity not only the laws of propagation of light but also those of the impact of bodies and, as Euler had demonstrated, the laws of the celestial motion. However, the demonstration was not merely a mathematical derivation. Maupertuis thought of his principle as the mathematical formulation of an effect in nature that can be comprehended against the background of a permanent creation by God. The quintessence of his reflections upon the action principle is to be seen in the fact that there had to be a kind of entities that are revealed to us following an optimisation principle, God’s wisdom even in nature. Maupertuis often warned against misunderstanding his ideas, stressing that he would argue neither for a physical influence of God nor for a mathematical demonstration of the creator. All he insisted upon was that the action principle corresponded adequately to God’s wisdom since this was all that was needed to gain the certainty that a scientist possibly could achieve. The validity of definite physical laws like the various quantities of force, therefore, resulted from the fact that phenomena were effects of underlying agents, like actions were, and that they played the same role in nature as did the activities of monads on a metaphysical level of thinking. At least, this was the essence of Maupertuis’ “Principe de la moindre quantité d’action” as a metaphysical principle. Natural entities existed in space and time. They were of special quantities that made them amenable to measurement and calculation. Furthermore, they were ordered by causality, and according to Maupertuis this property was a relationship between mere phenomena. But when the validity of the least action quantity principle was assumed, this also guaranteed the existence of certainty in nature. Once this was accepted, one arrived at different representations of distinct branches of nature by fixing the conditions alternatively: elastic bodies led to Leibniz’ physics, and attraction to Newtonian physics. All these descriptions were, then, genuine descriptions of respective parts of the universe since they all built on the underlying least action principle. The activities of monads, in turn, rendered physical things calculable and measurable without themselves being furnished with such a quality, i.e., monads acted beyond space and time. Moreover, they formed bodies and generated their motions. The final myth of the Theodicy may serve as an illustration of the differences between Leibniz’ and Maupertuis’ natural philosophy. After having explained that there was one, and only one, world that was the best and most beautiful of all possible worlds, Leibniz gave an interpretation of this condition in terms of geometry:  “[…] qui produite de nouveau, & créée pour ainsi dire à chaque instant, est toujours créée avec la plus grande économie qu’il soit possible. Par là l’Univers annonce la dépendance & le besoin où il est de la présence de son auteur; & fait voir que cet auteur est aussi sage qu’il est puissant. Cette force est ce que nous avons appellé l’action: c’est de ce principe que nous avons déduit toutes les loix du mouvement, tant des corps durs que des corps élastiques.” 15

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

45

And whenever the conditions are not determinate enough, there will be as many such worlds differing from one another as one shall wish, which will answer differently the same question, in as many ways as possible. You learnt geometry in your youth, like all well-­ instructed Greeks. You know therefore that when the conditions of a required point do not sufficiently determine it, and there is an infinite number of them, they all fall into what the geometricians call a locus, and this locus at least (which is often a line) will be determinate. Thus you can picture to yourself an ordered succession of worlds, which shall contain each and every one the case that is in question, and shall vary its circumstances and its consequences. But if you put a case that differs from the actual world only in one single definite thing and in its results, a certain one of those determinate worlds will answer you. (Leibniz, Theodicy, 371)

Applying this image to Maupertuis we continue with our interpretation. It was shown that Maupertuis recognised different laws of motion for different kinds of bodies, and that he argued for a common basis of all physical phenomena as revealed by his treatment of the action principle. Yet this principle was no overarching one. It guaranteed the existence of laws for well-defined areas of nature only by sacrificing the idea of a general quantity of force governing all possible changes in the world. It was Maupertius’ abandonment, mentioned further above, of any further attempt to unite bodies and motion within the framework of a single principle of generation that prompted this outcome. In terms of the image from the above passage of the Theodicy, the conditions were not sufficiently determined, and the acceptance of divergent laws for divergent areas of nature was thus a consequence that flowed from an incomplete metaphysical and physical foundation. Maupertuis sacrificed those entities like monads in his attempt to establish a plurality of physical laws that corresponded to different areas of nature (or different physical worlds). Maupertuis’ principle of least action quantity that seemed to be informed by the spirit of Leibniz, shares with Leibniz the idea of a general economy in God’s creation and, consequently, of certainty in nature. Yet it leads to a set of possible worlds as possessing real existence because their defining features are built only of motion, but not the things undergoing motion. We will see now, how Euler tackled this problem.

2.7 A Final View to Euler Euler postulated that a body is to be characterised basically by the properties of extension, mobility, inertia and of impenetrability, which was equal to saying that forces no longer possess the character of primary natural agents. Forces emerge rather from the interaction of bodies which are impenetrable. In the 78th of his letters to a German Princess, Euler argues that forces cannot be described as the effect of the impenetrability of one single body. They are, correctly understood, the result of a universal property of bodies, i.e., of impenetrability, and because this property is the inexhaustible source of forces it guarantees the existence of the corporeal world as a whole. Such a world then, Euler completed his reflections, must obey an optimisation principle, and he wrote in the letter just mentioned:

46

H. Hecht But it must be carefully remarked, that, in general, bodies do not act upon each other, but in so far as their state becomes contrary to impenetrability; from whence results a force capable of changing it, precisely so much as is necessary to prevent any penetration; so that a small force would not have been sufficient to produce this effect. […] Since, then, the force is the smallest, the effect which it produces, that is, the change of state which it operates, in order to prevent penetration, will be proportional; […] You will find here, therefore, beyond all expectation, the foundation of the system of the late Mr. de Maupertuis, so much cried up by some, and so violently attacked by others. His principle is that of the least possible action; by which he means that in all the changes which happen in nature, the cause which produces them is the least that can be. From the manner in which I have endeavoured to unfold this principle to you, it is evident that it is perfectly founded in the very nature of body [...]. (Euler, Letters, 78th letter, I 235f.)

This statement shows that Euler accepted the results of Maupertuis’ analysis. Nevertheless, he did not understand the ‘actions’ as being the least true natural agents but as a mode of acting forces. According to Euler one could not sacrifice the concept of forces in a portrayal of the physical world, and they had to be derived from interacting impenetrable bodies. These physical forces entered into the Newtonian equation of motion and also obeyed a variational principle, and they gave rise to a methodological distinction that Euler qualified as the distinction between the direct and indirect method in natural philosophy. Whereas the direct method gave a physical explication in terms of effective causes through the integration of a differential equation, the indirect one, resolving a variational problem, made reference to final causes. The aim of natural philosophy then was, according to Euler, to demonstrate the correspondence of these two modes of method in physics that he endeavoured to elaborate, following the general conviction: In my opinion, a distinction must be carefully made between the plans of a world which should contain corporeal substances only, and those of another world, which should contain beings intelligent and free. In the former case, the choice of the best would be involved in very little difficulty; but in the other, where beings intelligent and free constitute the principal part of the world, the determination of what is best is infinitely beyond our capacity [...]. (Euler, Letters, 60th letter, I 180f.)

For a world built solely of physical bodies Euler believed he would be able to realise the Leibnizian program of philosophy. Since such a world was governed by a principle that met the conditions of choice, an optimisation principle had to apply, and Euler concluded by resuming his analysis of Leibniz’ Monadology: That what Herr von Leibniz has proved in such an ingenious manner about the precise combination of all parts in the world, and the derivation of the monads thereby, remains fully valid on this investigation as long as the remarks pertaining to the monads are applied to all parts of the bodies. [...] This is so because due to this most perfect combination, and universal harmony in the world resulting therefrom, every part is combined with all other parts in such a manner that it would be possible to know the state of the whole world as soon as one knew fully the state of a unitary part. Hence, what Herr von Leibniz proposes about the monads may be affirmed with equal justification for all finite parts of the world.16 (Euler, Lehr-Gebäude, 366)

 “Was übrigens Herr von Leibniz auf eine so sinnreiche Art von der so genauen Verknüpfung aller Theile in der Welt bewiesen, und daraus auch die Monaden hergeleitet, behält nach dieser 16

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

47

Thus each single body followed its own path in space and time and all these paths taken together made up the corporeal world. Even if a single body deviated from its path we would no longer be in the same world. But we could, in turn, arrive at the unique real path of the system by a variation of possible or virtual paths. This procedure was fundamental to Euler’s physics. It demanded the equivalence of the so-­ called direct method and of its inversion in terms of an optimisation principle. Euler’s analysis of motion sheds some more light on this principle. According to Euler, motion in general could be rendered as the path of a geometrical point characterised by space (s), time (t) and velocity (v). Since the velocity was given by the relation v  =  ds/dt, its calculation was possible in terms of total length or total time, i.e.,



s = ∫ vdt

t=∫

ds v

Hence velocity was time-dependent or location-dependent, and Euler concluded: All investigations of mechanics amount to two alternatives: (1) if the forces affecting bodies are given, the changes which they bring about in motion need to be determined; (2) to ­determine the forces when the changes with regard to the state of the bodies are known.17 (Euler, Recherches, 112)

While the first case is equivalent to the problem of how to integrate the motion equation, the second one addresses of the variational problem. Representing the components of the force by P, Q, R, and the corresponding coordinates by x, y, z, Euler was able to formulate the equations of motion to be solved as:

2 = Mddx nPdt = , Mddy nQdt 2 , Mddz = nRdt 2

with M expressing the mass and n a proportionality factor. The variational problem he presented in terms of the action integral:

∫ Pdx + ∫ Qdy + ∫ Rdz

Untersuchung seinen vollkommenen Werth, wann nur dasjenige, was von den Monaden gesagt worden, auf alle Theile der Körper bezogen wird. [...] Denn wegen dieser vollkommensten Verbindung und daraus entstehenden allgemeinen Übereinstimmung in der Welt, ist ein jeglicher Theil dergestalt mit allen andern Theilen verbunden dass wenn man den Zustand eines einigen Theils vollkommen einsähe, man daraus den Zustand der ganzen Welt erkennen könnte. Dieses also, was der Herr von Leibniz von den Monaden behauptet, lässt sich mit ebenso gutem Grunde von allen endlichen Theilen der Welt bejahen.” 17  “C’est aussi à quoi aboutissent toutes les recherches de la Mécanique, où l’on s’applique principalement à deux choses: l’une les forces qui agissent sur un corps étant données, de déterminer le changement qui doit être produit dans son mouvement; l’autre, de trouver les forces mêmes, lorsque les changemens, qui arrivent aux corps dans leur état sont connus.”

48

H. Hecht

The result shows that the action principle is of a physical meaning without immediately metaphysical implications. This does not mean that metaphysical reflections were entirely neglected in Euler’s scheme. Euler needed them to posit the interaction of forces as caused by impenetrability as a universal property of bodies and, in order to legitimise his general methodological scheme, i.e., the equivalence of the direct and the indirect method.

2.8 A Priority Problem and Its Recent Discussion Leonhard Euler formulated his main ideas on the relationship between the fundamental dynamic quantities as his scientific conclusion from the controversy on the priority of the Principle of Least Action that took place at the Académie Royale des Sciences et Belles Lettres de Prusse in Berlin. The controversy itself focussed on the fragment of an alleged Leibniz-letter that Samuel König quoted in an article, written for the scientific journal Nova Acta Eruditorum 1751. The author, a German scholar, who studied Leibniz’ mathematics, metaphysics and physics under the guidance of Johann (I) Bernoulli together with Maupertuis in Basel, was later appointed to a professorship at the University of Franeker in the Netherlands. About the same time Maupertuis took his presidency of the Berlin academy of science, which he successfully reorganized. He appointed many new members into the academy and among them Samuel König, who thanked him with the mentioned publication. It was a Danaer gift. Starting with general remarks on the universal principle of the equilibrium of forces, König analyzed the relationship between the action quantity and the Leibnizian vis viva. It was his goal to demonstrate that the vis viva is sufficient to solve the mechanical problems and, therefore, the recourse to the Principle of Least Action would be without any benefit. Actually he understood this principle as a derivation of the vis viva, and he quoted a letter from Leibniz to Jacob Hermann at the end of his article, which seemed to prove that already Leibniz was in possession of the principle, to which Maupertuis had registered priority. Thus, the priority problem was born, and the now incipient quarrel between the two scholars Maupertuis and König quickly divided the European scientific community into two parts with the Leibniz Wolff school on the one hand and the followers of Newton on the other. However, not only scientists were involved in the priority debate. Even the king of Prussia took part in it, and especially Voltaire appealed emotions, publishing the Diatribe du Docteur Akakia, a pamphlet that attacked with deadly irony the president Maupertuis. From a more scientific point of view this Europe-wide and hard-fought debate focused on the authenticity of the quoted passage of the Leibniz letter. That is why Samuel König presented only a copy of a letter fragment, whereas Maupertuis and his partisans wanted to see the original document that König could not furnish. The fate took its course. The Berlin academy of science decided to install a commission in order to examine the authenticity of the Leibniz letter Samuel König had quoted

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

49

in his paper. And it was the famous Leonhard Euler, who undertook it to search for references or at least allusions in the papers of Leibniz that could justify the assertion of the letter in question. Euler could not find any, and the academy followed him in his conclusion that the letter could only be a forgery. This judgement of the academy was subject of controversies from the very beginning. Samuel König returned his certificate of appointment, and many scholars in Europe distanced themselves from the procedure of the Berlin academy. Nevertheless, the interest in the question whether the Leibniz letter has to be accepted as authentic continued. And nearly 150 years had passed when it was reanimated in the context of the academic Leibniz edition. It was Carl Immanuel Gerhardt, the editor of several collections of Leibniz’s letters and writings, who analyzed the fragment of the Leibniz letter to Jacob Hermann again. Just like Samuel König and all the others before him, he could not present the autograph of the letter. In spite of that he took it for granted that the letter in question had been written by Leibniz. However, as he presumed, it had been addressed not to Hermann, but to Pierre Varignon. And 15  years after this statement another Leibniz editor, Willy Kabitz, demonstrated that the letter could have been addressed neither to Hermann nor to Varignon. He concluded his detailed analysis mentioning that the autograph of the Leibniz letter in question could not be found yet. Moreover, it was not possible to insert it into one of the known Leibniz correspondences. Against this background a Leibniz editor of our days, Herbert Breger, published a paper on the famous Leibniz-letter once again. In contrast to Carl Immanuel Gerhardt and Willy Kabitz, he not only focused on the accordance with other Leibniz letters in style of writing, but carefully analyzed the letter in question. Breger found a series of incompatibilities, which attracted his attention, and he formulated eight topics that provoked him to doubt about the authenticity of the letter, Samuel König has quoted. The publication of his analysis rekindled the old controversy a few years later, and it was Ursula Goldenbaum who disagreed with Breger’s results in all its parts. In a booklet entitled Ein gefälschter Leibnizbrief? Plädoyer für seine Authentizität (A forged Leibniz-letter? Plea for its authenticity) she undertook it to rebut Breger’s arguments step by step. In order to give an impression of the renewed controversy I will draw the attention to some of the discussed topics. Breger’s first point of interest is concerned with the technical term limes. And his interest in it is caused by the formulation La géométrie n’étant que la science des limites et de la grandeur du continu (Berger, Leibniz-Brief, 365) in the controversial Leibniz-letter. Breger translated it in the sense that geometry is nothing but the science of the limes and the dimension of the continuum, i.e. he refers to the mathematical limes concept that only after Leibniz’ death had been introduced into mathematics – a strong argument against the originality of the letter, as he believed. Unfortunately this translation is not compelling, and Goldenbaum rejects Breger’s understanding of the cited sentence showing that the better translation of limites is limits instead of limes – a translation that is in conformity with the level of mathematical thinking at the Leibniz-time. Breger’s second point repeats an old argument that always Maupertuis and Euler brought to the debate. It is based on the fact that there is no other reference to a

50

H. Hecht

Principle of Least Action in the known Leibniz-manuscripts than the passage that Samuel König quoted in his paper. It reads: I have observed that in movement processes it [the action quantity] usually assumes a maximum or a minimum.18 In oder to underline the significance of this sentence, Herbert Breger points out that Leibniz sometimes speaks about maxima and minima in his manuscripts, and that he also uses the action quantity, but nowhere a formulation of such a generality could be found in them. In her answer to these arguments Ursula Goldenbaum refers to Leibniz’ Discours de métaphysique (Metaphysical discourse) and remarks that König’s quotation is in line with Leibniz’ reflections on the significance of teleological principles in nature (Goldenbaum. Leibnizbrief. 57). It is evident that this apology is nothing but an attempt to save the authenticity of the letter, because the problem to be solved is not to remark any accordance between final causes and the Principle of Least Action but to demonstrate how, i.e. in what manner, this principle is connected to final causes. In Leibniz this relationship leads to the vis viva conservation and not to Maupertuis’ principle as I have shown above. Summarizing the recent controversy on the alleged Leibniz-letter one can say that it brought about some new arguments, the result however, did not overcome the historical standoff. Nevertheless, there is one point in the mentioned discussion that has the power to steer the previous debates in a new direction. This point concerns with the significance of Leibniz’ principle of continuity in biology, which Breger discusses in his sixth argument. It draws the attention to natural philosophy and removes the restriction of the Principle of Least Action to the physical meaning only. In this context the possible world problem gets interesting. I demonstrated above that the problem of choosing the best of all possible worlds in Leibniz is a metaphysical problem. Possible worlds differ from one another by its quality to represent a special degree of perfection. And all these possible worlds are characterized by unique general laws. In the case of our world this general law is the vis viva conservation. Based on this law Leibniz developed his physics as a physics of conservation laws. Compared with Maupertuis we have a similar situation. Instead of Leibniz’ conviction, however, the result of God’s choice is not the best of all possible worlds. In Maupertuis the possible world problem is no longer a metaphysical one. It appears as a continual creation caused by entities Maupertuis called actions, and the general law of their activities is given by the Principle of Least Action. It is a principle that governs all the processes in nature – in physics as well as in biology. In other words: it appears in different forms, which depend on the different branches in nature. In biology it explains the development of species (Maupertuis. Cosmologie. 11–12) and in mechanics it is mathematically formulated as the variational principle of the action quantity (Maupertuis. Cosmologie. 42–43).

 J’ai remarqué que dans les modifications des mouvemens elle devient ordinairement un Maximum, ou un Minimum. (König. Dissertatio. 324) 18

2  Leibniz’ Concept of Possible Worlds and the Analysis of Motion…

51

In contrast to Maupertuis the nature in Leibniz is governed by metaphysically based forces, which apply to a conservation principle, whereas the actions Maupertuis’ follow an extremal principle, and these two principles – understood as general laws based on forces and actions respectively – are inconsistent with one another. They indicate different steps in the history of the dynamical principles, and that’s the reason why they are not to be mixed. From my point of view this result justifies the assumption that the alleged letter is a forgery.

2.9 Resume It has been the aim of this paper to show that the analysis of motion in eighteenth century physics drew an important motivation from, and was strongly influenced by, the thinking of Leibniz and especially by his well-known problem of how to choose the best of all possible worlds. I have attempted to show that this problem was a driving force in development of physics after Newton. Yet the conceptions of Maupertuis and Euler were not merely an extension of the Leibnizian philosophical program. Indeed, they had their own points to make and yielded independent results owing to an independent and new methodology. This does not preclude that they also derived from the spirit of Leibniz in that they all built on optimisation principles, by which existence as well as motion were comprehended. This was, in my opinion, the context in which eighteenth-century physics appeared to embody the transformation of a major problem set by Leibniz. And this is why Leibniz as well as Maupertuis and Euler, though giving different interpretations of the concept of ‘possible worlds’, all agreed on the main point that all certainty in nature and physics arises from the application of an optimisation principle. Thus we observed in Leibniz a total dynamics of monads that required physics to encompass a perspective on the whole world. Maupertuis’ action principle then, focussing on the same goal, arrived at a position that limited the Leibnizian worldview to one of nature whereas Euler transformed it into a physical problem. In doing so, he – among others – paved the way for further progress in physics.

References Académie des Sciences de Paris, Fonds Maupertuis, n° 17. Beeson, David. 1992. Maupertuis: An Intellectual Biography. Oxford: Voltaire Foundation at the Taylor Institution. (= Studies on Voltaire and the Eighteenth Century 299). Breger, Herbert. 1999. Über den von Samuel König veröffentlichten Brief zum Prinzip der kleinsten Wirkung. In Pierre Louis Moreau de Maupertuis. Eine Bilanz nach 300 Jahren, ed. Hartmut Hecht. Berlin: Arno Spitz. Euler, Leonhard. 1823. Letters of Euler on Different Subjects in Natural Philosophy Addressed to a German Princess, ed. D. Brewster. 3rd edition in two volumes, Edinburgh: printed for W. & C. Tait.

52

H. Hecht

Euler, Leonhard. “Recherches sur l’origne des forces.” Opera Omnia, ser. II vol. 5. Euler, Leonhard. “Von dem Lehr-Gebäude der Monaden und den Gründen desselben.” Opera Omnia, ser. III vol. 1. Goldenbaum, Ursula. 2016. Ein gefälschter Leibnizbrief? Plädoyer für seine Authentizität. Hannover: Wehrhahn. König, Samuel. „De universali principio aequilibrii et motus in vi viva reperto, deque nexu inter vim vivam et actionem utriusque minimo, dissertatio.” In: Euler, Leonhard, Opera omnia, ser. II, vol. 5. Leibniz, Gottfried Wilhelm. 1966. Briefwechsel zwischen Leibniz und Bayle. 1687–1702. In Die philosophischen Schriften, ed. C.I. Gerhardt, vol. 3. Hildesheim: Olms. ———. 1956a. Correspondence with Arnauld 1686–87. In Philosophical Papers and Letters, ed. Leroy E. Loemker, vol. 1. Chicago: Chicago University Press. ———. 1956b. Correspondence with De Volder 1699–1706. In Philosophical Papers and Letters, ed. Leroy E. Loemker, vol. 1. Chicago: Chicago University Press. ———. 1956c. Discourse on Metaphysics. In Philosophical Papers and Letters, ed. Leroy E. Loemker, vol. 1. Chicago: Chicago University Press. ———. “Discours de métaphysique.” Sämtliche Schriften und Briefe (Akademie-Ausgabe), vol. VI, 4B. ———. 1971. Mathematische Schriften, ed. C. I. Gerhardt. Vol. 6, Hildesheim: Olms. ———. 1956d. Monadology. In Philosophical Papers and Letters, ed. Leroy E. Loemker, vol. 2. Chicago: Chicago University Press. ———. 1956e. Specimen Dynamicum. In Philosophical Papers and Letters, ed. Leroy E. Loemker, vol. 2. Chicago: Chicago University Press. ———. 1956f. Tentamen Anagogicum. In Philosophical Papers and Letters, ed. Leroy E. Loemker, vol. 2. Chicago: Chicago University Press. ———. 1956g. The Metaphysical Foundations of Mathematics. In Philosophical Papers and Letters, ed. Leroy E. Loemker, vol. 2. Chicago: Chicago University Press. ———. 1951. Theodicy. Essays on the Goodness of God the Freedom of Man and the Origin of Evil. London: Routledge & Kegan Paul. Maupertuis, Pierre Louis Moreau de. 1965a. “Accord des différentes loix de la nature qui avoint jusqu’ici paru incompatibles.” Oeuvres IV, Hildesheim: Olms. ———. 1974a. “Discours sur les différentes figures des astres avec une exposition des systèmes de MM. Descartes et Newton.” Oeuvres I, Hildesheim: Olms. ———. 1974b. “Essay de Cosmologie.” Oeuvres I, Hildesheim: Olms. ———. 1965b. “Lettre sur la comète.” Oeuvres III, Hildesheim: Olms. ———. 1965c. “Lois du repos des corps.” Oeuvres IV, Hildesheim: Olms.

Chapter 3

The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s Philosophy François De Gandt

Abstract  The chapter examines the change in the role and understanding of metaphysics that took place in the seventeenth and eighteenth centuries, as reflected in d’Alembert’s philosophy of science. D’Alembert based in an unmistakably Cartesian manner scientific truth on the intact chain of scientific knowledge that links the fundamental cognition of the most abstract properties of natural beings at the top to a series of descending levels of knowledge about entities with increasingly compound and complex properties. But he did not hide the numerous gaps and lacunae existing in this chain which had to be filled in by underived propositions. This is even true of the famous d’Alembert principle, that was, indeed, regarded by its author only as a methodical means that facilitates the “geometers” the appropriate use of the proper principles of composition of motion and of equilibrium. Moreover, as this chapter substantiates, the fundamental course of ascending by abstraction of properties and descending by restoring them step by step, on which the Cartesian chain of scientific knowledge rests, was taken by d’Alembert to be a methodical “strategy” rather than a procedure that secures the ontological foundations of physics. Where should we look if we want to know what physics meant to d’Alembert? To his real work in mathematical physics or to his philosophical professions of faith? After the great successes of Galileo and Newton, after the triumph of the new analytical methods of Varignon, the Bernoullis and Euler (whose Mechanica sive motus scientia analytice exposita appeared in 1736), comes the time for theoretical

The work presented here is linked to the vast enterprise of a complete and critical edition of d’Alembert’s writings; see Chouillet et al., L’édition.

F. De Gandt (*) Sciences Humaines, Lettres et Arts, Université Charles de Gaulle, Lille, France © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_3

53

54

F. De Gandt

reorganisation, for systematic presentation. But it is also time for new inquiries, into celestial perturbations, fluid phenomena, mechanical systems. D’Alembert was a practicing scientist as well as a theorist. He was very inventive in celestial mechanics, in fluid theory, in the study of mechanical systems and vibrations, and on the other hand, for the purpose of the Encyclopédie and in quest of philosophical clarity, he spent much effort in delineating the general structure of sciences, their overall map or tree, in tracing their relations of dependence and formulating carefully their respective principles. He also tried, in the Discours préliminaire de l’Encyclopédie and in his Essai sur les élémens de philosophie, to sketch a sort of history of human mind in his ascent to knowledge. These different endeavours are not easily reconcilable. To define physical science or any other given discipline in a d’Alembertian way, we therefore have to follow several paths, and to test their agreement: –– according to its mode of operation, we can indicate its level on an abstracting ladder from sensation to understanding: a genetic path; –– according to the nature of its domain, we can determine its place in the tree of knowledge: a deductive or systematic path; –– according to its real results and questions, we can inspect its actual content as a practicing inquiry: a factual inspection.

3.1 Abstraction Let us start with the genesis of the sciences given in the Discours Préliminaire de l’Encyclopédie, “the genealogy and filiation of the parts of our knowledge” (Alembert, Preliminary discourse, 5).1 According to d’Alembert, human knowledge is a process of abstraction from sensory evidence (the “objects that affect us by their presence” (ibid. 10). The system of innate ideas must be definitively abandoned – “we owe all our ideas to our sensations”2 – but the ideas of our existence, of justice between men, and the “sentiment intérieur” which attests the existence of God, are to be counted among first ideas.3 Then we reach, step by step, through comparison and reflection, the more abstract properties of bodies. Necessity and curiosity lead us on this ascending path. “In our study of nature, which we make partly by necessity and partly for amusement, we note that bodies have a large number of properties.” (Alembert, Preliminary discourse, 16) Some properties are common to all bodies, as movement and rest, and the capacity of communicating movement. We discover a property more fundamental, impenetrability, upon which all other properties depend. We gradually  “la généalogie et la filiation de nos connaissances” (Alembert, Discours Préliminaire, i).  “c’est à nos sensations que nous devons toutes nos idées” (ibid. ii). 3  More precisely, they are “the fruits of the first reflective ideas that our sensations occasion.” (Alembert, Preliminary discourse, 14) 1

2

3  The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s…

55

come to a differentiation between two sorts of extension, one impenetrable, the body itself, the other simply “occupied by the bodies” (ibid. 18). “We now see bodies only as shaped and extended parts of space,” and “we are led to ascertain the properties of extension simply as to shape.” This is geometry. The complexity of qualities and features of the bodies is progressively reduced; “by a few successive operations and abstractions of our minds we divest matter of almost all its sensible properties” (Alembert, Preliminary discourse, 19). The human mind is capable of that sort of selective attention which retains only certain features of the given bodies: “abstraction is nothing else than the operation by which we consider in an object a particular property without paying attention to others.”4 Geometry is at a high level on the abstracting ladder; it studies bodies only as they are shaped and extended. “The properties of extension simply as to shape” are the object of geometry (Alembert, Preliminary discourse, 18 f.). Beyond geometry, the summit is occupied by the study of combinations and comparisons, under the various chapters of arithmetic and algebra, the science of magnitudes in general (ibid. 19 f.). All sciences find their origin and occasion in nature, they all are in a certain sense, sciences of nature. They consider physical objects as..., or as..., that is as endowed only with a given stock of properties.5 The difference is only that some disciplines are poor in physical properties, while others are rich. Each science has its object placed on a certain level of the abstracting ladder.

3.2 Restoration At the end of the abstracting process comes a “restoration.” To the object of our study we give back one property or another: But such is the progress of the mind in its investigation that after having generalized its perception to the point where it can no longer break them up further into their constituent elements, it retraces its steps, reconstitutes anew its perceptions themselves, and, little by little and by degrees, produces from them the concrete beings that are the immediate and direct objects of our sensations. (Alembert, Preliminary discourse, 20f.)6

During that inverse procedure of restoration, we generate one science after another, graded according to their degree of complexity:  “l’abstraction en effet n’est autre chose que l’opération par laquelle nous considérons dans un objet une propriété particulière, sans faire attention aux autres.” (Alembert, Elémens de philosophie, 29) 5  An interesting comparison could be made, surprisingly, with the Aristotelian description of mathematics in Physics B 2. 6  “Telle est la marche de l’esprit humain dans ses recherches, qu’après avoir généralisé ses perceptions jusqu’au point de ne pouvoir plus les décomposer davantage, il revient ensuite sur ses pas, recompose de nouveau ces perceptions mêmes, et en forme peu à peu et par gradation les êtres réels qui sont l’objet immédiat de nos sensations.” (Alembert, Discours Préliminaire, vi) 4

56

F. De Gandt Having so to speak exhausted the properties of shaped extension through geometric speculation, we begin by restoring to it impenetrability, which constitutes physical bodies and was the last sensible quality of which we had divested it. (ibid. 21)

The first step on the descending ladder is thus mathematical physics, or more precisely mechanics: The restoration of impenetrability brings with it the consideration of the action of bodies on one another, for bodies act only insofar as they are impenetrable. It is thence that the laws of equilibrium and movement, which are the objects of mechanics, are deduced. (ibid.)

Then we make use of geometry and mechanics for the study of bodies, for instance in astronomy and in all the branches of “physico-mathematical sciences.”

3.3 Properties The progression and restoration are guided by the notion of properties. Our sensory experience is an experience of bodies, and in these bodies, we notice various properties. “In our study of nature, […] we note that bodies have a large number of properties.” (Alembert, Preliminary discourse, 16). Questions could be posed at that stage: what forces us to decompose the world into pieces which we call bodies and into constituents which we call properties? Is it even true that we in fact do so? D’Alembert is not very helpful in such inquiries. His description of human experience is probably biassed, as we shall see, by the habits of scientific understanding. We separate properties from the magma in which they are present together: we note that bodies have a large number of properties. However, in most cases they are so closely united in the same subject that, in order to study each of them more thoroughly, we are obliged to consider them separately. (Alembert, Preliminary discourse, 17)

The abstracting operation consists in filtering certain of these properties, according to whether they are common to many bodies, or to all of them, or even by noting that some properties are more fundamental. (What a strange task for a strictly empirical strategy to decide which properties are more fundamental!) The speculation on the properties of matter, the philosophical task of establishing the list and order of precedence of the properties of matter is a common theme of discussion in those years (Maupertuis, Voltaire, Diderot, et  al.). Cartesians and Lockeans agreed that some qualities of the bodies are more fundamental or more essential. Descartes proved it in the Second Part of his Principia Philosophiae,7 and Locke admitted that some qualities (solidity, extension, figure, mobility) are such that the finest division of a material body will never take them away (Locke, Essay, II.8 § 9). He called them “primary.”

 Using the intellect only, since the senses are inapt to teach the real nature of things (Descartes, Principia, II § 3), we “perceive” “that the nature of bodies does not consist in weight, hardness, colour or such things, but only in extension” (ibid. § 4). 7

3  The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s…

57

Cartesians had strong reasons to limit the properties belonging to matter, whereas empiricists were more lenient in their admittance. Since we do not know the nature of things, even strange qualities like thought and gravitation could be considered. The discussion became more acute when readers of Locke were scandalised by his suggestion that nothing prevents God from granting thought to a piece of matter (Locke, Essay, IV.3 § 6), and when followers of Newton felt inclined to admit attraction as a quality of matter.8 What then should we count as belonging to matter qua matter? Extension, solidity, weight, attraction, colour, irritability, sensitivity, thought?

3.4 Simplicity This back-and-forth movement in the consideration of physical objects has some roots in the philosophical tradition. The abstracting path is well known through the description given by Locke; we could even trace it back to Aristotle’s Physics B 2. The descending path is more original. Why two ways, up and down? Is the first genetic and the second systematic? Where shall we find the various sciences, on the way up or on the way down? The double path is much better understood and justified if we see it as mirroring or paralleling exactly the strategy of the scientist when confronted to a given phenomenon. The most striking description, a sort of geometer’s profession de foi, is given at the beginning of the study of winds in 1747: Most physico-mathematical questions are so complicated that it is necessary to consider them first in a general and abstract manner, and to climb by degrees from simple cases to more composite ones. If any progress has been done up to now in the study on nature, it is due to the constant application of this method.”9

Mathematics is most certain because simple: “Certainty of mathematics is an advantage which these sciences owe mainly to the simplicity of their object.”10 Therefore it is useful to strip objects of their complexity in order to reduce them to a simple pattern, the study of which can be easily achieved by mathematics, and raised to a high degree of certainty. Once a simplified pattern has been studied in its principal aspects (the corresponding mathematical situation, reduced to a skeleton of geometrical and arithmetical data), the scientist has to “restore” the complexity step by step.

 See the preface to the third edition (1726) of Newton’s Principia, by Cotes, the first of those attractionists: “either gravity must have a place among the primary qualities of all bodies, or extension, mobility and impenetrability must not.” (Newton, Mathematical principles, I xxvi) 9  “La plupart des questions physico-mathématiques sont si compliquées qu’il est nécessaire de les envisager d’abord d’une manière générale et abstraite pour s’élever ensuite par degrés des cas simples aux composés. Si on a fait jusqu’ici quelques progrès dans l’étude de la nature, c’est à l’observation constante de cette méthode qu’on le doit.” (Alembert, Reflexions, VIII) 10  “La certitude des mathématiques est un avantage que ces sciences doivent principalement à la simplicité de leur objet.” (Alembert, Traité de dynamique, first sentence) 8

58

F. De Gandt

Newton’s Principia is the best illustration of this procedure: we start with point masses under the influence of the centripetal force attached to a single point, then progressively the situation is enriched by admitting several moving bodies, or massive attractive bodies, introducing a resisting medium, and so on. Archimedes or Galileo could also be invoked as grandfathers of this mathematical method.

3.5 Winds Take the example of winds, a very difficult object, so impalpable and unpredictable. The more tractable winds are the regular ones, the trade winds, which form the theme of the Reflexions sur la cause générale des vents (1747). D’Alembert’s guess is that gravitation could explain trade winds. He starts by a very simple situation and enriches it step by step. The inquiry proceeds on several levels, from the simplest to the richest and most concrete (my list is somewhat simplified compared to the actual argumentation of the text): 1. The geometer begins by determining the shape of a thin layer of fluid surrounding a spherical solid core: what is the figure of equilibrium of that fluid layer under the action of a centrifugal force? 2. Then d’Alembert studies the evolution of the shape from an initial perfectly spherical situation to the equilibrium state. 3. Then he comes to the oscillations around the equilibrium state. 4. External action is added, via the outward gravitational influence of an immobile planet. 5. The planet is made to rotate. 6. The reciprocal attraction of the particles of fluid is taken into account. 7. Elasticity of the fluid is introduced. 8. The behaviour of the fluid currents is studied in narrow rectilinear channels oriented East to West or North to South. Oblique or curvilinear currents must be obtained as combinations and superpositions of those simple streams. Do we recover the real and effective trade winds as a result of the theoretical reconstruction? At the end, alas, all the business fails since a major cause has not been considered: the variation of heat in the atmosphere. D’Alembert alludes to that cause, but he discards it because it is not amenable to mathematical precision. The interest for our purpose is in the systematic impoverishment and re-­ enrichment of the data. The object or the phenomenon under investigation is stripped from its concrete nuances and qualities, stripped to the purest skeleton, then progressively reinvested with well-determined new properties. Mathematics guides the progression.

3  The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s…

59

3.6 Essences The reduction is a strategy, not an ontology. Nothing guarantees that the abstract properties reached in the ascending path are the essential properties of bodies. “Is the being which we call matter similar to the idea which we form of it? We must accept our ignorance on this question.”11 Descartes saw extension and motion as first properties in an essential sense. D’Alembert has doubts about the accessibility of essence of bodies: the most sensible properties which we discover in matter by observation […] belong to the essence, and so to speak to the intimate constitution of matter, of which we know nothing, and shall never know.12

He even has some doubts about the simplicity and intelligibility of nature. And yet, surprisingly, there is one case where d’Alembert accepts the notion of essence and grants to men some access to matter itself: impenetrability is an essential quality of matter, maybe the very essence of matter, and upon it rests the most robust and demonstrative part of physics.

3.7 Impenetrability Various qualities of bodies are linked to the various senses. In the 1740s the Parisian Salons became warmly interested in the privilege of sight or of touch. Thus a new turn occurred in the debate on the properties of matter. Diderot had first asked about the best place for the soul – heart, foot, nose, eye, jewel13? – and tried to separate the contribution of each sense to our experience and to our science.14 Buffon,15 disputing with Condillac about the hierarchy of senses, described Adam discovering the world through his five senses, giving the precedence to touch. D’Alembert’s solution, in his Essai of 1759, is that touch is first, because no man can be totally deprived of touch, and because solidity is more essential to bodies: “impenetrability, this quality essential to bodies, is known to us only through touch.”16 This is an unexpected note: now we have a quality essential to matter. In  “Cet être que nous appelons matière, est-il semblable à l’idée que nous nous en formons? C’est ce que nous devons nous résoudre à ignorer.” (Alembert, Elémens de philosophie, 46) 12  “les propriétés les plus sensibles que l’observation nous découvre dans la matière […] tiennent elles-mêmes à l’essence, et si je puis m’exprimer ainsi, à la constitution intime de la matière que nous ne connaissons nullement, et que nous ne parviendrons jamais à connaître.” (Alembert, Elémens de philosophie, 217) 13  Diderot, Les Bijoux indiscrets. 14  Diderot, Lettre sur les aveugles (1749) and Lettre sur les sourds et les muets (1751). 15  Buffon, Histoire naturelle, vol. III (1749). 16  “l’impénétrabilité, cette qualité essentielle des corps, ne nous est connue que par le toucher.” (Alembert, Elémens de philosophie, 41) 11

60

F. De Gandt

the empiricist landscape it is not totally new: Locke called it “solidity” and he viewed it as “the idea most intimately connected with, and essential to Body,” or “inseparably inherent in Body.” (Locke, Essay, II.4 § 1) This quality has an eminent privilege over all others: we soon discover another property upon which all of these depend: impenetrability, which is to say, that specific force by virtue of which each body excludes all others from the place it occupies, so that when two bodies are put together as closely as possible, they can never occupy a space smaller than the one they filled separately. Impenetrability is the principal property by which we make a distinction between the bodies themselves and the indefinite portions of space in which we conceive them as being placed – at least the evidence of our senses tells us such is the case. (Alembert, Preliminary discourse, 17)17

In the general construction of knowledge sketched by d’Alembert, impenetrability is a decisive element. It marks the frontier between geometry and mechanics.18 D’Alembert is incredibly positive about the privilege of impenetrability: “bodies act only insofar as they are impenetrable” (Alembert, Preliminary discourse, 21).19 Should we then believe that all sorts of action in nature flow from the unique source of impenetrability? “Bodies act only insofar as …”: All other modes of operation in nature are inacceptable or incomprehensible; they are beyond our understanding, which does not entail that they are impossible in Nature.

3.8 Necessity Impenetrability must be conceived of as an active property, causing positive effects when several bodies meet. Locke was already aware of this: “That which thus hinders the approach of two bodies, when they are moving one towards another, I call Solidity.” (Locke, Essay, II.4 § 1). Thence comes the construction of pure and rational mechanics (Firode, Lois du choc). That is, mechanics is rational insofar as it can be generated from the first properties of matter. There are laws of mechanics, and they result only from the admission of extension, shape, motion and impenetrability. Mechanics is able to deduce with certitude the laws of equilibrium and motion. The three laws (inertia, composition of motions and equilibrium) are necessary truths – such is d’Alembert’s answer to the question posed by the Berlin Academy in 1758 (Alembert, Essai, 138ff.). Impact is the only case where a sort of causal reconstruction is possible:

 Note the use of the term “force,” which is so rare and meaningful in d’Alembert’s writings.  A confrontation would be useful here with Euler’s conception of the privilege of impenetrability in the study of nature and force: “la raison ou la cause de ce changement existe infailliblement dans l’impénétrabilité des corps mêmes.” (Euler, Lettres à une princesse d’Allemagne (2nd part, letter IX “sur l’origine et la nature des forces”), 201). 19  “les corps n’agissent qu’en tant qu’ils sont impénétrables” (Alembert, Discours Préliminaire, vi). 17 18

3  The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s…

61

among all causes, occasional or direct, which influence the motion of bodies, impulsion is the only one of which we are able to determine the effect from the knowledge of the cause […]. All other causes are entirely unknown to us.20

We have to start from the situation where equilibrium manifests itself in a clear and distinct way: equal masses with equal and opposite velocities.21 Deduction of the general laws proceeds from the simple case, where equal bodies with equal and opposite velocities must simply stop: If two bodies are equal and their velocities are equal, it is obvious that they will stay at rest. For there is no reason why the one rather than the other, should move in his direction.22

By decomposing the more complex cases into components of equal mass and velocity, d’Alembert reduces them to the simple case of equilibrium: “Thence comes the axiom that bodies whose quantities of motion are equal and directly opposite are in equilibrium.”23 It is an axiomatic truth, because impenetrability forces the bodies to stop, and because the principle of sufficient reason does not allow any particular preeminence of one of the equal bodies nor any arbitrary deviation from equilibrium. The destruction of the motion is the perfectly intelligible situation.

3.9 Springs and Other Gaps But these laws establish only the behaviour of bodies in abstract and restricted cases of impact. Two equal bodies with opposite velocities must remain in equilibrium. That is, they have to stop. The Cartesian idea of a communication of motion through impact is not included in the strict derivation of mechanics from first properties. What makes the bodies rebound? What causes the whole fabric of nature to move and live, bodies pushing one another? For a more adequate study of the fate of

 “de toutes les causes, soit occasionnelles, soit immédiates, qui influent dans le mouvement des corps, il n’y a tout au plus que l’impulsion seule dont nous soyons en état de déterminer l’effet par la seule connaissance de la cause […]. Toutes les autres causes nous sont entièrement inconnues.” (Alembert, Traité de dynamique, (2nd. ed.) 22) 21  “si l’on y fait attention, on verra qu’il n’y a qu’un seul cas où l’équilibre se manifeste d’une manière claire et distincte; c’est celui où les masses des deux corps sont égales et leurs vitesses égales et opposées. Le seul parti qu’on puisse prendre, ce me semble, pour démontrer l’équilibre dans les autres cas, est de les réduire, s’il se peut, à ce premier cas simple et évident par lui-même.” (Alembert, Traité de dynamique, (1st. ed.) xiv) 22  “Si deux corps sont égaux et leurs vitesses égales, il est évident qu’ils resteront tous deux en repos. Car il n’y a point de raison pourquoi l’un se meuve plutôt que l’autre dans la direction qu’il a.” (Alembert, Traité de dynamique, (1st. ed.) 37, (2nd. ed.) 51). See also Alembert, Essai, 132. 23  “De là naît cet axiome, que les corps qui ont des quantités de mouvement égales et directement opposées, se font équilibre.” (ibid. (1st. ed.) 39 f., (2nd. ed.) 55) 20

62

F. De Gandt

colliding bodies, we must add a new notion, subject to many difficult questions: the notion of “ressort” (spring).24 The rigorous theory deals only with perfectly hard bodies which stop after impact (in the case of equal and opposite quantity of motion). The “ressort” is introduced and defined as the device (whatever it may be, physically speaking) which allows the restitution of the motion in the opposite sense: If any number of bodies strike one another in such a way that, supposing them perfectly hard and without spring, they stay at rest after impact, I say that, if they are endowed with perfect spring, they will return backwards each with the velocity it had before impact. For the effect of the spring is to restitute to each body in contrary sense the velocity lost by the action of other bodies.25

If one asks what a “ressort” may be, the answer is evasive: I also suppose, as a truth of experience, that spring gives back to each body in a contrary sense the amount of motion it lost in impact, without examining in which manner this restitution may be effected.26

The only property of springs is that they restitute entirely the lost motion in opposite direction. We know nothing more, and we do not need it.

3.10 Well-Known Facts About Forces In the three basic laws (inertia, composition, equilibrium), there is no mention of acceleration. D’Alembert admits the law of the proportionality of the element of velocity to the accelerating force, dv :: F dt, and he re-demonstrates this from geometrical considerations in the first pages of his Traité de Dynamique (1st ed. §§ 14–19). D’Alembert has some strong reservations about the proportionality between force and the element of velocity: 1. He shows that this law is not verified in the case of collisions.27  The strange and difficult notion of “ressort” or “elaster,” in its use by Jean Bernoulli (Discours sur les loix de la communication des mouvemens, 1726) and others, has not received the attention it deserves. 25  “Si tant de corps qu’on voudra viennent se choquer de manière, qu’en les supposant parfaitement durs et sans ressort, ils demeurent tous en repos après le choc; je dis que s’ils sont à ressort parfait, ils retourneront en arrière chacun avec la vitesse qu’il avoit avant le choc. Car l’effet du ressort est de restituer en sens contraire à chaque corps le mouvement qu’il a perdu par l’action des autres.” (Alembert, Traité de dynamique, (2nd. ed.) 217 f.) 26  “Je suppose aussi comme une vérité d’expérience, que le ressort rend à chaque corps en sens contraire ce qu’il a perdu de mouvement par le choc, sans examiner de quelle manière se fait cette restitution.” (ibid. 218) 27  “le principe des forces accélératrices proportionnelles à l’élément de la vitesse ne doit point être employé pour déterminer les mouvemens qui résultent de l’impulsion.” (Alembert, Traité de dynamique, (1st ed.) 139) 24

3  The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s…

63

2. He refuses to think of it as a causal principle. A justification of the law in terms of cause and effect (like Euler’s reasoning in his Mechanica from 1736) is much too vague and inconclusive. (Alembert, Traité de dynamique, (1st. ed.) 18 f.)28 In his own research, when he has to pass from forces to trajectories, he does not treat the formula dv:: f dt as an important novelty, but as an elementary and well-known fact. For instance, he uses it as a basic tool in his first creative study, devoted to the resistance of fluids and the “refraction of the sphere” (manuscript in the Paris Registres Manuscrits de l’Académie des Sciences, dating from 1741).29 In doing so he is in agreement with all his fellow geometers of the time. Even Newton already considered his second law as discovered by Galileo,30 and Jean Bernoulli viewed it as a traditional truth of mechanics.31 There are other important results which d’Alembert treats as accepted facts in his studies of mechanical phenomena. In his first Mémoire on celestial mechanics, he inserts without any precaution or justification the relation vdv = f dx, or the area law for central forces (Alembert, Méthode, 367). The formula vdv = fdx is derived elsewhere, in the opening section of the Traité de dynamique (1st ed. 16), the area law is not re-demonstrated by d’Alembert. Since he is not writing a textbook (and d’Alembert always refused to write a textbook), he does not feel obliged, as Euler did in his Introductiones or Institutiones, to re-expose the basic arguments of every item of science he uses. He simply relies on the treasure of hundred years of mathematical physics which had become a sort of common property, the accepted and refined culture of a thin layer of philosophers since Galileo and Huygens.

3.11 Attraction as a Last Recourse The status of universal gravitation is the crux of the systematic derivation. Gravitation is not an essential property, and we must take a fresh start, made acceptable in the general strategy by the admission of provisional concepts. There are properties which we admit provisionally at first, and from which we derive others:

 “cet unique axiome vague et obscur que l’effet est proportionnel à sa cause” (Alembert, Traité de dynamique, (1st. ed.) xi). 29  See F. De Gandt, 1744. The occurrence of the acceleration formula is on the top of folio 373 of the Registres for 1741: “Or cet effort multiplié par le carré du temps /.../ doit être égal au produit de la masse m du cercle par la petite ligne oi {second difference}.” Then the trajectory is obtained by integration. See Alembert, Traité de l’équilibre, book II ch. 2 (= the published version of this study), in particular page 223. 30  “Per leges duas primas et corollaria duo prima adinvenit Galilaeus descensum gravium esse in duplicata ratione temporis, et motum projectilium fieri in parabola […].” (Newton, Principia, 20) 31  “Or les Méchaniques faisant voir aussi que les accroissements de vitesse qui résultent de ces forces dans des corps égaux, sont entre eux en raison composée de ces forces et des temps élémentaires employés par elles à produire ces accroissements de vitesse.” (1710, Jean Bernoulli, Opera, I 473) 28

64

F. De Gandt Why should we really bother with penetrating into the essence of bodies, so long as, supposing that matter is such as we conceive it, we are able to deduce from certain properties which we consider as primary the other secondary ones which we perceive in it, and so long as the general system of the phenomena, always uniform and continuous, nowhere presents a contradiction.32

3.12 Fluids The study of fluids introduces another gap in the deductive chain. Since we do not know the internal constitution of fluids (“the form and disposition of fluid particles”  – Alembert, Traité de l’équilibre, vii), we cannot construct a decisive and certain science of fluids. If we knew the figure and mutual disposition of the particles which compose fluids, the principles of ordinary mechanics would be sufficient to determine the laws of their equilibrium and motion. (ibid.)

But this is not the case, and we have to add certain other provisional assumptions: As the mechanics of solid bodies is resting only on principles which are metaphysical and independent of experience, we can determine exactly the principles which must be used as foundations for the others. The theory of fluids, on the contrary, must necessarily rest on experience.33

For instance, the third principle of ordinary mechanics, concerning equilibrium, cannot be applied directly to fluids, since we cannot compare the particles separately. Relying on experience, the theory of fluids must start from a new “foundation”: “that the pressure of particles is spread equally and in all directions.”34 The unjustifiable transition from solids to fluids, with the insertion of new hypotheses, is placed by d’Alembert on a par with the acceptance of gravitation. In both cases our ignorance of the essence and internal structure of the bodies forces us to accept certain hypotheses, or to reduce the phenomena to a small number of “primary and fundamental facts.”35  “Que nous importe au fond de pénétrer dans l’essence des corps, pourvu que la matière étant supposée telle que nous la concevons, nous puissions déduire des propriétés que nous y regardons comme primitives les autres propriétés secondaires que nous appercevons en elle, et que le système général des phénomènes, toujours uniforme et continu, ne nous présente nulle part de contradiction.” (Alembert, Elémens de philosophie, 46) 33  “La méchanique des corps solides n’étant appuyée que sur des principes métaphysiques et indépendants de l’expérience, on peut déterminer exactement ceux de ces principes qui doivent servir de fondement aux autres. La théorie des fluides, au contraire, doit nécessairement avoir pour base l’expérience.” (Alembert, Traité de l’équilibre, vi) 34  “que la pression des particules se répand également et en tous sens” (ibid. x). 35  “Condamnés comme nous le sommes à ignorer l’essence et la contexture intérieure des corps, la seule ressource qui reste à notre sagacité est de tâcher au moins de saisir dans chaque matière l’analogie des phénomènes et de les rappeler tous à un petit nombre de faits primitifs et fondamentaux.” (Alembert, Elémens de philosophie, 440) 32

3  The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s…

65

3.13 Fluids as Systems: D’Alembert’s Principle The conservation of living forces is not included in the first principles, and its validity in the case of fluids, for instance, is dubious. It must be demonstrated in each case, and cannot serve as a general tool – as opposed to Daniel Bernoulli, who tried to demonstrate it from unacceptable assumptions about the elastic corpuscles which could compose fluids (Alembert, Traité de l’équilibre, xvi). Instead of the conservation of living forces, d’Alembert uses his own “principle”: the sum of destroyed motions in a system must be equal to zero. The possibility of replacing living forces by that statement is certainly not obvious, and must be explained. Why is d’Alembert’s principle here equivalent to the conservation of vis viva? The general problem, in the case of fluids as in any complex arrangement of moving masses, is to take into account the internal actions or influences of each component upon the others. In a complex pendulum where several masses are suspended by a common string or rigid bar, the lower masses tend to retard the common motion, while the higher ones tend to accelerate it. Is it possible to quantify exactly this mutual influence, and to derive a law for the common motion? Huygens, in his study of complex pendula, posed the problem: I had considered […] that the weight nearest to the suspension made an effort to hasten the motion of the lowest weight; but, since it was difficult to say the amount by which it hastened it, I investigated that using an established method and following quite certain principles.36

Huygens found his way through conservation of the global vis viva, applied to the centre of gravity.37 The difficulty is the same with fluids: each part of the fluid in motion has its own velocity, which would be the actual velocity if the part were left alone and free. For instance, the velocity of a given volume of fluid may vary according to the width of the various sections in an irregular pipe. To determine the total motion of a large mass of fluid, it is necessary to combine the particular motions of the components, but not as a simple sum, because the motions are not all compatible: one component is too fast, the other is too slow, and they “embarrass” each other. The resulting global motion is not the exact magnitude of all motions. We have to evaluate the motion which is lost or gained by the mutual actions of the parts. To determine the global motion, conservation of vis viva can be helpful at this stage,38 but other instruments may be used. D’Alembert performs the same operation of globalisation in his first studies on fluids, by considering “slices” (“tranches”) inside the mass of fluid, and writing that the total amount of motion lost and gained  “J’avais considéré comme eux [sc. Bernoulli and L’Hospital] que le poids le plus proche de la suspension faisait effort pour hâter le mouvement du poids d’en bas; mais étant difficile de dire de combien il devait le faire hâter, j’ai cherché cela par une voie plus assurée et où je suivrais des principes plus certains.” (Huygens, Oeuvres, XVI 44O, note 2) 37  Cf. his Horologium oscillatorium, section on the center of oscillation. 38  Daniel Bernoulli follows that line of reasoning in his Hydrodynamica (1738). 36

66

F. De Gandt

by mutual actions of slices (“l’action mutuelle des tranches”) must be zero (Alembert, Traité de l’équilibre, 69 f.). A disciple of d’Alembert, the Abbé Bossut, explains the idea for a case which is elementary and paradigmatic, a mass of fluid flowing downwards inside a cylindrical and vertical pipe of variable width: Imagine the fluid to be divided into an infinity of horizontal and equal slices […] which move down always remaining parallel to each other, and each of which having the same vertical velocity over its entire extension. All of these slices act upon each other, either by pushing the next or by dragging it; so that if the velocity of one is retarded from one instant to the next, the velocity of the others is accelerated. In this respect, the same things happen in the motion of fluid particles as in the motion of several solid bodies forming one system, each body unable to move unless it acts upon the others and is acted upon in return.39

3.14 The Privilege of Destruction The motivation and meaning of d’Alembert’s principle appear more clearly in such a context. Commentators speak of a reduction of dynamics to statics, or of an extension of statics. It is true in a sense: the “principle” institutes a fictitious equilibrium, it operates via mutual destruction of motion. D’Alembert, in his Traité de dynamique, presents the principle in an indirect way: the motion impressed on each body of a system must be decomposed into two components, one which the bodies could have conserved “without mutual damage” (“sans se nuire réciproquement” – 1st. ed. 51), the other totally destroyed. If only the last motions had taken place, the system would have remained at rest. These last components are then the portions of motion destroyed by the mutual hindrance or “embarrassment” of the bodies; they annihilate each other because of the interactions between the parts of the system. The particular nature of the system is irrelevant: slices of fluid, masses suspended, etc. The computational trick consists in summing those components and equalling them to zero. The so-called principle is not a new and independent hypothesis; it is not an addition to the stock of three principles (inertia, composition and equilibrium). In some texts d’Alembert presents his “principle” as a new method enabling geometers to make use of composition of motion and equilibrium. The situation may appear slightly disappointing: D’Alembert himself does not grant a high dignity to his main innovation in theoretical science.

 “Imaginons que le fluide est partagé en une infinité de tranches horizontales et égales […] et qui s’abaissent parallèlement à elles-mêmes, et dont chacune a la même vitesse verticale dans toute son étendue. Toutes ces tranches agissent les unes sur les autres, soit en se poussant ou en s’entraînant; ensorte que si la vitesse des unes est retardée d’un instant à l’autre, la vitesse des autres est accélérée. Il en est à cet égard du mouvement des particules fluides comme de celui de plusieurs corps solides, formant un même système, dont aucun ne peut se mouvoir sans agir sur les autres et sans éprouver leur réaction.” (Bossut, Traité, 328ff.) 39

3  The Limits of Intelligibility: The Status of Physical Science in D’Alembert’s…

67

The principle – or the method – is linked with d’Alembert’s fundamental ideas in physics. Destruction of motion is the only rational situation in the behaviour of bodies, as we saw above. The most intelligible, and maybe the only perfectly intelligible situation, is equilibrium. The principle reduces the behaviour of systems to the state of equilibrium, a strategy comparable to the one used for impacts: the perfectly intelligible situation is the case of frontal impact between equal masses with equal and opposite velocities; from it all other cases must be derived (Firode, Lois du choc; Firode, Recherches).

3.15 Broken Branches The general structure of physics in d’Alembert’s work has striking rationalist and, so to speak, Cartesian features, especially in his tendency to deduce the laws of mechanics. But, even in that case, d’Alembert himself was not satisfied with the result, since up to his final days he tried to improve his own demonstrations of the three basic laws.40 He also acknowledged the numerous lacunae of the systematic chain of sciences. We noted several important gaps in the deductive architecture: –– the adjunction of “ressort” to hard bodies to account for the continuation of motion after impact, –– the difficult passage from solid bodies to fluids, –– the insertion of gravitational attraction. The demonstrative part of science which stems from the admittance of extension, movement and impenetrability is merely an initial segment of the long chain. Other parts of the great chain must be reconstructed independently. Descartes saw human knowledge as a large unitary tree, with metaphysics as the roots, physics as the trunk and the branches as medicine, mechanics and ethics.41 D’Alembert tried to reconstruct a comparably beautiful structure, but his “tree of knowledge” has many missing parts and many branches hanging separately.42

 Manuscript of the ninth volume of Opuscules, Bibl. de l’Institut de France. See Dhombre et al., Contingence). 41  See the Lettre-Préface of the French translation of the Principia Philosophiae: Descartes, Oeuvres, IX.2 14. 42  See the additional Eclaircissements to his Essai sur les Elemens de Philosophie and the comments in Hankins, Jean d’Alembert, 104–131 and De Gandt, D’Alembert et la chaîne des sciences, 39–53. 40

68

F. De Gandt

References Alembert, Jean LeRond d’. 1743. Traité de dynamique. Paris: David. ———. 1990. Traité de dynamique (1758). 2nd ed. Sceaux: J. Gabay. ———. 1744. Traité de l’équilibre et du mouvement des fluides. Paris: David. ———. 1745 Méthode générale pour déterminer les orbites et les mouvemens de toutes les planètes. Histoire de l’Académie Royale des Sciences. ———. 1747. Reflexions sur la cause générale des vents. Berlin: Haude & Spener. ———. 1751. Discours Préliminaire de l’Encyclopédie. In Encyclopédie ou dictionnaire raisonné des sciences, des arts et des métiers, vol. 1. Paris: Briasson. ———. 1985. Preliminary discourse to the Encyclopedia, transl. R. Schwab. Library of Liberal Arts, Indianapolis: Bobbs-Merrill. ———. 1986. Essai sur les élémens de philosophie (1759). Paris: Fayard. ———. 1761–1780. Opuscules mathématiques, ou Mémoires sur différens sujets de géométrie, de méchanique, d’optique, d’astronomie. Paris: David. Bernoulli, Jean. 1742. Opera omnia, ed. J.E. Hofmann. Lausannae; Genevae: Bousquet. Bossut, Charles. 1771. Traité élémentaire d’hydrodynamique. Paris: Claude-Antoine Jombert. Chouillet, A.M., F.  De Gandt, and I.  Passeron. 1998, July. L’édition des oeuvres complètes de d’Alembert. Gazette des Mathématiciens: 59–71. Descartes, René. 1644. Principia Philosophiae. Amsterdam: Ludovicum Elzevirium. ———. 1964. Oeuvres complètes, ed. Ch. Adam and P. Tannery. Paris: Vrin. Dhombre, Jean, and Patricia Radelet-de Grave. 1991. Contingence et nécessité en mécanique. Etude de deux textes inédits de Jean d‘Alembert. Physis – Rivista Internazionale di Storia della Scienza XXVIII: 35–114. Euler, Leonhard. 1843. Lettres a une princess d’Allem agne sur divers sujets de physique & de philosophie, ed. Emile Saisset. Paris: Charpentier. Firode, Alain. 1996, October. Les lois du choc et la rationalité de la mécanique selon d’Alembert. Recherches sur Diderot et sur l’Encyclopédie 21. ———. 1999. Recherches sur la philosophie de d’Alembert et son contexte intellectuel. Thèse de doctorat, Univ. de Lille III – Charles de Gaulle. De Gandt, François. 1994. D’Alembert et la chaîne des sciences. Revue de Synthèse. ———. 1999. 1744: Maupertuis et D’Alembert entre mécanique et métaphysique. In Pierre Louis Moreau de Maupertuis, Eine Bilanz nach 300 Jahren, ed. H. Hecht, 277–292. Berlin: Berlin Verlag. Hankins, Thomas L. 1990. Jean d’Alembert, Science and the Enlightenment. New York: Gordon and Breach. Huygens, Christiaan. 1888–1950. Oeuvres complètes. The Hague: M. Nijhoff. Locke, John. 1690. An Essay Concerning Humane Understanding. London: Printed for Th. Basset, and sold by Edw. Mory. Newton, Isaac. 1687. Philosophioae naturalis principia mathematica. London: J. Streater. ———. 1966. Mathematical principles of Natural Philosophy (1729), ed. F. Cajori. Berkeley/Los Angeles/London: California University Press.

Chapter 4

“In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate on the Physical Significance of Mathematical Objects Aaron Wells Abstract  Du Châtelet holds that mathematical representations play an explanatory role in natural science. Moreover, she writes that things proceed in nature as they do in geometry. How should we square these assertions with Du Châtelet’s idealism about mathematical objects, on which they are ‘fictions’ dependent on acts of abstraction? The question is especially pressing because some of her important interlocutors (Wolff, Maupertuis, and Voltaire) denied that mathematics informs us about the properties of material things. After situating Du Châtelet in this debate, this chapter argues, first, that her account of the origins of mathematical objects is less subjectivist than it might seem. Mathematical objects are non-arbitrary, public entities. While mathematical objects are partly mind-dependent, so are material things. Mathematical objects can approximate the material. Second, it is argued that this moderate metaphysical position underlies Du Châtelet’s persistent claims that mathematics is required for certain kinds of general knowledge, including in natural science. The chapter concludes with an illustrative example: an analysis of Du Châtelet’s argument that matter is continuous. A key premise in the argument is that mathematical representations and material nature correspond.

4.1 Introduction A familiar early modern doctrine is that mathematical objects aptly represent the physical world, such that physics can and should be mathematical. But this was contested. One source of vigorous resistance was the difficulty in giving a metaphysical account of mathematical objects. It was widely agreed that mathematical A. Wells (*) Institut für Humanwissenschaften, Center for the History of Women Philosophers and Scientists, Universität Paderborn, Paderborn, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_4

69

70

A. Wells

objects, unlike the subject matter of physics, are not substances that wield causal powers. It was also hard to see how mathematical objects, with their definitional exactness, could be regarded as accidents or modes of physical things. A related epistemological question concerns how inferences from mathematics to the natural sciences might be justified. Third, there were methodological worries: it was often thought that science must deal with substances and offer causal demonstrations. Since mathematics does not seem to deal with primary substances or offer causal demonstrations, it is not clear how it meets these criteria for proper science.1 These controversies persisted in the wake of Newton’s Principia. In the first half of the eighteenth century, this work was often treated, both by critics and sympathizers, as a work in pure mathematics. Many German and French thinkers adopted a broadly anti-realist approach to Newton’s physics, holding that despite its impeccable mathematics, Principia did not constitute proper, causal physics. Yet it was difficult to dismiss Newton’s arguments, which have causal conclusions, as in his famous defense of universal gravitation. And his empirical results in optics and orbital mechanics were widely accepted. François De Gandt has called this a “crisis of causality” in the reception of Newton (2001, 129).2 Emilie Du Châtelet develops an intriguing and still neglected position on these issues.3 As I show, three of her contemporary interlocutors—Maupertuis, Voltaire, and Wolff—are skeptical about inferences from mathematics to physics, despite their broadly Newtonian sympathies. Du Châtelet has been read as likewise regarding the assertions in Principia as merely mathematical, rather than genuinely causal (Shank 2018, 273–74). But in fact, I’ll argue, she is confident about these inferences from mathematics to physics, and therefore about the standing of Newtonian physics as she understands it. This stance regarding the epistemic bona fides of mathematics is compatible with her idealist metaphysics of mathematical objects, which are fictions and products of abstraction. The objects of physics are also ideal and partly mind-dependent, for Du Châtelet, if to a lesser degree. This may help with the problem of understanding the success of inferences from mathematics to physics. This problem is still much discussed by philosophers of science and mathematics, but usually in a physicalist and metaphysically realist framework.4  For example, in a 1669 letter to Thomasius, Leibniz endorses these two broadly Aristotelian criteria for science, and adds that the “scholastici”—though not Leibniz himself—deny they can be met by geometry (1875–90, IV.168–70). 2  See further Gingras (2001), Janiak (2007), and Shank (2008, 49–104). Thanks to Anat Schectman for insightful comments on these issues. 3  I focus here on Du Châtelet’s Institutions de Physique, and still more narrowly on the foundational and methodological discussions early in the Institutions, as opposed to more specific discussions of physics later in the work. It is undisputed that mathematics plays a pivotal role in the Institutions. The puzzle is why and how Du Châtelet takes this to be justified. 4  One recent statement: “there must be some kind of correspondence between the mathematics in which we formulate our theories and the nature of the physical world, a correspondence that helps explain, on the one hand, the effectiveness of the mathematics in describing the world, and on the other, the success of our inferences about the world on the basis of that mathematics” (North 2021, 5). 1

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

71

I conclude by considering Du Châtelet’s frequently overlooked arguments for the continuity of matter and change. These arguments, which are important for her physics, rely on the correspondence between nature and mathematics.

4.2 The Ambivalent Reception of Newton’s Mathematical Physics Du Châtelet’s Preface to the Institutions frames the work as an exposition of Newton’s “system” (Du Châtelet 1742, 7). That system is presented as mathematical physics. On her telling, Newton played a critical role in a scientific “revolution” by which modern physics acquired “solid foundations” through a combination of “geometry” and “observations” (12; 5; 9; cf. 1738, 535, 1759, 7–8). Geometry, she holds, is “the key to all discoveries” in science, without which “progress in the study of nature” is impossible (1740, 3–4; 2018, I:500). Much remains unexplained in physics, but this is because of a failure to make sufficient use of geometry, which here includes post-Cartesian algebraic geometry (1740, 3–4; 14). Geometrical demonstrations, moreover, are maximally rigorous and link necessary truths (14; 17; 20–21; 26). The Preface also makes clear that while the Institutions is intended to be understood by a reader who knows only ordinary geometry, more advanced physicists make use of “algebra” (3). The task of “making Newton accessible” to a wider public, especially the “mystery” of his mathematical techniques, is already stated as a goal in her earlier, anonymous review of a work on Newton by Voltaire (Du Châtelet 1738a, b, 534–5; 538; 541). The Institutions also refers to calculus, though usually in passing (e.g. 1742, 308). Du Châtelet later calls calculus the “geometry of the infinite” (1759, 9).5 She considers it to be just as certain as classical geometry. But how exactly is mathematics a “means,” as she writes, to foundations for physics (1742, 12)? In working out the answer to this question, it’s helpful to consider Du Châtelet’s historical context, and especially three figures in the reception of Newton’s Principia who were of particular significance for her: Maupertuis, Voltaire, and Wolff. She disagrees with all three about the role of mathematics in physics. Maupertuis’s short treatise on the Figures des Astres (1732) is a work that Du Châtelet knew well (Du Châtelet 2018, I.350). Maupertuis presents the work as defending Newtonianism. The second chapter is an excursus on the metaphysics of Newtonian attraction or gravitational force. Maupertuis notes that Newton’s theory was accused of being unparsimonious, and of reviving “the doctrine of occult qualities” (Maupertuis 1732, 11).

 This follows eighteenth-century usage. For example, in 1702 Leibniz presents his infinitesimal calculus as a type of “geometrical reasoning” (Leibniz 1849, IV:91–92), and in 1743 D’Alembert places calculus within pure geometry (D’Alembert 1743, vi–viii). 5

72

A. Wells

Let’s consider the second of these accusations. Maupertuis does not say what he means by occult qualities. But epistemological worries about occult qualities often turned on their alleged causal efficacy (Pasnau 2011, 540–46). The problem was not just positing unobserved qualities, but taking these to be causal powers that explain what is observed, for example when fire is allegedly explained by a power to burn. The identification of occult qualities with unobserved causal powers sheds light on Maupertuis’s response to this objection. He argues that Newton never advanced attraction as a causal explanation (“explication”) of the behavior of bodies, such as the “heaviness [pesanteur] of some bodies towards others” (1732, 11). Instead, Newtonian theory gives a merely mathematical account of regular effects that are “susceptible” to being considered as greater or lesser in quantity (“de plus & de moins”) (12). A mathematical account is within our “means,” whatever the “nature” of the underlying cause turns out to be (“quelle que soit sa nature”) (12). It is clear from Maupertuis’s examples that the ‘mathematicians’ he has in mind include thinkers we’d now consider natural scientists or physicists. In addition to Newton, for example, Maupertuis discusses Galileo. He presents the theory of falling bodies in Galileo as mathematically “explaining the phenomena,” while leaving an account of causes to “more sublime philosophers” (1732, 12–13). Maupertuis does not elaborate on just what this would involve, and there is room for interpretive debate here. But Maupertuis favors the merely mathematical, acausal approach. He deflates the question of whether Newtonian force is an “inherent” property of matter: it can be usefully regarded “as if it were [comme si elle étoit]” such a property, but no metaphysical commitment is supposed to follow from this (10; cf. Maupertuis 1735, 343). A helpful point of comparison here is classical geometrical optics. Euclid’s Optics precisely described many observed aspects of vision, even though the causal mechanism of sight remained unknown for centuries.6 In the eighteenth century, optics was often still distinguished from the proper causal science of nature. Leibniz used the analogy with classical optics to stress the explanatory limitations of the Newtonian project, which he described as merely abstract and geometrical.7 Voltaire’s 1738 Eléments de la Philosophie de Newton went through twenty-six editions in fifty years. Du Châtelet was closely involved in its composition and may have even written portions of it, although she raised criticisms of the results, both publicly and in private letters.8  Aristotle’s Physics distinguishes between pure geometry and optics, which is “hupó” or subordinate to it (194a6–11). But optics is still a mathematical rather than natural science: the Meteorology expounds observations about reflection drawn “from the theory of optics” (1984, 372a29), then separately lays out causal natural-scientific theses concerning halos, rainbows, and so on (372b13–378b6). Early modern optical texts continued to classify optics as applied mathematics, citing Aristotle as an authority (Dear 1995, 41–58). 7  See for example a letter to Hartsoeker of 8 February 1712 (Leibniz 1875–1890, III:534–5; cf. VII:452). 8  On the publication history, see De Gandt (2001, 126). Zinsser (2006, 145–51) argues for Du Châtelet’s involvement. See Du Châtelet (1738a, b, 1740, 7, 2018, I:345–6; I:353) for her mixed assessments of the work. Lu-Adler (2018, 183–88) examines divergences between Voltaire and Du Châtelet. 6

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

73

Voltaire is explicitly indebted to Maupertuis’s Figure des Astres, and especially to its chapter on the metaphysics of attraction. He praises it as perhaps the best philosophical work in French (Voltaire 1738, 84). Behind the scenes, already in 1732, Voltaire had turned to Maupertuis for help in understanding the Principia (De Gandt 2001, 136–39). Like Maupertuis, Voltaire seeks to defend Newton’s system broadly speaking, while also driving a wedge between mathematics and causal physics. Many chapters are devoted to “proofs” and “demonstrations” of Newton’s theory of gravitation (Chapters XVIII–XXII), or to refutations of its Cartesian rivals (Chapters XV– XVI). But in a set of ‘Eclairissements’ added to the second edition, Voltaire defends gravity, while denying that Newton revealed its “principle” or “cause” (xiv–xv; cf. Voltaire 1734, 65; Du Châtelet 1738a, b, 539–40). Newton is depicted as a mere mathematician, lacking the time for the deeper metaphysical investigations Voltaire takes to be required in natural philosophy (1738, vii). Voltaire raises comparisons to classical optics, which as “simple geometry” cannot apply to empirical problems (iii–v).9 These remarks suggest that for Voltaire, natural science ought to give an account of causes, and that Newton fails to do so. This is hard to reconcile with Voltaire’s repeated claims that Newtonian theory is strictly proven. One case where Voltaire’s position is clear, however, is that of inferences from mathematics to physics. In Chapter X, Voltaire criticizes the Newtonian John Keill. For Keill geometry is foundational for all philosophy, and there is no other way to obtain knowledge of “the forces of nature” (Keill 1733, viii). Voltaire denies both these claims. Voltaire objects with particular zeal to Keill’s arguments for the infinite divisibility of matter. Keill’s basic move is to claim that, because space can be proven to be infinitely divisible within Euclidean geometry, matter must be infinitely divisible as well (Keill 1733, 20–32). This argument, then, moves from mathematical premises—Keill gives five examples of how indivisibles conflict with Euclidean assumptions—to conclusions about the physical world.10 We will see below that Du Châtelet could endorse Keill’s argument, so long as it is not taken to show that matter is made up of an infinity of actual parts (Du Châtelet 1742, 191–92). Consider one of Keill’s examples, which was discussed by thirteenth-century thinkers such as Roger Bacon in his Opus Maius (1962, 173), and originally found in Book X of Euclid’s Elements. The assumption of indivisibles, Keill points out,  Instead, Voltaire praises the psychological account given in Berkeley’s New Theory of Vision. Voltaire presents Berkeley’s theory as both empirical and metaphysical: the intended contrast is with the merely mathematical and acausal style of classical optics. Du Châtelet seems sympathetic to this point (1738a, b, 537). But given the broad scope of the term ‘metaphysics’ here, we cannot assume that Voltaire influenced Du Châtelet’s shift towards the a priori metaphysical systems of Leibniz and Wolff in the Institutions, as Gessell (2019, 868–71) has argued. 10  Kant, in 1790, still cites Keill as giving an authoritative “demonstration” of matter’s infinite divisibility (2004, 8:202). We will see below that Du Châtelet could endorse Keill’s argument, so long as it is not taken to show that matter is made up of an infinity of actual parts (Du Châtelet 1742, 191–92). 9

74

A. Wells

would allow one to build up both a square and its diagonal out of some finite number of spatial parts. The lengths of the side of the square and its diagonal would then be commensurate (i.e., have a common divisor) (Keill 1733, 30). But as a consequence of the Pythagorean Theorem, the side and diagonal of a unit square are incommensurable, contradicting the assumption of indivisibles.11 Voltaire rejects Keill’s argument. He allows that within geometry, it can be proven with complete certainty that a line is infinitely divisible (Voltaire 1738, 102–3). But he also takes it to be proven a priori that there are indivisible physical atoms.12 Granting that this might seem “contradictory,” Voltaire insists that it is not: “geometry has as its object the ideas of our mind [esprit]” (102). He spells out the point on the following page. Geometrical objects have only a mental existence, and geometrical points, lines, and planes cannot exist in the natural world (103). Lines and planes are indefinitely divisible in thought (“en idée”), and Voltaire hints that we can indefinitely divide matter in thought, as well (103). But mere divisibility in thought “hardly prevents” physical atoms from existing (1738, 102–3). It follows that geometrical reasoning is not a reliable guide to the physical world. Geometrical objects are divisible, but merely mental. Real, extramental matter is discrete. Voltaire does not, however, consider what this might mean for the accuracy of mathematical physics. Christian Wolff’s so-called ‘German Metaphysics,’ first published in 1720, was available to Du Châtelet in translation by early 1737. She had some knowledge of Wolff’s Latin works as well, and his system influenced aspects of her Institutions. Wolff takes metaphysics to study more fundamental entities than does mathematics. Metaphysics is concerned with fundamental substances “in themselves,” which include finite souls, fundamental simple substances, and God (Wolff 2001/1731, 336; cf. 1720, §593). Such substances are causally active, and in turn, causal activity is the criterion of substantiality (1720, §116). The objects of mathematics, by contrast, are not causally active (1965/1726, §18). Since causal activity is the criterion of substantiality, mathematical objects are not substances, but indeterminate and ideal entities, essentially dependent on our imagination (2001/1730, §§110–11).

 Voltaire comments that this example shows how the mathematics of the infinitely large and small, despite its apparent absurdity (“déraison”), is “founded on simple ideas” (1961/1734, 71; 76). Yet he denies that we can directly draw any physical consequences from it. 12  If the division of matter were actually completed, there would only be empty “pores,” not matter; thus the actual existence of matter contradicts its infinite divisibility (1738, 102). Clarke’s Fourth Reply to Leibniz presents a similar argument that also identifies pores with void (Leibniz and Clarke 2000, 35). But Aristotle already discusses the gist of this argument, attributing it to the Presocratic atomists (1984, 324b25–5a16). In the same passage, Aristotle discusses a theory of pores (poroi)—though as it appears in the Empedoclean theory of causation and change, rather than an atomist argument. 11

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

75

Wolff takes philosophy to be the study of possible things, in the strict sense of substances or res.13 Mathematical objects are not substances or res, and do not fall within the domain of philosophy. That is, mathematical statements do not have a place in the ideal system of philosophical “truths” (1965/1726, §36). They instead serve to make the contents of that system clearer and more distinct. For Wolff, even Euclid’s first principles are not primitive, but have an ontological basis (Buchenau 2013, 32–33). Accordingly, Wolff’s account of mathematics focuses on its applications. The goal of mathematics is, through measurement, to make clearer and more distinct our knowledge of qualities and quantities in substances, such as forces (1713, Vorbericht, XV, 2001/1730, §442; §742). Even here, Wolff is cautious about regarding forces as literally quantifiable. While he does endorse degrees of force for which arithmetical operations seem to be well-defined, these degrees are merely “imaginary” (2001/1730, §752–54; §747). His idea is that magnitudes for which operations such as addition are well-defined—often called extensive magnitudes—must consist of homogeneous parts that can be added together. Forces have no such parts: they are merely intensive magnitudes. For Wolff, then, we cannot infer from the properties of mathematical objects to the properties of things (1965/1726, §6; §17; 2001/1730, §110). Such inferences can only lead to contradictions, preventing progress in both physics and metaphysics (2001/1730, §110). For example, although Wolff accepts that geometrical objects are continuous, he holds that the world is made up of simple, discontinuous elements (1720, §76; §81). In a 1731 essay on the differences between mathematical and metaphysical concepts, Wolff draws on this account in assessing Newton’s Principia (Wolff 2001/1731, 286–348). As Katherine Dunlop (2013) has emphasized, Wolff dismisses Newtonian forces as “imaginary” (Wolff 2001/1731, 316). For Wolff, the core concepts and causal inferences of physics need to be grounded in metaphysics (1965/1726, §§94–95). But Newton is “no metaphysician” (2019, 1:209). The Principia’s propositions refer only to phenomena, and describe their regularities. They are merely mathematical (Dunlop 2013, 466). So they do not get at underlying causes, and cannot yield genuine explanations without metaphysical supplementation.14

 Wolff famously claims to follow a mathematical method in philosophy, though Lambert and other  critics soon objected that his method has little to do with mathematical practice (Basso 2008). Wolff presents the method as in the first instance logical: it could be grasped “even if mathematics did not exist” (Wolff 1965/1726, §139). 14  The Wolffian Samuel Formey, secretary of the Berlin Academy, took this position to extremes. He argued in a reply to Euler that quantity, as an essentially imaginary concept, cannot be applied to “real and existing” objects at all (1754/1747, 281). For Formey, then, attempts at mathematical physics, including Newton’s, issue in “absurdity,” “occult qualities,” and contradictions (282; 285; 294). He rejects not only geometrical arguments for the indivisibility of body (284), but all quantitative conceptions of motion and force, taking these to be based on “notions imaginaires & confuses” (292). 13

76

A. Wells

4.3 Du Châtelet on the Metaphysics of Mathematical Objects I now turn to surveying claims Du Châtelet makes in the Institutions about the metaphysical status of mathematical objects, which are non-fundamental and mind-­ dependent. I discuss the location of mathematical objects in her global metaphysics, her general account of magnitude, and her claims that mathematical objects are fictions and products of abstraction. While I cannot treat these topics in full detail, I hope to provide enough information to set up a later discussion of Du Châtelet’s confidence in the role of mathematics in physics.

4.3.1 Mathematical Objects and Metaphysical Idealism The metaphysical status of mathematical objects must be understood in terms of Du Châtelet’s multi-level idealist metaphysics. She holds that the fundamental level of created reality consists of simple, active substances (1742, 141–46; 155–58). Some simple substances are souls (45; 128; 133–34; 149–50; 156–58). Souls represent the whole universe, although confusedly. Other simple substances do not seem to be endowed with representational capacities at all. Simple substances lack spatiotemporal properties and are not directly perceived. But we can indirectly infer their existence and activity (138–41; 185–87). Matter is non-mereologically grounded in these simples. As we’ll see in Sect. 4.4.2, matter has no lowest level of mereological structure because it is indefinitely divisible. Apparently, Du Châtelet is committed to genuine causal interaction and dependence among at least some fundamental created substances (147–48; Stan 2018). It seems that souls represent the whole universe partly in virtue of being causally affected. If the rest of the universe were different, their representational states would differ as well (1742,  151–52). Simple substances themselves, however, cannot depend just on other finite substances. Their existence can be shown to depend on God (142). Du Châtelet’s views may be reminiscent of Leibniz’s multi-level idealist metaphysics.15 But there are important differences. Leibniz’s simple substances or monads are all conceived as perceiving and hence as mind-like in at least a minimal sense (Leibniz 1875–90, II:270; IV:479; VI:598). It is in virtue of expressing or representing the rest of the world from a unique point of view that simple substances are individuated (II.47).16 Furthermore, Leibniz famously forbids efficient causation

 Leibniz also distinguishes between mereological and non-mereological grounds. Monads are not literally parts of bodies (Leibniz 1875–90, II:268–69; II:436). See further Rutherford (1990). 16  The 1740 edition of the Institutions suggests that souls (but not all simple substances) are individuated by their unique representational states, and cites Leibniz (§128). However, Du Châtelet deletes this discussion from the 1742 edition. 15

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

77

among created substances: monads have no windows (II:264; II:271; IV:509–10; VI:607–8). On these points, Du Châtelet diverges from Leibniz. Like Leibniz, however, Du Châtelet does not take space and time to be fundamental, mind-independent entities. Instead, she regards them as mind-dependent (1742, 101–4; 120–22). Material beings are essentially spatiotemporal, so their existence and properties are also mind-dependent (155–56; 176–82). Thus the properties of material things relevant for physics are at least partly mind-dependent: extension, motion, and force are “phenomena” (176). Such phenomena are not wholly mind-dependent, however, because they are also grounded in non-mind-like simples (143–44). This brings us to mathematical objects, which Du Châtelet presents as still more mind-dependent than material things (Carson 2004, 170). This is a complex claim that will need to be unpacked. We can begin with a contrast Du Châtelet draws between material things as “real and determined” and mathematical objects as ideal and indeterminate (1742, 112). An important application of this point I’ll return to later is that only real things have determinate, actual parts. The number of parts in a geometrical object, by contrast, is “absolutely indeterminate”: these parts are merely potential (190; cf. Leibniz 1875–90, II:282; IV:491). The determinacy of material things is one indication that they are more real than mathematical objects, along with the fact that material things are endowed with force (163–64). These differences between material things and mathematical objects are presumably explained by their standing in different grounding relations to simple souls and non-mind-like simple substances. The indeterminacy of mathematical objects also means they are not subject to a principle of the identity of indiscernibles that is based on qualitative properties. According to this principle, neither fundamental substances nor material things can be alike in all of their qualitative properties, such that they differ only numerically (30). The individuality of a part of geometrical extension, however, is grounded solely in its numerical distinctness, and this holds for other mathematical objects as well (103). Du Châtelet is not a strict Cartesian mechanist, and does not seek to reduce qualitative properties to mereological properties. Thus the qualitative indeterminacy of mathematical objects seems to be an additional claim, over and above the thesis that they have an indeterminate number of parts. Du Châtelet concludes that no mathematical object can be identical to (“la même chose que”) a real, material thing (1742, 112). A mathematical object, as indeterminate, must lack the determinate qualitative properties that make a material thing what it is, so it cannot have the same qualitative properties as a material thing. By the principle of the identity of indiscernibles, she argues, a mathematical object cannot be identical to a material thing, since identity requires sharing all qualitative properties. Nevertheless, as we’ll see in the following section, Du Châtelet apparently holds that magnitudes are in material things, even if these magnitudes are not identical to mathematical objects proper.

78

A. Wells

4.3.2 The Metaphysics and Epistemology of Magnitude Considering some of Du Châtelet’s remarks on magnitudes will shed light on the metaphysical status of mathematical objects. In brief, she describes magnitudes as internal properties of material things. Du Châtelet further distinguishes between magnitudes as such and the conditions under which we fully understand magnitudes and communicate differences between them. Paradigmatic objects of mathematics, such as numbers or geometrical lines, plausibly depend on the conditions for understanding magnitudes. Communicating about magnitudes, in turn, requires units, and often an element of convention. An especially detailed discussion of magnitudes appears only in the longer manuscript version of Chap. 1 of the Institutions. These remarks are echoed in various parts of the published work, however, and are not canceled out in the manuscript, so they may have remained unpublished for reasons of space. The manuscript defines magnitude (grandeur) as an “internal” property of a “thing” (chose) in virtue of which it can differ from other entities that are in other respects “similar” to it (Du Châtelet 1738–1740, ff. 33r–33v).17 The things in question are, paradigmatically, material bodies. For example, “particles of matter” have a volume, and this is a magnitude (f. 32v). Elsewhere, Du Châtelet refers to forces standing in proportion to one another. Thus forces are also magnitudes or quantities (1742, 83). Quantitative equality is something above and beyond being qualitatively “similar” or “alike” (semblable) (Du Châtelet 1738–1740, ff. 33r–33v; 1742, 103–4; cf. Aristotle 1984, 6a26–35; 1021a). Given this distinction, two objects may differ in magnitude even if they are qualitatively alike, as with two similar triangles that are different sizes and hence not congruent. For two qualitatively identical things, a “real difference” in magnitude can metaphysically individuate those things (1738–1740, f. 43v).18 Magnitudes per se, then, exist in concrete, physical things. They serve to metaphysically individuate things from qualitatively similar things. So magnitudes do not have a merely mental existence. This is significant for assessing the metaphysical status of mathematical objects. Having answered the metaphysical question of what magnitudes are, the manuscript turns to further questions about how we can fully understand magnitudes and communicate about them. First, regarding understanding: even though magnitude is  By an internal property, in turn, I take Du Châtelet to mean one that reliably appears intrinsic to a thing. Because of Du Châtelet’s idealist commitments, magnitudes are not absolutely intrinsic properties of material things. Material magnitudes are partly mind-dependent, and so can’t be instantiated in worlds without minds. But for practical purposes, one can abstract from the dependent status of material beings and draw a contrast between the intrinsic and the relational at the level of what Du Châtelet calls substantial phenomena. 18  Wolff also emphasizes that qualitatively similar things can differ in quantity (1720, §20–22, 2001/1731, §196). He denies, however, that things can be individuated by difference in quantity (1720, §20; 1973/1710, 118). It is debatable whether this is a merely epistemic point, or also concerns metaphysical individuation. 17

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

79

an internal property of things, “it can only be understood [comprise] through the comparison our senses make of one object to another” (f. 33r). For two magnitudes to be compared, they must have some degree of qualitative similarity (f. 33v). The volumes of two particles can be compared, for example, because each particle is extended in three dimensions. Even if magnitudes are internal properties of things, then, they can only be fully understood through comparison with other objects. For example, a token length is an internal property of a thing that does not metaphysically depend on acts of comparison. When we wish to understand the size of this length, for example, we must compare it with a class of lengths. This class defines a type of magnitude. (In Du Châtelet’s French there is just one word, grandeur, for both magnitude and size, but context indicates she is drawing a distinction here.) While the epistemological details are not spelled out, the reference to understanding implies that cognitive faculties such as the understanding are constitutively involved in grasping size. By contrast, a token magnitude seems to be an object of mere perception. Du Châtelet does not claim that understanding a size requires apprehending it in terms of units. This tracks the Euclidean conception of unit-free comparison between magnitudes, which can afford a grasp of ratios. However, units of measure do play a role in Du Châtelet’s account. Here we can turn to the condition she lays out for communicating a magnitude to someone. To do this, “it is required to tell him the relation [raport] it has [to] a measure that is known [connuëe] to him” (f.33v).19 Our choice of unit may turn out trivially conventional or up to us. Du Châtelet mentions various more or less arbitrary units of time, for example. However, magnitudes themselves, as internal features of things, are not conventional. This partly explains why some ways of measuring time are objectively better than others. A wellmade pendulum clock, for example, is more accurate than a sundial (1742, 132–3). This account of measurement  does not meet the structures of a traditional Euclidean theory. For Euclid, measurement was defined in terms of the composition of rational magnitudes out of aliquot parts that are multiples of the whole that they compose.20 The magnitudes of the parts can then be used to measure the magnitude

 Compare Wolff: “If I am supposed to tell someone how large something is, I must tell him what relation it has to a certain measure that he is familiar with” (1720, §20; 1713, I, 38). Wolff concludes from this that magnitude cannot be grasped by the understanding, but must be sensibly “given” (gegeben) (§20; cf. Sutherland 2005, 147). Du Châtelet does not explicitly draw this epistemological consequence. 20  This is the sense of ‘part’ (méros) at issue in Definition 1 of Book V of Euclid’s Elements: “A magnitude is a part of a magnitude, the less of the greater, when it measures the greater” (Euclid 1908, II.113). In turn, Definition 4, the so-called Axiom of Archimedes, stipulates that magnitudes in ratio to one another must be “capable, when multiplied, of exceeding one another” (II.114; White 1992, 148–154). Thus, infinitely small or large magnitudes are incommensurable with finite ones. In Commandino’s widely used edition of the Elements (1572) this was presented not just as a definition of magnitudes in ratio, but as a genuine axiom, ranging necessarily over all magnitudes whatsoever (De Risi 2016, 626). The point was contested even before the development of calculus, however. Cavalieri and Torricelli, among others, treated infinite collections of indivisibles as summing to finite magnitudes, thus violating the Axiom of Archimedes (608). 19

80

A. Wells

of the whole directly. Euclid calls magnitudes that permit this type of measurement homogeneous, or “of the same kind” (Euclid 1908 II.114). This Euclidean conception of measurement appears in many early modern mathematics texts (e.g. Arnauld 1683, 5). And it seems to inform Wolff’s approach to mathematics. While Wolff denies that forces are literally made up of homogeneous parts, for example, he thinks they must be treated as composed of such parts, even if these are strictly speaking imaginary. Plausibly, Wolff is trying to get forces to satisfy Euclid’s criteria for measurement. It is not so clear how Wolff can account for the soundness of mathematical reasoning that relates heterogeneous quantities, as in algebra. Du Châtelet, meanwhile, endorses the (early) modern conception of algebra as the science of magnitude in general. Although the Institutions officially uses geometrical rather than algebraic methods for pedagogical purposes, she is willing to use algebraic definitions, and also stresses the power of algebraic geometry, where unknowns are computed from given quantities (14).21 In turn, Du Châtelet claims that her conception of magnitude is especially apt for algebra (1738–1740, f.33v). Algebra presumably works at the level of sizes and magnitude-types that arise from comparison, and only indirectly applies to token concrete magnitudes. As Descartes, Leibniz, Wallis, and others argued, algebra relates magnitudes of many kinds, whether continuous or discrete.22 It is unclear, meanwhile, how Wolff would account for sound algebraic reasoning that relates heterogeneous quantities. In discussing basic arithmetic, however, Du Châtelet hews closer to the traditional Euclidean account. For  the integers, she takes ultimate “units,” that is, the number 1, to be “combined” in order to form larger numbers (1742, 70). Numbers can thus be regarded as composed of units, and as homogeneous with those units (compare Aristotle 1984, 1057a3–4). It is “hardly necessary” that numerical units actually get composed into a given number (1742, 70). Numbers are partly mind-­ dependent, and some large numbers will never be reached by finite minds like ours. Yet Du Châtelet attributes a kind of necessity to arithmetical units themselves, comparing them to the simple positive properties that make up the essences of possible things (70). Obscure as this comparison may be, it indicates that at least in the case of arithmetic, we do not have a choice of the unit of measure. Numbers, however, are strictly speaking not internal properties of things, like the magnitudes discussed in the manuscript. Numbers are partly dependent on “things numbered,” but their existence also depends on an active “power to form” mathematical objects through abstraction (1742, 112–13; 110). As discussed further in Sects. 4.3.3 and 4.3.4, mathematical objects such as numbers are presented as ideal, abstract, and fictional. While matter and its properties are partly mind-dependent, they are not described as ideal, abstract, or fictional. So in the end, the ontological status of the integers seems comparable to that of algebraic quantities.  For example, she defines the “measure” of dead force algebraically, as the product of mass and initial velocity, rather than in terms of parts of a homogeneous magnitude (1742, 438–39). 22  See e.g. Leibniz (1849, IV:451–2; V:178–9) and the discussions in Hill (1996) and De Risi (2021, 15–17). 21

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

81

These points may help understand Du Châtelet’s claims that extension, number, and other mathematical objects are products of mental abstraction, and therefore fictions. Not just mathematics but “all the sciences” are “full of…fictions” and crucially rely on them, even if mathematics is most of all dependent on fictions (1742, 111–12). One reason for this is the prevalence of mathematical representations in science. Before turning to her account of fictions as such, I briefly discuss the faculty of abstraction, which Du Châtelet thinks makes fictions possible.

4.3.3 The Power of Abstraction Du Châtelet would have been aware of a range of theories of abstraction—from the Port-Royal Logic, Locke, Wolff, and others—but she does not commit to any one of these in detail.23 Instead, she focuses on the applications of this mental faculty. Some basic features of her account emerge in the following passage. This power that our mind has of forming by abstraction imaginary Beings that contain just the determinations we want to examine—and of excluding from these Beings all the other determinations, by means of which they could be conceived in another way—is of great use in meditation, for the imagination then rescues the understanding, and helps it to contemplate its idea. (Du Châtelet 1742, 111; cf. 182–83; 343–45; 352–53)

Abstraction, then, is characterized as an active or creative power of our faculty of imagination. This already distinguishes Du Châtelet’s account from a purely negative conception on which abstraction merely strips away irrelevant properties from objects. For Du Châtelet, abstraction does, negatively, ignore select features of things, notably “internal” qualitative “determinations” (1742, 113). But it also, positively, creates new intentional objects. As we’ve already seen, the intentional objects of mathematics are indeterminate, with only potential parts, whereas physical objects have fully determinate, actual parts. Hence mathematical objects are designated abstract entities (“les Abstraits”), and contrasted with spatiotemporal, concrete entities (“les Concrets”) (111). For Du Châtelet, then, abstracta are partly dependent on acts of abstraction. But they are also grounded in material things. An abstract entity “cannot subsist without a concrete entity [ne peut subsister sans un Concret]” (112). That is, every actual abstract entity y counterfactually depends on some concrete entity or entities x: if x does not exist, then necessarily, y does not exist.

 The Port-Royaliens define abstraction in terms of analysis into parts or aspects (Arnauld and Nicole 1996, 37). Du Châtelet does not define abstraction this way. Locke and Wolff introduce abstraction to give a nominalist account of how we acquire general ideas (Locke 1975, 2.11.9; Wolff 1713, I, 26). Du Châtelet does not explicitly share this aim, or their nominalism. Abstractionism about Lockean general ideas need not go together with abstractionism concerning mathematical objects. Kant and the Frege of the Grundlagen, for example, retain an abstractionist account of concepts such as or , but deny that it applies to mathematical objects. Conversely, one could endorse mathematical abstractionism without applying the theory to other general ideas. 23

82

A. Wells

While the passage quoted above links acts of abstraction to the faculty of imagination, it also emphasizes that the imagination assists the understanding in contemplating its proper ideas or concepts. In fact, some “geometrical truths” defy our mere imagination, understood as a capacity to “represent our ideas by way of sensible images” (1742, 158). By contrast, algebra “speaks only to the understanding,” as its objects cannot be represented in images (3; cf. 158). Cases such as the employment of algebraic techniques in geometry and calculus highlight how the imagination on its own is insufficient for mathematics (159). Moreover, Du Châtelet’s account of mathematics is set in a broader rationalist framework, in the sense that it presupposes a priori rational principles that are not themselves produced by abstraction, as they might be for empiricists. Du Châtelet does not make very explicit what role these principles play in the origins of our mathematical concepts. Nevertheless, these background principles illuminate the above passage’s claim that we can abstract whatever “we want to examine.” Elsewhere, Du Châtelet writes that “to make a number [pour faire un nombre], one combines some units, of which the combination is not at all necessary, but only possible” (1742, 70). These passages need not be read as implying that mathematical truths themselves are in the voluntary control of agents. There can still be constraints on the way a process of mathematical abstraction proceeds, and on the objects it yields. The context of the passage, which is a genealogy of our ideas of space, provides further evidence on this point (Du Châtelet 1742, 101–10). Throughout this discussion, Du Châtelet uses expressions of constraint. Extension “must” (doit) be conceived as uniform and homogeneous (103); space “must” seem empty to us (107); we “must represent” space to ourselves as immutable (108), and so on. Sources of these constraints may include the content of the understanding’s ideas or concepts, the aims or goals for which these concepts are employed, and psychological facts about our abilities to mentally represent space and its objects. A drawn geometrical diagram can be seen as constrained in one sense by concepts such as , but also by our goals in using these concepts and by our representational capacities. The example of absolute space, however, raises a question about the ontological status of abstract entities. Not only does nothing correspond to our abstracted idea of absolute space, but “nothing similar [semblable] to this idea could exist” (Du Châtelet 1742, 110; emphasis added). This is an idea of an impossible object. The question is then: are all abstract objects impossible objects, on Du Châtelet’s view? Not at all. While material absolute space is on her view incoherent, geometrical extension is properly founded in actual physical things that ground or “constitute” it (1742, 112). Numbers, likewise, are partly grounded in the actual concrete things they number (113). As we’ve seen, not only mathematics but “all the sciences” are full of “abstractions” or fictional entities, on her view (111). Here ‘abstractions’ include positive products of our mental activities that more recent philosophers of science often call idealizations.24 As discussed further in Sect. 4.4.1, Du Châtelet’s understanding of  In the recent literature, idealizations standardly “characterize ideal cases that do not, perhaps cannot, occur in nature” (Elgin 2004, 118). However, the verb idéaliser and its derivatives did not 24

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

83

the positive role of abstraction appeals to practices in physical science (notably in the work of Galileo and Newton). The success of abstraction in physics can allay worries that abstraction is up to the whims of individuals. Du Châtelet’s views on the modal status of abstract objects are further developed through a distinction between real or actual abstract entities and those that are merely possible or conceivable. For numbers to be “real and existent,” they must be grounded in concrete, countable things (Du Châtelet 1742, 113). Even if no such grounding relation obtained, however, it would still be coherent to speak of “possible numbers,” apparently grounded in the divine intellect (113). Such merely possible mathematical objects would be less dependent on our minds than actual mathematical objects. Appeal to possible mathematical objects also suggests a way around a common objection to mathematical abstractionism, namely that there are far more mathematical objects than can be produced by finite minds and their activities of abstraction. Moreover, it allows Du Châtelet to do justice to the intuition that mathematical truths are necessary. Necessary truths hold for any possible mathematical objects, and do not depend on actualization. Invoking possible mathematical objects does raise problems of its own. Some deny that the distinction between possibility and actuality applies for mathematical objects, and Du Châtelet does not make it explicit why she thinks such a distinction does hold. One could also ask how there can be knowledge of merely possible mathematical objects. Du Châtelet compares mathematical objects to the essences of possible things (1742, 70–71). In both cases, our knowledge relies in part on intellectual insight into possibilia, as something like ante rem universals grounded in the divine intellect (63–64). This insight is fairly mysterious. But Du Châtelet is committed to insight into essences anyway, independently of her stance on merely possible mathematical objects. So there need not be any special epistemological problem raised by her endorsement of merely possible mathematical objects.

4.3.4 Abstraction and Fictions Du Châtelet, as we’ve seen, describes the products of abstraction as “fictions” (1742, 111). Fictionalism is now a much-discussed position in the philosophy of mathematics. Recent articulations of fictionalism often rely on an analogy to literary fictions such as novels. This analogy is not new. Du Châtelet would likely have known, for example, Jean-Pierre Crousaz’s 1714 comparison of Newtonian physics to a mere novel (roman) (Crousaz 1714, 112–14; Shank 2008, 110–12).25 Du Châtelet herself considers the “fabulous world” depicted in “fairy tales” an

enter French until the end of the eighteenth century (Rey et al. 2011, s.v. “idéal”). 25  Crousaz also objected to Leibnizianism, and initiated a correspondence on this point with Du Châtelet in 1741 (Du Châtelet 2018, II.43–47). Du Châtelet commented to Maupertuis two months later that “les Institutions m’ont encore attiré une drôle d’adversaire, c’est Crousaz” (II.54), and sent a cutting reply to Crousaz the next day (II.56).

84

A. Wells

instructive contrast with properly grounded scientific explanation (1742, 26). Novels also provide her with examples of merely logically possible worlds (46). But we cannot presume that Du Châtelet relies on an analogy between mathematical fictions and literary works, and we’ll see that there are important differences between literary creation and mathematical abstraction. In an early modern context, the French term ‘fiction’ often had broad, non-literary connotations of creation, fashioning, or establishment by convention (Rey et al. 2011, s.v. “fiction”). And as a Scholastic term of art, ficta were mind-dependent concepts or objects of thought, introduced to solve a general epistemological problem.26 An earlier historical reference point is Aristotelian abstractionism about mathematical objects. Aristotle often emphasizes eliminating or subtracting features from an object (Aristotle 1984, 1061a28–b2). What remains after this process has a non-­ arbitrary basis in the object. The nature of the soul places further constraints on the process of abstraction, such that abstraction yields the same, publicly accessible results for different individual thinkers. As for existence, Aristotle states that mathematical objects can be said “without qualification” to “exist …with the character ascribed to them by mathematicians” (Aristotle 1984, 1077b33–34).27 In turn, Leibniz came to hold that some mathematical objects, namely infinitely small and large magnitudes, are mere “fictions of the mind” (Leibniz 1875–90, II:305; V:157–58).28 He connects them to acts of mental abstraction (Leibniz 1849, VI:234–54). Unlike truths of arithmetic and classical geometry, which for Leibniz hold true at every possible world in virtue of the divine intellect, such fictions exist only at worlds where there are finite minds of a certain kind (Leibniz 1875–90, II:262–65; Jauernig 2010, 175–76). Yet infinitesimals are of great use in discovering truths, even though claims about them are strictly speaking false (Rabouin and Arthur 2020, 406–7). Their usefulness is not up to us but stems from general features of our cognitive faculties. I take Du Châtelet, like these earlier thinkers, to reject at least three possible implications of conflating fictions in general with literary or artistic fictions. One implication is that mathematical claims are more or less arbitrarily dreamed up by mathematicians. This is how Du Châtelet describes novels. A novelist plays with possibilities in a way that lacks constraint from the actual world (1742, 45–46).

 For the early Ockham, ficta exist in the mind, but lack the reality of the soul’s powers or dispositions: they have intentional existence. Ockham went on to eliminate ficta from his epistemology. Pasnau (1997, 82) argues that Ockham found a more parsimonious alternative to ficta, but never had “doubts about the concept of fictive existence” itself. 27  Nonetheless, the manner in which mathematical objects exist is “special” and qualified (1984, 1077b16). Substances exist in an unqualified way. So Aristotle’s mathematical objects are not substances: they are in substances. Interpreters disagree on further details (Hasper 2021). 28  A letter from Leibniz to Varignon—published in 1702 and perhaps known to Du Châtelet— sketches this position, though Leibniz is cautious about labelling infinitesimals as fictions (Leibniz 1849, IV:91–95; Reichenberger 2016, 152n54). Further details were not publicly available, and remain controversial (Jesseph 2015; Rabouin and Arthur 2020). 26

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

85

A second implication she rejects is that, because mathematical objects do not exist, mathematical claims are essentially falsehoods (Field 1989, 2; Elgin 2004, 123). In her view, a fiction is not a thing (chose) or substance. Nevertheless, it can count as a “being” (être), so long as it has a logically consistent essence (1742, 61). So, unlike in contemporary fictionalism, fictional beings exist and claims about them can be true. Third, whereas she holds that some works of literature are like dreams, in that both “furnish us with the idea of a fabulous world” that is private and depends on our individual psychological constitution, she does not consider mathematical fictions in the same class as dreams (1742, 25). Mathematical objects, unlike dreams, are public and shared. Amie Thomasson (1999, 2007) has advanced a more neutral analytical framework for thinking about fictions. Literary fictions, she suggests, are one species in a genus of abstract artifacts, which also include legal systems and scientific theories (xii; 147–53). Such artifacts are “jointly dependent” on physical things and on human mental states (150). Literary works illustrate some features of abstract artifacts, but they are not the paradigm for all abstract artifacts. If mathematical fictions fall under the genus of abstract artifacts, they need not share the specific features of novels or fables. Many concrete artifacts are end-directed in a way that distinguishes them from works of literature. To be fit for purpose, such artifacts must have specific and non-­ arbitrary features (Thomasson 2007). Thomasson’s conception of an abstract artifact permits us to view mathematical fictions along similar lines, in contrast with literary fictions. Furthermore, Thomasson thinks we should “postulate” literary fictional objects (111–14; 147). That is, we should take them to exist, albeit in a dependent and non-fundamental way. Finally, abstract artifacts such as legal systems or scientific theories are patently public and shared, unlike dreams. Thomasson’s framework is apt insofar as Du Châtelet develops her account of mathematical fictions through analogies with general grammar, rather than artistic or literary creation. The Institutions notably never uses the word ‘fiction’ to directly describe works of literature. It is mainly used for mathematical and grammatical entities, though also, with a more negative valence, for speculative scientific hypotheses (1742, 79; 93). While cautioning against speculative hypotheses, she stresses that they are advanced in order to rationally explain observed facts, are sometimes historically inevitable (as in Descartes), and do not turn philosophy into “a heap of fables” (88; 79; 93). So here too, fictions in general are not equated with literary fictions. “Substances by fiction” are an important case of fictions in a grammatical context (1742, 76). These are substantive terms that may not refer to anything substantial. For example, the substantive ‘whiteness’ refers to a mere accident: “whiteness can never be a true substance” (76). Arguably, whiteness could not be an accident of any fundamental, simple substance. It is only ever an accident of bodies, which are mere substantial phenomena. Bodies are apparent rather than genuine and primary substances (181).

86

A. Wells

Frequently, grammatical fictions are not even approximately true of the material world. I will argue in Sect. 4.4 that in this respect many mathematical fictions have epistemic advantages over grammatical fictions. But even grammatical fictions have a universality and (quasi-)objectivity that distinguishes them from literary fictions.29 Grammatical facts, though in some sense products of human activity, are not arbitrary or false. For while the distinctive features of individual languages are contingent, all languages are founded in an implicit, humanly universal “natural logic” (logique naturelle) (Du Châtelet n.d., f. 133r).30 Falsehood results not from grammatical fictions as such, but from confusing grammar with an account of real things. Thus she cautions against taking (for example) grammatical substantive terms to reliably pick out “true substances of nature” (76). In the background is her view that “error” is the result of mistaken judgments, rather than stemming from any particular type of singular representation, including false representation (1742, 112; 124; 206). A similar point appears in the Port-Royal Logic, where error is said to arise “only from judging badly” (Arnauld and Nicole 1996, 59).31 Du Châtelet’s discussion of grammar and fiction also plausibly draws on the Port-Royal Grammar, which treats at length the case of substantive terms such as ‘whiteness.’ For the Port-Royaliens, substantive terms originate from the need to refer to real substances. In standard Cartesian fashion, they contrast these substances with attributes and modes. Many substantive terms, such as ‘soul,’ do refer to substances in this way. But the usage of such terms goes “beyond” this (Arnauld and Lancelot 1975, 69–70): Since substance is that which exists by itself, people came to call all those words which exist by themselves in discourse without requiring another noun substantive nouns, even though they in fact signified accidents.

Grammatical substantives reflect genuine facts about grammar that are not up to any particular speaker. ‘Whiteness,’ for example, can appear alone in a sentence while ‘white’ must be accompanied by a subject term designating some subject that is  Du Châtelet wrote, but never published, a Grammaire Raisonée. The known surviving chapters discuss substantive terms in detail, stating that the grammar of substantives is based on a generalization from the metaphysics of substance (Du Châtelet n.d., ff. 133v–135v; 138r; 145r). 30  Similarly, when the Port-Royal Grammaire turns from linguistic signs themselves to their signification, it asserts that understanding the latter requires an account of “what occurs in our minds” (Arnauld and Lancelot 1975, 65–68). These mental operations include conceiving concepts and objects of perception, judging propositions, and reasoning through syllogisms, which are all discussed in the Port-Royal Logic. Humanly universal logical principles, then, underlie all languages qua “signifying…thoughts” (41). We find similar assumptions in Maupertuis’s (1740) essay on the origin of language, which treats mental capacities expressed in all language, rather than the features of any specific language. For broad discussion of early modern general grammar as irreducible to either formal logic or empirical linguistics, see Foucault (1966, 92–136). 31  Descartes makes the still stronger claim that ideas “cannot strictly speaking be false” (1984, 26). Leibniz, for his part, stresses that an “abstraction n’est pas une erreur,” including in mathematics, so long as one “knows” that the material world is not really as the abstraction presents it (1875–1890, V.50; these New Essays were only published after Du Châtelet’s death). 29

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

87

white. Moreover, these facts are straightforwardly expressible by truths about the term ‘whiteness.’ It is true that ‘whiteness’ is a substantive term, for example, even though ‘whiteness’ does not refer to a substance. What lessons can we draw from these grammatical examples for Du Châtelet’s conception of fictions more generally? First, fictions can be seen as jointly dependent on human mental states and on mind-independent things. Though fictions are partly dependent on our activities, they stand under robust constraints grounded in common features of our mental faculties (notably the understanding and imagination). Second, this joint dependence raises the possibility that the mind-dependence of fictions is a matter of degree. There may be a spectrum ranging from highly mind-­ dependent fairy tales, through grammatical fictions, to mathematical fictions. Third, Du Châtelet distinguishes the accuracy of fictional representations from the further question whether they bring about error. Error arises from misusing these representations and confusing them with fundamental, mind-independent entities, rather than from sheer inaccuracy of representation. The fact remains that both literary and grammatical fictions are typically false, and are more or less arbitrary. In the following section I further discuss how, especially in geometry, mathematical fictions are not sheer falsehoods, but can approximately represent physical entities.

4.4 Du Châtelet’s Defense of Inferences from Mathematics to Material Nature Recall that for Du Châtelet, the use of mathematics is a necessary condition for scientific progress. Mathematics is needed to explain what, for physics, has so far been “inexplicable” (1742, 3). Moreover, she praises general inferences from mathematics to the physical world: mathematics is a source of physical knowledge.32 So it may be puzzling that Du Châtelet is also an avowed fictionalist and abstractionist about mathematical objects. In Sect. 4.3.4, I began to dispel this puzzle by stressing how for Du Châtelet, abstract and fictional objects can be public and subject to robust constraints. I now examine some epistemic advantages that mathematical fictions enjoy even over grammatical fictions. Mathematical fictions may not be exactly true of the physical world, but even so, they can and ought to approximately represent the physical world. By contrast, fictions in grammar are more or less arbitrary and need not seek to represent the physical world, even approximately. Literary fictions represent the physical world but do not quantitatively approximate it.  Du Châtelet’s later commentary on the Principia confirms this point. She holds for example that the mathematical Lemmas in Book I of the Principia not only lay out Newton’s “method of first and last ratios,” but also establish “general solutions” for Newton’s “entire theory” of gravitation (1759, 9; 32). These solutions then “explain astronomical phenomena” in Principia Book III (9). 32

88

A. Wells

4.4.1 Mathematical Fictions and Approximate Truth Du Châtelet’s position is summed up in the dictum that “the same thing happens in nature as in geometry” (1742, 34). She does not claim that nature corresponds in this way to grammar or works of literature. I’ll now explicate this claim, and note some important qualifications on it. In brief, we’ll see that this sort of inference works only for certain general facts about nature: physics cannot be spun out of pure geometry. For Du Châtelet, ‘nature’ sometimes refers the actual world in general. It is in this broad sense that she describes God as the author of nature (1742, 472). However, her “same thing” dictum does not range over nature in this broad sense. She does not hold that simple substances and souls correspond to, or are describable in, geometry. So by “nature,” she means the subject matter of physics: matter and its properties, such as force.33 This is confirmed by her claim that, because things are in nature as they are in geometry, one can use the law of continuity to “find and demonstrate the true laws of motion” (1742, 35). Recall that Du Châtelet is an idealist about matter and force: they are partly mind-dependent. This mind-dependence is linked to the spatial and temporal properties of matter and force. But geometrical objects are essentially spatial, and numbers are connected to succession in time. Events in material nature thus have something in common with mathematical facts: they are essentially spatial and temporal. Du Châtelet’s metaphysics of quantity, as we’ve seen, allows for quantities to exist in physical things: quantitative properties are not confined to mathematical entities. Therefore, the objects of nature and of mathematics can have the same kinds of properties, although they are not “the same” in the sense of being numerically identical. Du Châtelet’s idealism and her conception of mathematical objects thus provide a framework in which mathematical representations may be approximately true of the material world. Approximate truth, in turn, suffices for at least some kinds of scientific explanation, on Du Châtelet’s view (1742, 203–5). For example, a body in motion has a volume, and so does a geometrical solid. We can therefore use geometry to represent a property of bodies, even if bodies do not behave exactly as geometrical figures do. In an example made famous by Galileo, a geometrical sphere in contact with a plane would touch it at exactly one point, but this does not hold for a physical sphere resting on a surface (cf. 1742, 111). Still, geometrical proofs can legitimately apply to physical nature, even if perfect geometrical spheres and planes are never physically realized. By contrast, volume is not even a possible property of Du Châtelet’s non-spatial, non-composite substances (177; 141). To illustrate the correct use of fictional representations, she considers the case of the Ptolemaic system. Even though it is false, it yields sufficiently accurate  The law of continuity could also be applied to mental changes, insofar as these take place in time (cf. Kant 1998, A208–209/B253–54; 2004, 4:471). Du Châtelet may well do this (1742, 152). But my focus is on the physical significance of mathematics, so I leave this issue aside 33

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

89

solutions for some problems in astronomy (1742, 111–12). More broadly, strictly false assumptions can be made in physics in such a way that they do not lead to “error” in “experiments and…explications” (206). Here too, she may rely on the Port-Royal idea that error properly speaking is the product of judgment. This point can apply to any mathematical representation used in science, insofar as it is fictional and never exactly realized in material nature. Du Châtelet considers, for example, the mathematical consequences of the theory of universal gravitation. The theory predicts observations such as the moon’s orbital period to a very high degree of accuracy, so much so that “calculations” can be “taken for observations” (1742, 332–33).34 This is consistent with the theory’s being “more or less [à peu près]” rather than exactly correct (1759, 66). More positively, Du Châtelet contends that because of the limitations of our cognitive faculties, abstract and fictional representation is unavoidable for us. Without it, we would need to represent far more particulars than we could effectively reason about (1742, 111). To take one of her examples, a token iron bar has a vast array of properties (103–4). Describing all of these properties is a potentially infinite task. For many purposes, we will need to characterize the iron bar in mathematical terms, as a three-dimensional object in Euclidean space. We can then hold this characterization fixed even if some of the bar’s internal properties change, for example, if it loses or gains some microscopic parts. So even if mathematical representations are a step removed from material things, they provide a privileged way of knowing the general properties of matter.

4.4.2 From Mathematical to Physical Continuity One important case where Du Châtelet draws conclusions about the material world from principles of mathematics is her treatment of the continuity of matter and of material change. Since her principle of the continuity of change draws on Leibniz, it would be all too easy to portray Du Châtelet as upholding a ‘Leibnizian’ material continuum against the ‘Newtonian’ atomism of Voltaire’s Eléments. We’ll see, however, that Du Châtelet cannot be seen as simply recapitulating Leibniz on this point. Nor did Newton and Leibniz have simple positions on these issues.35

 Other examples Du Châtelet considers include treating the moon as a point-mass, comets as subject solely to gravitational forces, outer space as if it were a void, and so on. These ideas are further developed in her commentary on the Principia. 35  In the early manuscript “Of Attomes,” for example, Newton contends that objections to the indefinite divisibility of body apply equally in mathematics. But they have absurd consequences in the mathematical case. Therefore, these objections are unpersuasive in the case of bodies as well (Janiak 2000, 213). Leibniz, throughout his career, regards matter as actually infinitely divided (1875–1890, II:77; II:268; Rutherford 1990, 544–49). Yet in early works, he presents infinite division as compatible with atomism (IV:15–26; IV:228–29). 34

90

A. Wells

A further complication is that Du Châtelet’s views on this topic were not static. In the manuscript of the Institutions and the 1740 first edition—but not in the second edition of 1742—some parcels of matter are treated as if they were atoms or at least natural minima, for practical purposes in physics (1738–1740, f. 216r; 1740, 185–6; cf. 1742, 194–5). Here I focus on outlining Du Châtelet’s position in the 1742 second edition, which is altered to stress the infinite divisibility of time and matter (e.g. 1742, 265). Reichenberger (2016, 146–69) provides a broader discussion of Du Châtelet’s development and sources on the topic. In brief, Du Châtelet holds that matter is continuous, but her account of material parts is potentialist. She does not hold that between any two material parts, there actually exists another part. Rather, matter can always be further divided into parts, and is never actually divided into ultimate parts.36 She also holds that all material change is continuous. Her official statement of this point is that if a thing is changing from state A to state B, it necessarily passes through all conceivable intermediate states (1742, 32). What this means in practice is that changes in material things, such as motions, can always be further divided into smaller units of change or motion. These continuity claims have straightforward consequences for actual material things. They entail that atomism is false and that change in matter is continuous. Du Châtelet’s optical theory also relies on continuity assumptions (Gessell 2019, 872–73). I disagree, then, with Reichenberger’s (2016, 163) suggestion that these continuity principles are mere regulative guidelines for inquiry, in a Kantian sense, that lack objective purport. At several points, Du Châtelet appeals to the principle of sufficient reason to support these claims about continuity (1742, 32ff.; 137–40; 151–52). But it is unclear how, on its own, the principle of sufficient reason could establish them. Atoms as ultimate parts might seem to provide a conclusive, unqualified explanation for the composite bodies they compose. A material continuum, meanwhile, courts an unsatisfying infinite explanatory regress, one that might not satisfy the principle of sufficient reason. Here Leibniz helps himself to the premise that if atoms existed, then God would have arbitrarily decided, without sufficient reason, that a certain fundamental mereological level for matter obtains rather than some other possibility (Leibniz and Clarke 2000, 28). But it is unclear why a parallel problem does not arise for levels of non-mereological metaphysical dependence. What is God’s sufficient reason for making monads the fundamental created beings, with no level below them? In any case, Du Châtelet is cautious about reading off conclusions about divine choice

 Aristotle’s Physics defines the continuous as that which can be endlessly divided into further divisibles (1985, 200b19; 232b25). While apparently allowing some completed actual infinities, Aristotle does not countenance actual infinite collections of parts of continua (White 1992, 111–12n54; 156–61; Coope 2005, 80–81). Broadly Aristotelian approaches to continuity were still authoritative in the eighteenth century. Outside of relatively isolated mathematical works, continuity lacked a clear, positive definition; it was usually conceived as a mere lack of division or determination (De Risi 2021). See for example Wolff’s definition of continuity (2001/1730, §554). 36

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

91

from observed facts in nature. She does not present this Leibnizian premise in her arguments for material continuity. Attempts to prove the continuity of change merely from the principle of sufficient reason also risk begging the question. Supposing that change did occur in discrete stages, why couldn’t each stage find its sufficient reason in the stage prior to it? Atomists about change could argue that these discrete stages are more intelligible and explanatory than Leibniz’s alternative. Stages provide ultimate units of change, and hence an unconditioned explanatory bedrock, as opposed to the explanatory regress suggested by continuous change. This is where Du Châtelet’s views on the relationship between mathematics and physics come in. These continuity theses, on her account, follow not just from the principle of sufficient reason, but require the additional principle that things are in spatiotemporal nature as they are in mathematics. More specifically, she appeals to the idea that, for at least some theses that hold in geometry, we can infer that they hold of matter. The continuity of geometrical extension is one such thesis. On this basis, Du Châtelet can use the following argument schema: 1 . A continuity thesis C holds in geometry. 2. If C holds in geometry, then it holds for physical matter. 3. Therefore, C holds for physical matter. This schema is then applied both to the continuity of matter itself, and to the continuity of change.37 To begin with the continuity of matter, consider one of Du Châtelet’s arguments against atomism. Any alleged atom takes up some space, thus has spatial parts and can in principle be further divided, even if this is “physically” impossible (1742, 139). This argument seems to presuppose premises elaborated in Du Châtelet’s account of matter. Extension is an essential property of matter, and in turn, extension logically implies indefinite divisibility (160). Therefore, matter is essentially indefinitely divisible. But why does extension logically imply indefinite divisibility? Here she is relying on the assumption, from geometry, that extension is always potentially divisible into further parts. We can compare the argument from Keill discussed in Sect. 4.2: since in geometry extension is provably infinitely divisible, matter must be infinitely divisible as well. Du Châtelet thus accepts arguments from mathematical truths to physical truths that Voltaire and Wolff rejected. This geometrical assumption makes it easier to see the principle of sufficient reason’s relevance to the question of matter’s continuity. For if matter is composed of atoms, then these atoms ground the size and shape of whatever they mereologically compose. But the atoms themselves are extended, and therefore, by the premise from geometry, must have some size and shape. Their size and shape cannot be grounded in further parts, on pain of contradicting the hypothesis that they are  Leibniz’s arguments for continuity sometimes use the premise that “nature…observes the same [rule]” as does geometry (1875–1890, IV:375–76; IV:568–69). Du Châtelet probably did not know these texts, however. 37

92

A. Wells

atoms. But what other grounds for their size and shape could there be? Some atomists fall back on “the will of the creator” to “give a reason for the extension of the atom” (1742, 140). Du Châtelet rejects this solution: God is volitionally responsible for the existence of matter, but not for its essence or possibility (73–74). The demand for a reason arises, she holds, even for possible or conceivable atomic parts of matter, so long as we assume that matter is essentially spatial and so corresponds to geometry. So she concludes that there are no material atoms: the size and shape of any part of matter is (partly) grounded in the size and shape of its parts. Du Châtelet uses similar reasoning to defend the continuity of material change. An equivalent to the continuity of change holds in geometry, on her view. For example, the deformation of a parabola must proceed continuously (Du Châtelet 1742, 36–37). She also discusses inflections (points de rebroussement) in third-degree algebraic curves. A “concave” curve, for example, becomes “convex” by “infinitely small degrees” (33). By the “same principle,” the quantity of motion of a given body can be continuously decreased until it is at rest (37). Like some earlier authors, she considers geometrical curves as abstracted from the motions of bodies.38 A continuous geometrical curve is one traced by (idealized) continuous motion. The continuity of geometrical curves, then, can be seen as governed by the same principle as the continuity of motion. So although continuous motions are metaphysically prior to geometrical curves, one can deduce properties of motions from properties of curves. Given these arguments from geometry, it is easier to see why for Du Châtelet, failures of continuity in the material world violate the principle of sufficient reason. If the arguments from geometry are successful, then matter and change are continuous. If one attempts to explain matter or change in terms of an arbitrary number of discrete parts or stages, some intervening parts or stages will always be missed by an explanatory account. Before concluding, let’s consider a passage that has been taken to support a quite different reading of Du Châtelet on the relationship between physics and mathematics. “The divisibility of extension to infinity,” she writes, “is at the same time a geometrical truth and a physical error,” citing Keill as confused on this point (1742, 194). At first glance, this might seem to contradict her doctrine of the continuity of matter, as well as the correspondence between geometry and nature (cf. Carson 2004, 169–70). This passage, however, needs to be read in its context, which is an attempt to resolve ancient paradoxes about continuity. It is in confusing geometrical extension and physical extension, and in assuming that physical extension is always composed of extended parts to infinity, that the Ancients [sc. Zeno and Melissus] formed these so very false and specious arguments against the possibility of motion. (Du Châtelet 1742, 191–92)

 Descartes identified “the subject-matter of pure mathematics” with “corporeal nature” or “material things” (1984, 49; 264; 55). Newton arguably took lines and circles to be, in the first instance, physical motions (Guicciardini 2004). 38

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

93

Du Châtelet also accuses Keill of reasoning that, because a grain of sand has an infinite number of parts, these parts could “fill the entire universe” (194). This is a variant of Zeno’s second paradox of plurality, which is standardly read as arguing that because a line is divisible into an infinite number of parts and each part has some size, the line must, absurdly, have infinite size (Vlastos 1971). Despite her remarks about confusing geometrical and physical extension, however, Du Châtelet is not objecting to the continuity of matter and change as such. Nor is she ruling out inferences from general geometrical principles to conclusions about material nature. For the “physical error” she diagnoses here is not the continuity of matter, but rather that Zeno and Keill present matter as actually “composed of” an infinite number of parts, such that these parts are prior to the whole. This is also a point of disagreement with Wolff, who regarded simple substances as prior to and collectively composing spatial wholes, even though each simple substance “does not…fill a space” (1720, §602). Du Châtelet, by contrast, upholds the infinite potential divisibility of matter. In this sense, physical extension is divisible “to infinity.” But it is not actually divided into atoms, either.39 What does Du Châtelet mean by the claim that the actual infinity of extended parts is a “geometrical truth”? Euclid defines points as partless (1908, I.153). Presumably, she does not want to give this up. Given her dictum that things are in nature as they are in geometry, if she accepts infinite collections of actual geometrical points, then it might seem that she must accept infinite collections of actual physical points, despite her official potentialism about parts of matter. But it is only the “ideal division” of geometrical objects that can go to infinity, because we can conceive of geometrical points (1742, 194). The points in question are merely ideal “possible parts” (1742, 190). She supports this point by first appealing to the familiar process of dividing a line into parts. We can “mentally proceed to infinity” by conceiving of this process as extending indefinitely: there is no principled reason this “ideal division” cannot continue (193). Next, we reflect on this capacity to divide continuous geometrical objects ad indefinitum or “to infinity,” and finally conceive of the logically “possible” ultimate result of such boundless division (193; 109). But given our finite cognitive capacities, such an “infinite” result is not in our power (193). With geometrical points, it seems we have reached a limitation on Du Châtelet’s dictum that things are in nature as they are in geometry. Perhaps this limitation rests on an epistemological distinction between different kinds of mathematical object. Figures and lines can be given to us, at least approximately, in perception. Geometrical points cannot be perceptually given in this way: they are merely conceivable. More precisely, Du Châtelet’s dictum that things are in nature as they are in geometry is plausibly restricted to geometrical objects with determinate magnitude. A  An influence here may be Jacques Rohault’s introductory work on physics, which Du Châtelet owned (Du Châtelet 2018, I.367). Near the beginning of this work, Rohault offers a proof that matter cannot have simple parts, but he also rules out an actual infinity of material points. Instead, “matter is indefinitely divisible” and has no definite number of actual parts (Rohault 1723, I.32). 39

94

A. Wells

physical object such as a watch has a “fixed number” of determinate parts, each with a measure, and these parts are largely mind-independent, even if they are in principle further divisible (1742, 191). By contrast, the number of points in a line is “absolutely indeterminate”: it is nonsensical to speak of the determinate length of these points, even though the line has a determinate length (190; cf. Rohault 1723, I.32–33). A line should be treated not as made up not of an infinity of points but as divisible into some “non-finite” but unknown “quantity of parts” (193). Geometrical points, as merely conceivable, lack determinate magnitude or number. This circumvents the difficult question of whether points are Archimedean or non-Archimedean magnitudes. To historically situate Du Châtelet’s position on the continuity of matter, I want to conclude by juxtaposing it with Kant’s taxonomy of traditional accounts of the part–whole structure of the world in the Second Antinomy.40 The Antithesis of the Second Antinomy denies that there are any simples in the created world. Du Châtelet is by contrast committed to simple or at least non-­composite substances, namely the non-spatiotemporal souls and elements making up the fundamental level of the created world. Therefore, she would not accept the Antithesis. Nor would Du Châtelet endorse the Thesis of the Second Antinomy: Every composite substance in the world consists of [besteht aus] simple parts, and nothing exists anywhere except the simple or what is composed [zusammengesetzt] of simples. (Kant 1998, A434/B462)

Du Châtelet take there to be some composite substances, although these are merely phenomenal substances. But she denies that matter is mereologically composed of simples. Matter is indefinitely divisible into further material parts. Simple substances—or more precisely, non-composite substances—partly ground matter. But this is not a standard mereological composition relation, since these non-composite substances are non-spatial and cannot compose spatial wholes. This is particularly clear from Du Châtelet’s discussions of souls. Given these properties of matter and Du Châtelet’s commitment to the existence of material things, it follows that (i) not every composite substance in the world consists of simple parts and (ii) something exists somewhere that is neither simple nor composed of simples. In turn, (i) and (ii) negate the two clauses of the Thesis of Kant’s Second Antinomy. Du Châtelet is not committed, then, to either of the apparently contradictory propositions making up the Second Antinomy. Kant seemingly resolves the Antinomy by claiming that both the Thesis and the Antithesis are false (1998, A485/B513). The truth, on his view, is that the “division” of matter into parts can be continued “in infinitum,” but because of our finitude cannot actually reach a complete division into “infinitely many parts” (A523–4/B551–2; A515–17/B543–45; Marschall 2019). This solution resembles Du Châtelet’s potentialist approach to the division of matter.

 As for the continuity of change, McNulty (2019) argues that Kant considers it an “a priori…truth of metaphysics,” linked to a demand for intelligible explanation, though also grounded in the “geometric” continuity of space and time (1595; 1600; 1605–7). McNulty’s reading suggests similarities between Du Châtelet and Kant on the continuity of change. 40

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

95

4.5 Conclusion I began by examining the positions of some of Du Châtelet’s influential contemporaries on the application of mathematics to physics. Maupertuis, Voltaire, and Wolff take relatively conservative positions on this issue, often leaving it unclear what role is to be played by the mathematics in post-Newtonian physics. Du Châtelet’s position, I then sought to show, contrasts vividly with theirs. Even though mathematical objects are abstracted from the physical world, they are partly grounded in magnitudes that are in material things. This allows for relations of approximation between mathematical objects and physical things. And although Du Châtelet takes these objects to be fictions, a closer look at her account reveals that they are public, and under a number of objective and non-voluntary constraints which do not apply to literary fictions. I argued that these commitments underwrite Du Châtelet’s claim that the same thing happens in nature in geometry. And I showed that Du Châtelet, in turn, uses the parallel between nature and geometry to establish two important metaphysical theses, namely the continuity of matter and change.41

References Aristotle. 1984. In The Complete Works of Aristotle. Two volumes, ed. J.  Barnes. Princeton: Princeton University Press. Arnauld, A. 1683. Nouveaux élémens de géométrie. 2nd ed. Paris: Desprez. Arnauld, A., and C. Lancelot. 1975. General and Rational Grammar: The Port-Royal Grammar, J. Rieux et al., Eds. and Trs. The Hague: Mouton. Arnauld, A. and P. Nicole. 1996. Logic, or, The Art of Thinking (trans: Buroker, J. V.). New York: Cambridge University Press. Bacon, R. 1962. Opus Maius (trans: Burke, R. B.). New York: Russell & Russell. Basso, L. 2008. Rien de mathématique dans la methodus mathematica wolfienne. In Christian Wolff et la pensée encyclopédique européenne, ed. J. Mondot and C. Larrère, 109–124. Bordeaux: Presses Universitaires de Bordeaux. Buchenau, S. 2013. The Founding of Aesthetics in the German Enlightenment. New  York: Cambridge University Press. Carson, E. 2004. Metaphysics, Mathematics and the Distinction Between the Sensible and the Intelligible in Kant’s Inaugural Dissertation. Journal of the History of Philosophy 42 (2): 165–194.

 Many thanks to Wolfgang Lefèvre and Anat Schechtman for helpful written comments, as well as to William Marsolek for discussion. I presented drafts of some of this material at the Philosophy of Science Association meeting in Baltimore, a Du Châtelet discussion group at Paderborn University, and the British Society for the History of Philosophy conference in Edinburgh. I thank the participants on these occasions, particularly Clara Carus, Manuel Fasko, Ruth Hagengruber, William Harper, Jil Muller, Hanns-Peter Neumann, Areins Pelayo, and Edward Slowik. I also thank Katherine Dunlop, Andrea Reichenberger, and Maja Sidzińska for sharing relevant work in progress. Research on this paper was partly supported by the Deutsche Forschungsgemeinschaft (DFG), project number 435124693. Section 4.4.1 draws on my “Du Châtelet on the Need for Mathematics in Physics,” Philosophy of Science 88, 1137–48 (2021). 41

96

A. Wells

Coope, U. 2005. Time for Aristotle: Physics IV.10–14. Oxford: Clarendon Press. Crousaz, J.-P. 1714. Traité du beau. Amsterdam. D’Alembert, J.-B. 1743. Traité de dynamique. Paris. De Gandt, F. 2001. Qu’est-ce qu’être newtonien en 1740? In Cirey dans la vie intellectuelle : la réception de Newton en France, ed. F. De Gandt, 126–147. Oxford: Voltaire Foundation. De Risi, V. 2016. The Development of Euclidean Axiomatics. Archive for History of Exact Sciences 70: 591–676. ———. 2021. Did Euclid Prove Elements I, 1? The Early Modern Debate on Intersections and Continuity. In Reading Mathematics in Early Modern Europe, ed. P. Beeley, Y. Nasifoglu, and B. Wardhaugh, 12–32. London: Routledge. Dear, P. 1995. Discipline and Experience. Chicago: University of Chicago Press. Descartes, R. 1984. The Philosophical Writings of Descartes: Volume II (trans: Cottingham, J. et al.). New York: Cambridge University Press. Du Châtelet, E. 1738a. Lettre sur les Elémens de la Philosophie de Newton. In Le Journal des Sçavans: Septembre 1738, 534–541. Paris. ———. 1738b–1740. Manuscript of Institutions de Physique. MS fr. 12265, Bibliotheque nationale de France, Paris. ———. 1740. Institutions de Physique. 1st ed. Paris: Prault. ———. 1742. Institutions Physiques. 2nd ed. Amsterdam. ———. 1759. Exposition Abregée du Systême du Monde. In Principes Mathématiques de la Philosophie Naturelle, by Isaac Newton, vol. 2. Paris: Gabay. ———. 2018. La Correspondance d’Émilie Du Châtelet. Ferney-Voltaire: Centre International d’étude du XVIIIe siècle. ———. n.d. Manuscript of Grammaire Raisonée [Chapters VI–VIII]. MS BV 5-240 (vol. 9, ff. 133–49), National Library of Russia, St. Petersburg. Dunlop, K. 2013. Mathematical Method and Newtonian Science in the Philosophy of Christian Wolff. Studies in History and Philosophy of Science Part A 44 (3): 457–469. Elgin, C.Z. 2004. True Enough. Philosophical Issues 14: 113–131. Euclid. 1908. In The Thirteen Books of Euclid’s Elements, ed. T.L. Heath, vol. Three. Cambridge: Cambridge University Press. Field, H. 1989. Realism, Mathematics, and Modality. Oxford: Blackwell. Formey, S. 1754/1747. Recherches sur les Elémens de la matière. In Mélanges Philosophiques, vol. 1, 263–388. Leiden: Luzac & Fils. Foucault, M. 1966. Les mots et les choses. Paris: Gallimard. Gessell, B. 2019. ‘Mon petit essai’: Émilie du Châtelet’s Essai sur l’optique and her early natural philosophy. British Journal for the History of Philosophy 27 (4): 860–879. Gingras, Y. 2001. What did Mathematics do to Physics? History of Science 39 (4): 383–416. Guicciardini, N. 2004. Geometry and Mechanics in the Preface to Newton’s Principia. Graduate Faculty Philosophy Journal 25 (2): 119–159. Hasper, P.S. 2021. Mathematische Gegenstände. In Aristoteles-Handbuch, ed. C.  Rapp and K. Corcilius, 2nd ed., 299–303. Berlin: Springer. Hill, K. 1996. Neither Ancient nor Modern: Wallis and Barrow on the Composition of Continua. Part One. Notes and Records of the Royal Society of London 50 (2): 165–178. Janiak, A. 2000. Space, Atoms and Mathematical Divisibility in Newton. Studies in History and Philosophy of Science 31 (2): 203–230. ———. 2007. Newton and the Reality of Force. Journal of the History of Philosophy 45 (1): 127–147. Jauernig, A. 2010. Disentangling Leibniz’s Views on Relations and Extrinsic Denominations. Journal of the History of Philosophy 48 (2): 171–205. Jesseph, D.M. 2015. Leibniz on the Elimination of Infinitesimals. In G.W. Leibniz: Interrelations between Mathematics and Philosophy, ed. N.B. Goethe et al., 188–205. Dordrecht: Springer. Kant, I. 1998. In Critique of Pure Reason, ed. P. Guyer and A.W. Wood. New York: Cambridge University Press.

4  “In Nature as in Geometry”: Du Châtelet and the Post-Newtonian Debate…

97

———. 2004. In Theoretical Philosophy after 1781, ed. H.  Allison and P.  Heath. New  York: Cambridge University Press. Keill, J. 1733. Introduction to Natural Philosophy: or, Philosophical Lectures Read in the University of Oxford, Anno Dom. London: 1700. Fourth edition. Leibniz, G. W. 1849–63. In Leibnizens mathematische Schriften, ed. C.I. Gerhardt, Seven vols. Halle: Schmidt. ———. 1875–1890. In Die philosophischen Schriften, ed. C.I.  Gerhardt, Seven vols. Berlin: Weidmann. Leibniz, G.W., and S. Clarke. 2000. In Correspondence, ed. R. Ariew. Indianapolis: Hackett. Locke, J. 1975. In An Essay concerning Human Understanding, ed. P.H.  Nidditch. Oxford: Clarendon Press. Lu-Adler, H. 2018. Between Du Châtelet’s Leibniz Exegesis and Kant’s Early Philosophy. Philosophiegeschichte und Logische Analyse 21: 177–194. Marschall, B. 2019. Conceptualizing Kant’s Mereology. Ergo 6 (14): 374–404. Maupertuis, P.-L.M. 1732. Discours sur les différentes figures des astres. Paris. ———. 1735. Sur les loix de l’attraction. In Mémoires de mathématique & de physique de l’academie royale, 343–362. Paris: l’Imprimerie Royale. ———. 1740. Reflexions Philosophiques sur L’Origine des Langues et la Signification des Mots. [Basel.]. McNulty, M.B. 2019. Continuity of change in Kant’s dynamics. Synthese 196: 1595–1622. North, J. 2021. Physics, Structure, and Reality. Oxford: Oxford University Press. Pasnau, R. 1997. Theories of Cognition in the Later Middle Ages. New  York: Cambridge University Press. ———. 2011. Metaphysical Themes 1274–1671. Oxford: Clarendon Press. Rabouin, D., and R.T.W. Arthur. 2020. Leibniz’s Syncategorematic Infinitesimals II. Archive for History of Exact Sciences 74: 401–443. Reichenberger, A. 2016. Émilie du Châtelets Institutions physiques: Über die Rolle von Prinzipien und Hypothesen in der Physik. Wiesbaden: Springer VS. Rey, A., et  al. 2011. Dictionnaire Historique de la Langue Française. Paris: Les Dictionnaires Le Robert. Rohault, J. 1723. Rohault’s System of Natural Philosophy, Illustrated with Dr. Samuel Clarke’s Notes. Fourth edition. London. Rutherford, D. 1990. Leibniz’s “Analysis of Multitude and Phenomena into Unities and Reality.” Journal of the History of Philosophy 28 (4): 525–552. Shank, J.B. 2008. The Newton Wars and the Beginning of the French Enlightenment. Chicago: University of Chicago Press. ———. 2018. Before Voltaire: The French Origins of ‘Newtonian’ Mechanics. Chicago: University of Chicago Press. Stan, M. 2018. Émilie Du Châtelet’s Metaphysics of Substance. Journal of the History of Philosophy 56 (3): 477–496. Sutherland, D. 2005. Kant on Fundamental Geometrical Relations. Archiv für Geschichte der Philosophie 87: 117–158. Thomasson, A. 1999. Fiction and Metaphysics. New York: Cambridge University Press. ———. 2007. Realism and Human Kinds. Philosophy and Phenomenological Research 67 (3): 580–609. Vlastos, G. 1971. A Zenonian Argument against Plurality. In Essays in Ancient Greek Philosophy, ed. J.P. Anton and G. Kustas, 119–144. Albany: State University of New York Press. Voltaire. 1738. Elémens de la Philosophie de Neuton. London: 2nd. ———. 1961/1734. Lettres Philosophiques. In Mélanges de Voltaire, ed. J. van den Heuvel, 2–133. Paris: Gallimard. White, M.J. 1992. The Continuous and the Discrete: Ancient Physical Theories from a Contemporary Perspective. Oxford: Clarendon Press.

98

A. Wells

Wolff, C. 1713. Vernünfftige Gedancken von den Kräfften des menschlichen Verstandes [‘German Logic’]. Halle. ———. 1720. Vernünfftige Gedancken von Gott, der Welt und der Seele des Menschen, auch allen Dingen überhaupt [‘German Metaphysics’]. First edition. Halle. ———. 1965/1726. Preliminary Discourse on Philosophy in General (trans: Blackwell, R.  J.). Indianapolis: Bobbs-Merrill. ———. 1973/1710. Anfangsgründe aller Mathematischen Wissenshaften [Reprint in Christian Wolff Gesammelte Werke, I. Abt. Bd. 12], ed. J. Ecole. Hildesheim: Olms Verlag. ———. 2001a. Philosophia prima sive Ontologia [II.  Abt. Bd. 3], ed. J.  Ecole. Hildesheim: Olms Verlag. ———. 2001b. Von dem Unterschiede metaphysischer und mathematischer Begriffe. In Kleine Schriften und Einzele Betrachtungen, 286–348. Hildesheim: [I. Abt. Bd. 22]. Olms. ———. 2019. Briefwechsel zwischen Christian Wolff und Ernst Christoph von Manteuffel, ed. J. Stolzenberg, D. Döring, K. Middell, and H.-P. Neumann. Hildesheim: Olms. Zinsser, J.P. 2006. Emilie Du Châtelet: Daring Genius of the Enlightenment. New York: Penguin.

Chapter 5

Order of Nature and Orders of Science On the Mathematical Philosophy of Nature and Its Changing Concepts of Science from Newton and Euler to Lagrange and Kant Helmut Pulte Abstract  It is common knowledge that, next to experimentation, mathematics is the most important pillar of modern natural science. Less well known is how strongly the mathematical ideal of knowledge shaped modern science, especially so-called ‘rational mechanics’, which was regarded by most scientists and philosophers as the foundation and backbone of all natural sciences. The following chapter examines how this ideal of a ‘mechanical Euclideanism’, as I call it, shaped different programmes of mathematical natural philosophy in the late seventeenth and eighteenth centuries. It shows that this ideal was in opposition to the modern, hypothetico-decuctive understanding of science, and reveals how it was supported by epistemological and methodological arguments from both traditional rationalism and empiricism. The analysis of these processes is directed against an understanding of the development in question as one that was shaped primarily by Newton’s mechanics (as Ernst Mach, Thomas S.  Kuhn and others claimed). Rather, it attempts to reconstruct this development as a dispute and competition between different programmes, guided by different scientific metaphysics and striving for different conceptual foundations of rational mechanics. It also tries to reveal how the attempts to integrate the achievements of these programmes into a unified formal framework of analytical mechanics alter and ultimately undermine the ideal of mechanical Euclideanism. The first edition of ‘Between Leibniz, Newton and Kant’ already contained a slightly different version of this paper as a chapter. As the former one was quite widely received and positively evaluated by the readership, this new version could make do with some updates and a few corrections. Readers interested in a more detailed account than can be given in this outline, perhaps also in continuing the story beyond Lagrange and Kant into the nineteenth century up to Neumann and Einstein, are referred to my book Axiomatik und Empirie. H. Pulte (*) Institut für Philosophie, Ruhr-Universität Bochum, Bochum, Germany © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_5

99

100

H. Pulte

[…] to derive two or three general Principles of Motion from Phaenomena, and afterwards to tell us how the Properties of all corporeal Things follow from those manifest Principles, would be a very great step in Philosophy, though the Causes of those Principles were not yet discover’d. (Isaac Newton, Opticks, Qu. 31) Les principes de la Mécanique sont déja si solidement établis, qu’on auroit grand tort, si l’on vouloit encore douter de leur vérité. Quand même on ne seroit pas en état de les démontrer par les principes généraux de la Métaphysique, le merveilleux accord de toutes les conclusions qu’on en tire par le moyen du calcul, avec tous les mouvemens des corps […] seroit suffisant pour mettre leur vérité hors de doute. (Leonhard Euler, Réfléxions sur l’espace et le tems, § 1) Je me suis proposé de réduire la théorie de [Méchanique], & l’art de résoudre les problêmes qui s’y rapportent, à des formules générales, dont le simple développement donne toutes les équations nécessaires pour la solution de chaque problême. (Joseph Louis Lagrange, Méchanique Analitique, Avertissement) So konnten also jene mathematische Physiker metaphysischer Prinzipien gar nicht entbehren […]. Darüber aber bloß empirische Grundsätze gelten zu lassen, hielten sie mit Recht der apodiktischen Gewißheit, die sie ihren Naturgesetzen geben wollten, gar nicht gemäß, daher sie solche lieber postulierten, ohne nach ihren Quellen a priori zu forschen. (Immanuel Kant, Metaphysische Anfangsgründe der Naturwissenschaft, Vorrede)

5.1 Preliminaries: Three Points of Departure and One Aim The role of mathematics in eighteenth-century science and philosophy of science can hardly be overestimated, though it was and is frequently misunderstood. From today’s point of view, one might be tempted to say that philosophers and scientists in the seventeenth and even more in the eighteenth century became aware of the importance of mathematics as a means of ‘representing’ physical phenomena or as an ‘instrument’ of deductive explanation and prediction. According to this view, the rise of mathematical physics is a peripheral aspect of the new experimental sciences, and the mathematical part of physics is a methodologically directed, constructive enterprise that is somehow ‘parasitical’ with respect to experimental and observational data. But such modernising outcomes of logical empiricism are missing the central point, i.e., the ‘mathematical nature of nature’ according to mechanical philosophy. I will start with some general considerations about mathematics under the premise of mechanism before coming to the aim of my paper.

5.1.1 ‘Semantical Ladenness’ of Mathematics On the premise of mechanism, the primary aim of natural philosophy was the determination of the motion of material particles under different physical conditions and the science of motion was the ‘hard core’ of natural philosophy. Motion itself being regarded as a genuine mathematical concept, natural philosophy had to

5  Order of Nature and Orders of Science

101

be not only an experimental, but also a mathematical science. Taking this idea seriously, the attribute ‘mathematical’ should be understood not as ‘mathematics applied to science’ but rather as ‘science, having essentially to do with mathematical entities’. This is the reason why the new science of motion should be called mathematical philosophy of nature rather than mechanics. The traditional meaning of mechanics as an art which is directed against the ‘nature’ of bodies obscures the fact that the ‘new’ mechanics dealt with natural motions and aimed at the uncovering of their primary laws. While Newton made this intention quite clear when he chose the title Philosophiae naturalis principia mathematica for his chief work, it was the name mechanica rationalis,1 used by him in the preface in order to underline his foundational claims, that became prominent in the eighteenth century – perhaps for the sake of brevity, and for this reason only I will use it throughout this paper. It is important to note, however, that in the course of the eighteenth century, rational mechanics – even in the abstract, ‘analytical’ form that can be found in the works of Euler, d’Alembert and Lagrange – never became a ‘purely’ mathematical exercise without physical meaning: its concepts and primary laws were located in natural reality, and (therefore) its deductive consequences were expected to be empirically meaningful. Hence mechanics between Leibniz, Newton and Kant should not be understood as ‘applied’ mathematics in the modern sense (a syntactic structure to be ‘filled’ with semantic content by empirical data and rules of correspondence), but as the most important part of mathesis mixta in the traditional sense, i.e., as a part of mathematics that is eo ipso a part of natural philosophy, because it was the science of the (mathematical) laws of (natural) motion. Within the frame of rational mechanics, mathematical symbols and even the most abstract mathematical formulas are, so to speak, ‘semantically laden’.

 “[…] rational mechanics [mechanica rationalis] will be the science of motions resulting from any forces whatsoever, and of the forces required to produce any motions, accurately proposed and demonstrated. This part of mechanics, as far as it extended to the five powers which relate to manual arts, was cultivated by the ancients, who considered gravity (it not being a manual power) no otherwise than in moving weights by those powers. But I consider philosophy rather than arts and write not concerning manual but natural powers, and consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore I offer this work as the mathematical principles of philosophy, for the whole burden of philosophy seems to consist in this—from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena […]” (Newton, Mathematical Principles, XVII–XVIII). In one of his early papers on the history of rational mechanics, Clifford Truesdell asked for any precursor of Newton using the term ‘rational mechanics’, and I. Bernard Cohen later put forward the same question. Alan Gabbey has shown that it was used in Goclenius’s Lexicon philosophicum Graecum and therefore “was in (probably common) use during the first decade of the seventeenth century, at the latest” (Gabbey, 309, n. 13). His argument, that Newton’s Principia “was and was not a treatise on mechanics” (ibid., 308) seems to be in line with my understanding of ‘mathematical philosophy of nature’; see Pulte, Axiomatik und Empirie. 1

102

H. Pulte

5.1.2 Euclideanism A second common feature of mathematical philosophy of nature between Leibniz, Newton and Kant is of equal importance with respect to the role of mathematics: Rational mechanics follows the ideal of Euclidean geometry, or, to be more precise, its concept of science is best described as ‘Euclideanism’ (in Lakatos’ sense). I will confine myself in this introduction to its most important feature: its first principles are not only true, but certainly true, i.e., infallible with respect to empirical ‘anomalies’. This means, first and above all, that rational mechanics should not be understood as a hypothetical-deductive, but rather as an axiomatic-deductive science. In other words: If the hypothetical-deductive method is “at the core of modern science [neuzeitliche Wissenschaft]” (Böhme, Alternativen der Wissenschaft, 84), as is sometimes claimed, rational mechanics from Newton to Kant is not modern, and if it is defined as ‘modern’ [neuzeitlich], which is probably desirable for a science that was widely regarded as a prototype by both scientists and philosophers of science in the course of the eighteenth and nineteenth centuries, this characterisation cannot be true. The ‘historical stability’ of classical mechanics from Newton to Einstein is not only due to its empirical success, but also to its Euclideanistic leanings, and the decline of ‘mechanical Euclideanism’ was a necessary historical premise for the replacement of classical mechanics at the beginning of the twentieth century. Newton, in his Principia, used a noteworthy phrase which makes these two sides of mathematics in natural philosophy visible: axiomata sive leges motus. As leges motus, his well-known mathematical propositions act as primary laws of nature which govern the behaviour of (possibly all) material bodies. As axiomata they act as first principles of the theory of mechanics, they govern the known laws and examples (especially from Kepler’s celestial and Galilei’s terrestrial mechanics) in order to gain a deductive organisation of the whole body of mechanical knowledge. It is, however, by no means evident that primary laws of nature are ‘prime candidates’ for axioms of a deductively organised theory, nor is it clear whether such a ‘metatheoretical coincidence’ is possible at all: From natural laws the philosopher-­ scientist expects truth, empirical generality, explanatory power (mechanical explanation of possibly all phenomena of nature), a certain plausibility and intuitiveness with respect to his scientific metaphysics and (perhaps) necessity. From first principles or ‘axioms’ of a theory he expects, above all, truth, deductive power (entailment of all the other laws of a theory); moreover they are thought to be neither provable by other propositions nor – due to their evidence – to be in need of such a proof. These demands correspond to each other, but they do not coincide. Why should they be granted by the same principles? Why should the basic laws of nature be identical with the axioms of a mathematical theory of nature? Kant, in his Critique of Judgement and elsewhere, discusses the possibility that this may not be the case: Though basic laws exist, their deductive power might be insufficient in order to build up a coherent order of science. Despite universal lawfulness, nature might, so to speak, refuse logical order. In this case man would come only to an ‘aggregate’ of regularities, i.e., to a number of diverging empirical laws, but not to order and unity. This is a central point of my discussion: Laws have to explain nature, axioms have to organise theories. But a ‘congruence’ of the order of nature and the orders

5  Order of Nature and Orders of Science

103

of science is increasingly difficult to guarantee when science produces a growing body of knowledge. Traditional mechanical Euclideanism is at stake here.

5.1.3 Orders of Science The plural ‘orders’ refers to a third point which should be mentioned at the outset: At the beginning of the eighteenth century, there were indeed fundamentally different attempts to gain a coherent system of ‘mathematical principles of natural philosophy’: At the least, Descartes’ ‘geometrical’ mechanics, based on his laws of impact, Newton’s mechanics of forces, based on his three laws and the law of gravitation, and Leibniz’ dynamics, based on laws of impact and the conservation of vis via, should be sharply separated. With respect to its empirical bearing Newton’s Principia was obviously the most successful attempt, but it was neither unique in its intention, nor was it faultless or complete in its execution, nor was it understood as ‘revolutionary’ by the first generation of its readers, as far as the principles of mechanics2 are concerned. That Newton laid down principles which are sufficient to solve all problems of mechanics is a legend which was invented by so-called ‘Newtonians’ of the first generation, spread by Lagrange, Montucla and others until it became a ‘canon law’ of history of science with Mach’s Mechanics.3 In recent times, Thomas Kuhn was its most prominent advocate,4 but this did not improve the ‘law’: it is simply false. It was mainly  Concerning the foundations of mechanics, Newton’s principles (axiomata sive leges motus) and his law of gravitation should be distinguished. What was soon understood as ‘revolutionary’ (in the sense of an obvious and irreversible break with the past) was his celestial mechanics, i.e., the application of his three laws and the law of gravitation to the motion of the moon and the planets. In the last decades, however, more and more publications have shown that Newton’s three laws of motion were neither entirely new, nor understood as new by his contemporaries and his immediate successors; for an overview see Bos, Mathematics and Rational Mechanics. 3  “Die Newtonschen Prinzipien sind genügend, um ohne Hinzuziehung eines neuen Prinzips jeden praktisch vorkommenden mechanischen Fall […] zu durchschauen. Wenn sich hierbei Schwierigkeiten ergeben, so sind dieselben immer nur mathematischer (formeller) und keineswegs mehr prinzipieller Natur” (Mach, Mechanik, 272). Mechanics after Newton is characterised by Mach as a deductive, formal and mathematical development on the basis of his principles (ibid., 179). 4  “The Principia […] did not always prove an easy work to apply, partly because it retained some of the clumsiness inevitable in a first venture and partly because so much of its meaning was only implicit in its applications. For many terrestrial applications, in any case, an apparently unrelated set of Continental techniques seemed vastly more powerful. Therefore, from Euler and Lagrange in the eighteenth century to Hamilton, Jacobi and Hertz in the nineteenth, many of Europe’s most brilliant mathematical physicists repeatedly endeavoured to reformulate mechanical theory in an equivalent but logically and aesthetically more satisfying form. They wished, that is, to exhibit the explicit and implicit lessons of the Principia and of Continental mechanics in a logically more coherent version, one that would be at once more uniform and less equivocal in its application to the newly elaborated problems of mechanics. Similar reformulations of a paradigm have occurred repeatedly in all of the sciences, but most of them have produced more substantial changes in the paradigm than the reformulations of the Principia cited above.” (Kuhn, Structure, 33). Kuhn’s marginal note (“Principia and of Continental mechanics”) reveals the main problem which he failed to address because of the ‘Machian shaping’ of his history of mechanics. 2

104

H. Pulte

Clifford Truesdell’s enormous contribution to the history of rational mechanics which made obvious that it was during the eighteenth century rather than the seventeenth century that classical mechanics, as it is known today, took shape. Therefore, ‘Classical mechanics’ and ‘Newtonian mechanics’ (understood as mechanics laid down by Newton) are by no means synonymous. As far as the foundations of rational mechanics are at stake, the great ‘Newtonian revolution’ did not take place. Today, we see better than some decades ago that rational mechanics in the eighteenth century emerged from different sources and grew into a coherent system not before the end of the eighteenth century. Descartes, Newton, Leibniz, Huygens, Euler, d’Alembert, Lagrange and others contributed to the conceptual and mathematical framework that is known today as ‘classical mechanics’: The three first mentioned tried to establish fundamentally different sciences of mechanics, driven by different systems of ‘scientific metaphysics’5 and therefore based on different basic concepts and different ‘first’ laws of motion. I have elsewhere proposed that the development of rational mechanics in the first half of the eighteenth century could be essentially interpreted as a competition of these three great research programs of Descartes, Newton and Leibniz. If there is some truth in this conjecture – and a detailed analysis of the numerous controversies about the ‘nature’ of space and time, the conservation of vis viva and the concept of Newtonian force (esp. gravitation) might show that it is – the Mach-Kuhnian picture of eighteenth century rational mechanics as a ‘normal’ and ‘formal’ elaboration of the Newtonian paradigm cannot be upheld. To put it in the nutshell of Kuhnian terminology: with regard to the foundations of rational mechanics the eighteenth century was not ‘normal’, because the seventeenth century was not ‘revolutionary’ (Pulte, Prinzip, esp. 18). At least the first half of the siècle du lumière is characterised rather by the competition among fundamentally different endeavours to clear up the conceptual and formal framework of rational mechanics, and its outcome is by no means ‘Newtonianism’ in its original meaning. During a period of ‘revolution in permanence’, however, so-called ‘formal’ elements of science gain a peculiar quality: While a ‘conceptual discourse’ across the boundaries of actual scientific metaphysics was hardly possible and almost futile (as is best illustrated by the famous Leibniz-Clarke correspondence), the language of mathematics became even more important for a small (and in a way isolated) scientific community that promoted rational mechanics as is best illustrated by the continental reception of Newton’s Principia (see the respective chapters in Pulte and Mandelbrote, The Reception of Isaac Newton in Europe). This is not to share the  In this paper, I will use the term ‘scientific metaphysics’ for all assumptions which define the ‘hard core’ of a scientific research program in the sense of Lakatos. They belong to metaphysics, in so far as they are immune from empirical falsification, and they are scientific, in so far as they determine the problems, basic concepts and acceptable explanations of the science in question. Elkana, inspired by Lakatos, defines scientific metaphysics as “those untestable hypotheses which deal with the structure of the physical world and which direct scientists in their research” (Elkana, Euler and Kant, 278). The scientific metaphysics of mechanics shapes the understanding of matter and motion. It has genuinely to do with the concepts of space, time, mass and (eventually) with the concept of force and (or) energy and their mutual relations. 5

5  Order of Nature and Orders of Science

105

somehow naive view that mathematics in the age of reason worked as a kind of ‘meta-language’, capable of solving even philosophical problems of rational mechanics and, as it were, ‘replacing’ the Babylonian confusion of the different tongues of metaphysics – a view obviously shared by Lagrange.6 It means, however, that mathematics played a key role in making accessible the results of one research program of mechanics to the others, that it was indispensable in integrating those parts which seemed valuable and that it was the only means of formulating ‘towering’ principles (like those of least action and virtual displacements) from which all the accepted laws of mechanics, whether or not they emerge from the ‘native’ research program, could be derived. Scientific metaphysics tends towards a separation, mathematics tends towards an integration of different programs. At the end of the eighteenth century, we have one (and only one) system which represents all of the accepted ‘mathematical principles of natural philosophy’: Lagrange’s Méchanique Analitique. But how could this integration happen? And what was its price, i.e., did it hold what mathematical philosophy of nature, a century earlier, promised? These questions address the central point of my paper, the change of concepts of science within rational mechanics and the reasons for this change.

5.1.4 Understanding the Change of Concepts of Science ‘Semantical ladenness’ and ‘integrative potential’ of mathematics as well as ‘global’ Euclideanism (i.e., Euclideanism of all programs of rational mechanics) are three points of departure of my survey. Its aim is a better understanding of the metatheoretical change of rational mechanics which took place in the course of the eighteenth century and is most obvious if we compare Newton’s Principia (1687) and Lagrange’s Méchanique Analitique (1788). Jürgen Mittelstraß has described the difference between both works as a replacement “of a ‘Euclidean’ [synthetical] construction of physics by an ‘analytical’ construction,”7 and he has criticised this development as part of a methodological ‘degeneration’ that started with Newton. I have criticised the shortcomings of this view elsewhere (Pulte, Axiomatik und Empirie, 217–223). Here, I will try to explain the development from Newton to Lagrange by showing that both approaches are in the same ‘Euclidean line’ (though my definition of ‘Euclidean’ is different), the latter fulfilling, however, a different function: no decline of method, but rather a change of theoretical demands. In general, I will argue that there is a growing tension between the order of nature and the orders of science that led to a dissolution of Euclideanism, beginning at the end of the eighteenth century and becoming most obvious in a crisis of  See Lagrange’s letter to d’Alembert of January 27, 1778 (Lagrange, Oeuvres, XIII 336).  See Mittelstraß, Neuzeit, esp. 302. ‘Euclidean’ and ‘synthetical’ are obviously used as synonyms; see Mittelstraß, Möglichkeit, 119 and 236 note 19. The case study ‘analytical mechanics’ is also picked up in Mittelstraß, Rationale Rekonstruktionen. 6 7

106

H. Pulte

meaning of so-called ‘axioms’ or ‘principles’ of mechanics. (This development, promoted by the rise of analytical mechanics, opened the way for conventionalism and instrumentalism in mechanics over the course of the following century, starting with Jacobi, Riemann and Carl Neumann and continued by Mach, Hertz, Poincaré, Duhem and others.) As I am aiming at a structural outline of these developments, examples, hopefully representative and illuminating, are reduced to a minimum.

5.2 Mechanical Euclideanism: The Case of Newton’s Principia 5.2.1 Mechanical Euclideanism Lakatos’ metatheoretical concept of ‘Euclideanism’ seems to me for several reasons an appropriate label for rational mechanics as pursued by most8 of the eighteenthand early nineteenth-century mathematicians, physicists, and philosophers: First, Euclideanism means that the “ideal theory is a deductive system with an indubitable truth-injection at the top (a finite conjunction of axioms)  – so that truth, flowing down from the top through the safe truth-preserving channels of valid inferences, inundates the whole system.” And its basic aim “is to search for self-evident axioms  – Euclidian [sic!] methodology is puritanical, anti-speculative.” (Lakatos, Philosophical Papers, II 28 and 29). Secondly, Lakatos’ concept is epistemologically neutral, i.e., Euclideanism includes both empirical and rationalistic foundations of the science in question.9 For mechanics this means that it includes theories whose first principles are allegedly revealed by ‘the light of reason’ (Descartes) as well as theories whose first principles are allegedly ‘deduced from phenomena’ (Newton). Both kinds of justifications can be found in eighteenth-century mechanics, and in many textbooks they are inseparably interwoven. D’Alembert, Euler and Lagrange could well illustrate the (more general) thesis that the decisive philosophical feature of rational mechanics at this time cannot be understood in terms of the traditional dichotomy ‘rationalism/empiricism’. This epistemological pattern is hardly suitable for grasping the development of mechanics into a highly organised body of knowledge. Largely independent of epistemological fixations, it is probably the search for certain,  A remarkable, though not very influential exception is Lazare Carnot; see his Principes. A detailed analysis of Carnot’s work can be found in Gillispie, Lazare Carnot Savant. 9  Lakatos makes clear that the dichotomy ‘Euclidian/Empiricist’ (or later: ‘Euclidian/Quasi-­ empirical’) applies for whole theories, while single propositions are traditionally qualified as ‘a priori/a posteriori’ or ‘analytic/synthetic’: “[…] epistemologists were slow to notice the emergence of highly organized knowledge, and the decisive role played by the specific patterns of this organization” (ibid., 6) This holds true especially for mechanics. The traditional empirical/rationalistic dichotomy conceals the common basis of infallibility and is not very useful historiographically (ibid., 70–103). 8

5  Order of Nature and Orders of Science

107

evident and general first principles and for suitable procedures of deductive inference with the overall aim of arriving at (possibly all) valid ‘special’ laws, which characterises mechanics at the time in question: different epistemological justifications, but equal metatheoretical fixations. Thirdly, Lakatos’ concept, used as a label, makes explicit that Euclidean geometry served as the model science for mechanics. This does not only mean that all relevant mechanical knowledge can be brought under an axiomatic-deductive structure, but also that it possesses the same distinctive characteristic as any other mathematical knowledge: infallibility. In applying ‘Euclideanism’ in Lakatos’ sense to rational mechanics from Newton to Lagrange,10 I would like to add some metatheoretical features which are not to be found in Lakatos’ work, but seem to be in line with his understanding of Euclideanism as the dominating ‘classical’ concept of science: First, I regard it as a general characteristic of mechanical Euclideanism that its principles are true in isolation. This does not necessarily mean that they are logically independent from other principles, but rather expresses the fact that holism (in the sense of Duhem and Quine) is alien to mechanical Euclideanism: The set of principles at the top is not interpreted as one logical conjunction, which (as a whole) is true, but as an aggregate of individual principles which are true and therefore applicable to the same physical system without ‘interfering’. That is, for example, the reason why two principles like the law of inertia and the law of gravitation, though they seem to contradict each other in a certain sense,11 can coexist in Newton’s Principia as axioms. A second addition refers to the metatheoretical status of each element of a theory: This status is immutable, i.e., it cannot change with the context of application. The law of inertia, for example, being understood as a synthetic axiom, cannot ‘degenerate’ into an analytic definition (of being free of external forces).12 Thirdly, the set of principles of mechanics is understood not only as necessary and sufficient to deduce all accepted special laws (thereby altogether making them into proper laws) and to explain all phenomena in question. It is also understood as unique in the sense that no second, fundamentally different set is possible. The order of science is a unique representation of the order of nature. There is one (and only one) true mathematical science of nature, and it is defined by their mathematical principles or axioms. The fourth and last addition is of limited range in the temporal aspect: I claim that the early programs of classical mathematical philosophy of nature (Descartes’, Newton’s, Leibniz’ program) have in common that the irreducible, basic concepts of mechanics, as they appear in its principles, bear ontological burdens, i.e., to these concepts is ascribed a fundamentum in re in their actual scientific metaphysics: To space, time and mass, indispensable for any kind of mechanics, are added the  In case of Lagrange, the term “Rubber Euclideanism” (ibid., 7, 9) would be more appropriate; see Sect. 5.4.3 of this paper. 11  For a detailed discussion see Hanson, Newton’s First Law. 12  Ronald N.  Giere exemplifies in ch. 3 of his Explaining Science that this classical demand of ‘metatheoretical invariance’ is not accepted by modern philosophy of science. 10

108

H. Pulte

concept of vis viva in Leibniz’ program, rooted in his ontology of primary and derivative forces,13 and the concept of (external and directive) force in Newton’s program.14 As no concept enters the level of mathematical principles which is not ontologically relevant in itself or ‘derived’ from ontological principles (Leibniz), we can characterize the early programs as different types of mathematical realism15 or (partly) even of mathematical essentialism: Their first principles reflect the causal relations of nature.

5.2.2 Axiomatic Structure and Empiristic Methodology In how far does Newton’s program fit to these characteristics? It has often been stressed that the Principia ‘follows’ the standard of Euclid’s Elements: The formal structure of the Principia, distinguishing definitions, axioms, propositions, corollars etc., makes this quite clear. It is, of course, easy to see that the definitions and so-­ called axiomata sive leges motus do not ‘contain’ the lower-level propositions of the deductive structure in the sense of Euclid’s geometry. Newton frequently introduces hypothetically16 further propositions (for example laws of forces), concrete examples etc. and than uses the axiomata in order to derive conclusions which are empirically testable. But it has to be kept in mind that the empirical verification (or falsification) aims only at the hypothesis introduced, not at the axiomata. Are they hypothetical in the broadest (modern) meaning, i.e., propositions not yet acknowledged to be true and therefore regarded as revisable in the light of new experience? This is part of the question of whether Newton’s mechanics is Euclideanistic in Lakatos’ sense. Euclideanism in Lakatos’ sense obviously means more than a formal analogy to Euclid’s Elements. It implies, first and above all, truth and infallibility of the first principles (or axioms) of the science in question. This ascription is perhaps easy to accept in the case of Descartes, but might be somehow provocative in the case of Newton.17 The reason seems obvious: Newton claimed that he ‘deduced’ all of his  The concept of force in Leibniz’s physics is analysed in some detail by Stammel, Kraftbegriff.  “Force was an entity ontologically existent in the universe” (Westfall, Force, 87). 15  It has to be kept in mind that mathematical realism in my sense only implies the ontological relevance of all concepts which are actually used in mathematical principles. This does not mean, however, that all ontologically relevant concepts enter these principles. The concept of impenetrability, for example, is ontologically relevant for all important programs of the time in question but does not (and cannot) play a role in its mathematical formulation, because it has no quantitative meaning. It is a concept which later disappears from the textbooks of mechanics, though it is still present in some textbooks of general physics in the first decades of the nineteenth century. 16  This is probably the reason why it was frequently presented as a model of the ‘hypothetical-­ deductive’ concept of science (see, for example, Blake, Isaac Newton). 17  Therefore, I can and will restrict my attention to Newton in this context: I take it for granted that mechanics in the tradition of Cartesian or Leibnizian rationalism is accepted as ‘Euclideanistic’ in the sense described above. 13 14

5  Order of Nature and Orders of Science

109

laws, the axioms or laws of motion included, from phenomena. His discussion of the method of ‘analysis and synthesis’ and his methodologically articulated empiricism in general are most often understood as an implicit rejection of all Euclideanistic leanings, as they are (‘clearly’ and ‘distinctively’) to be found in Descartes’ philosophy of science: a hallmark not of an axiomatic-deductive, but of a hypothetical-­ deductive science. I do not agree with such a view, the outcome of the efforts of logical empiricism to make Newton its patron saint. Classical empiricism, as represented by Newton, does not ‘automatically’ imply fallibility of laws or even of first principles: Hertz’ famous dictum, “that which is derived from experience can again be annulled by experience” (Hertz, Principles, 9) is not a part of this doctrine. Quite on the contrary, its basic attitude can be described like this: ‘That which is derived from experience (by careful, gradual induction) can never be annulled by (further) experience’. Without going into the details of Newton’s allegedly ‘empirical’ foundation of his axioms18 and without discussing the vast literature on his philosophy of science, I would like to focus on the status of Newton’s so-called ‘axioms’. (For recent general accounts of his methodology, see Ducheyne, The Main Business, Harper, Isaac Newton’s Scientific Method, for its reception in the eighteenth century see Pulte, ‘Tis much Better to do a Little with Certainty.) Interestingly enough, Newton is pretty cautious with statements about the ‘axiomatic’ status of his laws of motion, the difference between axioms and ‘lower level’-laws, the possibility of excluding all ‘hypothetical’ elements from law statements in general, and from the laws of motion in particular. The reason is that his empiricism yields no epistemological criteria of demarcation between axioms, laws and hypothesis though he obviously wants to distinguish axioms and ‘usual’ laws as well as laws and hypothesis. The whole methodology, as it is laid down in the Regulae philosophandi of the Principia, in the Queries of the Opticks and elsewhere, contains but one positive instruction of what to do when an inductive generalisation (“conclusion”) conflicts with experience: “[…] if no Exception occur from Phaenomena, the Conclusion may be pronounced generally. But if at any time afterwards any Exception shall occur from Experiments, it may then begin to be pronounced with such Exceptions as occur.” (Newton, Opticks, 404). Conflicting observations or experiments cannot falsify general conclusions, but only restrict their range of application. Falsification is even excluded, because according to Newton’s empiricism both the conflicting phenomenon (“Exception”) and the inductive conclusion are indisputably true. But Newton’s solution – restriction of the range of applicability by the enumeration of ‘exceptions’  – bears a problem in the case of axioms: According to his  Remember, for example, the instances given as ‘empirical’ support of his first law, according to which “every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it”: We find projectiles, “so as far as they are not retarded by the resistance of the air,” a rotating top which “does not cease its rotation,” and “even the greater bodies of the planets and comets” (Newton, Mathematical Principles, 13). There is obviously no observation which shows the uniformity and rectilinearity of ‘natural’ motion. 18

110

H. Pulte

empiristic methodology, they can work as axioms for the (one and only) reason that they are most general, or even of unrestricted generality. On the other hand they should be open for restriction, if we take his methodology seriously. But what Newton really does, in contrast to his methodology, is to ‘immunise’ his axioms not only from falsification, but also from restriction. “As in Geometry […] so in experimental Philosophy,” he says, hypotheses and “first Principles or Axioms” have to be sharply separated: “These Principles are deduced from Phaenomena & made general by Induction: wch is the highest evidence that a Proposition can have in this philosophy […]”; with respect to a possible falsifier (more appropriate: ‘restrictor’) he argues that “there is no such phaenomenon in all nature.”19 Newton sometimes parallels his laws of motion with the axioms of geometry in order to underline the certainty he ascribes to these laws. “Hypothetical philosophy,” as proposed by “[Des]Cartes, Leibnitz & some others” is contrasted with his own “experimental philosophy,” which starts from “the three Laws of motion [which] are proposed as general Principles of Philosophy tho founded upon Phaenomena by no better Argument then that of Induction without exception of any one Phaenomenon” (Newton, Correspondence, V 398f.). He also reveals essentialistic leanings when he compares the knowledge of these principles with knowledge of the impenetrability of bodies (ibid. 399) – a property understood as most general and belonging to “the foundation of all philosophy” (Newton, Mathematical Principles, 399). Newton obviously saw that his Euclideanism could not be founded on his empiristic methodology, though methodology was necessary to ‘disguise’ a certain essentialism with respect to first laws which cannot be established empirically. He therefore uses several other arguments in order to underpin the assumed certainty of principles – for example physico-theological arguments, especially with respect to his law of gravitation.20 Furthermore, the laws of motion and their corollaries are summed up by the comment “Hactenus principia tradidi a mathematicis recepta & experientia multiplici confirmata,”21 a phrase that might appeal to the koinai ennoiai or communes animi conceptiones at the time of Euclid’s Elements (Szabo, Geschichte, 378–389), i.e., to principles which are neither demonstrated nor in need

 Newton to Cotes on March 28, 1713 (Newton, Correspondence, V 396–397). Newton’s statement was provoked by an example which was used by Cotes in order to explicate his foundations of mechanics: “[…] ‘till this Objection be cleared I would not undertake to answer any one who should assert You do Hypothesim fingere […]” (ibid., 392). Though Cotes’ thought experiment is untenable (and therefore is not discussed here), it should be noted that Newton’s rejection relies on the undubitable truth and generality of his axiomata. 20  See, for example, his famous letter to Bentley of December 10, 1692 (Newton, Correspondence, III 233). The law of gravitation does not, of course, belong to his axioms in a strict sense. But its certainty is vital for Newton in order to show that his celestial mechanics (presented in Book III of the Principia) can be based on a set of certain principles, i.e., his three laws of motion and the law of gravitation. 21  Newton, Principia, 64. Wolfer’s German translation (“von den Mathematikern angenommen”; Newton, Mathematische Prinzipien der Naturlehre, 39) promotes ‘conventionalistic’ misinterpretations, while the brand-new translation by Volkmar Schüller (“von den Mathematikern allgemein anerkannt.”; Newton, Mathematische Prinzipien der Physik; 40) does justice to the original meaning. 19

5  Order of Nature and Orders of Science

111

of demonstration, though accepted as true by all mathematicians. In a different context, Newton even describes a violation of the first law as an event which would disturb “the whole frame of nature, & in the general opinion of mankind is as remote from the nature of matter as […] [penetrability]” (Newton, Correspondence, V 399). ‘The general opinion of mankind’: Remember that for Galileo, a generation earlier, Newton’s first law was less than evident  – it was unknown to him in the ‘linear’ form presented by Newton.

5.2.3 Newton’s Euclideanism These references are meant to throw some light on an antagonism between Newton’s empiristic methodology and his actual attitude towards his axiomata: He claims that they are most general results of induction, and therefore can be understood as laws of nature. But he actually introduces a set of ingeniously chosen mathematical principles which function as axioms of the deductive structure of the Principia: Truth is ‘injected’ from the top, and its flow down to the level of phenomena cannot be turned round by conflicting observations. They work de facto as synthetic propositions a priori. Kant’s interpretation of the Principia was closer to the historical truth than later, ‘modernising’ attempts. The certainty of principles Newton supposed is only included in his methodology ex negativo, i.e., only to the extent that notable exceptions from valid inductions are not counted as falsifiers, but as ‘restrictors’. But axioms are obviously exempted from restriction without methodological justification: greatest generality and certainty coincide in his philosophy of science. This coincidence is not (and cannot be) explained by his methodology, but is rather rooted in his ontology: The material truth of axioms, inundating the whole system of propositions, stems from mathematics itself. Newton holds the view that geometry is not a science that can be separated or abstracted from mechanics, but a science which shows how to apply mechanically constructed entities to physical reality.22 This application poses no problem in itself: As they stem from nature, they are applicable to it. Rectilinearity, for example, is ‘natural’; Euclidean geometry and simple algebraic relations (proportionality, for example) are empirically relevant. This may serve as an illustration of the thesis that mathematics – in Newton’s case as in classical mathematical philosophy of nature in general – is ‘semantically laden’.

 “[…] for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us how to draw these lines, but requires them to be drawn, for it requires that the learner should first be taught to describe these accurately before he enters upon geometry, then it shows how by these operations problems may be solved. To describe right lines and circles are problems, but not geometrical problems. The solution of these problems is required from mechanics, and by geometry the use of them, when so solved, is shown; and it is the glory of geometry that from those few principles, brought from without, it is able to produce so many things” (Newton, Mathematical Principles, XVII). 22

112

H. Pulte

Without going into the details of Newton’s philosophy of mathematics, it seems clear that his mathematical realism23 is at the core of what I described as his mechanical Euclideanism. This is the reason why the ontology of ‘absolute, true and mathematical space’ and ‘absolute, true and mathematical time’ is indispensable for his attempt to found rational mechanics. With respect to these entities, his axioms function as synthetic principles a priori. The traditional, rationalistic-minded Euclideanism demanded metaphysical support for these principles (as causes are equal to its effects). Newton rejects such support, though he cannot renounce metaphysics in his attempt to provide mechanics a ‘secure’ foundation: Methodological inductivism is not sufficient to reach this end. In general, it can be said that for Newton’s safeguarding of epistemic claims regarding the certainty of ‘empirical’ principles the role of mathematics can hardly be overestimated (see Guicciardini, Isaac Newton).

5.3 Newtonian and Analytical Perspectives: Euler’s Program of Rational Mechanics It was Clifford Truesdell’s huge contribution to eighteenth-century rational mechanics which has shown that Euler is its towering figure. Especially with respect to the development of its principles, his oeuvre is unique: We owe to him a sound formulation of the principle of least action (1744), the general formulation of ‘Newton’s’ second law (1750), the law of conservation of moment of momentum (1755), the differential equations of an ideal liquid (1755), the general equations for the rotation of rigid bodies (1760) and numerous other achievements. Truesdell made Euler’s immense work accessible to the history of science, thereby changing our understanding of its development in the course of the eighteenth century dramatically.24 Nevertheless, Truesdell’s presentation of Euler’s rational mechanics is one-sided and, in a way, misleading: According to him, “the history of rational mechanics is neither experimental nor philosophical, it is mathematical,” (Truesdell, Program, 11) and consequently he presents Euler’s contribution by and large as a mathematical one. But Euler has more to offer. As Ernst Cassirer remarked, he is “the true and classical witness of the spirit of mathematical philosophy of nature,” and the philosopher-­ scientist who “most completely represents the scientific consciousness in the middle of the eighteenth century.”25 While Euler’s work by and large can support Truesdell’s claim that rational mechanics was not experimental, it is by no means suitable to 23  A label already applied to him by Jammer, Problem des Raumes, 110; see Burtt, Metaphysical Foundations and Strong, Newton’s Mathematical Way, for similar judgements. 24  See Sect. 5.1.3 for the ‘non-Kuhnian’ implications of this change. 25  Cassirer, Erkenntnisproblem, 472. According to Cassirer the second description was given by a historian of mathematics of his time, but he agrees with this judgement, especially “with respect to the methodological manner of the interpretation and treatment” of scientific problems.

5  Order of Nature and Orders of Science

113

show that it was not philosophical. Quite the contrary: Euler’s rational mechanics is both mathematical and philosophical in its character, and I claim that both parts are indispensable in understanding the coherence and continuity of his program. The reason, however, why I chose Euler’s mechanics as the ‘fulcrum’ between Newton and Lagrange is not so much its broad scope, nor its mere success in uncovering mechanical principles. The main reasons are rather that his program can serve, first, as a prototype of Euclideanism in the middle of the eighteenth century. Euler frequently states that rational mechanics has to start with a few necessary principles and that all changes in nature have to be explained by these principles in a deductive manner. His Euclideanism can be further described as essentialism in Popper’s sense, because it proceeds from the idea that “all laws of nature can be deduced necessarily from one analytical principle (the essential definition of ‘body’).” (Popper, Logik der Forschung, 385). It was Euler’s main concern to base mathematical mechanics on a theory of matter in which primary forces – regarded as incompatible with inertia  – have no place. As I tried to show earlier, his scientific metaphysics and his philosophy of science were strongly influenced by Descartes (Pulte, Prinzip, esp. 110–121). The Cartesian ideal of a rational mechanics on an equal footing with geometry is always present in Euler’s works, as it is in d’Alembert’s.26 Euler’s Mechanica (1736), d’Alembert’s Traité (1743) and Euler’s Theoria motus (1765) are the three major textbooks in the second third of the eighteenth century, and their most important common feature is Euclideanism. Notwithstanding its Euclideanism, Euler’s program is, secondly, successful in integrating the results of other programs, namely Newton’s and Leibniz’, though Euler rejects the Newtonian mechanics of forces as well as Leibniz’ dynamics on philosophical grounds. There is a ‘peaceful coexistence’ of diverging elements of different programs to be found in his work. In particular, we find both an elaboration of a ‘Newtonian’ axiomatisation (a label which will need some qualification) and the beginnings of an ‘analytical’ axiomatisation of mechanics (principle of least action, conservation of vis viva) in his work. I am interested in how this integration worked and to what extent it changed the character of mechanical Euclideanism in the middle of the eighteenth century. For the sake of brevity, I will concentrate on four points which seem to me illuminating in these two respects.

5.3.1 ‘Synthetical’ Beginnings of Analytical Mechanics Lagrange, in his Méchanique Analitique, called Euler’s Mechanica (1736) the first book “in which analysis was applied to the science of motion.”27 Euler himself remarked that predecessors like Hermann and Newton treated mechanics “in the

26 27

 See Hankins, Jean d’Alembert, for a detailed discussion of d’Alembert’s Cartesian leanings.  Lagrange, Mécanique Analytique (2nd ed.), I 243. This passage is not included in the first edition.

114

H. Pulte

way the ancients did, by synthetic geometrical demonstrations,” while he preferred the “smooth and uniform method” of analysis (Euler, Mechanik, I 3). Pierre Varignon and others paved the way for the use of the calculus in mechanics (see Blay, La Naissance; Shank, Calculus-Based Mathematical Physics). However, as far as the extensive use of the higher calculus28 for the organisation of mechanical knowledge is concerned, Euler’s Mechanica was indeed the starting point of what we today call ‘analytical’ mechanics. But from a metatheoretical point of view, Euler’s first mechanics is a traditional, synthetic one: It begins along ‘Newtonian lines’ with a discussion and definition of basic concepts like space, place, time, motion, rest, mass (via inertia) force, and proceeds with the laws of motion, which are, contrary to Newton, ‘demonstrated’ and therefore “not only true, but necessarily true.”29 Nearly the whole first chapter (§§ 1–82), parts of the second (§§ 99–117) and smaller parts of the following chapters are devoted entirely to the conceptual foundations of mechanics and problems of measurement. The same could be shown for Euler’s second major work on mechanics, his Theoria motus (1765) and for numerous smaller articles. It has been asserted that the appearance of analytical mechanics eo ipso marked a ‘methodological turn’ and even a fundamental change in the ‘concept of science’ to the extent that analytical mechanics disregarded conceptual and methodological foundations and made experimental data its methodological starting point.30 This thesis, however, does not withstand detailed historical examination.

5.3.2 ‘Newtonian’ Axiomatisation Without Newtonian Ontology Aside from all novelties with respect to content, there is also a new metatheoretical element in Euler’s program, though not the one rejected above. I would like to illustrate this new element with just one example: Euler’s axiomatisation of mechanics is, by and large, a Newtonian one. He accepts Newton’s first and third laws as starting points of his mathematical theory and tries to ‘demonstrate’ their a priori status, and he was the first who established the general form of Newton’s second law in his Découverte d’un nouveau principe de mécanique (1750).31 At this time he believed that it would “include all the laws of mechanics” and could serve as the “unique fundament” of the whole of  To be more precise: the ‘explicit’ use. It is well known that Newton made use of calculus, but later ‘translated’ his results in a geometric language in order to facilitate the reception of his Principia. 29  See Euler, Mechanik, I 49. I cannot discuss his various ‘demonstrations’ in this paper. 30  See Mittelstraß, Neuzeit, esp. 301–302; see endnote 7 above, and Pulte, Axiomatik und Empirie, ch. IV.6. 31  The relevance of Euler’s Découverte is underlined by Truesdell, Program and Pulte, Prinzip, esp. 151. 28

5  Order of Nature and Orders of Science

115

mechanics (including the movement of continua, percussion and all processes which were presumed to be based on action at a distance).32 Euler did not, however, accept Newtonian, ‘directive’ forces as primary ontological entities, neither in his Mechanica nor later. There is a discrepancy between his ontology on the one hand and the basic concepts33 of his mathematical theory on the other. This seems to contradict the essentialism I ascribed to him, and has indeed provoked interpretations of his program as being ‘instrumentalistic’. But as was shown elsewhere, Euler never accepted this ‘gap’ between the mathematical part of his mechanics and his scientific metaphysics as final. He always looked for an explanation of forces by ‘matter and motion’ and found such an explanation in the impenetrability of matter, determining forces by the principle of least action and thereby basing his mathematical, ‘Newtonian’ mechanics on a ‘quasi-Cartesian’ theory of matter.34 Though Euler’s solution is ‘conservative’, in so far as it sticks to traditional essentialism, the fact remains that mathematical axiomatisation and ontological foundation differ: Force is a central and irreducible concept of his mathematical mechanics, but alien to his concept of matter. This marks a difference between Euler’s program and ‘earlier’ programs of mathematical philosophy of nature, as characterised above. The case of Euler shows, as other cases (like d’Alembert and Maupertuis, for example) would show likewise, a growing tension between the mathematical treatment of rational mechanics and its foundation in scientific metaphysics. But what was its root?

5.3.3 ‘Inflation of Principles’ and Metatheoretical ‘Sliding of the Center of Gravity’ It has often been claimed that Newtonian mechanics made its way on the continent, despite all philosophical resistance, because it was empirically successful, especially in celestial mechanics. Applied to Euler, this might serve as a convenient explanation of how he dealt with forces: He was too much of a mathematician to dispense with the fruitful Newtonian mechanics of forces, and too much of a (Cartesian) philosopher to recognise forces as primary entities. This argument should not be rejected indiscriminately, but it is of limited range with respect to the foundations of mechanics: First, it presupposes a prevalence of ‘empirical success’ over ‘rational foundation’, which seems problematic for the

 Euler, Découverte, 88–89. Later he discovered that the principle of moment of momentum has to be added as a separate ‘axiom’. 33  ‘Basic concepts’ in this context always means ‘concepts which are used in the actual axiomatisation of mechanics’. 34  For all details see Pulte, Prinzip, 150–181, esp. 176. 32

116

H. Pulte

working philosopher-scientists in this period, especially for Euler. Secondly, it is applicable only in favour of the Newtonian program. But how to explain, for example, that Maupertuis – first an ardent disciple of Newton’s philosophy and opponent of Leibniz and Descartes – rejected Newtonian forces in his later career and tried to replace Newton’s laws by his ‘non-causal’ or ‘descriptive’ principle of least action, thereby making Leibniz’ concept of action the primary concept of his mathematical mechanics? How to explain the general tendency towards general principles without causal claims (least action, virtual velocities etc.)? It seems to me that questions like these cannot be answered satisfactorily by ‘empirical success’, nor by a general epistemological switch from ‘rationalism to empiricism’. We need to consider the practice of mathematical physics (under the premise of diverging forms of Euclideanism) in order to understand these features. What characterises rational mechanics above all in the second third of the eighteenth century is an inflation of principles: Numerous principles of statics which had to be integrated into a general science of mechanics, the principle of the conservation of momentum (or impulse, in modern terminology) for impact, the principle of vis viva conservation for (elastic) impact and central force problems, the three so-called Newtonian principles, the principle of moment of momentum, Maupertuis’ loi du repos and the general principle of least action, d’Alembert’s principle and the principle of virtual velocities, d’Arcy’s principle, Koenig’s principle etc. – not to mention the numerous principles of continuum and fluid mechanics which had to be integrated into the rational mechanics of mass points. All of these principles grew out of the study of special problems and idealised physical situations, whose relevance for a mathematical theory of nature was determined by the current scientific metaphysics. They were confirmed by applications to different problems, and often gained their status as ‘principles’ by this restricted applicability alone. They were not ‘deduced’ from higher principles, nor ‘deduced’ from phenomena (in Newton’s sense), but revealed their relevance by their (possibly limited) explanatory power. In a word: Their status as a ‘principle’ was not due to metaphysical or empirical foundation, but to the deductively proceeding practice of mathematical physics alone. But Euclideanism cannot tolerate a plurality of principles, especially when they grew out of ‘alien’ scientific metaphysics. It strives for a small number of axioms, from which lower-level principles must be deduced: Plurality of principles is a result of different scientific metaphysics, unity is the aim of Euclideanism.35 So if a (possibly ‘basic’) principle of one program turns out to be of (probably limited) deductive power for a different program, it has to be integrated in the deductive structure of the latter program, thereby ‘explaining’ its applicability. The ‘mania of demonstration’ (Mach, Mechanik, 72) and the fact that it was sometimes unclear  As d’Alembert put it in the title of his great textbook: “Traité de Dynamique, dans lequel les loix de l’equilibre & du Mouvement des Corps sont réduites au plus petit nombre possible, & démontrèes d’une manière nouvelle, & où l’on donne un Principe général pour trouver le Mouvement de plusieurs Corps qui agissent les uns sur les autres, d’une maniére quelconque.” 35

5  Order of Nature and Orders of Science

117

that ‘something must be assumed’ (Truesdell, Program, 10) illustrate the efforts made in order to reach systematic order and, at the same time, that the ties to current scientific metaphysics were loose. To give a concrete example: Conservation laws have no place in Newton’s program. They were alien to Euler’s scientific metaphysics, too: Euler was suspicious that vis viva and impulse (to use the modern word), introduced as basic concepts of mechanics, would mean introducing ‘indestructable’ entities – essential forces (or active principles), which are not allowed by his theory of passive matter. Johann Bernoulli and other ‘Leibnizians’ convinced him, however, that the concept of vis viva is of considerable interest to understand the different cases of elastic impact, and it also became important for his own investigation of central force problems. Euler therefore introduced vis viva as a derived concept, i.e., as the line integral of (Newtonian) force, and he also introduced impulse as a derived concept, i.e., as the time integral of (Newtonian) force.36 Problems of conservation of vis viva and impulse were thereby transformed into problems of Newtonian mechanics and, in a way, to a problem of mathematics: When does an integrable force function exist? It depends on the answer to this question, in which (special) case the famous vis viva controversy can be decided in favour of Leibniz or not. The problem of force conservation, which was at the bottom of one of the most tedious disputes between the different programs of mechanics in the eighteenth century, thus became, as Euler said, a mere dispute about words (“logomachie”) (Euler, De la force, 34). Conservation of vis viva, an ‘axiom’ of Leibniz’ mechanics, and conservation of impulse, (in nuce) an axiom of Descartes’ mechanics, are no longer axioms or ‘principles’ in Euler’s program, but derived laws, which still can be used, however, in order to explain special physical phenomena. This example, too, refers to the importance of the ‘Newtonian’ conceptual framework for Euler’s program. But Euler’s Newtonian leanings on the level of mathematical presentation are in this context not the main point of my argument, and it is neither the immediate empirical success of this framework (i.e., the deductive explanation of phenomena) nor the idea that certainty and evidence of basic axioms must be assured by proper ‘demonstrations’, based on scientific metaphysics. Here, my main point is rather the deductive organisation of mechanics itself: It is not sufficient to have ‘certain and evident’ axioms, it must be shown that the whole mechanical knowledge accepted as true falls under these axioms. To use Lakatos’ metaphor: It is not sufficient to introduce ‘truth from the top’ by indubitable axioms, it is also essential to be able to lead truth down to the bottom by building ‘truth-­ preserving channels’ (Lakatos, Philosophical Papers, II 28). This is a characteristic feature of Euclideanism in a developed (or advanced) stage: it focusses no longer on how to come to evident and certain axioms, but on the deductive structure of the growing body of knowledge. Alwin Diemer, who seems to have been the first German philosopher of science who tried to find criteria of demarcation between

36

 See, for example, Euler’s De la force and his Anleitung.

118

H. Pulte

‘classical’ and ‘modern’ science, used the metaphor of the “decline of the centre of gravity” to illustrate such a ‘structural’ development within classical science.37 In the course of the eighteenth century, a lot of mathematical and conceptual work was done in order to build ‘truth-preserving channels’ for the deductive structure of rational mechanics. Its outcome was, as already becomes visible in Euler’s huge oeuvre, a hierarchically organised system, including elements of the different programs, but ‘crowned’ by Euler’s transformation of Newton’s three laws of motion. But remember the ‘decline of the centre of gravity’: What counts here is the truth of the whole body of mechanical knowledge, which is – according to the Euclidean concept of science – ‘represented’ by its axioms in a formal way rather than ‘condensed’ in these axioms in a material way. From this shift results a growing independence of mathematical physics from the philosophical foundations of its principles, be these foundations ‘empirical’ or ‘rational’: It is the deductive power of principles rather than their empirical contents, their axiomatic status rather than their status as ‘laws of nature’, their formal truth rather than their material truth, which become important. To borrow again from Lakatos’ picture: If the deductive channels are filled with truth, and the truth flow down to the phenomena can be guaranteed, the source of truth becomes less important. Euclideanism continues to shape the concept of science, but it becomes a syntactical rather than a semantical concept of science. This development of rational mechanics in the course of the eighteenth century is reflected by two main features: a decline of metaphysical discussions and a rise of deductive organisation by appropriate mathematical techniques. The great controversies about the ‘nature’ of space and time, about the status of gravitation, about the existence of entities which are conserved in all nature, belong to the first half of the century rather than to the second, while ‘technical’ discussions about the calculus of variations, potential theory, differential equations and perturbation theory were prominent in the second half rather than in the first.

 “Wenn von der geistigen oder logischen Evidenz als einem Wissenschaftskriterium [klassischer Wissenschaft] gesprochen wird, so soll ein relativ neutraler und umfassender Begriff verwendet werden, da damit ein Komplex mit vielerlei Nuancen gemeint ist. Genau genommen gilt das Wort nur für die frühe Wissenschaft, später tritt mehr und mehr die Idee der logischen Struktur, schließlich der logischen Ordnung als System an seine Stelle. Im einzelnen ist dazu folgendes zu sagen: Daß Wissen im Sinne des später so verstandenen wissenschaftlichen Wissens keine unmittelbare Evidenz in sich trägt, keine unmittelbare Wahrheit in sich birgt, ist eine implizite Voraussetzung der Theorie—eigentlich bis zur Gegenwart. So stand wie über der episteme der nous, so über [der] scientia als der ‘mittelbaren’ der intellectus bzw. Die intelligentia als die eigentliche unmittelbare Einsicht der letzten Wahrheiten, der Axiome. Durch die Evidenz der Ableitung, der ‘De-duktion’—(‘Apagoge’)—wird dann die Sicherheit und Gewißheit der anderen Sätze garantiert. Die wissenschaftliche Gewißheit und insofern die Wissenschaftlichkeit liegt also nicht so sehr in der ursprünglichen Schau als der gesicherten, d.h. systematischen Ableitung. Dies wird zunächst unmittelbar gesagt und sinngemäß versucht, die entsprechenden Syllogismusstrukturen als die entsprechenden Wege zu entwickeln. In zunehmendem Maße verlagert sich dann später der Schwerpunkt; er rutscht gewissermaßen ‘abwärts’ […].” (Diemer, Begründung, 30–31). 37

5  Order of Nature and Orders of Science

119

Euler himself saw this shift fairly early, and used it as an argument to restrict the impact of traditional metaphysics on science: In his famous Réflexions sur l’espace et le tems (1748) he explicitly stated that it is mistaken to think that mechanics or mathematical physics in general receive true foundations from metaphysics, but that, vice versa, metaphysics has to model its basic ideas in such a way that its conclusions agree with the “indisputable” principles of mechanics (Euler, Réflexions, esp. 376f.; Cassirer, Erkenntnisproblem, 475–479). Mathematical physics does not (and cannot) dispense with philosophical foundations, but it can (and must) determine what has to be founded. Not autonomy of science from philosophy, but a certain ‘equilibrium’ of science and philosophy is his object  – a model which resembles Hilbert’s distinction of mathematics and philosophy of mathematics (‘metamathematics’).

5.3.4 Analytical Principles of Mechanics The development sketched above is perhaps best illustrated by analytical mechanics,38 to which Euler contributed substantially, too. The rise of analytical principles like the principle of least action or the principle of virtual velocities cannot be understood by the Mach-Kuhnian pattern of rational mechanics as ‘normal science’ in the tradition of Newton’s Principia (see Sect. 5.1.3). These principles originated from concrete problems, and their development was driven, at first, by other programs and (partly) by substantial philosophical difficulties of the Newtonian program – and not by ‘formal’ demands. The principle of least action, for example, was understood as an alternative to Newton’s foundation of mechanics by Maupertuis as well as Euler. Both underlined its descriptive and, so to speak, ‘phenomenological’ character in contrast to its explanatory function in terms of a Newtonian mechanics of forces. While the concepts of causality and force ran into a crisis, it was meant to provide a new foundation of mechanics, which had not to make use of these problematic concepts. Only later, with Lagrange, it became a merely formal alternative to a ‘Newtonian’ axiomatisation of mechanics,39 i.e., a part of ‘normal Newtonian science’ in Kuhn’s sense.40 I am mentioning this ‘context of discovery’ because it is part of the development described above (see Sect. 5.3.3.) and might best illustrate some of its implications. Again, I will use mainly the principle of least action for illustration.  Note my general use of this technical term: Not all mechanics which uses calculus is called ‘analytical’ (Euler’s Mechanica, for example, is not ‘analytical’ in this sense), but only mechanics in so far as it makes use of principles, which are based on analytical principles, i.e., integral variational principles (like the principle of least action) or differential variational principles (like the principle of virtual velocities). 39  See Pulte, Prinzip, 230–261, for a more detailled discussion of this development. 40  See endnote 4 above; see also Sect. 5.4 for more details. 38

120

H. Pulte

First, the concept of action used in this principle is no longer a concept which is determinated as ‘basic’ by actually scientific metaphysics: Maupertuis picked it up from Leibniz, but it had no genuine meaning in his own mechanics. Being forced to give a ‘higher’ justification of his principle (a demand of traditional mechanical Euclideanism), action became a measure of ‘divine force’ – a retrogression to occasionalism which was not rooted in Maupertuis’ genuine scientific metaphysics. Euler, too, was initially worried about the fact that action could not be justified by clear philosophical arguments. It made its way into his mechanics not because it was rooted in his scientific metaphysics, but because it turned out to be useful. It can generally be said that concepts like action, effort and potential energy, in the case of the least action principle (and Maupertuis’ lois du repos), or virtual work (virtual displacement), in the case of d’Alembert’s principle and the principle of virtual velocities, do not have the same semantic relevance as the basic concepts in the earlier programs of mechanical Euclideanism (like force, velocity, vis viva, etc.). The rise of analytical principles is accompanied by a ‘semantical unloading’ of their basic mathematical concepts. This process is, secondly, parallel to the changing role of analytical principles. They started from special problems, but soon turned out to be applicable to a wide range of phenomena and even to derive a number of more special laws of motion and other laws. Maupertuis and Euler41 extended the principle of least action to optics (derivation of the law of reflection and refraction), to the statics of point masses and continua (derivation of Maupertuis’ lois du repos, the principle of the lever, special forms of ‘Dirichlet’s principle’), to the mechanics of impact (conservation of impulse and, in the case of elastic collision, of vis viva) and to central force problems (derivation of Kepler’s laws and special forms of the equations of motion). This applicability to a wide range of ‘heterogeneous’ problems was unique in the history of mechanics, and it led Euler and Maupertuis to the view that the principle of least action can work as an organising principle of the whole of mechanics, i.e., a principle from which a great variety of special laws of motion and rest can be deduced.42 While metaphysical discussions were prominent in the early career of the principle of least action, its later development was determined by the extension and analysis of its integrative and deductive power. This seems to me exemplary for analytical mechanics in general: The rise of analytical mechanics in the second half of the century highlights the striving of Euclideanism for an axiomatic-deductive organisation of science. But it has to be noted that in the course of this process an important change takes place in so far as principles become formal axioms of science rather than laws of nature. Lagrange’s mechanics is most significant in this respect.  Here I do not distinguish between Maupertuis’ and Euler’s formulations, though they do differ in various details. It is noteworthy that Euler and Maupertuis always stressed that they discovered and elaborated the same principle. 42  This emerges even from the titles of some of Maupertuis’ and Euler’s essays on the principle of least action. See, for example, Maupertuis, Accord de différentes Loix de la Nature qui avoient jusqu’ici paru incompatibles and Les Lois du Mouvement et du Repos déduites d’un Principe Metaphysique and Euler, Harmonie entre les principes générales de repos et de mouvement de M. de Maupertuis. 41

5  Order of Nature and Orders of Science

121

5.4 The Edge of Certainty: Lagrange’s Analytical Mechanics In a way, Lagrange’s mechanics completes the development sketched above though, in a different way, it marks a break with the older tradition, thereby revealing the basic philosophical problems of mechanical Euclideanism. In short, Lagrange’s approach can be described as Newtonian with respect to the philosophy of nature, leading to an ideal of mechanics which tries to explain all phenomena by central forces acting between discrete particles. His philosophy of science, however, was strongly influenced by d’Alembert and Euler. As both his predecessors, he wanted to base mechanics on certain and evident principles: “Mechanics can be understood as a geometry with four dimensions, and the analysis of mechanics can be understood as an extension of geometrical analysis.” (Lagrange, Théorie des fonctions (2nd ed.), 337). Geometry continues to be the ideal of mechanics, though the shape of Euclideanism changes considerably. In trying to illustrate this change, I will confine myself to three major points.

5.4.1 Changing Principles and Concepts Before I come to what I regard to be the main features of Lagrange’s concept of science, I would like to refer to a remarkable, though widely neglected development in Lagrange’s foundations of mechanics: For reasons to be discussed later (see Sect. 5.4.2) Lagrange started his mechanics with analytical principles. In his early career, he had chosen Euler’s principle of least action as “the universal key to all problems, both of statics and dynamics.”43 In his first paper on analytical mechanics, he not only derived from it different ‘integrals of movement’, but also the ‘Newtonian’ (or rather ‘Newton-Eulerian’, see Sect. 5.3.2) differential equations of motion for all conservative forces (Lagrange, Application, 369). This was a remarkable achievement within eighteenth-century rational mechanics, because Lagrange’s paper was the first work “in which an adequate statement of the laws of a fairly extensive branch of mechanics was gotten without the use of an a priori concept of force” (Truesdell, Program, 33). This could have been the starting point of a new conceptual foundation of mechanics which actually was not elaborated until the last decades of the nineteenth century by Helmholtz, Hertz and others. But actually it was no starting point, because Lagrange did not even take notice of it – at least he discussed it nowhere. In later papers as well as in his Méchanique Analitique he rather replaced the principle of least action with his ‘variational’ form of the principle of virtual velocities, thereby reintroducing forces as basic concepts of his mechanics. If the reconstruction given elsewhere (Pulte, Prinzip, 252–258) is right, this switch was due primarily to the fact that the latter principle turned out to be more useful in deductive respects: ‘Deductivity’ wins over conceptual 43

 Letter to Euler of May 19, 1756 (Lagrange, Oeuvres, Vol. 14, 391–392).

122

H. Pulte

foundation – or at least makes conceptual foundation a problem which no longer requires discussion. This is one of the features of Lagrange’s approach to which I will come now.

5.4.2 No Geometry, No Methodology, No (Explicit) Scientific Metaphysics: The New Meaning of ‘Analytical’ From the beginning, Lagrange’s main aim was a coherent deductive system of the laws of rest and motion. Both the history of mechanics and its dominating concept of science (i.e., Euclideanism) make this aim plausible: When Lagrange started his scientific career in the fifties, he was confronted with a totally different state of mechanics than Euler was 20 years earlier. As already mentioned, the mechanics existing then presented a great number of generally accepted laws and so-called principles, including Newton’s laws of motion (in Euler’s form), d’Alembert’s principle and the principle of least action. Lagrange’s Euclideanism could (and had to) operate beyond the level of special examples (as Euler’s), but on the level of more or less general propositions. These propositions were actually presented in an algebraic or even analytic fashion, in which geometry possibly served as a means of illustration,44 but no longer had important foundational or inferential tasks. This is the reason why Lagrange focussed on analytical principles as ‘candidates’ for axioms of his system (see Sect. 5.4.1) and disregarded synthetical or geometrical means. That “no figures are to be found in this work,” (Lagrange, Méchanique Analitique, vi) as he later proudly remarked, is an outcome of the state of affairs of the mechanics of his time and of his Euclideanistic striving for a unique order of science – and not of personal preference, as was sometimes presumed. Nor does this mean, in and of itself, a fundamental change in the concept of science. In modern terms, geometry remained important for Lagrange in the context of discovery (Grattan-Guinness, Recent Researches, 679), but had to be eliminated from the context of presentation and justification. No principles other than the ‘analytical’ could actually do the job of deductive organisation. So much for Lagrange’s neglect of geometry. More serious with respect to a possible change in the concept of science is the absence of nearly any kind of methodology or explicit metaphysical foundation of mechanics (Pulte, Jacobi’s Criticism, esp. 158). Lagrange’s Méchanique Analitique (1788) is the first major textbook in the history of mechanics which I know of which abandons any kind of explicit philosophical reflection. It says nothing about how space, time, mass, force (in Newton’s sense) or vis viva (in Leibniz’ sense) are to be established as basic concepts of mechanics, nor about how a deductive mathematical theory on that basis is possible. Neither are the metaphysical premises of his

 Euler, for example, frequently makes use of geometrical figures, even if he deals with ‘analytical mechanics’ (in the narrow sense defined in endnote 38). 44

5  Order of Nature and Orders of Science

123

mechanics made explicit, nor is there any epistemological justification given for the presumed infallible character of the basic principles of mechanics. Lagrange’s silence about foundational issues is in striking contrast not only to seventeenth-­ century programs of mechanics such as those of Descartes, Leibniz and Newton, but also to the approaches of Lagrange’s immediate predecessors in the analytical tradition, i.e., Maupertuis, d’Alembert and Euler. In short, a century after Newton’s Principia, Lagrange gives an ‘update’ of the mathematical principles of natural philosophy, while abandoning traditional subjects of philosophia naturalis. His bold claim to make mechanics “a new branch” of analysis (Lagrange, Méchanique Analitique, vi) by ‘reducing’ it to calculus and reducing the calculus to a sound algebraical basis in order to achieve a secure foundation of the whole of mechanics (Grabiner, The Calculus as Algebra, 7–10) can and should be understood not only as a rejection of geometrical means, but also as a rejection of explicit philosophical foundations in the broadest sense. This is the most important metatheoretical novelty of Lagrange’s program. Insofar as Lagrange is not interested in the conceptual foundations of his mechanics, and even changes his basic concept for reasons of ‘formal economy’ (see Sect. 5.4.1), his mechanics can no longer be understood as a Euclideanistic enterprise (in the ‘traditional’ sense, see Sects. 5.1.2 and 5.2.1), but rather as an example of mathematical instrumentalism.45 Lagrange obviously shares, by and large, the scientific metaphysics underlying the Newtonian program (Pulte, Prinzip, 230–240), but this fact is not reflected in his ‘purely mathematical’ mechanics. Central forces, free mass-points, absolute space, absolute time and intuitive natural laws on the one hand, mathematical concepts of potential and kinetic energy, masses under ideal constraints, a ‘structural’ (with respect to the invariance properties of variational principles) rather than Euclidean space, time as a mere ‘fourth coordinate’ and abstract variational principles on the other hand: Mathematics serves as a formal frame, but is ‘unloaded’ of meaning. We saw that in Euler’s program, too, basic assumptions about nature and mathematical presentation deviated (no primary ontological forces here, but basic ‘mathematical’ forces there, for example). But this deviation could be cleared up by a

 In order to avoid misunderstandings, I must emphasise that ‘instrumentalism’ here refers to philosophy of nature (I1) rather than to philosophy of science (I2): Lagrange did not base his mathematical formulation of mechanics on an analysis of the fundamental concepts of philosophy of nature like matter, force, space and time, as did Descartes, Newton, Leibniz, d’Alembert, or Euler. Instead, he chose the basic concepts and laws of his theory in a mathematically convenient manner. This is what I call instrumentalism (I1) and which is best illustrated by Lagrange’s switch described in Sect. 5.4.1. In contrast, instrumentalism with respect to philosophy of science (I2) is characterised by the view that the whole theory of mechanics or at least one of its principles is only a tool to describe and predict phenomena without having any real content itself. Lagrange certainly would not have accepted being called an instrumentalist in this second sense (see Sect. 5.4.3, but also Sect. 5.4.1). He could not, however, have refuted such an ascription: A consistent instrumentalism (I1), which is not supported by an adequate theory of representation inevitably leads to (I2). Therefore the distinction is generally unnecessary, but as Lagrange’s view is not consistent in this respect, it has to be kept in mind. 45

124

H. Pulte

reconstruction of his philosophical thinking: it was explainable by his own scientific metaphysics. In Lagrange’s case, however, we are left with the simple fact that ‘order of nature’ and ‘order of science’ differ. An explanation cannot be found in his scientific metaphysics (because there is no explicit scientific metaphysics to be found in his work), but has to be sought in the wider historical context. It is my thesis that Lagrange’s mechanics is a logical consequence and, at the same time, a dissolution of Euclideanism in its original meaning: While the ‘sliding of the centre of gravity’ (in Diemer’s sense, see Sect. 5.3.3) continues, axioms become formal principles rather than principles with regard to content; the whole system is held together by logical coherence rather than by material truth. This is what happened in eighteenth-century rational mechanics, this is what later happened in geometry. I claim that this development is, as far as the mathematical sciences are concerned, somehow inevitable under the conditions of ‘global’ Euclideanism and successfully competing research programs: Each program tends towards building up deductive structures (filled with different contents), global Euclideanism tends towards building up a unique ‘superstructure’ (left with the problem of what its content is). To put it more precisely: Lagrange was confronted with an abundance of different laws (Newton’s laws, conservation laws, variational laws etc.) which emerged from different programs, and he had good reasons to accept them as valid, because they had turned out to be appropriate to describe (and deductively ‘explain’) different classes of mechanical problems. Lagrange’s Euclideanism now operates on the level of these laws which are already expressed in algebraical or analytical form. It aims at a hierarchy of laws, starting with most general ones and ending with special ones and single problems. Higher calculus serves as the uniting element in the deductive chains. Insofar as order and unity become the main targets and the calculus the main means, this mechanics is rightly called analytical. To sum up: Lagrange’s main concern is a deductive organisation of the different laws, not the discovery of new ones.46 Along with the aim of ‘reducing’ all mechanical problems to general equations, this is the main object of his program: “The various principles presently available will be assembled and presented from a single point of view in order to facilitate the solution of the problems of mechanics. Moreover, it will also show their interdependence and mutual dependence and will permit the evaluation of their validity and scope.” (Lagrange, Analytical mechanics, 7).47

 That is the main reason why Lagrange’s mechanics was sterile in some respects: It contains no truly new principles, nor new concepts of mechanics, as Truesdell and others have justly remarked. 47  The Méchanique Analitique “réunira & présentera sous un même point de vue, le différens Principes trouvés jusqu’ici pour faciliter la solution des questions de Méchanique, en montrera la liaison & la dépendance mutuelle, & mettra à portée de juger de leur justesse & de leur étendue.” (Lagrange, Méchanique Analitique, v) 46

5  Order of Nature and Orders of Science

125

5.4.3 Loss of Evidence: ‘Rubber Euclideanism’ Regardless of his ‘mathematical instrumentalism’ (see Sect. 5.4.2), Lagrange stuck to the idea that mechanics can be built up from evident and certain axioms. The combination of new instrumentalism (with respect to philosophy of nature) and old Euclideanism (with respect to philosophy of science) seems to me the decisive characteristic of his mechanics as well as the weakest point of his approach.48 This combination bears a significant tension of which Lagrange himself was partly aware, and some of his successors in the French tradition of mathematical physics were even more so: the conjunction of Euclideanism and instrumentalism suggests that the ‘deductive chain’ can be started by first principles without recourse to any kind of geometrical and physical intuition or metaphysical arguments. This leads inevitably to a conflict with the traditional meaning of ‘axiom’ as a self-­ evident first proposition which is neither provable nor in need of a proof. Lagrange wanted to start with one principle, i.e., the principle of virtual velocities. In the first edition of his Méchanique analitique, he introduced this “very simple and very general” principle in statics as “a kind of axiom” (Lagrange, Méchanique Analitique, 12). He appeased his tangible discomfort with the title ‘axiom’ by extensive references to its successful use by great authorities of the past like Galileo and Descartes.49 In the second edition, he stuck to the title ‘axiom’, but had to admit that his principle lacks one decisive characteristic of an axiom in the traditional meaning: It is “not sufficiently evident to be established as a primordial principle” (Lagrange, Mécanique Analytique (second ed.), I 23 and 27). Euclideanism demands evidence; instrumentalism tends to dissolve it. This is the basic dilemma of Lagrange’s mechanics.50 In two different so-called ‘demonstrations’ he tried to prove his primordial principle by referring to simple mechanical processes or machines (Lagrange, Sur le principe des vitesses (second ed.), 350–357), thus trying to bring back intuitive truth to his axiom. Lagrange’s formulation and/or demonstration of the principle of virtual velocities posed a challenge for a number of mathematicians.51 There was a “crisis of principles,” (Bailhache, Introduction et commentaire, 2) and it was caused by the Méchanique Analitique.

 Regardless of its philosophical shortcomings, the Méchanique Analitique became for some time a model of how mathematics should be used in physics. It is its advanced mathematical and anti-­ metaphysical style which made his textbook attractive for working mathematicians like Fourier as well as for positivistic philosophers like Comte (see Fraser, Lagrange’s Analytical Mechanics). It was widely accepted as the best realisation of a ‘purely mathematical’ Euclideanism in physics. 49  ibid., 8–12. Lagrange uses the history of mechanics partly as a substitute for missing philosophical justification. 50  It was probably brought to his attention by Fourier’s Mémoire from 1798. 51  From Fourier (1798), de Prony (1798), Laplace (1799), L. Carnot (1803) and Ampère (1806) to Cournot (1829), Gauss (1829), Poisson (1833), Ostrogradsky (1835, 1838), and Poinsot (1806, 1838, 1846). They aimed at an extension of Lagrange’s principle, taking into account conditions of constraints given by inequalities (Fourier, Cournot, Gauss, Ostrogradsky) and/or at its better foundation. 48

126

H. Pulte

All attempts to solve it, however, aimed at better demonstrations, giving the principle of virtual velocities a more secure foundation and making it more evident. Like Lagrange, they applied their refined logical and mathematical methods to mediate evidence to the principle of virtual velocities. Lakatos, in a different context, aptly described such a position as “a sort of ‘rubber-Euclideanism’” because it “stretches the boundaries of self-evidence.” (Lakatos, Philosophical Papers, II 7). This episode can be interpreted as a ‘metatheoretical turning point’ with respect to ‘practised’ mathematical physics: Some decades later, mechanical Euclideanism became suspicious, a development which opened the way to other concepts of science. But this story is certainly ‘beyond Leibniz, Newton and Kant’.52

5.5 Kant and Eighteenth-Century Rational Mechanics: Two Projections Notwithstanding the development of ‘practiced’ Euclideanism as outlined above, the ideal of a theory of mechanics on equal footing with geometry continued to attract scientists and philosophers until the twentieth century. As is well known, Kant’s philosophy of science was (and possibly is) the most important bastion of this ideal: Though ‘revolutionary’ in its philosophical approach, it was ‘conservative’ in its objective to found the theory of mechanics upon certain and apodictic principles. The preface of Kant’s Metaphysical Foundations of Natural Science is perhaps the best articulated representation of a classical concept of science as distinct from a modern one53 to be found in the whole history of philosophy of science. Apodictical certainty, a priori principles, systematic order and the necessity of a metaphysics of nature as well as mathematics in order to establish such a science are the main features of this concept. Kant borrowed it from the mathematical physics of his time, and he aimed at a philosophical foundation which the scientists themselves were unable to provide.54 Newton’s mechanics was his main object, but his attempt to gain a sufficient foundation also relied on Leibniz, Euler and other philosopher-scientists of the Age of Enlightenment. It may appear daring or even misleading to discuss Kant’s foundational attempt in the context of this paper: Kant next to Lagrange? This might be offensive to any philosopher (and perhaps to some mathematicians as well). Though I do not share such ‘isolating’ views, I will not discuss any details of Kant’s mathematical philosophy of nature in this article.55 I will rather confine myself to some observations on how Kant perceived contemporary rational mechanics and tried to save its Euclideanism by new means. 52  In the passage above I reported upon the interpretation of Pulte, Jacobi’s Criticism, 158–160; see 160–181 for the subsequent development of analytical mechanics, especially with respect to C.G.J. Jacobi. 53  See Diemer, Begründung, as well as Diemer and König, Was ist Wissenschaft?. 54  Kant, Metaphysische Anfangsgründe, A XIII; see also the mottos of this paper. 55  See Pulte, Axiomatik und Empirie, Ch. IV.7 for Kant’s contribution in the context of the general decline of ‘mechanical Euclidianism’.

5  Order of Nature and Orders of Science

127

5.5.1 The ‘Synthetical’ Projection: Metaphysical Foundations The Metaphysical Foundations are synthetic in at least three different (though not independent) senses: in a new or epistemological Kantian sense (‘pure’ synthesis of a priori concepts; S1), in a traditional or methodological, especially Newtonian sense (‘proved’ explanation of phenomena and special laws by deduction from principles; S2) and, close to this, in a traditional mathematical sense (relying on Euclidean geometry; S3). It was the primacy of geometrical construction (S3) which prevented Kant from considering approaches to mechanics which are basically different from Newton’s as possibly relevant for his foundation of natural philosophy: Though he could have learned from the analytical tradition (see Sect. 5.4.1) that mechanics was actually established on different conceptual bases (S2), and therefore might have come to the tempting philosophical problem of whether this can be done, i.e., whether a metaphysical foundation (S1) for such attempts can be provided, Kant restricted the Metaphysical Foundations, by and large, to a modified Newtonian mechanics: (S3) obviously was too evident for Kant – or was this restriction really brought about by (S1), as a ‘true’ Kantian would argue? Though Kant did not want to pursue empirical science, he wanted to show how (on the basis of synthetic a priori principles) an empirically successful and mathematical science of mechanics is possible and that (as a science) it forms a system, i.e., “an interrelation of reason and consequence.” (Kant, Metaphysische Anfangsgründe, A V). The preface of the Metaphysical Foundations is promising, and many interpreters did not go beyond it. Kant’s accomplishment of his plan in the following parts (Phoronomy, Dynamics, Mechanics, Phenomenology) is, however, less encouraging. Where does he ‘demonstrate’, for example, the assumption made in the addition to the second definition of his Dynamics “that all movement which one body [eine Materie] can impress to another must be regarded as applied along the straight line between both points”? (ibid., A 35). Other ‘lacunae’ could easily be added. The main reason for Kant’s limited success with respect to ‘contents’, however, is the fact that he nowhere deduces Newton’s second law of motion or an equivalent law of motion, and, it seems to me that from the conceptual frame chosen in the Metaphysical Foundations, no successful empirical science can arise without such a law. Kant, however, does not even mention it in his book.56 By and large it must be said that only the first part (Phoronomy) was sufficiently developed by him.

 This gap was—curiously enough—often ignored (see, for example, Gloy, Die Kantische Theorie, Schäfer, Kants Metaphysik) or belittled. Eric Watkins shows in his The Laws of Motion in some detail that Kant’s omission was by no means unique in eighteenth-century German attempts to justify the laws of motion. Euler and others, however, tried to give a justification of the second law, and Kant’s strong orientation towards the introductory part of Newton’s Principia also urges toward further explanation. Some notes in his Opus postumum suggest that Kant (later) might have regarded the relation between force and motion as a matter of empirical investigation. This would mean, however, a serious drawback for his claim to provide a foundation of mathematical philosophy of nature including dynamics, mechanics and phenomenology (in his terms). 56

128

H. Pulte

If we try to sum up the achievements of the Metaphysical Foundations not from an ‘internal’ point of view,57 but placing it in the wider context of contemporary science and philosophy of science, the result might look like this: They offered synthesis (along S3), they promised empirical relevance (S2) on the basis of its synthetic a priori frame (S1) and they gained only beginnings of the systematic order, which (according to Kant) is characteristic to ‘proper science’ and which, in a formal, mathematical (though not synthetical, i.e., geometrical) manner, largely was achieved by mathematical physics itself (see Sect. 5.4).

5.5.2 The ‘Analytical’ Projection: Critique of Judgement Though analytical mechanics played no role in Kant’s ‘critical’ foundations of natural philosophy, he did not completely ignore it. He paid special attention to Maupertuis’s principle of least action, because it seemed to include not only “the most general laws, by which matter actually acts,” but also a plentitude of special laws for quite heterogenous areas of phenomena, thereby giving “unity to the infinite manifold of the universe, and order to blind necessity.” (Kant, Beweisgrund, A 63). In his pre-critical period he shared Maupertuis’ physico-theological interpretation of this principle and made it a part of his argument that “a necessary order of nature derives the harmonious arrangements of matter from the necessary laws of interaction constituting the very essence of matter itself,” as Michael Friedman aptly put it (Friedman, Kant, 13). In Lakatos’ above-quoted metaphor: Using the physicotheological argument, Kant injects truth at the top (principle of least action) and claims that it can be spread over the whole system of science (plentitude of special laws of nature) by deductive inference, thus making these special laws (which start as mere inductive generalisations – ‘empirische Regeln’) not only true, but necessarily true, and their connections necessary, too. His ideal of a systematic order of science, which in a way should be isomorphous to the order of nature, is thus guaranteed. This thought evolved into one of the central problems of Kant’s philosophy of science during his ‘critical period’, when the physico-theological argument was no longer acceptable. While the old ‘solution’ was given up, the problem remained: We possess, as a matter of fact, a number of special laws [“besondere Gesetze”]  – empirical rules, which are obviously true, but which have not yet been proved to be necessary. They form a mere ‘aggregate’ of possible laws, but no system: Nature reveals regularities, even possible laws, but no order58; it might be structured in a  See for example Gloy, Die Kantische Theorie, Plaass, Kants Theorie and Schäfer, Kants Metaphysik. 58  In a certain sense this was, restricted to the area of mechanics, Lagrange’s problem, too: His attempt to organise mechanics by means of analytical principles starts with the fact that there are a number of accepted laws, but that no order and unity can be found among these laws. This may serve as a second reason for calling this projection ‘analytical’. 57

5  Order of Nature and Orders of Science

129

such way that we are left in a “labyrinth of a manifold of possible [and] special laws of nature” (Kant, Erste Fassung, 19) forever: No order of nature, no order of science. This problem belongs to the Critique of Judgement, because it is reflecting judgement which has to subsume special laws under (possibly existing) more general laws or principles. Kant introduced the ‘transcendental principle of judgement’ in order to save his ideal of order and unity: We must assume that nature forms a well-­ conceived system for our mind. In our context, i.e., in the context of mathematical order of nature, this premise can be labelled Kant’s subjective formal teleology of nature. This kind of teleology is explicitly introduced by Kant as a regulative, not as a constitutive principle.59 He himself, however, ‘transcends’ this distinction when he tries to show that subjective formal teleology implies the necessity of the special laws of nature (i.e., their very lawfulness). This attempt has no sound basis in his ‘critical’ philosophy of science, and it cannot yield the necessity of special laws and thereby the existence of a scientific system Kant was looking for.60 It is as a relapse to the pre-critical period, an appeal to the both discoursive and intuitive divine understanding which man can never reach. Thus the ideal of mechanical Euclideanism – an ‘order of science’ in agreement with the ‘order of nature’ – continues to exist in Kant’s philosophy of science as a regulative idea of reason, but cannot constitute a scientific system in an objective sense.

5.6 Conclusion I tried to describe and explain some developments of eighteenth-century mathematical philosophy of nature from a unified point of view, regarding mechanical Euclideanism as its dominant concept of science. Regardless of epistemological fixations, this concept of science shaped mechanics up to the end of the century. It strives, above all, for certain (infallible) and evident principles, but also for unity and completeness: It aims at an axiomatic-deductive structure of the whole ‘order of science’. From Euclid’s Elements to Newton’s Principia two thousand years passed without overcoming this ideal and its dogmatic implications. So, if an all-out hypothetical-­deductivism is regarded as the essential feature of modern science, rational mechanics in the age of reason was not modern. If, on the other hand, we want to integrate this key discipline into modern science  – certainly desirable according to the common understanding of modernity – we have to look for reasons for metatheoretical change which ultimately led to a consequent fallibilism (i.e., a fallibilism with respect to principles) within mechanics.  This kind of teleology bears some similarities to the ‘architectural’ function of mathematics in Leibniz’ programme; see Pulte, Mathesis pura und Mathesis mixta, 233–238. 60  For a criticism of Kant’s approach see Pulte, Physikotheologie, esp. 320–327. I have tried to show that Kant’s adherent J. F. Fries gave a more satisfying methodological solution of this problem (ibid., 327–341 and Pulte, Kant, Fries and the Expanding Universe of Science). 59

130

H. Pulte

In this paper, I tried to locate one important reason for this change within ‘mechanical Euclideanism’ itself: in order to save the ideal of order and unity, rational mechanics in the course of the eighteenth century had to rely increasingly on abstract mathematical tools and techniques, thereby ‘unloading’ its axioms of that meaning and intuition which was initially (relative to the scientific metaphysics in question) their characteristic. This process ended in Lagrange’s mechanics: The Méchanique Analitique makes use of ‘first’ principles only as formal axioms with great deductive power which can no longer be understood as laws of nature in the original sense. This is what, in the end, caused a ‘crisis of principles’ and promoted phenomenalistic, conventionalistic and instrumentalistic concepts of mechanics in the course of the nineteenth century (for this, see Pulte, Axiomatik and Empirie, chs. VI, VII, and From Axioms to Conventions and Hyphotheses). Kant, on the other hand, tried to ‘synthesise’ mechanical knowledge in some principles, which are, under the premises of his system, certain and evident, but he made by no means clear how the whole body of accepted knowledge could be based on these principles. In his philosophy of mechanics, the unique ‘order of science’ remained an ‘projected’ ideal and nothing more. Though there were more reasons to believe in the ideal of Euclideanism – the very possibility of certain foundations and an axiomatic-deductive order of science – in the eighteenth century than today, this metatheoretical concept cannot be ‘refuted’ – not, of course, by history, and not by philosophical arguments either.61 It must be kept in mind, however, that it is “the Programme of Trivialization of Knowledge.”62 This holds true for mathematics at the turn towards the last century and shortly beyond, where all ‘reductions’ to logic failed, this holds even more true for mathematical physics in the eighteenth century. Nevertheless I regard Euclidianism as a historiographically useful category, especially with respect to the history of mathematical physics. Metatheoretical concepts like this are necessary if we want to understand fundamental changes in the sciences and their philosophy. But they have to be supplemented by guiding historical questions and filled with ‘factual’ history in order to uncover reasons for historical change: Perhaps no unique history of reason will be possible, but there is certainly more reason in history than some of our ‘postmodern’ contemporaries would imagine.

 As Lakatos aptly states: “An Euclidean never has to admit defeat: his programme is irrefutable. One can never refute the pure existential statement that there exists a set of trivial first principles from which all truth follows. Thus science may be haunted for ever by the Euclidean programme as a regulative principle, ‘influential metaphysics’” (Lakatos, Philosophical Papers, II 6). 62  Ibid, 5. 61

5  Order of Nature and Orders of Science

131

References63 Alembert, Jean le Rond d. 1743. Traité de Dynamique. Paris: David. Bailhache, Patrice. 1975. Introduction et commentaire.” Louis Poinsot. In La Théorie générale de l’équilibre et du mouvement des systèmes, ed. P. Bailhache, 1–199. Paris: Vrin Blake, Ralph M. 1966. Isaac Newton and the Hypothetico-Deductive Method. In Theories of Scientific Method: Renaissance through the Nineteenth Century, ed. E.H. Madden, 119–143. Seattle/London: University of Washington Press. Blay, Michele. 1992. La Naissance de la Mécanique analytique. La Science du Mouvement au tournant des XVIIe et XVIIIe Siécles. Paris: Presses University France. Böhme, Gernot. 1984. Alternativen der Wissenschaft. Frankfurt am Main: Suhrkamp. Bos, Henk J.M. 1980. Mathematics and Rational Mechanics. In The Ferment of Knowledge: Studies in the Historiography of Eighteenth-Century Science, ed. G.S. Rousseau and R. Porter, 327–355. Cambridge: Cambridge University Press. Burtt, Edwin A. 1932. The Metaphysical Foundations of Modern Physical Science. London: Routledge/Kegan Paul. Carnot, Lazare N.M. 1803. Principes fondamentaux de l’équilibre et du mouvement. Paris: Deterville. Cassirer, Ernst. 1974. Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit. Vol. II. 3rd ed (1922). Darmstadt: Wissenschaftliche Buchgesellschaft. de Maupertuis, Pierre L.M. 1744/1748 Accord des différentes Loix de la Nature qui avoient jusqu’ici paru incompatibles. Mémoires de l’Académie Royale des Sciences de Paris: 417–426. [with changes in: Oeuvres 4: 3–28]. ———. 1746/1748. Les Lois du Mouvement et du Repos déduites d’un Principe Métaphysique. Histoire de l’Académie Royale des Sciences et Belles-lettres de Berlin 2: 267–294. [with changes in: Oeuvres 4, 31–42]. ———. 1974. Oeuvres. Oeuvres. 4 vols. (Lyon 1768), Hildesheim/New York: Olms. Diemer, Alwin. 1968. Die Begründung des Wissenschaftscharakters der Wissenschaften im 19. Jahrhundert  – Die Wissenschaftstheorie zwischen klassischer und moderner Wissenschaftskonzeption. In Beiträge zur Entwicklung der Wissenschaftstheorie im 19. Jahrhundert, ed. A. Diemer, 3–62. Meisenheim: A. Hain. Diemer, Alwin, and Gert König. 1991. Was ist Wissenschaft? In Technik und Wissenschaft, ed. A. Hermann and Ch. Schönbeck, 3–28. Düsseldorf: VDI Verlag. Ducheyne, Steffen. 2012. The Main Business of Natural Philosophy: Isaac Newton’s Natural-­ Philosophical Methodology. New York: Springer. Dugas, René. 1988. A History of Mechanics (1955). New York: Dover. Duhem, Pierre. 1980. The Evolution of Mechanics. Alphen an den Rijn/Germantown: Sijthoff & Nordhoff. Elkana, Yehuda. 1974. Scientific and Metaphysical Problems: Euler and Kant. Boston Studies in the Philosophy of Science 14: 277–305. Euler, Leonhard. 1736. Mechanica sive motus scientia analytice exposita. 2 vols., Petersburg: Academiae Scientiarum, [Opera omnia (2)1 and 2].

 References to publications in academic periodicals usually bear two dates (1748/1750, for example). The first refers to the year when the contribution was read (in the Berlin Academy, for example), the second to the year when the volume in question (of the Berlin Histoires, for example) was published. Abbreviations to collected works etc. are added in square brackets (as [AA] in case of Kant’s Gesammelte Schriften, for example). Quotations and references taken from these editions are indicated by square brackets at the end of the contribution in question (as [AA 2, 63–163] for Kant’s Der einzig mögliche Beweisgrund). 63

132

H. Pulte

———. 1744a. Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes sive solutio problematis isoperimetrici latissimo sens accepti. Lausanne/Genf: Bousquet. [Opera omnia (1)24]. ———. 1744b. De la force de percussion et de sa véritable mesure. Histoire de l’Académie Royale des Sciences et Belles-lettres de Berlin 1: 21–35. [Opera omnia (2)8: 27–53]. ———. 1746. Gedancken von den Elementen der Cörper, in welchem das Lehr-Gebäude von den einfachen Dingen und Monaden geprüfet, und das wahre Wesen der Cörper entdecket wird. Berlin: Haude und Spener. [Opera omnia (3)2: 349–366]. ———. 1748/1750. Réflexions sur l’espace et le tems. Histoire de l’Académie Royale des Sciences et Belles-lettres de Berlin 4: 324–333. [Opera omnia (3)2: 376–383]. ———. 1750/1752. Découverte d’un nouveau principe de mécanique. Histoire de l’Académie Royale des Sciences et Belles-lettres de Berlin 6: 185–217. [Opera omnia (2)5: 81–108]. ———. 1751/1753. Harmonie entre les principes générales de repos et de mouvement de M. de Maupertuis. Histoire de l’Académie Royale des Sciences et Belles-lettres de Berlin 7: 169–198. [Opera omnia (2)5: 152–176]. ———. 1765. Theoria motus corporum solidorum seu rigidorum ex primis nostrae cognitionis principiis stabilita et ad omnes qui in huiusmodi corpora cadere possunt accommodata. Rostock/Greifswald: Röse. [Opera omnia (2)3 and 4]. ———. 1848/1850. Mechanik oder analytische Darstellung der Wissenschaft von der Bewegung. 2 Vols., Greifswald: Koch’s Verlagshandlung. ———. 1853. Mechanik. Dritter Theil: Theorie der Bewegung fester und starrer Körper. Greifswald: Koch’s Verlagshandlung. ———. 1911–1986. Opera omnia sub speciis societatis scientiarium naturalium helveticae. 73 vols. [in progress], Leipzig/Berlin/Basel: Teubner and (from 1952): Zürich/Birkhäuser. ———. “Anleitung zur Naturlehre, worin die Gründe zur Erklärung aller in der Natur sich ereignenden Begebenheiten und Veränderungen festgesetzt werden” (posthumously ed.). Opera omnia 3 (1): 16–178. Fourier, Jean B. 1798. Mémoire sur la statique, contenant la démonstration du principe des vitesse virtuelles, et la théorie des momens. Journal de l’Ecole Polytechnique 1 (2 Cah. 5): 20–60. Fraser, Craig. 1983. J.L.  Lagrange’s Early Contributions to the Principles and Methods of Mechanics. Archive for History of Exact Sciences 28: 197–241. ———. 1990. Lagrange’s Analytical Mechanics, Its Cartesian Origins and Reception in Comte’s Positive Philosophy. Studies in the History and Philosophy of Science 21: 243–256. Friedman, Michael. 1992. Kant and the Exact Sciences. Cambridge, MA/London: Harvard University Press. Gabbey, Alan. 1992. Newton’s Mathematical Principles of Natural Philosophy: a Treatise of ‘Mechanics’? In The Investigation of Difficult Things, ed. P.M.  Harman and A.E.  Shapiro, 305–322. Cambridge: University Press. Giere, Ronald N. 1988. Explaining Science. A Cognitive Approach. Chicago/London: The University of Chicago Press. Gillispie, Charles C. 1971. Lazare Carnot Savant. Princeton: University Press. Gloy, Karen. 1976. Die Kantische Theorie der Naturwissenschaft. Berlin: De Gruyter. Grabiner, Judith V. 1990. The Calculus as Algebra: J.-L.  Lagrange, 1736–1813. New  York/ London: Garland Publishing. Grattan-Guinness, Ivor. 1981. Recent Researches in French Mathematical Physics of the Early Nineteenth Century. Annals of Science 38: 663–690. ———. 1990. Convolutions in French Mathematics, 1800–1840. Vol. 3 vols. Basel/Boston/ Stuttgart: Birkhäuser. Guicciardini, Niccolò. 2009. Isaac Newton on Mathematical Certainty and Method. Cambridge, MA/London: The MIT Press. Hankins, Thomas L. 1970. Jean d’Alembert. Science and the Enlightenment. Oxford: Clarendon Press.

5  Order of Nature and Orders of Science

133

Hanson, Norwood R. 1965. Newton’s First Law: A Philosopher’s Door into Natural Philosophy. In Beyond the Edge of Certainty, ed. R.G. Colodny, 6–28. Englewood Cliffs: Prentice-Hall. Harper, William L. 2011. Isaac Newton’s Scientific Method: Turning Data into Evidence about Gravity and Coscmology. Oxford: Oxford University Press. Hertz, Heinrich. 1956. In The Principles of Mechanics. Presented in a New Form, ed. R.S. Cohen. New York: Dover. Jammer, Max. 1980. Das Problem des Raumes. Die Entwicklung der Raumtheorien. 2nd ed. Darmstadt: Wissenschaftliche Buchgesellschaft. Kant, Immanuel. 1763. Der einzig mögliche Beweisgrund zu einer Demonstration des Daseins Gottes. Königsberg: Kanter. [AA 2, 63–163]. ———. 1786. Metaphysische Anfangsgründe der Naturwissenschaft. Riga: Hartknoch. [AA 4, 465–565]. ———. 1787. Kritik der reinen Vernunft. 2nd ed. Riga: Hartknoch. [AA 3]. ———. 1790. Kritik der Urtheilskraft. Riga: Lagarde und Friederich. [AA 5, 165–485]. ———. 1910–1983. Gesammelte Schriften, ed. by (Königlich) Preußische Akademie der Wissenschaften and (Deutsche) Akademie der Wissenschaften (der DDR). 29 vols., Berlin/ Leipzig: Akademie-Verlag, [AA]. ———. 1958. Erste Fassung der Einleitung in die Kritik der Urteilskraft. Werke 8: 171–232. ———. 1983. Werke in zehn Bänden, ed. W.  Weischedel. Darmstadt: Wissenschaftliche Buchgesellschaft, [Werke]. Kuhn, Thomas L. 1996. The Structure of Scientific Revolutions. 3rd ed. Chicago: The University of Chicago Press. Lagrange, Joseph-Louis. 1760/1762. Application de la méthode exposée dans le mémoire précédent à la solution de différens Problèmes de Dynamique. Miscellanea Taurinensa 2: 196–268. [Oeuvres 1: 365–468]. ———. 1788. Méchanique Analitique. Paris: Desaint. ———. 1798. Sur le principe des vitesses virtuelles. Journal de l’École polytechnique 1 (2 Cah. 5): 115–118. [Oeuvres 3: 315–321]. ———. 1813. Théorie des fonctions analytiques. Nouvelle édition, revue et augmentée par l’auteur. Paris: Bachelier. ———. 1853/1855. Mécanique Analytique, revue, corrigée et annotée par J. Bertrand. 3rd ed. Paris: Courcier. [Oeuvres 11 and 12]. ———. 1867–1892. Oeuvres. In , ed. J.A.  Serret and G.  Darboux, vol. 14 vols. Paris: Gauthier-Villars. ———. 1997. Analytical mechanics, Trans. A.  Boissonnade and V.N.  Vagliente. Dordrecht/ Boston/London: Kluwer Academic Publishers. Lakatos, Imre. 1978. Philosophical Papers, ed. J.  Worrall and G.  Currie. 2 vols., Cambridge: University Press. Mach, Ernst. 1982. Die Mechanik in ihrer Entwicklung, historisch-kritisch dargestellt. 9th ed ed. (1933). Wissenschaftliche Buchgesellschaft: Darmstadt MacLaurin, Colin. 1971. An Account of Sir Isaac Newton’s Philosophical Discoveries (1748). Hildesheim/New York: Olms. Mittelstraß, Jürgen. 1970. Neuzeit und Aufklärung. Studien zur Entstehung der neuzeitlichen Wissenschaft und Philosophie. Berlin/New York: De Gruyter. ———. 1974. Die Möglichkeit von Wissenschaft. Suhrkamp: Frankfurt a. M. ———. 1981. Rationale Rekonstruktion der Wissenschaftsgeschichte. In Wissenschaftstheorie und Wissenschaftsforschung, ed. P. Janich, 89–148. München: Aspekte Verlag. Newton, Isaac. 1952. Opticks: Or a Treatise of the Reflections, Refractions, Inflections Colours of Light. 4th ed. (1730), ed. I.B. Cohen, New York: Dover. ———. 1959–1977. The Correspondence, ed. H.W.  Turnbull et  al. 7 vols., Cambridge: University Press. ———. 1963. Mathematische Prinzipien der Naturlehre (1872). Darmstadt: Wissenschaftliche Buchgesellschaft.

134

H. Pulte

———.1972. Philosophiae naturalis principia mathematica. 3rd ed. (1726), ed. A.  Koyré and I.B. Cohen, 2 vols., Cambridge MA: Harvard University Press. ———. 1982. Mathematical Principles of Natural Philosophy and His System of the World (1729), ed. F. Cajori. 2 vols. (1934) Berkeley/Los Angeles/London: University of California Press. ———. 1999. In Die Mathematischen Prinzipien der Physik, ed. V. Schüller. Berlin/New York: De Gruyter. Plaass, Peter. 1965. Kants Theorie der Naturwissenschaft. Göttingen: Vandenhoeck & Ruprecht. Popper, Karl R. 1982. Logik der Forschung. 7th ed. Tübingen: Mohr (Siebeck). Pulte, Helmut. 1989. Das Prinzip der kleinsten Wirkung und die Kraftkonzeptionen der rationalen Mechanik. Eine Untersuchung zur Grundlegungsproblematik bei L. Euler, P. L. M. de Maupertuis und J. L. Lagrange. Stuttgart: Steiner. ———. 1998. Jacobi’s Criticism of Lagrange: The Changing Role of Mathematics in the Foundations of Classical Mechanics. Historia Mathematica 25: 154–184. ———. 1999. Von der Physikotheologie zur Methodologie. Eine wissenschaftstheoriegeschichtliche Analyse der Transformation von nomothetischer Teleologie und Systemdenken bei Kant und Fries. In Jakob Friedrich Fries. Philosoph, Naturwissenschaftler und Mathematiker, ed. W. Hogrebe and K. Hermann, 301–351. Frankfurt a.M.: Peter Lang. ———. 2005. Axiomatik und Empirie. Eine wissenschaftstheoriegeschichtliche Untersuchung zur Mathematischen Naturphilosophie von Newton bis Neumann. Darmstadt: Wissenschaftliche Buchgesellschaft. ———. 2006. Kant, Fries and the Expanding Universe of Science. In The Kantian Legacy in the Nineteenth-Century, ed. M. Friedman and A. Nordmann, 101–121. Cambridge, MA/London: The MIT Press. ———. 2009. From Axioms to Conventions and Hypotheses: The Foundation of Mechanics and the Roots of Carl Neumann’s ‘Principles of the Galilean-Newtonian Theory’. In The Significance of the Hypothetical in the Natural Sciences, ed. M. Heidelberger and G. Schiemann, 71–92. Berlin/New York: De Gruyter. ———. 2012. Rational Mechanics in the Eighteenth Century. On Structural Developments of a Mathematical Science. Berichte zur Wissenschaftsgeschichte 35: 183–199. ———. 2019a. Mathesis pura und Mathesis mixta: Die Leitfunktion der Mathematik als Vernunftund Anwendungswissenschaft im Zeitalter der Aufklärung. In Theatrum naturae et artium – Leibniz und die Schäuplätze der Aufklärung, ed. D. Fulda and P. Stekeler-Weithofer, 222–244. Stuttgart/Leipzig: S. Hirzel. ———. 2019b. ‘Tis Much Better to do a Little with Certainty’: On the Reception of Newton’s Methodology. In The Reception of Isaac Newton in Europe, ed. H. Pulte and S. Mandelbrote, vol. 2, 355–384. London: Bloomsbury. Pulte, Helmut, and Scott Mandelbrote, eds. 2019. The Reception of Isaac Newton in Europe. 3 vols. London: Bloomsbury. Schäfer, Lothar. 1966. Kants Metaphysik der Natur. Berlin: De Gruyter. Shank, John B. 2019. How Calculus-Based Mathematical Physics Arose in France after 1700: A Historicized Actor-Network Narrative as Explanation. Isis 110: 312–316. Stammel, Hans. 1980. Der Kraftbegriff in Leibniz’ Physik. Mannheim: Diss. University. Strong, Edward W. 1951. Newton’s Mathematical Way. Journal of the History of Ideas 12: 90–110. Szabó, István. 1979. Geschichte der mechanischen Prinzipien und ihrer wichtigsten Anwendungen. Basel/Boston/Stuttgart: Birkhäuser. Truesdell, Clifford A. 1960a. A Program toward Rediscovering the Rational Mechanics of the Age of Reason. Archive for History of Exact Sciences 1: 1–36. ———. 1960b. “The Rational Mechanics of Flexible or Elastic Bodies: 1638-1780”. Introduction to Leonhardi Euleri opera omnia Vol. X et XI seriei secundae. Turici: Orell Füssli. ———. 1968. Essays in the Hi story of Mechanics. Berlin/Heidelberg/New York: Springer. Voss, Aurel. 1901. Die Prinzipien der rationellen Mechanik. Encyclopädie der mathematischen Wissenschaften mit Einschluß ihrer Anwendungen 4 (1): 1–121. Leipzig: Teubner.

5  Order of Nature and Orders of Science

135

Watkins, Eric. 1997. The Laws of Motion from Newton to Kant. Perspectives on Science 5: 311–348. ———. 1998. Kant’s Justification of the Laws of Mechanics. Studies in the History and Philosophy of Science 29: 539–560. Westfall, Richard S.  Force in Newton’s Physics. The Science of Dynamics in the Seventeenth Century. London/MacDonald/New York: Elsevier, 1971.

Part III

Avenues of Newtonianism

Chapter 6

Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique, and How They Contributed to Popularising Newton’s Physics Volkmar Schüller Abstract  Isaac Newton published his important Philosophiae Naturalis Prinicpia Mathematica in 1687. However, considerable skills in mathematics or geometry are completely necessary to follow Newton’s thoughts and therefrom only a few contemporaries of Newton comprehended his great book fully. As a result the knowledge of Newton’s physics remained limited to a small circle of mathematicians and physicists. It was only when Samuel Clarke published his new Latin translation of Jacques Rohault’s Traité de Physique in 1697 that a wider audience, e.g. philosophers and theologians, got the opportunity to read up on Newton’s physics. In those days Rohault’s Traité de Physique was a widely-read textbook of the Cartesian physics. Fortunately, Clarke added a large number of annotations presenting Newton’s opinions to his new Latin translation. Since Clarke hardly ever made use of mathematical reasoning or calculations for presenting Newton’s views the common reader who could not comprehend Newton’s mathematical considerations in the Principia had a chance to get to know Newton’s physics. Furthermore, it was possible for the common reader to compare the then predominant Cartesian physics with Newton’s physics. In this way Clarke’s new Latin translation of Rohault’s Traité de Physique served as a Trojan horse for Newton’s physics.

6.1 Newton’s Physics Disseminated by a Cartesian Textbook Certainly, the publication of Isaac Newton’s Philosophiae Naturalis Principia Mathematica in 1687 marks a turning point in the history of physics, but it took many years before his physics (of which “Newtonian physics” of the eighteenth and nineteenth century is a derivative) began to assert itself against the then dominant V. Schüller (*) Max Planck Institute for the History of Science, Berlin, Germany © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_6

139

140

V. Schüller

Cartesian physics. “Cartesian physics” generally meant the physics of Descartes’ inclusive of the “physics” of all those scientists who accepted the fundamentals of Descartes’ philosophy and endeavoured to improve upon it by adding various alien ingredients. Between 1687 and approximately 1740 Newton’s physics and Cartesian physics stood irreconcilably opposed to each other. In the pursuit of truth, no two methodologies and philosophies could have been more different, and this is equally true of the basic tenets and the consequences following therefrom. Only few contemporaries of Newton appreciated the outstanding significance of his Principia. Owing to the extremely high standards of mathematical and geometrical skill that were needed to follow Newton’s reasoning, it was left to a few great scientists of the day like C. Huygens and G. W. Leibniz to disseminate the news – and often through attack rather than promotion. For instance, it is well known how Newton, in the first edition of the Principia of 1687, quietly treated the principle of universal gravitation like a force acting at a distance. This was immediately noticed by those of his contemporaries who could follow him, and for them this was unacceptable because of the philosophical consequences such a daring hypothesis would entail. But for a long time these disputes remained limited to a small circle of individuals able to understand.1 Textbooks that made Newton’s thinking palatable to a broader audience had not yet been written. And when they were,2 they contributed a great deal to the dissemination of Newton’s physics among students of mathematics and physics who, again, possessed sufficient preliminary skill, though not among the yet less educated in this regard, like philosophers and theologians. In the end, it was a strong circulating textbook on Cartesian physics that played, circumstantially, a significant role in making Newtonian physics palatable among these latter circles, namely the Traité de physique by Jacques Rohault  – that is, Samuel Clarke’s edition of this textbook. The importance of this edition has not yet found appropriate attention among scholars of the history of science. This is also true of a recent review of textbooks written by the first generation of Newtonians (Snobelen, Reading Isaac Newton’s Principia).

 Contemporary reviews were symptomatic of the ambiguity of reception of the first edition of Newton’s Principia. Whereas in the Journal des Sçavans (1688 153–154) an unknown reviewer explicitly rejected Newton’s idea of universal gravity and along with it the whole book, other reviewers gave a more tolerable treatment of universal gravity but remained insensitive toward the foundational problems involved in the concept. See the reviews by Chr. Pfautz (Acta Eruditorum), by E. Halley (Philosophical Transactions), by N.F. de Duillier (?) or J. Locke (?) (Bibliothéque Universelle). German translations in: I. Newton, Mathematische Prinzipien, 581ff. 2  Keill, Introductio ad veram physicam; Gregory, Astronomiae physicae et geometricae elementa; Whiston Praelectiones physio-mathematicae; Keill, Introductio ad veram astronomiam; Pemberton, A view of Sir Isaac Newton’s philosophy. The authors of these textbooks were important exponents of Newtonianism in Britain. Soon after their publication these Latin books were translated into English. 1

6  Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique...

141

6.2 Jacques Rohault and His Traité de Physique In spite of his historical merits, Rohault has fallen into oblivion (except for specialists in seventeenth-century French Cartesianism), and no reliable biography is available, let alone a complete edition of his works.3 We know little of his life. He was born in 1620 in Amiens and was given a conventional scholastic education at the Jesuitical college. He studied in Paris, and there he became acquainted with Descartes’ philosophy, but the circumstances are unknown. Be that as it may, soon he became a disciple of Claude Clerselier (1614–1686) who was a pen-friend of Descartes and who edited Descartes’ writings posthumously. In 1648 Jacques Rohault married Clerselier’s daughter, and he earned fame among his contemporaries throughout France for his lectures in Cartesian physics in Paris which he took up in the mid-1650s. Soon he was considered an authority on Cartesian physics, and he is reported to have conducted experiments during his lectures. The Traité de physique originated from these lectures, probably written together with Claude Clerselier who may also have provided the preface.4 The significance of this treatise consists in the fact that it is no longer purely Cartesian but attempts a compromise between Aristotle’s and Descartes’ system. This has been shown well by P. Mouy (Dévelopment, 116). In spite of his bowing to Aristotelianism, Rohault was indeed an incarnation of French Cartesianism among the physicists, as shown already by F. Boullier (Histoire, I 51). At the end of the preface doubts are expressed as to whether the treatise will meet fully with the approval of the French audience “Time will show how my honest intentions will be accepted here. I am, however, preparing a Latin version for foreigners, of whom I expect a friendly acceptance.” These fears were groundless; already the first French edition of the Traité de physique was received with enthusiasm both in France and in Britain as the reviews attest.5 Owing to Rohault’s masterly presentation of Cartesian physics, chemistry, astronomy and physiology, the treatise went through numerous editions,6 and in 1674 the Genevan physician Théophile Bonet (1620–1689) published a Latin translation which was republished in 1682 and 1700 together with annotations made by the Cartesian Antoine le Grand

 The most complete, but far from exhaustive representation of his life and work is: Clair, Jacques Rohault. 4  Both are reported in: Jöcher, Gelehrten-Lexikon, I col. 1662 5  Philosophical Transactions of the Royal Society 70 (April 17, 1671) 2138–2141; Journal des Sçavans (June 22, 1671) 624–625. 6  The following French editions were published in Paris: 1671 (first ed.), 1672 (second ed), 1676/5 (third ed. corrigée), 1676 (fourth ed. reveuë et corrigée), 1682 (fifth ed. tres-exactement reveuë et corrigée) 1683 (sixth ed.), 1692 (sixth ed. tres- exactement reveuë et corrigée), 1705, 1708 (12th ed.), 1723, 1730. Moreover in 1672 and 1676 French editions were published in Amsterdam and in Lyon the fourth French edition (reveuë et corrigée) was published in 1681. 3

142

V. Schüller

(ca. 1620–1700).7 Soon, Rohault’s volume became the leading textbook of its time, and it was used at the universities of Utrecht, Frankfurt, Groningen, Louvain and Leyden (Sarton, Early Scientific Textbooks).

6.3 Rohault’s Traité Translated and Annotated by Samuel Clarke With the advent of Newton’s Principia in 1687, a fairly complete presentation of a new physics was launched that not only amounted to a comprehensive rejection of Cartesian physics, but indeed disproved it convincingly. Newton was fully convinced to have given a successful disproof of Descartes’ vortex hypothesis as one of the most important propositions of Cartesian physics. In Britain and on the Continent mathematicians and physicists swiftly took notice of Newton’s Principia, and in Britain the first generation of Newtonians aligned and began to further develop Newton’s ideas. The same was true of the Continental physicists, though they were often sceptical of Newton’s views, e.g., of the notion of universal gravity that is to be treated like forces acting at a distance. But through application of Leibniz’ infinitesimal calculus they excelled in the mathematical derivation of important physical insights in ways unattainable by their British colleagues who in terms of mathematics still adhered to Newton’s more awkward method of fluxion. This paved the way towards a more general acceptance of the superiority of Newton’s over Cartesian physics. In philosophy, however, having recently freed itself from scholastic tradition and leaning towards Descartes’ ideas, Newton’s physics and its philosophical implications met with almost universal disapproval. The lack of an handy and popular textbook by which students could have acquainted themselves with the new physics presented a formidable obstacle to the propagation of Newton’s thinking outside of the community of mathematicians and physicists. Although it was known in Britain that Rohault’s Traité de physique no longer presented the most recent state of the art, students continued to use it because there was no better textbook available. However, owing to a happy coincidence, the scientific community soon was to be presented with such a textbook in the near future. It was left to the activity of the English theologian Samuel Clarke (1675–1729) who published his own Latin translation of Rohault’s Traité de physique in 1697, and this translation was to figure so significantly in the propagation of Newton’s physics. Also Samuel Clarke has fallen largely into oblivion, except for the now-famous correspondence with G. W. Leibniz in 1715 and 1716. In his letters Clarke defended among other things Newton’s  Jacobi Rohaulti tractatus physicus gallice emissus et recens latinitate donatus per Th. Bonetum, Genevae 1674; J. Rohaulti tractatus physicus gallice emissus et latinitate donatus per T. Bonetum cum animadversionibus A. Le Grand, Londini 1682; Jacobi Rohaulti tractatus physicus cum animadversionibus Antonii Le Grand. Accedit huic editioni ejusdem tractatus mathematicus de arte mechanica, Amstelaedami 1700. 7

6  Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique...

143

physics against the attacks launched by Leibniz. Today there is documentary evidence that Newton contributed to the formulation of some passages in Clarke’s letters, and as a consequence the significance of Clarke is often overly down-graded. But Clarke’s metaphysics and theology contained elements that were most certainly not always identical with those of Newton’s. Later on, Clarke became more intimately associated with Newton and translated the second edition of Newton’s Opticks into Latin in 1706 which promoted its propagation on the continent. Two sources (written nearly simultaneously) are available that give us important details on the genesis of Clarke’s Latin translation of Rohault’s Traité de physique, provided they are read critically, because they also contain passages that obviously lack historical truth.

6.3.1 Hoadley’s Account The first source, entitled “Essay on the Life, Writings, and Character of Dr. Samuel Clarke” stems from the theologian Benjamin Hoadley (1676–1716). First being a preface to Hoadley’s ten-volume edition of Clarke’s “Sermons” of 1730, he republished it under the title of “The Preface, Giving some Account of the Life, Writings and Character of the Author” in his large four-volume edition in 1738 of The Works of Samuel Clarke that appeared in London. Hoadley tells us that Samuel Clarke studied at Caius College in Cambridge beginning in 1691 where he became a disciple of Mr. Ellis, the later Sir John Ellis. Cambridge was fully dominated by Cartesian philosophy at the time, and Ellis, according to Hoadley, was a zealot of this philosophy. Nevertheless, Samuel Clarke, who was interested in ancient languages and philology and showed a keen interest in philosophy and physics, became sensitive towards Newton’s physics. This is the way Hoadley puts it: And in This Study He made such uncommon Advances, that He was presently Master of the Chief parts of the Newtonian Philosophy; and, in order to his First Degree, performed a Publick Exercise in the Schools, upon a Question taken from thence, which surprized the Whole Audience, both for the Accuracy of Knowledge, and Clearness of Expression, that appeared through the Whole. […] As soon as He had taken that first Degree, Young as He was, He made an Effort for the Service of the Students, which ought not to be forgotten. The System of Natural Philosophy then generally taught in the University, was That written by Mons. Rohault; entirely founded on the Cartesian Principles; and very ill translated into Latin. He justly thought that Philosophical Notions might be express’d in pure Latin: And if He had gone no farther than This, He would have merited of All Those who were to draw their Knowledge out of that Book. But His Aim was much higher than the making a Better Translation of it. He resolved to add to It such Notes, as might lead the Young Men insensibly, and by degrees, to Other and Truer Notions than what could be found there. And this certainly, was a More Prudent Method of introducing Truth unknown before, than to attempt to throw aside this Treatise entirely, and write a New one instead of it. The Success answered exceedingly well to His Hopes: And He may justly be stiled a Great Benefactor to the University, in this Attempt. For, by this Means, the True Philosophy has without any Noise prevailed: and to this Day, His Translation of Rohault is, generally speaking, the Standing

144

V. Schüller

Text for Lectures; and His Notes, the first Direction to Those who are willing to receive the Reality and Truth of Things in the place of Invention and Romance. And thus before he was much above 20 years old, He furnished the Students with a System of Knowledge, which has been ever since, and still continues to be, a Publick Benefit to All who have the happiness of a Liberal and Learned Education in that University.8

6.3.2 Whiston’s Account The second source is William Whiston’s Historical Memoirs of the Life and Writings of Dr. Samuel Clarke published 1730  in London. William Whiston (1667–1752) was one of the first Newtonians and took over Newton’s chair when Newton left Cambridge to become head of the mint in London. Whiston published numerous works in mathematics and physics, among them the introductory textbook on Newton’s physics (Whiston, Praelectiones), but mostly he wrote theological works in which he revealed him (among other things) as an anti-Trinitarian. This aroused the allied protest of many theologians in England, and ultimately he lost his chair at Cambridge. This is Whiston’s report on how Clarke’s translation of Rohault’s Traité de physique came about: About the Year 1697, while I was Chaplain to Dr. John Moor, then Bishop of Norwich, I met at one of the Coffee-houses in the Market-place at Norwich, a young Man, to me then wholly unknown, his Name was Clarke, Pupil to that eminent and careful Tutor, Mr. Ellis, of Gonvil and Caius College in Cambridge. Mr. Clarke knew me so far at the University, I being about 8  years elder than himself, and so far knew the Nature and Success of my Studies, as to enter into a Conservation with me, about that System of Cartesian Philosophy, his Tutor had put him to translate; I mean Rohault’s Physicks; and to ask my Opinion about the Fitness of such a Translation. I well remember the Answer I made him; that ‘Since the Youth of the University must have, at present, some System of Natural Philosophy for their Studies and Exercises; and since the true System of Sir Isaac Newton was not yet made easy enough for that Purpose; it was not improper for their Sakes, yet to translate and use the System of Rohault (who was esteemed the best Expositor of Des Cartes) but that as soon as Sir Isaac Newton’s Philosophy came to be better known, that only ought to be taught, and the other dropp’d.’ Which last Part of my Advice, by the way, has not been followed, as it ought to have been, in that University: But, as Bishop Hoadly truly observes, Dr.Clarke’s Rohault is still the principal Book for the young Students there. Though such an Observation be no way to the Honour of the Tutors in that University, who in reading Rohault, do only read a Philosophical Romance to their Pupils, almost perpetually contradicted by the better Notes thereto belonging. And certainly, to use Cartesian fictitious Hypotheses at this Time of Day, after the principal Parts of Sir Isaac Newton’s certain System have been made easy enough for the Understanding of ordinary Mathematicians, is like the continuing to eat old Acorns, after the Discovery of new Wheat, for the Food of Mankind. However, upon this Occasion, Mr. Clarke and I fell into a Discourse about the wonderful Discoveries made in Sir Isaac Newton’s Philosophy. And the Result of that Discourse was, that I was greatly surprized, that so young a Man as Mr. Clarke then was, not much, I think above twenty-two Years of Age, should know so much of those sublime Discoveries, which were then almost

 Clarke, Works, I 1: “Preface […] by Benjamin, now Lord Bishop of Winchester,” i.e., Benjamin Hoadley. 8

6  Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique...

145

a Secret to all, but to a few particular Mathematicians. Nor did I remember above one, or two at the most, whom I had then met with, that seemed to know so much of that Philosophy as Mr. Clarke. (Whiston, Historical Memoirs, 2–4.)9

6.3.3 A Document Unparalleled in the History of Physics Through the adding of Clarke’s annotations in which the views entertained by Rohault are immediately contrasted with those contained in Newton’s Principia of 1687, Clarke’s translation has become a document unparalleled in the history of physics. The main text being a Latin translation of Rohault’s Traité de physique, the student-reader was offered at once the opportunity to glean the essentials of Newton’s physics from the abundant annotations with which Clarke has furnished the volume. True, this was no systematic presentation of Newton’s ideas, for Clarke’s role was always limited to that of a responder to a text designed as a thoughtful exposition of Cartesian physics. Yet he was able to infuse through these annotations a sufficiently coherent picture to serve adequately as a first impression of the new physics. The importance of this book in introducing and propagating Newton’s physics among all those who were less interested in the mathematical details of physical processes, but rather in the new explanatory quality, can hardly be overrated. The new Latin translation with Clarke’s varied annotations was the masterstroke of his own. And it really served as a Trojan horse for Newton’s physics.10 Although Rohault stated explicitly in the preface that a quantitative or mathematical description of nature was desirable, he, nevertheless, hardly ever employed mathematical reasoning or calculation for justifying his views, and this was also true of Descartes. It can be well assumed that for many a philosopher, theologian and physician this book provided the first source of acquaintance with Newton’s physics. After having first appeared in 1697, Clarke’s translation went through its fourth edition by 1710.11 He continually enlarged upon his annotations, and in 1710 they amounted to roughly 20 per cent of the whole text. While in the first edition annotations were relatively sparse and mainly added to the passages on experimental designs, the subsequent editions were furnished increasingly with critical comments on Rohault’s text and references to Newton as well as lengthy quotes taken from the  Note especially the role played by the Cartesian “zealot” Mr. Ellis, who seems to have been friendly with the Newtonians and who suggested the new translation of the Traité de physique. 10  A. Koyré Newtonian Studies page 54 footnote 3 11  Jacobi Rohaulti Physica latine reddit et annotatiunculis quibusdam illustravit S. Clarke, Londini 1697. In the title-page of the later editions it is explicitly said that Clarke’s annotations were written on the basis of Newton’s Principia. The hitherto known editions are: 1697 (first version of Clarke’s annotations), 1702 (second version of Clarke’s annotations), 1708 (second version of Clarke’s annotations, in addition annotations by La Grand), 1710 (third version of Clarke’s annotations), 1713 (second version of Clarke’s annotations, in addition annotations by La Grand), 1718 (third version of Clarke’s annotations), 1739 (designated as sixth edition). 9

146

V. Schüller

Principia and Opticks. Michael Hoskin (Clarke’s Notes) was the first to point out these alterations and improvements taking place across the editions. Due to their limitations in Latin, it seems, many students were unable to read the Latin edition. Therefore John Clarke (1682–1757), who was the younger brother of Samuel Clarke, undertook the task of translating the book into English, and the English version appeared in 1723.12 On this occasion Samuel Clarke made his fourth amendment to the annotations. His brother was a highly competent translator. He was not only highly educated in theology and philosophy, which provided the subject matter of some books written by himself, but also well acquainted with Newton’s physics, as his commentary A Demonstration of some of the principal sections of Sir Isaac Newton’s Principles of Natural Philosophy (London 1730) shows. More than ten editions of the English version appeared between 1697 and 1739. We may assume that originally the readers were motivated in the first instance by Rohault’s text, but also that with increasing popularity of Newton’s physics among mathematicians and physicists an interest in Clarke’s annotations was increasingly generated among the students of other subjects. The reports by Hoadley and Whiston attest to the fact that Clarke’s edition of Rohault’s Traité de physique (including his annotations) continued to be read at the universities for a long time. We may laugh at the somewhat simplistic explanation for the lasting success of Clarke’s edition given by the mathematician John Playfair (1748–1819), yet it contains a kernel of truth: “Error is never so sure of being exposed, as when truth is placed close to it, side by side, without anything to alarm prejudice, or awaken from its lethargy the dread of innovation. Thus, therefore, the Newtonian philosophy first entered the University of Cambridge under the protection of the Cartesian” (Dugas, Mechanics, 548). Clarke’s translation was read in Cambridge as well as at various English academies (Bishop, Physics Teaching), likewise in America, for instance at Yale and Harvard. Thus George Sarton was able to state: “The RohaultClarke treatise became the outstanding scientific textbook in England (and America) in the first half of the eighteenth century. […] the Rohault-Clarke treatise could be defined not as a Cartesian Newtonian textbook (that would be nonsense) but as a Cartesian textbook including, in the footnotes, a Newtonian refutation. […] Many generations of English and American students (at Yale until 1743) learned Newtonianism in a Cartesian textbook.” (Sarton, Early Scientific Textbooks, 144–145).

 Rohaults’s System of Natural Philosophy: Illustrated with Dr. Samuel Clarke’s Notes, Taken Mostly out of Sir Isaac Newton’s Philosophy, Done into English by John Clarke, London 1723. Later editions: 1728/9 and 1735. Reprint: A System of Natural Philosophy by Jacques Rohault, vol. 1 and 2, with a new introduction by L. L. Laudan, New York; London 1969 (The Sources of Science No. 50). 12

6  Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique...

147

6.4 The Structure of Rohault’s Traité It was most reasonable for Rohault to mould the structure of his Traité de physique according to the then prevailing Aristotelian tradition, for his intention was, on the one hand, to refute the peripatetic natural philosophy that was still very wide spread, and on the other, to give an introduction to Cartesian natural philosophy. This is why his Traité de physique consisted of four parts. The first part is concerned with the foundations of physics and with general explanations of matter and its divisibility, motion and rest, the void, the elements of matter, and universal mechanical laws. On this grounding Rohault attempts a mechanical explanation of hydrostatic and optical phenomena, and also of elasticity, capillarity, sound, light and colours. The structure of the first part agrees with that of the second part and some sections of the fourth part of Descartes’ Principia. The second part of Rohault’s Traité de physique deals with problems in astronomy and agrees with the third part of Descartes’ Principia. After having given descriptions of a number of astronomical phenomena, the hypotheses of Ptolemy, of Copernicus and of Tycho Brahe are explained in great detail, and Rohault himself decides explicitly in favour of Copernicus. The nature of stars and comets is considered at some length, and Rohault endeavours to give a mechanical explanation of gravity and lightness and of the tides according to the principles formulated in the first part. The third part deals with terrestrial phenomena and corresponds to the fourth part of Descartes’ Principia. The treatise comes to an end after the fourth part, which is concerned with living beings and corresponds to some sections in the fifth and sixth part of Descartes’ Principia.

6.4.1 Matter, Inertia, and Conservation of the Quantity of Motion Truthful to Descartes, Rohault attempts to derive all phenomena of nature by means of a few principal axioms of natural philosophy. Descartes’ principle that the essence of matter lies solely in extension is among his best-known (Rohault, Traité, I 7 Art. 8), and this principle is rejected by Clarke in an annotation stating that otherwise matter and space would be identical. In the opinion of Clarke, a piece of space qualifies more properly as matter when it is solid and impenetrable and is endowed with the potential to resist. Elsewhere in his annotations he states more succinctly that the essence of matter does not consist in extension, but in impenetrable solidity (Rohault, Traité, I 8 Art. 1, Clarke’s annotation 1). Also the Cartesian law of inertia – that every thing endeavours to continue in that state in which it is (Rohault, Traité, I 5 Art. 8) – reappears in Rohault, albeit in a more refined sense: All things will continue in the state they once are unless external causes intervene, so that a body at rest never will begin to move of itself, nor a body in motion cease to move of itself (Rohault, Traité, I 11 Art. 1).

148

V. Schüller

In this context, Rohault explicitly rejects as groundless the law of Aristotle  – which Kepler still considered correct – that all things in motion tend toward rest (Rohault, Traité, I 11 Art. 2). Very surprisingly, no annotation by Clarke is found at this position that would have acquainted the reader with Newton’s law of inertia, i.e., of inertia as a force inherent to matter. Clarke did indeed reject Rohault’s presentation of Descartes’ law, according to which the quantity of motion which God impressed upon the world is always preserved. He did so by quoting the passage from Query 31 of Newton’s Opticks, in which Newton denied the possibility of conservation of the total quantity of motion in the world (Rohault, Traité, I 10 Art. 13, Clarke’s annotation 1), inclusive of Newton’s example of a rotating dumb-bell moving forward in a straight line of which Newton believes that it shows how the quantity of motion in the world may vary. At the time, Leibniz referred positively to this example of Newton’s and gave his support to it in § 99 of his fifth letter to Clarke. Surely we know today that the dumb-bell example was ill-chosen. (It is extremely doubtful that Newton’s example can be rescued by a retrospective invention of modes of calculation which Newton is unlikely to have ever heard of.)13 Like Descartes, Rohault seems to maintain that there are only matter and motion in the world and everything else (except mind) follows therefrom. Though not completely explicit on this point in the Traité, Rohault’s general strategy of explanation of natural phenomena makes it very likely that this was his opinion.

6.4.2 Vacuum and Elements From his principal axioms of natural philosophy Rohault inferred that a vacuum was impossible. A vacuum would be a space devoid of matter, but since space (or extension) was supposed to be the same thing as matter, it followed that space without matter was the same as matter without matter, which was a contradiction (Rohault, Traité, I 8 Art.1). Clarke in turn, in his attempt to rehabilitate vacuum, quoted in his annotation a passage from Opticks, where Newton concluded from the continual motions of comets that the heavenly spaces must be devoid of sensible matter. And Clarke added the example of a pendulum whose motion is unchangeable in a void and thus attests evidently to the absence of matter (also of Descartes’ subtle matter). It seemed obvious to him that vacuum existed in nature, and moreover that vacuum provided nature’s largest part. At this point, Clarke also emphasised that the whole world is composed of solid bodies moving in a vacuum, and he assured the reader that there was no danger that those phenomena hitherto explained in terms of a plenum now would become inexplicable. Quite to the contrary, they could be explained much better by the new principles, while those phenomena not dependent on these principles would continue to be explained in Newton’s framework in the same way the Cartesians did.

13

 See for, instance, Sepper, Newton’s Optical Writings, Appendix D.

6  Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique...

149

Also Rohault’s teachings on the elements was a recapitulation of Descartes’ teachings (Rohault, Traité, I 21). Matter was said to be composed of three elements. When the world was created, there was only one kind of matter that consisted of an infinity of minutest particles of different forms and motion. Rohault called these particles first elements. Owing to their mutual collisions they grew increasingly smaller, and their forms smoothed down until nearly all had become of spherical shape. These particles qualified as second elements and possessed the potential to vast aggregations or visible compositions, which were called third elements. The sun and stars consisted of first elements, i.e., minutest, swiftly moving luminous particles. The heaven was composed of second elements, i.e., minute, swiftly moving spherical particles that were transparent. The earth, the planets and nearly all things encountered on earth were composed mainly of third elements, i.e., of opaque particles of irregular shape that move rather slowly. Clarke rejected the whole doctrine of elements because of their fictitious and imaginary nature (as he saw it). This was so because they depended on the plenum which Clarke had already rejected. In his annotation Clarke quoted two lengthy passages from Opticks, where Newton explained that in the beginning of the world God formed matter in solid, massy, impenetrable and moveable particles of which all bodies are composed. But Clarke not only took objection to the Cartesian theory of the three elements. He also claimed that nothing could be more absurd than their assumption that in the beginning motion was imparted to these particles once and forever so that no future intervention of God himself or some other intelligent cause was needed. Because in the eyes of Rohault there was no vacuum in nature, the spaces between the second elements must have been filled by first elements. Similarly, the spaces between the particles of which the visible bodies are composed must be filled by second elements. Expansion and contraction of bodies always was a difficult subject to explain for the protagonists of a plenum, and Rohault invokes the presence of a subtle matter (that is, matter of the first and the second element) that fills the lacuna originating during the expansion of bodies. Though Boyle’s, Pascal’s and Toricelli’s experiments made the presence of a vacuum in nature a very likely possibility, Rohault contrived “to explain and prove” the impossibility of such a vacuum (Rohault, Traité, I 12). Clarke rejected this undertaking in several annotations through a careful examination of Rohault’s experiments and of his interpretations of these experiments, and also gave an alternative explanation of the experiments in terms of Newton’s physics.

6.4.3 Rules of Collision From Descartes’ principle that all things will continue in the state they once are in unless any external cause intervenes (Rohault, Traité, I 11 Art.1), it followed that a body moving with a given velocity would continue in this way until it collided with another body. As a consequence of such a collision, the body in question would either continue in an altered direction but with an unaltered velocity or it would lose

150

V. Schüller

some quantity of its motion by imparting this quantity to the body encountered. The overarching principle was, of course, that none of the motion would be lost because the total quantity of motion in the world remained constant. According to Descartes, when God created matter he impressed a certain quantity of motion upon its parts and by his providence always the same quantity of motion was preserved in the world (Rohault, Traité, I 10 Art. 13). Thus whenever two bodies encountered each other, the total quantity of motion involved had to remain constant before and after. In spite of Rohault’s proper insight, his rules of collision were incomplete and mistaken (Rohault, Traité, I 11 Art. 5ff.). Though Rohault refrained from repeating the seven rules that govern collision according to Descartes’ Principia (of which six were wrong and one was inconclusive), it was also true that he made no reference to the correct rules derived by Huygens, Wren and Wallis in 1668/9. This is indeed surprising because they are by no means inconsistent with the principles of Cartesian physics and they would have provided Rohault with the proper tools to support the Cartesian system by empirical experiment. Perhaps Rohault was unaware of the relevant publications by Huygens, Wren and Wallis. For Clarke, of course, this is a welcome opportunity to insert an elaborate correction by presenting the correct rules of collision. Rohault was able to explain a variety of phenomena by means of his theory of collisions. He assumed that a body’s heat arose from a specific kind of motion of the body’s particles, but excluded rectilinear motion in favour of a rotary motion of these particles as its cause (Rohault, Traité, I 23 Art. 10).

6.4.4 Attractive and Repulsive Forces In his Traité de physique Rohault deliberately excluded attractive and repulsive forces (i.e., forces acting at a distance) because he was part of the purely mechanic tradition, which endeavoured to explain everything in terms of mutual collisions of solid-matter particles, i.e., only through immediate contact. Like most contemporary protagonists of corpuscular philosophy, Rohault tried to explain all natural phenomena in terms of magnitude, shape and motion of invisible material particles. His major objection against the hypothesis of attractive and repulsive forces was that they were chimerical and fictitious and had been posited by some unworldly philosophers for want of an explanation of numerous natural phenomena. In his opinion such explanations were below the standards of respectable natural philosophy. Magnetism was a case in point. Though everybody said that a magnet attracted a piece of iron, this is an explanation of neither its nature nor this manifest property (Rohault, Traité, I 11 Art. 14, 15). But respectable natural philosophy must not take recourse to occult qualities. Clarke responded to this objection in a most remarkable annotation: Since nothing acts at a Distance, that is, nothing can exert any Force in acting where it is not; it is evident, that Bodies (if we would speak properly) cannot at all move one another, but by Contact and Impulse. […] Yet because, besides innumerable other Phaenomena of

6  Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique...

151

Nature, that universal Gravitation of Matter […] can by no means arise from the mutual Impulse of Bodies (because all Impulse must be in proportion to the Superficies, but Gravity is always in proportion to the Quantity of solid Matter, and therefore must of Necessity be ascribed to some Cause that penetrates the very inward Substance it self of solid Matter) therefore all such Attraction, is by all means to be allowed, as is not the Action of Matter at a Distance, but the Action of some immaterial Cause which perpetually moves and governs Matter by certain Laws. (Rohault, Traité, I 11 Art. 15 Clarke’s annotation 1).

Clarke repeated this argument in a more elaborate way in his correspondence with Leibniz.14 Clarke also quotes on this occasion two long passages from Opticks in which Newton formulates his ideas of attraction. Clarke also says much the same thing in his A Discourse concerning the unchangeable obligations of natural religion, and the truth and certainty of the Christian revelation: That most universal Principle of Gravitation itself, the Spring of almost all the great and regular inanimate Motions in the World, answering […] not at all to the Surfaces of Bodies, (by which alone they can act one upon another,) but entirely to their Solid Content; cannot possibly be the result of any Motion originally impressed on Matter, but must of necessity be caused (either immediately or mediately) by something which penetrates the very solid Substance of all Bodies, and continually puts forth in them a Force or Power entirely different from that by which Matter acts on Matter. Which is, by the way, an evident demonstration, not only of the World’s being made originally by a supreme Intelligent Cause; but moreover that it depends every Moment on some Superior Being, for the Preservation of its Frame; and that all the great Motions in it, are caused by some Immaterial Power. (Clarke, Works, II 601).

The partial overlap with some of the passages of Newton’s Scholium generale which Newton added to the second edition of his Principia of 1713 is conspicuous; all the more remarkable is the fact that Clarke had written his Discourse already in 1705.

6.4.5 Light and Colour Light and colour are explained by Rohault, again, in terms of motions of invisible particles. The original (primary) source of light consisted “in a certain Motion of the Parts of luminous Bodies.” (Rohault, Traité, I 27 Art. 15). As a consequence of this motion, some pressure was generated in subtle matter which filled the whole of space, especially the pores of transparent bodies. This pressure, in turn, produced in subtle matter a tendency toward motion, but without leading to actual motion. This disposition, however, yielded the light perceived by us, which Rohault called secondary, or derived light. Hence, only secondary light was visible. The pressure of light spread instantaneously (like pressure in a liquid); i.e., the velocity of light was infinite. In Rohault’s opinion light formed no independent substance, but consisted solely of this disposition of subtle matter towards motion. So it happens that it is reflected and refracted in the same way the motion of a body is reflected, when it bounces against a wall, or is refracted, when it enters a medium that slows down its 14

 See § 45 in Clarke’s fourth letter and §§ 110ff. in Clarke’s fifth letter to Leibniz

152

V. Schüller

velocity. “The light is nothing else but a particular motion of the small Globules of the second element, or at least a disposition to a particular sort of motion.” (Rohault, Traité, I 27 Art. 53). This was Rohault’s explanation of the causes of optical phenomena. In his annotations, Clarke, once more, contrasted this explanation with that given by Newton according to which light was made of particles that were emitted by luminescent bodies. Light consisted no longer in a mere tendency to move, but in the actual motion of light-particles. Clarke also quoted elaborately from Newton’s Opticks and stressed that the light-particles must move with an extraordinarily high velocity because otherwise the rectilinear propagation of light could not be understood. According to Clarke the velocity of light lay above seven million miles per minute (Rohault, Traité, I 27 Art. 15 Clarke’s annotation 1). Rohault’s theory of colour flowed smoothly from his theory of light (Rohault, Traité, I 27 Art. 51 f.). He thought of colour as light modified by coloured bodies. Whiteness, for instance, was a modification that resulted from the reflection of light on a rough surface through which it became scattered in all directions. Blackness, in turn, was the result of the total absorption of light by a body, and this also explained why black bodies more easily heat up than white ones. Because light was a disposition of subtle matter toward motion and heat was one kind of motion, it followed that every body that absorbed light received an additional quantity of motion and thus increased in temperature. Other colours were a consequence of the rotary motion of the spherical particles of the second elements, the specific colour depending on their speed of rotation. The dispersion of light into spectral colours when passing through a prism was explained by Rohault like this: When a light-beam passed through the prism, it was not only refracted, but the light-particles also collided with those of which the prism was composed. Such a collision, however, not only caused a deflection of light-particles from their original path, but also set the light-particles into a rotary motion around their axes. Their speed of rotation depended on the degree of deflection or refraction. Because blue light was most strongly refracted, its particles were supposed to have the highest speed of rotation. Speaking of light-particles, we must always keep in mind that Rohault’s views did not allow for light particles proper. Strictly speaking, only the disposition toward motion of the particles comprising the second element was affected when some particular light arrived at the location in question. Again, Clarke presented in his annotation Newton’s alternative theory. He pointed out that it was experimentally proven that white light was a composition of the spectral colours. Different colours, according to Newton, arose as a consequence of the differing velocities of light particles, which also explained why different colours were refracted to different degrees when passing through a medium. This provided an explanation for the dispersion of white light of utmost simplicity, and Clarke discusses various experimental situations through which white light might be dispersed. Though Clarke refers to Newton, it is somewhat surprising to note that he does not quote from his Opticks like he did in so many other instances.

6  Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique...

153

6.4.6 Planetary Motion and Free Fall After he had described the planetary motions and the hypotheses of Ptolemy and of Tycho Brahe (Rohault, Traité, II 24), Rohault sided with Copernicus’ hypothesis that the planets revolve round the sun, for “the hypothesis of Copernicus is, without doubt, the most simple of the three.” (Rohault, Traité, II 24 Art. 10) In his explanation of celestial motions, Rohault remained fully faithful to Descartes. The sun was in the centre of a huge vortex that consisted of extremely fluid and transparent matter, in which the earth and the planets floated. The vortex revolved around the sun, thus carrying along the earth and the planets (Rohault, Traité, II 25 Art. 5). Moreover, every planet possessed its own fluid and transparent vortex by which it was more immediately surrounded and through the rotation of which the rotation of the earth and planets was generated (Rohault, Traité, II 25 Art. 22). Like the sun, also the other stars owned separate vortices (Rohault, Traité, II 25 Art. 20). Clarke, in contrast, denied the existence of such vortices because of the regularity of motion among the comets and quotes extensively from Newton’s scholium at the end of the second book of Newton’s Principia. There Newton says that “the hypothesis of vortexes directly contradicts the astronomical phaenomena, and tends more to confound the celestial motion than to explain them.” (Rohault, Traité, II 25 Art. 22 Clarke’s annotation 1). According to Rohault the vortex responsible for the earth’s rotation also explained why bodies fell towards the earth, that is, he believed he had found an explanation for gravity (Rohault, Traité, II 28). As a consequence of the rotary process, all components of the vortex tended to move toward the outer limits of the vortex. The more bulky these components, the greater the difficulties to move to the vortex’s edge, while the smaller particles (i.e., those of the first and second elements) met with less obstacles and moved more swiftly to the fringes. In doing so, they displaced the larger ones and in effect pressed them, as it were, toward the direction of the earth. Consequently, bodies did not fall to the earth as the result of an attractive force but were pushed downward by the subtle matter that surrounded them. Clarke, in turn, explains in his annotation Newton’s law of universal gravitation. After having told the reader that “Every single Particle of all Bodies whatever, gravitates to every single Particle of all Bodies whatsoever; that is, they are impelled towards each other by Gravity” (Rohault, Traité, II 28 Art. 13 Clarke’s annotation 1), he argued for gravity as a universal force. A body possessed gravity irrespective of its location in space, of its shape or size, whether solid or fluid. Gravity was a universal property that could be neither diminished nor increased under set conditions. The magnitude of gravity was proportional to the quantity of matter contained in a body, and gravitation between two bodies was inversely proportional to their square distance. Gravity wasn’t the accidental outcome of some kind of motion or subtle matter, but was a universal law that had been impressed upon all matter by God. From the existence of universal gravity Clarke concluded that there was also vacuum in nature, and he said that the motion of falling bodies as well as celestial

154

V. Schüller

motions depended on universal gravity. Surprisingly for the historian of science, Clarke, instead of hailing Newton for his discovery of universal gravitation in his annotation, directed the reader’s attention to Johannes Kepler. Though he did not succeed in explaining celestial motions through gravity, Kepler claimed the existence of such a context. To show this, Clarke quotes thoroughly from Kepler’s Astronomy nova, and especially that famous passage in which Kepler maintains that gravity is a mutual corporeal affection that always takes place between two bodies and that gravity not only obtains between celestial bodies, but also between terrestrial bodies such as two stones. Another topic to which Rohault paid thorough attention in his Traité was the velocity of falling bodies, and he arrived at the correct conclusion that all bodies fell equally fast (Rohault, Traité, II 28 Art. 16). During fall the velocity of bodies was permanently accelerated because subtle matter continued to keep pressing them downwards. In the annotation added in this place, Clarke dealt in great detail with Newton’s theory of falling bodies. Remarkably, he argued here that gravity impels bodies to move downward and that the speed of such a body at any one time depended on the number of times it had received such impulses. This statement appears to contradict Newton’s opinion that it was the earth that attracted bodies. But Newton speaks of impulses, too. In the introduction to sect. XI book I of Newton’s Principia we can read that in strictly physical terms the attractions may be called more truly impulses.

6.5 Charles Morgan’s Annotations Now there is an important point that we must not suppress. Not all annotations contained in the Traité were written by Clarke; there are some that were written by Charles Morgan.15 This is already stated by Clarke in the preface to his edition of Rohault’s Traité de physique. Morgan’s annotations are notable for their extensive use of mathematical tools and their summary of Newton’s thoughts in ways easier comprehensible than the original; but they tend to neglect to some extent the differences between Cartesian and Newton’s physics. These were the annotations written by Morgan: (1) the annotation to I XI Art. 6 that explained the communication of motion from one body to another as a result of collision and how along with this communication the quantity of motion was preserved; (2) the annotation to I XIV Art. 9 that described the forces at work on a pair of scales, on an inclined plain, on a wedge, on a screw and on a pulley; (3) the annotation to II XXVIII Art 16 that  Probably identical with Charles Morgan who is the subject of a report by the British Biographical Archive (Fiche I 788, 016). The reported Charles Morgan was born 1659(?) and became member of Society of Jesus in 1689. In his preface Clarke designates him as Dominus Carolus Morgan, Reverendus Episcopus Eliensis a Sacris domesticis. According to Michael A.  Hoskin (Clarke’s Notes, 361), Charles Morgan was a contemporary of Clarke at Cambridge and later Master of Clare College. 15

6  Samuel Clarke’s Annotations in Jacques Rohault’s Traité de Physique...

155

described the motion of a falling body and of projectiles, and moreover the motion of heavy bodies falling in a cycloid, (4) the annotation to III XVII Art. 6 that explained the origin of the rainbow and its size, and the distribution of its colours. In 1770 these annotations were also published as an independent book.16 Here, we have been able to give no more than a preliminary impression of Clarke’s edition of Rohault’s Traite de physique by relating the contents of some of its more important passages, but at any rate, only he or she who reads the whole book carefully will gain a firm impression. In a sense this book will appear to the modern reader as a curiosity, that is, as a document that reflects the convoluted ways in which science uncovers new knowledge and equally, of disseminating its entangled news.

References Bishop, George Daniel. 1961. Physics Teaching in England from Early Times up to 1850. London: P.R.M. Publ. Limited. Bouillier, Francisque. 1868. Histoire de la Philosophie Cartèsienne. 3rd ed. Paris: C. Delagrave. Clair, Pierre. 1978. Jacques Rohault: (1618–1672); bio-biographie avec l’edition critique des Entretiens sur la philosophie, Recherches sur la XVII siècle III. Paris: Ed. du Centre National de la Recherche Scientif. Clarke, Samuel. 1978. Works (1738). New York: Garland. Dugas, René. 1958. Mechanics in the Seventeenth Century. Neuchatel: Editions du Griffon. Duillier (?), Nicolas Fatio de or Locke (?). John. ["Review of Newton’s Principia"]. Bibliothéque Universelle (Amsterdam) VIII: 436–450. Gregory, David. 1702. Astronomiae physicae et geometricae elementa. Oxford: Theatro Sheldoniano. Halley, Edmond. 1687. Review of Newton’s Principia. Philosophical Transactions XVI/186: 291–297. Hoskin, Michael A. 1961. Mining All Within, Clarke’s Notes to Rohault’s Traité de Physique. The Thomist 24: 353–363. Jöcher, Christian. 1981. Allgemeines Gelehrten-Lexikon (1750). Hildesheim: Olms. Keill, John. 1701. Introductio ad veram physicam. Oxford: Theatro Sheldoniano. ———. 1718. Introductio ad veram astronomiam. Oxford: Theatro Sheldoniano. Koyré, Alexandre. 1965. Newtonian Studies. London. Mouy, Paul. 1934. Le Développement de la Physique Cartesienne (1646–1712). Paris: Vrin. Newton, Isaac. 1999. Die mathematischen Prinzipien der Physik, ed. Vol. V. Schüller. Berlin: De Gruyter. Pemberton, Henry. 1728. A view of Sir Isaac Newton’s philosophy. London: S. Palmer. Pfautz, Christoph. 1688. Review of Newton’s Principia. Acta Eruditorum.: 303–315. Rohault, Jacques. 1671. Traité de physique. Paris: Vve de C. Savreux. Sarton, George. 1948. The Study of Early Scientific Textbooks. Isis 38 (3/4): 137–150. Sepper, Dennis L. 1994. Newton’s Optical Writings. New Brunswick: Rutgers University Press.

 Charles Morgan. Six philosophical dissertations on the mechanical powers. Elastic bodies. Falling bodies. The cycloid. The parabola. The rain-bow. Published by Dr. Samuel Clarke in his notes upon Rohaults Physics. Cambridge: printed by Fletcher and Hodson, and sold by J. Nicholson, 1770. 16

156

V. Schüller

Snobelen, Stephen D. 1998. On reading Isaac Newton’s Principia in the 18th century. Endeavour 22: 159–163. Whiston, William. 1748. Historical Memoirs of the Life and Writings of Dr. Samuel Clarke. 3rd ed. London: printed for John Whiston. ———. 1710. Praelectiones physio-mathematicae. Cambridge.

Chapter 7

Kant on Extension and Force: Critical Appropriations of Leibniz and Newton Eric Watkins

Abstract  This paper describes Kant’s complex position on extension, showing how it emerges from the various ways in which he reacts to the views of Descartes, Locke, Newton, and Leibniz. Specifically, the paper argues that Kant’s views are closer to Leibniz’s than they are to those of Descartes, Locke, and Newton, insofar as Kant and Leibniz both reject the view that extension is a fundamental property, holding instead that it is explicable (at least in part) on the basis of more fundamental forces. Kant disagrees with Leibniz, however, insofar as he rejects Leibniz’s distinctive commitments to certain metaphysical doctrines (such as pre-established harmony) and to active and passive primitive and derivative forces, opting, instead, for a Newtonian inspired conception of attractive and repulsive forces. In this way, the Critical Kant develops a hybrid position that attempts to make good use of aspects of both Leibniz’s and Newton’s accounts as he articulates his own distinctive position. In the history of modern philosophy Kant is often taken to be most fundamentally an epistemologist, with his revolutionary “Critical turn” bringing about a grand synthesis of the rationalist and empiricist traditions, each of which emphasizes either reason or the senses as the exclusive source of knowledge. He does so by famously arguing that “[w]ithout sensibility, no object would be given to us, and without understanding none would be thougt … Only from their unification can cognition arise” (A51/B75).1 However apt this description may or may not be, it is clear that

 I. Kant, Critique of Pure Reason, edited and translated by Paul Guyer and Allen Wood (Cambridge: Cambridge University Press, 1998). As is standard, A and B refer to the first and second editions of the Critique, respectively. All references to the Metaphysical Foundations and other works by 1

E. Watkins (*) University of California, San Diego, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_7

157

158

E. Watkins

it must be supplemented significantly. For in addition to his groundbreaking contributions outside theoretical philosophy in the realm of ethics and aesthetics, Kant has serious interests in physics throughout his career, and although Kant’s views in physics are heavily indebted to his epistemological doctrines, it is clear that epistemological issues alone are not always decisive.2 In this paper I argue that Kant’s treatment of extension illuminates how he resolves issues that arise at the level of physics in a way that goes beyond his epistemology. More specifically, I argue that on the issue of extension, against the background of Newton, Locke, Descartes, and Leibniz, Kant takes recourse to elements of a broadly Leibnizian metaphysical conception of force, albeit for reasons somewhat different from Leibniz’s. At the same time, he utilizes aspects of a Newtonian conception of force employed in physics so as to avoid what he takes to be indefensible aspects of Leibniz’s metaphysical position. In short, Kant appropriates in a unique and subtle way elements of both Leibniz’s and Newton’s positions to resolve the difficulties that he sees each one facing. Along the way, we can see that since the elements of Leibniz’s and Newton’s positions that Kant draws on and the ways in which he supplements and modifies them do not stem exclusively from his own epistemology, an accurate description of Kant’s goals and achievements must go beyond purely epistemological concerns to include issues in both physics and metaphysics.

7.1 Newton, Locke, Descartes, and Leibniz on Extension 7.1.1 Newton, Locke, and Descartes on Extension as a Primitive To see the complexities involved in Kant’s position on extension, first consider briefly Newton’s, Locke’s, and Descartes’s positions. What unites these three thinkers is their view that extension is a primitive feature of what they call body, matter, or corporeal substance, despite their disagreements about how it is perceived and what role it might play in different kinds of scientific explanation. Newton holds not only that extension (e.g., size and shape) is a primitive property of bodies, but also that bodies are not naturally divisible and thus must consist of atoms.3 Locke claims that extension (which he sometimes calls “Bulk, Figure, Texture”4) is an example of what he calls a primary quality, i.e. a property that is “utterly inseparable from the

Kant, except the Critique of Pure Reason, will indicate in parentheses the volume and page number of Kant’s Gesammelte Schriften ed. Königlich Preussische Akademie der Wissenschaften, Berlin 1902-, Volumes 1–29. All translations are my own. 2  See Watkins (2019), Chapter 4, for one broadly epistemological line of argumentation. 3  Cf. Newton’s Opticks. 4  John Locke, An Essay concerning Human Understanding II.8.10.

7  Kant on Extension and Force: Critical Appropriations of Leibniz and Newton

159

Body”5 and that cannot be explained by any more fundamental property of that body. Instead, other properties, so-called secondary qualities (e.g., colors, sounds, and tastes), are to be explained through recourse to such primary qualities. Descartes asserts that extension is not only a primitive property of bodies, but also their ­‘principal attribute’, which means that “everything else which can be attributed to body presupposes extension” because a thing’s principal attribute “constitutes its nature and essence and [is that] to which all of its other properties are referred”.6 Thus, Newton, Locke, and Descartes agree that extension is a primitive feature of matter that neither requires nor admits of further explanation. While one might suspect that a single set of epistemological concerns would underlie Newton’s, Locke’s, and Descartes’s acceptance of extension as a primitive, the full story is complicated. From an empiricist’s perspective (e.g., Newton’s and Locke’s), the fact that one can sense extension through sight and touch might seem to support its privileged status insofar as extension is thereby grounded in a fairly direct way in the senses rather than in innate ideas, of which empiricists are skeptical. However, according to an empiricist, having a sensible idea is at best necessary and certainly not sufficient for asserting the existence of a property, and one would need an additional reason to privilege one sensible property over any other, as is the case when extension is taken to be primitive. For Newton and Locke, extension would seem to be privileged primarily due to the explanatory role that it plays in the empirical sciences of the day (e.g., astronomy, optics, and chemistry). Moreover, even if empiricist considerations were to indicate that extension should be privileged, they are unlikely to apply to Descartes, who precedes Newton and Locke by several decades and is not typically classified as an empiricist. Now Descartes has a distinctive epistemological ground for privileging extension, for on his view the human intellect can perceive extension clearly and distinctly, a feature of perception that stands in contrast to the epistemological factors typically stressed by empiricists (e.g., sensory impressions). Further, clear and distinct perception would seem to be more closely related to the kind of certainty attainable in mathematical physics than to the evidence available in, say, chemistry or applied physics (e.g., astronomy and optics). Thus, while epistemological concerns play an important role in Newton’s, Locke’s, and Descartes’s acceptance of extension as a primitive, their concerns are significantly different. What’s more, it is clear that considerations at the level of particular sciences (i.e. different branches of natural philosophy) are important factors in extension’s special status insofar as extension appears to be a crucial element of the explanations each of these figures develops for whatever other properties bodies are supposed to possess. Thus, despite Newton’s, Locke’s, and Descartes’s agreement on the fundamentality of extension, no common epistemological rationale seems to underlie this agreement.

 Ibid., II.8.9.  René Descartes, Principles of Philosophy Part I, 53.

5 6

160

E. Watkins

7.1.2 Leibniz on Extension Unlike Newton, Locke, and Descartes, Leibniz does not accept extension as a primitive feature of reality. Consistent with the fact that no common epistemological rationale supports Newton’s, Locke’s, and Descartes’s endorsement of extension’s privileged status, Leibniz reacts to their views in different ways. Consider first Leibniz’s reaction to Descartes’s view. Leibniz criticizes Descartes’s assertion that extension alone constitutes the essence of body on several grounds. For example, Leibniz argues that Galileo’s free fall experiments show that Descartes’s purely geometrical quantity of motion as measured by ‘mv’ (mass or volume times velocity) is not in fact conserved in nature.7 Moreover, given that Descartes derives the fundamental principles of his physics (including the relevant laws of motion) from his metaphysics, Leibniz takes his objection to Descartes’s physics to be an indication that Descartes’s metaphysics must be flawed as well.8 At the metaphysical level, one of Leibniz’s primary objections to Descartes is that extension alone cannot account for the reality of body.9 If extension alone were to constitute the essence of body and extension implies infinite divisibility, then body would be infinitely divisible. But if body were infinitely divisible, then no body could be simple (given that every body would be divisible). Yet Leibniz holds as a conceptual truth that what is real must be one or simple. As he puts it: “Being is one thing and beings are another; but the plural presupposes the singular, and where there is no being, still less will there be several beings. What could be clearer?”.10 In this context, Leibniz states the following principle as an axiom or “identical proposition” namely “that what is not truly one being is not truly one being either”.11 Since no body, understood in terms of extension alone, can have the unity required to be one being, no body can be a being at all. Therefore, if a body is to be real, extension alone cannot constitute its essence. Accordingly, Leibniz has both physical and metaphysical grounds for rejecting Descartes’s claim for the primacy of extension. Since Newton’s and Locke’s accounts differ from Descartes’s significantly, Leibniz sees the need to provide an independent reason for rejecting their position on extension. Ironically, Leibniz’s main criticism of Newton’s and Locke’s positions derives from Descartes. The very notion of an atom, as Newton and Locke understand the term, that is, as a spatially extended, but indivisible particle, is a contradiction in terms for both Descartes and Leibniz. For the spatiality of an atom  Gottfried Wilhelm Leibniz, “Discourse on Metaphysics” §17 and “A Brief Demonstration of a Notable Error of Descartes”. 8  See René Descartes Principles of Philosophy Parts I-II. 9  Cf. Gottfried Wilhelm Leibniz, “A New System of Nature and Communication of Substances, and of the Union of the Soul and Body”. Late in his career Leibniz may hold that all relations must be reducible to monadic properties. If so, spatial relations must then be reducible to non-spatial properties of monads. 10  “From the Letters to Arnauld” in Philosophical Essays, translated by R. Ariew and D. Garber, Indianapolis/Cambridge: Hackett Publishing Company, p. 86. 11  Ibid. 7

7  Kant on Extension and Force: Critical Appropriations of Leibniz and Newton

161

necessarily implies that it is infinitely divisible, which in turn implies that it cannot be an atom, that is, indivisible. Thus, Leibniz concludes that Locke’s and Newton’s position with respect to extension is just as untenable as Descartes’s, even if his reasons for objecting to their understanding of extension are different.12 Leibniz’s own view is that extension, a purely geometrical property, must be supported by something more metaphysically fundamental, since only something metaphysically real is capable of supplying the unity that extension (with its infinite divisibility) lacks and that the reality of body requires. Leibniz describes this metaphysical entity in a variety of ways, sometimes as a metaphysical point, sometimes as an Aristotelian substantial form, or entelechia, and sometimes as a force. In his Specimen Dynamicum (1695), Leibniz develops a physics based on this notion of force by distinguishing, e.g., between active and passive forces as well as between primitive and derivative forces. Given these and other distinctions, Leibniz describes his own view in contrast to Descartes’s plenist position and Newton’s and Locke’s atomistic position as follows. Against Descartes, Leibniz asserts that bodies essentially have what he calls ‘living force’ or ‘mv2’, which signals a metaphysical component to bodies, and claims that it rather than what Descartes understands as the quantity of motion (or ‘mv’) is conserved in nature. With respect to Newton and Locke, Leibniz replaces their “material atoms” (where ‘material’ is taken to include ‘spatial’) with his own “formal atoms”. By describing his own forces (or metaphysical points, substantial forms, etc.) in this manner, he hopes to retain one desirable aspect of Newton’s and Locke’s atomistic position, namely that its ultimate constituents can stop an explanatory regress, but without being forced to give up the infinite divisibility of spatial bodies. By reacting to Descartes, Newton, and Locke in these ways, Leibniz hopes to provide a satisfactory physics and metaphysics for extension.

7.2 Kant’s Objections to Extension as Primitive With respect to extension, Kant sides with Leibniz against Newton, Locke, and Descartes on two crucial points. First, he rejects the claim that extension is a primitive property of reality. Second, he accepts the view that extension depends on force. In the Dynamics chapter of the Metaphysical Foundations of Natural Science Kant favors what he calls the metaphysical-dynamical mode of explanation over the mathematical-mechanical mode by arguing that (dynamical) force is necessary for matter to fill a space.13 Thus, for Kant as for Leibniz, extension is not a primitive, but rather stands in need of further explanation, an explanation that in both cases essentially involves force.

 Leibniz also objects that atoms would violate the law of continuity in impact.  Kant explicitly associates the dynamical mode of explanation with Newton due to (his understanding of) Newton’s introduction of the force of gravity. 12 13

162

E. Watkins

However, these fundamental points of agreement should not obscure important differences between Kant’s and Leibniz’s positions. First, Kant explicitly attacks Leibniz’s criticisms of Newton, Locke, and Descartes. Second, and in light of this, Kant must develop his own objections to Newton, Locke, and Descartes to be justified in accepting force as the ground of extension. Moreover, and most importantly, as we shall see in the next section (3), despite the fact that Kant accepts the core meaning of Leibniz’s concept of force, Kant’s notion of force departs from Leibniz’s in significant, in fact, ironically enough, in Newtonian ways.

7.2.1 Kant’s Rejection of Leibniz’s Criticisms of Extension as a Primitive Recall briefly Leibniz’s two main metaphysical criticisms of the view that extension is a primitive feature of body. Against Descartes, Leibniz objected that extension could not be the sole essence of body because its infinite divisibility (i.e. the lack of simple parts) is inconsistent with the unity that is required for real being. Against Newton and Locke he objected that a spatial atom is a contradiction in terms because spatiality implies divisibility. Kant rejects both of these objections or at least modifies them so significantly that they become his own. Let us start by considering Kant’s reaction to Leibniz’s objection that extension’s infinite divisibility is inconsistent with the reality of body. In this case, the basis for Kant’s rejection of Leibniz’s objection lies in his metaphysics, more specifically, in Transcendental Idealism. One might think that Kant’s Transcendental Idealism would provide an immediate and obvious reply to Leibniz’s criticism of Descartes as follows. Leibniz’s criticism is conditional in nature. If body is real, then extension alone cannot constitute the nature of body. Given that Kant is an idealist, it might seem that he would simply deny the antecedent and thus avoid the consequent.14 That is, body is not real and extension could therefore constitute its nature. However, Kant’s criticism of Leibniz’s objection is much more interesting than this. For what he rejects about Leibniz’s objection is the conceptual truth according to which being and unity are reciprocal concepts. His ground for rejecting this “truth” is that it holds only for things in themselves, not for appearances. In particular, Kant asserts that in the case of bodies, being does not require unity. How is that possible? As Kant explains in the Dynamics chapter of the Metaphysical Foundations (but in similar fashion in the first Critique’s Antinomies chapter): This platonic concept of the world that Leibniz developed is correct in itself insofar as the world is regarded not as an object of the senses but as a thing in itself, i.e. as merely an object of the understanding which nevertheless underlies the appearances of the senses. Now, the composite of things in themselves must certainly consist of the simple; for the parts must here be given prior to all composition. But the composite in the appearance does  Given that Leibniz is an idealist, it is clear that his point is supposed to be an internalist critique of Descartes. 14

7  Kant on Extension and Force: Critical Appropriations of Leibniz and Newton

163

not consist of the simple, because in the appearance, which can never be given otherwise than as composite (extended), the parts can be given only through division and thus not prior to, but only in the composite. (4:507–8)

Kant’s position is as follows. With respect to things in themselves, it is correct to maintain that a composite whole depends for its existence on the plurality of simple parts that compose it. For bodies, however, while Kant maintains that it is true that bodies depend on the parts that compose them, these parts must themselves be spatially extended and therefore, regardless of how much they are divided, can never be simple, pace Leibniz. As a result, the composition relation for bodies is significantly different. Bodies, as spatially extended beings, are not principles of unity and cannot be divided into principles of unity that would still be spatial, even if they are necessarily divisible into their parts. I return to some of the complexities that Kant’s account of body encounters below. For now, it suffices to see that Kant can reject Leibniz’s criticism of Descartes on this point and thus ends up with a position that is interestingly different from Leibniz’s.15 Let us now turn to Kant’s attitude towards Leibniz’s objection to Newton’s and Locke’s atomism. Kant agrees with Leibniz that spatiality implies infinite divisibility, but maintains that one must distinguish between mathematical and physical divisibility.16 Mathematical divisibility requires merely that the various parts of space can be differentiated (spatially, in thought), whereas physical divisibility implies that the parts of matter that fill space can be moved and thus separated from each other (4:503). Since separating parts from each other is but one of many possible ways of differentiating parts, physical divisibility is a much narrower concept than mathematical divisibility. Accordingly, the spatiality of matter immediately entails only its mathematical, not its physical divisibility to infinity. Thus, Kant can be seen as replying to Leibniz’s objection to atomism on behalf of Newton and Locke by suggesting that atoms could be mathematically, but not physically divisible to infinity. Kant is interested in the distinction between mathematical and physical divisibility not only because it has important implications for Newton’s and Locke’s atomistic position, but also because it is of crucial importance to a position he himself had held earlier in his career. In the Physical Monadology (of 1756) Kant thought of matter as consisting of physical points that fill space by means of the exercise of attractive and repulsive forces. In this way, he hoped to reconcile the infinite divisibility of space, which mathematicians insist on, with monads, which can satisfy the metaphysician’s desire for intelligibility by means of the principle of unity inherent in monads. The physical monadologist’s position is possible, however, only if one  Although Kant does not accept Leibniz’s main metaphysical objection to Descartes, he may share some of Leibniz’s physics-based objections. His stance on the vis viva debate is expressed in Thoughts on the True Estimation of Living Forces (1747) and in the Metaphysical Foundations, where he attempts to reconcile the two positions (though the importance of the issue is clearly much diminished in the latter work.) 16  As Kant puts it: “By the proof of the infinite divisibility of space, that of matter has not by a long way been proved” (4:504). 15

164

E. Watkins

can distinguish between mathematical and physical divisibility. For the physical monadologist needs to be able to claim that the sphere of activity of a monad is divisible, without asserting that the monad itself is divisible. By characterizing the sphere of activity as spatial and thus as divisible and the monad as physical and, since it is a point, indivisible, the physical monadologist can avoid the contradiction that the competing demands of the mathematician and the metaphysician can otherwise lead to. Without going into the details of Kant’s argument in the Metaphysical Foundations for the infinite physical divisibility of matter (which, if successful, demonstrates the falsity of his earlier physical monadology),17 it suffices to note that the argument presupposes that extension is not a primitive because it assumes the exercise of attractive and repulsive forces. In the context of the Dynamics chapter of the Metaphysical Foundations, where Kant develops extended arguments for attractive and repulsive forces, such a presupposition is appropriate. However, insofar as we are interested in understanding Kant’s rejection of Newtonian and Lockean atomism, it implies that Kant’s argument for the infinite physical divisibility of matter will not be of direct help. Since Kant cannot rely on Leibniz’s objection to Locke and Newton (given that he has developed the distinction between mathematical and physical divisibility in the way that he has), he must develop one of his own.

7.2.2 Kant’s Arguments Against Atomism Kant raises two main objections to Newton’s and Locke’s position.18 First, the concept of “absolute impenetrability”, which is implicit in Newton’s atomistic position, is, according to Kant, a “qualitas occulta”. His justification is as follows: “For if one asks what the reason is why matters cannot penetrate one another in their motion, one receives the answer: because they are impenetrable” (4:502). Whether or not Kant is accurate in labeling absolute impenetrability an occult quality,19 he does seem to be justified in exposing the emptiness of explanations that invoke absolute impenetrability in clarifying why matter cannot penetrate other matter, since to attribute absolute impenetrability to matter seems to say only that matter cannot be penetrated. In particular, such an account does not explain why or in virtue of what feature it is that matter cannot be penetrated. Kant’s own dynamical position has an advantage on this point over the atomistic one insofar as Kant can give at least a partial explanation of why matter is impenetrable, namely in terms of “the concept of an active cause and of its laws in accordance with which the effect, namely  See Eric Watkins, Kant on Laws, Chapter 6 for a detailed reconstruction of this argument.  Kant does consider the advantages and disadvantages of what he calls the mathematical-mechanical (which he seems to identify with the atomistic position) vs. the metaphysical-dynamical (of which his own is one instance) modes of explanation. However, he does not claim that he can establish either one of these explanations as being definitively preferable to the other. 19  Descartes raises a similar objection against the scholastics’ substantial forms. 17 18

7  Kant on Extension and Force: Critical Appropriations of Leibniz and Newton

165

resistance in the filled space, can be estimated according to its degrees” (4:502). As we shall see below and as Kant himself notes later in this passage, there are limits to the explanatory power (and consequently the advantage) of his position (over the atomistic position) insofar as the fundamental (attractive and repulsive) forces that are invoked to explain impenetrability cannot in turn be explained in terms of any other more fundamental force (4:513). Still, Kant takes even such a limited explanatory advantage as an advantage of his dynamical account over the atomistic position. Second, following his explicit proof of the necessity of moving forces in the Dynamics chapter (Proposition 1, 4:497), Kant explains how this proof applies to those, like Lambert, who accept “solidity” as a primitive feature of matter.20 According to their concepts the presence of something real in space would have to carry this resistance with it by its very concept, hence according to the principle of contradiction, and make it that nothing else could be in the space of the presence of such a thing at the same time. But the principle of contradiction does not repel any matter that approaches in order to penetrate into a space in which another matter is to be found. (4:497–8)

Kant’s objection in this passage is far from straightforward. It might appear as if he is attributing a rather uncharitable interpretation to his atomistic opponents insofar as he construes solidity as a concept, which then allows him to infer that it is supposed to be the principle of contradiction that excludes the possibility of penetration. Descartes, who does not accept either forces or solidity, will need to give a different explanation of why bodies do not penetrate each other, and Leibniz, who, on Kant’s analysis in the Amphiboly chapter of the first Critique, mistakes real for logical opposition, might be guilty of trying to give purely conceptual explanations by means of the principle of contradiction, but it does not seem appropriate to level the same charge against empiricists such as Locke or Newton, since they explicitly accept solidity as a feature that one can directly sense, not as an abstract concept accessible only through reason. I would suggest, rather, that Kant’s objection to solidity is based not on such an uncharitable reading of the atomistic position, but rather on understanding solidity as an intrinsic property of a body, i.e. a property that a body is supposed to have in virtue of its very existence and regardless of the existence of other things (and thus irrespective of the relations the body might or might not have to other things). If solidity is an intrinsic property of a body, then, so Kant wants to object, it cannot by itself explain why a body is impenetrable or why one body could not change the size and shape of another. For the question of whether one body could change the size and shape of another would seem to depend on the relation between the two bodies, and appealing only to their intrinsic properties cannot suffice. Now, the atomist might respond by granting that impenetrability expresses a relational property but then argue that such a relation depends on the intrinsic properties of each of the bodies, namely their solidity. However, in addition to his general thesis in the first

 Although Kant mentions only Lambert by name, it is safe to assume that he would also have Locke and Newton in mind as well. Locke explicitly mentions solidity as a primary quality (II.8.9) and with respect to Newton it is only in virtue of their solidity that atoms are indivisible. 20

166

E. Watkins

Critique (B66–67) that appearances consist entirely in relations (and thus would seem to lack intrinsic properties such as absolute solidity), Kant holds that the intrinsic property of solidity is not of the right kind to ground the relational property of impenetrability. For impenetrability is a dynamical or causal relationship between bodies (pertaining to changes in motion), whereas solidity is a property a body has merely by means of its existence, as opposed to one that it would have by means of its causal activity on other bodies. Consequently, solidity, an intrinsic, static property, cannot explain impenetrability, a relational, dynamic property, and thus the atomistic position cannot explain this crucial feature of body.21 Accordingly, we have now seen that Kant does not accept Leibniz’s criticisms of Newton and Locke, just as he did not accept Leibniz’s criticisms of Descartes. However, rather than accepting Newton’s, Locke’s, or Descartes’s position, he develops his own independent criticisms of their views with the result that he can side with Leibniz on the issue of extension as a primitive even if his reasons and ultimate position are different from Leibniz’s.

7.3 Force and Causality Given that Leibniz and Kant agree that extension is not a primitive property insofar as force is necessary to explain it, the crucial question becomes: How do Leibniz and Kant conceive of force and how do they think that it can be invoked to explain extension? In this section of the paper, I argue that Leibniz and Kant agree on several important features of force, namely on its links with causality, activity, and substantiality and on the general thesis that physics requires support from metaphysics, but that they disagree on two significant issues, namely, on the fundamental metaphysical principles underlying physics and on how to characterize the kinds of basic forces.

7.3.1 Leibniz on Force To compare Leibniz’s and Kant’s conceptions of force, it is necessary to keep in mind a few salient aspects of Leibniz’s broader position. As noted above, Leibniz makes a number of distinctions regarding force. There are active and passive forces, primitive and derivative forces, living and dead forces, to mention but a few. The most important ones for our purposes can be described as follows. Derivative active force causes a body’s velocity and acceleration, while derivative passive force causes a body’s resistance, impenetrability, and extension. Primitive active force is  For interesting discussions of the issues raised by this objection, see Rae Langton, Kantian Humility Oxford: Oxford University Press, 1998, and Daniel Warren “Kant’s Dynamics” in Kant and the Sciences, ed. Eric Watkins, Oxford: Oxford University Press, 2000. 21

7  Kant on Extension and Force: Critical Appropriations of Leibniz and Newton

167

responsible for the unity, identity, and activity of a substance just as primitive passive force is responsible for the passivity of a substance (that is, the fact that it can be acted upon and take on or resist taking on certain properties). Despite significant differences, there is a core notion of force that underlies many if not all of these different kinds of force. A force, for Leibniz, is a principle of activity by which a change of state can be brought about or caused. Two crucial constituent notions involved in force are thus activity and cause of a change of state. Also of crucial importance to Leibniz’s theory of forces is the way in which forces are involved in physics being grounded in metaphysics. As we have seen above, derivative forces are directly responsible for several common properties of bodies (such as velocity, extension, impenetrability, etc.), but the derivative forces are still derivative, i.e. they depend on primitive forces. Thus, the physical properties of a body ultimately depend on the primitive forces of substance. What exactly are the primitive forces and how do they ground or support the derivative forces? According to Leibniz, the primitive forces are the basic metaphysical components of substance. Primitive active force corresponds to the soul or substantial form of a substance, i.e. that which is supposed to make actual the various properties that a substance might have. By contrast, primitive passive force is supposed to be “primary matter in the schools, if correctly interpreted,”22 i.e. that which has the ability to take on or resist taking on a variety of properties. It is the former that contains the unity that is required for being and that extension per se lacks. The grounding relationship between metaphysics and physics is a complex issue for Leibniz. Still, we can identify two fundamental ways in which Leibniz thinks that physics stands in need of support from metaphysics. First, he thinks that metaphysics can give physics a kind of intelligibility that it does not have on its own. More specifically, certain concepts in physics may be understood properly only if analyzed in terms of metaphysical concepts. For only metaphysics is in a position to provide an ontological account of what is real and what is imaginary or ideal in bodies. Leibniz’s primary metaphysical criticism of Descartes nicely illustrates how physics depends on metaphysics in this sense. Extension, a geometrical concept, is not fully intelligible when applied to the bodies of physics, since it requires metaphysical or ontological concepts (e.g., parts, wholes, force, and true unities) to be understood properly. In other words, to understand what is real in a body (as opposed to what is imaginary or ideal), it cannot be understood merely as extended, since it would then would lack the unity required for being, but must rather be understood by taking recourse to ontological concepts (formal atom, substantial form, metaphysical point) that, by contrast, are intelligible on Leibniz’s view. Second, the laws of physics depend, for Leibniz, on the laws of metaphysics. This occurs in at least two ways. First, Leibniz asserts that the laws of physics cannot be systematically derived without the laws of metaphysics. For example, in Part I of the Specimen Dynamicum Leibniz claims that the laws of motion cannot be

22

 “Specimen Dynamicum” in Philosophical Essays, p. 120.

168

E. Watkins

derived from the (geometrical) laws of extension alone, but rather must be supplemented by metaphysical laws, such as the law of continuity, the law of the equality of the cause and its effect, etc. Second, Leibniz thinks that metaphysical laws can have direct implications for the laws of physics, even where the metaphysical laws do not explicitly figure into their derivation. This point can be illustrated by considering an implication for physics that Leibniz draws from one of his best-known metaphysical doctrines, namely pre-established harmony. According to pre-­ established harmony, each finite substance can act not on another, but rather only on itself. Despite the fact that finite substances cannot act on each other, their states will still harmonize with each other, since God created the best possible world (with as much harmony as possible) and he did so before the beginning of time (making the harmony pre-established). Late in his career, Leibniz describes the force by which a substance acts on itself as appetition, an activity by virtue of which a substance passes from one internal representational state to another (with the aim of increasing its degree of perfection by pursuing what appears to it to be good). Pre-­ established harmony thus opposes what was sometimes referred to as physical influx, according to which one finite substance can act on another, and occasionalism, which denies that a finite substance can have any causal efficacy at all, making room for God (an infinite substance) to display his omnipotence and omniscience by being the sole true or real cause of everything in the world at every moment.23 What Leibniz takes pre-established harmony to imply for physics is that, harmonious appearances to the contrary, bodies do not in fact act on each other, not even in impact. In A New System of Nature (1695) Leibniz explicitly (and, in fact, proudly) draws this consequence of pre-established harmony for physics by asserting that “in the impact of bodies, each body suffers only through its own elasticity, caused by the motion already in it”.24 In other words, although it looks as if two bodies actually strike each other (i.e. act on each other causally) in impact and thereby determine each other’s motion, in fact each body determines its own motion.25 In this way too, we can see how for Leibniz the laws of physics require the support of metaphysics. Given these two ways in which Leibniz takes metaphysics to support physics, one can now see how Leibniz’s account of primitive and derivative forces is based on his desire for an ontology that would render physics intelligible. The Specimen Dynamicum (1695) can be read as a detailed and systematic attempt to relate the metaphysical truths Leibniz has previously established with the principles of physics he is focussing on at the time. Based on his criticisms of Descartes’s physics, Leibniz holds that any adequate physics requires something more than mere extension insofar as extension does not have the kind of unity that being requires. He also knows that substance (as composed of form and matter) does have the requisite  See Watkins (2005), for fuller discussion of Leibniz’s and Kant’s views on causality.  Philosophical Essays, p. 145. 25  In Leibniz’s later period, where bodies are mere representations (as opposed to corporeal substances) he holds that, properly speaking, bodies cannot act at all (i.e. not even on themselves), since bodies do not really exist and only substances (which are real) can act. 23 24

7  Kant on Extension and Force: Critical Appropriations of Leibniz and Newton

169

unity and causality. Thus, he believes that he can explain extension as a property of bodies in physics if he can draw on the requisite metaphysical principles. Primitive and derivative forces are supposed to provide the requisite link. Later in his career, when emphasizing detailed issues in physics less and his fully idealistic metaphysics more, Leibniz tends to describe the way in which metaphysics grounds physics by asserting simply that bodies are nothing but well-founded phenomena that ultimately reduce to monads, that is, immaterial substances endowed with basic forces of representation and appetition, but without always explaining what “well-founded” means or how exactly bodies are to “reduce” to monads. In this way, we can see, at least in principle, if not in all of its details, how Leibniz thinks that force is supposed to explain extension and, at a more general level, how metaphysics is supposed to support physics. Extension, along with its related properties (e.g., impenetrability and motion), is accounted for by derivative forces (both passive and active), which, in turn, are to be explained in terms of primitive forces that are properly metaphysical insofar as they constitute substance. Further, the laws that pertain to substance at the metaphysical level (e.g., pre-­established harmony) can have direct implications for bodies (e.g., that bodies do not in fact act on each other). Metaphysics can support physics in this way because the primitive forces, which have unity, identity, and activity, are ontologically intelligible and, moreover, are (allegedly) capable of causing the properties that pertain to bodies because they are forces, that is, activities by which changes of state are brought about.

7.3.2 Kant on Force We can now turn to Kant’s conception of force by asking what he accepts and what he rejects in Leibniz’s conception of force. At the most fundamental level, Kant agrees with Leibniz that physics requires metaphysics and he even agrees about the general ways in which metaphysics grounds physics. Kant is quite clear in the Preface to the Metaphysical Foundations that physics requires metaphysical principles and in the course of his proofs of these principles he both provides what he hopes will be an adequate ontology for bodies by drawing on some of the first Critique’s central metaphysical concepts such as substance and causality, and he shows how some of the first Critique’s principles have implications for bodies at the level of physics.26 Thus, Leibniz and Kant agree in holding both that any adequate physical explanation of bodies must be supported by an ontological account in terms of substance, causality, and force, and that the laws of metaphysics can have implications for the laws of physics.

 Kant goes beyond Leibniz in maintaining that the metaphysical laws of physics in the Metaphysical Foundations require a priori rather than empirical proofs. This point is directed primarily against Newton, who gave what Kant calls merely “empirical proofs”, but the point of contrast could be relevant to Leibniz as well. 26

170

E. Watkins

Despite this fundamental agreement on the necessity of metaphysics for physics (and on the general ways in which metaphysics supports physics), Leibniz and Kant disagree on some significant features of the ontology required for physics. More specifically, according to what it is possible for human beings to cognize theoretically, Kant rejects Leibniz’s simple monads,; instead, he accepts infinitely divisible phenomenal substances that possess merely “derivative” forces.27 Consider first Kant’s rejection of the simplicity of substance. Kant still agrees with Leibniz that there must be substances that have causal powers or forces (thus involving activity) that are responsible for bringing about change in the world we experience. However, despite his attempts in the Physical Monadology to retain the simplicity of substance, in the Metaphysical Foundations Kant argues that one cannot provide a coherent explanation of impenetrability in terms of simples. Thus, he is ultimately forced to give up on simplicity for material substance, asserting instead the infinite divisibility of matter. Yet there is a sense in which Kant also rejects Leibniz’s primitive forces. As we saw above, Leibniz requires the primitive forces for the intelligibility of the notions of unity, activity, and causality of change of state involved in them. How can Kant retain the intelligibility so attractive in Leibniz’s metaphysics without retaining Leibniz’s particular version of metaphysics? By understanding matter as phenomenal substance, which, due to its spatiality, entails the rejection of the simplicity of substance, Kant denies that the particular kind of unity Leibniz posited at the level of monads has any special intelligibility with regards to matter.28 At the same time, by introducing substance at the phenomenal level of bodies Kant can retain the intelligibility of its activity and causality, which, because phenomenal, cannot be primitive.29 Thus, there is a way in which Kant can reject not just the simplicity of substance, but also Leibnizian primitive forces without the loss of intelligibility.

 If Kant thinks of things in themselves as roughly equivalent to Leibniz’s monads, then there is an important sense in which Kant retains Leibniz’s monads, but assigns them a different role. (One should note, however, that there are significant differences in detail between Leibniz’s monads and Kant’s things in themselves. Cf. Eric Watkins “Kant’s Theory of Physical Influx,” Archiv für Geschichte der Philosophie 77 (1995): 285–324, for an explanation of some important differences.) 28  This is consistent with viewing things as they are in themselves as providing metaphysical grounding for empirical objects. 29  In correspondence with De Volder (e.g., on June 20, 1703) Leibniz makes it clear (in response to De Volder’s attempt to construct bodies out of derivative forces alone) that there is another reason for claiming that derivative forces require primitive forces. Derivative forces are momentary and always changing. Consequently, their existence cannot be understood as that of a substance (an enduring principle of change) but rather presupposes such an existence. Accordingly, derivative force presupposes primitive force, because the existence of the former can be rendered intelligible (i. e. accounted for ontologically) only as a state or modification of the latter. However, because Kant attacks the identification of force and substance (that Wolff and Baumgarten explicitly embrace, following Leibniz), there is room for him to claim that constantly changing “derivative” forces require not immutable primitive forces that inhere in substance, but rather only an unchanging substance in which they themselves directly inhere. 27

7  Kant on Extension and Force: Critical Appropriations of Leibniz and Newton

171

Kant’s rejection of the simplicity of substance and Leibniz’s primitive forces is important because it suggests significant implications for the way in which metaphysics can support physics. As we saw above, Leibniz’s attempt to have metaphysics ground physics was motivated by the attempt to bridge the gap between the bodies of physics, which are not strictly speaking intelligible due to their lack of unity, and the simple substances of metaphysics, which alone possess unity in virtue of the simplicity of the monads and in virtue of the way in which primitive forces (of substantial form and matter) could constitute a substance. However, as soon as simplicity has been divorced from substantiality, from the perspective of physics one of the primary points of primitive forces has been removed.30 Consequently, from the standpoint of physics, the gap that has to be bridged between physics and metaphysics has been significantly diminished, even if not eliminated. Further, by limiting what one can cognize at the metaphysical level, it becomes possible for the grounding of physics by metaphysics to be driven more by physics. In other words, instead of thinking that one can start with complete intelligibility at the level of metaphysics (with, e.g., primitive forces) and proceed to physics (and its derivative forces) from there, rejecting simplicity seems to suggest that one start with physics and then simply see what it requires, fulfilling these requirements by whatever means one has at one’s disposal. In this way, one naturally ends up with “derivative” forces that may not depend on distinct and simple substances in any way that human beings can cognize.31 With respect to the concept of force, Kant agrees with Leibniz on many fundamental points, but he also disagrees with him on important details. The fundamental point of agreement is that Kant adopts the core metaphysical meaning of Leibniz’s notion of force. For both Leibniz and Kant, a force is an activity of a substance that brings about or causes a change of state.32 According to both Leibniz and Kant, the forces inherent in substance explain the fact that a body is, for example, extended and impenetrable. In fact, Leibniz’s and Kant’s acceptance of this core notion may be able to provide an additional (and even more fundamental) explanation of their rejection of extension as a primitive. If a body is extended, i.e. has a particular size and shape, it is natural to think that there must be some reason why it is extended to that degree, i.e. has that particular size and shape rather than any other. Given the different

Interestingly, Kant assumes, “indeed with high probability, that there must be a primitive power from which all others must come” (29:770), i.e. that the two forces he calls primitive, namely attractive and repulsive forces, are in all likelihood derivative. However, “we cannot reduce all powers to one, because the accidents are so different that we cannot take them as the same” (ibid.). 30  For discussion, see Watkins (2006). 31  For discussion of the complex relations between the objects at issue in physics and the things in themselves that must serve as their conditions in various respects, see Watkins (2019). 32  This core notion of force contrasts especially clearly with Hume’s account of causation in §§4, 5, and 7 of his Enquiry concerning Human Understanding. It also contrasts with Newton’s account of force in the Principia insofar as force can be described only mathematically, not metaphysically, because Newton explicitly denies attempting to provide an explanation of what nature is really like.

172

E. Watkins

possible states bodies can be in, it is difficult to concede, as atomists must, that the sizes and shapes of each and every body are all brute facts. Both Leibniz and Kant want to say that a force, which is a kind of cause, can explain why a body has the particular size and shape, i.e. extension, that it has. Against the background of this important agreement on the general concept of force, however, Kant disagrees with Leibniz on several crucial details. First, Kant rejects Leibniz’s pre-established harmony in favor of physical influx. In other words, force (e.g., appetition) for Leibniz is active only within a given substance, whereas Kant maintains that substances can act on each other. Part of the reason why Kant can reject Leibniz’s pre-established harmony is his prior rejection of significant aspects of Leibniz’s metaphysics (e.g., the simplicity of substance). However, one of Kant’s central reasons for rejecting pre-established harmony in favor of physical influx is based on considerations at the level of physics, since he wants to be able to say (as proponents of both common sense and Newtonian physics do) that bodies really do act on each other in collision. This point comes out very clearly in Kant’s discussion of his Third Law of Mechanics, where he provides an ontological interpretation of the equality of action and reaction according to which each body acts on the other. It also suggests that Kant’s metaphysics is driven (at least in part) by his physics more than is the case for Leibniz. Second, Kant rejects Leibniz’s characterization of the various kinds of forces that are required to explain bodies and their properties. As we saw above, Leibniz invokes primitive and derivative active and passive forces to explain bodies and their properties. By contrast, Kant invokes attractive and repulsive forces and even argues (in the Dynamics chapter of the Metaphysical Foundations, 4:498) that no more than these two are possible as fundamental physical forces. Why does Kant abandon Leibniz’s characterization of forces after having accepted his core notion of force (as a causal activity of a substance)? More specifically, if Kant thinks that we cannot have theoretical cognition of the existence of primitive forces, why does he not at least accept Leibniz’s account of active and passive derivative forces? As early as his Thoughts on the True Estimation of Living Forces (1747), Kant sees the general issue here in terms of the following dilemma. In invoking a force to explain the properties of a body (e.g., its motion or extension) one describes the force either as Newtonians do, namely by means of its effects (e.g., moving forces), or as Leibniz does, namely as an entelechia. The problem with the first horn of the dilemma is that such explanations are vacuous. To say that a moving force is a force that causes motion explains nothing, since the only content that one can attribute to a moving force is that it is whatever is associated with a motion. However, the other horn of the dilemma is not especially appealing either. For to say, as Leibniz does, that a force is an Aristotelian entelechia (which makes actual what is merely potential) is rather cryptic. In other words, Leibniz’s use of the notion of entelechia avoids the charge of vacuity, but only at the cost of obscurity. Kant attempts to resolve the dilemma by arguing that what is ultimately responsible for various central properties of bodies are attractive and repulsive forces. In part, Kant wants to guarantee intelligibility and avoid obscurity by characterizing forces in terms of their effects, which is precisely Newton’s view. However, one must

7  Kant on Extension and Force: Critical Appropriations of Leibniz and Newton

173

then ask how it is that Kant intends to avoid the charge of vacuity, given his adoption of what would appear to be Newton’s empiricist view. It is at this point that Kant will emphasize the core notion of a force that he has accepted from Leibniz, namely that a force is a causal activity of a substance that explains a change of state. Newton, who Kant understands to be trying to provide mathematical laws rather than metaphysical explanations, need not be committed to understanding forces in this way. By appealing to Leibniz’s core notion of force Kant can thus attribute a content to force that goes beyond its empirical effects such that explanations invoking forces are not vacuous. However, because Kant’s notion of force connects up not only with observable effects (bodies moving either closer together or further apart), but also with the ontology which he hopes to have shown in the first Critique to be intelligible in a non-Leibnizian way, he can assert that he has avoided the charge of obscurity. We can thus see how Kant’s account of force combines aspects of both Leibniz’s and Newton’s conceptions of force in an interesting and subtle way, while still avoiding, so Kant hopes, the difficulties he sees in their views. One should note, however, (as Kant himself does) that the forces he posits are not fully intelligible. For Kant asserts that attractive and repulsive forces are primitive, that is, we cannot explain them (even if they depend on metaphysically more primitive entities). These forces are primitive in part because they cannot be constructed in intuition a priori, clearly a limitation stemming from Kant’s unique epistemological concerns. However, they are also primitive in the sense that we do not have access to whatever it is in bodies that allows them to bring about changes by means of the activity of their forces. As Kant repeatedly remarks about any type of causality (therefore including the causality of forces), we simply cannot fully understand how one thing can bring about a change in another. Accordingly, Kant seems to think that this limitation is one that any account will have. As Kant notes: […] all natural philosophy consists in the reduction of given forces apparently diverse to a smaller number of forces and powers sufficient for the explication of the actions of the former. But this reduction continues only to fundamental forces, beyond which our reason cannot go (4:534).

7.4 Brief Methodological Conclusion We have seen not only that, but also why Kant thinks that fundamental physical forces are required for extension. Kant’s reasons for rejecting extension as a primitive and for characterizing force the way he does are not based primarily on his distinction between sensibility and understanding or between intuitions and concepts. Nor are they explicitly based on general features of what Kant refers to as possible experience. Rather, they stem from a variety of considerations, including those stemming from his own metaphysics and how, on his view, metaphysics can support physics. Appreciating Kant’s theoretical philosophy after the “Critical turn”

174

E. Watkins

thus quite naturally involves considerations that go beyond his revolutionary epistemology.33

References Descartes, René. 1644. Principia Philosophiae. Amsterdam: Ludovicum Elzevirium. Hume, David. 1961. In Enquiries Concerning the Human Understanding (1748, posthumously ed. 1777), ed. L.A. Selby-Bigge, 2nd ed. Oxford: Clarendon. Kant, Immanuel. 1910–1983. Gesammelte Schriften, ed. by (Königlich) Preußische Akademie der Wissenschaften and (Deutsche) Akademie der Wissenschaften (der DDR). 29 vols., Berlin; Leipzig: Akademie-Verlag, [AA]. Kant, Immanuel. 1998. Critique of Pure Reason, ed. and Trans. by Paul Guyer and Allen Wood. Cambridge: Cambridge University Press. [CPR]. Langton, Rae. 1998. Kantian Humility. Oxford: Oxford University Press. Leibniz, Gottfried Wilhelm. 1962. In Mathematische Schriften, ed. C.I.  Gerhardt, vol. 1–7, 1849–1863. Hildesheim: Olms. [GM]. ———. 1960–61. Philosophische Schriften, ed. C. I. Gerhardt. Vols. 1–7 (1875–90), Hildesheim: Olms. [GP]. ———. 1989a. Philosophical Essays, Trans. By R. Ariew and D. Garber. Indianapolis/Cambridge: Hackett Publishing Company. [PhE]. ———. 1686. [Discours de metaphysique]. [GP IV 427–63, PhE 35–68]. ———. “Brevis demonstratio erroris memorabilis Cartesii et aliorum circa legem naturae.” Acta eruditorum March 1686. [GM VI 117-19]. ———. “Syteme nouveau de la nature et de la communication de substances, aussi bien que de l’union qu’il y a entre l’ame et le corps.” Journal des savants June 1695. [GP IV 477-87, PhE 138–144]. ———. 1695. Specimen Dynamicum. Part I Acta eruditorum April 1695. [GM VI 234–54, PhE 117–138]. ———. 1989b. From the Letters to Arnauld. Philosophical Essays, Trans. By R.  Ariew and D. Garber, 69–90. Indianapolis: Hackett Publishing Company. Locke, John. 1690. An Essay Concerning Humane Understanding. London: printed for Th. Basset, and sold by Edw. Mory. Newton, Isaac. 1687. Philosophioae naturalis principia mathematica. London: J. Streater. Newton, Issac. 1730. Opticks: Or a Treatise of the Reflections, Refractions, Inflections and Colours of Light. 4th ed. London: printed for William Innys. Warren, Daniel. 2000. Kant’s Dynamics. In Kant and the Sciences, ed. Eric Watkins. Oxford: Oxford University Press. Watkins, Eric. 1995. Kant’s Theory of Physical Influx. Archiv für Geschichte der Philosophie 77: 285–324. ———. 1998a. The Argumentative Structure of Kant’s Metaphysical Foundations of Natural Science. Journal of the History of Philosophy 36: 567–593. ———. 1998b. Kant’s Justification of the Laws of Mechanics. Studies in the History of Philosophy of Science 29: 539–560.

 I thank the audience members at the conference held in the summer of 1999 at the Max Planck Institute for the History of Science in Berlin at which an earlier version of this paper was presented, in particular, Herbert Breger, Alan Gabbey, Konstantin Pollok, Wolfgang Lefevre, and Falk Wunderlich. I also thank Don Rutherford for helpful comments on the penultimate version of this paper. 33

7  Kant on Extension and Force: Critical Appropriations of Leibniz and Newton

175

———. 2005. Kant and the metaphysics of causality. New York: Cambridge University Press. ———. 2006. On the Necessity and Nature of Simples: Leibniz, Wolff, Baumgarten, and the pre-Critical Kant. In Oxford Studies in Early Modern Philosophy, vol. 3, 261–314. Oxford: Clarendon Press. ———. 2019a. Kant on Laws. New York: Cambridge University Press. ———. 2019b. Kant and the Grounding of Transcendental Idealism. Studi Kantiani 32: 103–118.

Chapter 8

Scotland’s Philosophico-Chemical Physics David B. Wilson

Abstract  The chapter focusses on the Scottish natural philosophy of the late eighteenth century represented by John Anderson (1726–1796) and John Robison (1739–1805), which is considered a link between Newton’s natural philosophy and nineteenth-century physics in Britain (Kelvin and Maxwell). Anderson and Robison have to be seen in a tradition of Scottish Newtonians established in the seventeenth century by David Gregory and John Keill and specifically shaped in the Mid-­ eighteenth century through the chemical-physical work of Joseph Black and the common-sense philosophy of Thomas Reid. These latter Newtonians built on Newton’s theory of matter and short-range forces as indicated in Query 31 of his Opticks (Black) but also on his Rules of Reasoning of the second edition of his Principia (Black and Reid) and in this way created the theoretical framework in which Anderson and Robison developed their natural philosophy. In the center of their natural philosophy, which was oriented on experimental investigations, were In addition to the lively discussion with the contributors of this volume at the Max Planck Institute for the History of Science, I am grateful for helpful comments and questions after I presented versions of this material in talks at: a conference on “200 Years of Useful Learning” at Strathclyde University; the Midwest Junto for the History of Science; the Institute for Advanced Studies in the Humanities of Edinburgh University (IASH); the Dibner Institute for the History of Science; a Conference on Medicine, Science, and the Enlightenment sponsored by IASH; a Seven Pines Conference; and the History of Technology and Science Program at Iowa State University. My research has been greatly assisted by visiting research fellowships at IASH and at the Dibner Insitute. It has been supported by grants from the National Science Foundation, the Royal Philosophical Society of Glasgow, and Iowa State University. For permission to quote from manuscripts that they hold, I am grateful to St. Andrews University Library, The Andersonian of Strathclyde University, Edinburgh University Library, and the Beinecke Library of Yale University. J. Malcolm Allan has been especially helpful to me regarding materials in the Anderson Collection. In Edinburgh, I have benefitted from the assistance of Michael Barfoot, Erica Thomas, and Jean Jones D. B. Wilson (*) Department of History, Iowa State University, Ames, Iowa, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_8

177

178

D. B. Wilson

the manifold open questions of the Baconian sciences of that time - theories of heat, light, electricity, magnetism as well as the understanding of the phlogiston. The chapter thus provides insight into the specific way in which the Newtonian camp participated in early modern natural philosophical speculations about minute particles of matter, fluids, or the propagation of light and heat. The physics of Lord Kelvin and James Clerk Maxwell drew on the natural philosophy of the Scottish Enlightenment. John Anderson and John Robison, both Newtonians of course, were the most significant Scottish professors of natural philosophy in the eighteenth century  – Anderson for four decades at Glasgow University, from 1757 until his death in 1796, and Robison for three decades at Edinburgh University, from 1774 until his death in 1805. Anderson taught William Meikleham, who was the Glasgow professor of natural philosophy during Kelvin’s undergraduate years there, and Anderson shaped the overall structure of the Glasgow natural philosophy course that continued through Kelvin’s early professorship. Robison, it has been argued, defined a particularly Scottish approach to natural philosophy that influenced Meikleham and later Kelvin and Maxwell. The most direct path from Newton to Kelvin and Maxwell passed through Enlightenment Scotland. Among scholars of this period, the prevailing thesis is that the influence of Scottish common-sense philosophy wrought a non-hypothetical physics. Thomas Reid scorned hypotheses in his An Inquiry into the Human Mind on the Principles of Common Sense, published in 1764, and his scorn carried the day. In the early nineteenth century, this Scottish view militated against acceptance of the wave theory of light with its luminiferous ether, and a few decades later, with Robison as intermediary, Scottish common-sense philosophy informed the revolutionary physics of the two Scottish physicists, Kelvin and Maxwell. (Laudan, Reid; Cantor, Brougham; Olson, Scottish Philosophy; Smith and Wise, Energy and Empire). This chapter revisits the earlier history of Reid’s book, the formative period, one would expect, of Reid’s long-lasting reputation. The years from about 1760 to about 1785 embraced not only the initial response to Reid’s Inquiry, but also much of the professorial tenures of Anderson and Robison. This period preceded the publication of Reid’s later works as well as Robison’s many articles for the Encyclopaedia Britannica written near the end of his life. It also preceded two other events that eventually influenced the story: publication of Lavoisier’s Elements of Chemistry and the outbreak of the French Revolution, both in 1789. This quarter century thus includes the Scottish context of Reid’s publication and marks a well-defined era in Scottish natural philosophy. To explore this period, we must first examine Glasgow University in the 1760s. Ideas forged by the remarkable group of intellects who were then there shaped Scottish thought for at least the next two decades, in both Edinburgh and Glasgow. Joseph Black and John Anderson are the men heretofore largely overlooked in this history. Black has attracted attention as a chemist, but not as a natural philosopher.

8  Scotland’s Philosophico-Chemical Physics

179

Anderson has attracted very little notice.1 Though Robison has hardly been ignored, the ideas of his early professorship for the most part have been. Hence, though much has been written about Reid, scholars have said little about him with respect to these men surrounding him in the early decades of his influence. Comprehending these decades requires both an appreciation of the importance of Black’s methodological differences from Reid and an understanding of the content of Anderson’s and Robison’s courses in natural philosophy. This chapter thus contains two main sections – the first on Glasgow in the 1760s focusing on Reid and Black, the second comparing Anderson’s and Robison’s courses in the years around 1780.

8.1 Joseph Black and Thomas Reid in the 1760s In the 1760s, Glasgow University had fourteen professors, distributed among four “faculties”: arts, medicine, theology, and law. There were only 400 to 500 students with just over twenty degrees granted each year. The professors met formally several times per session to conduct the business of the university. It is difficult to imagine their having been unaware of one another or of one another’s leading ideas. We know that they formed many close connections, the long friendship of Black, Robison, and James Watt probably being the best known (Robinson and McKie, Partners in Science). The following graph indicates the tenure at Glasgow during the 1760s of various major figures (Addison, Graduates; Coutts, History; Murray, Memories). Glasgow University 1760

1761

1762

1763

1764

1765

1766

1767

1768

1769

1770

Joseph Black (1728-1799) Adam Smith (1723-1790)

Thomas Reid (1710-1796) John Anderson (1726-1796) John Robison (1739-1805) James Watt (1736-1819) William Irvine (1734-1787) Alexander Wilson (1714-1786)

Black was the pre-eminent man of science in mid-1760s Glasgow. He had studied chemistry at Glasgow University under William Cullen before going to Edinburgh where he received his M.D. in 1754. His M.D. thesis embodied his

 He was not included in the Dictionary of Scientific Biography or Olson, Scottish Philosophy, for example. But see Muir, Anderson, and, more recently, Wood, Science and Jolly Jack.

1

180

D. B. Wilson

path-­breaking discovery of fixed air, the first-known chemically active air, whose discovery preceded that of many other such “airs” in the next few decades. Replacing Cullen in 1756 as lecturer in chemistry at Glasgow, Black began his equally fundamental research on heat, discovering what he called latent heat and what was later called specific heat. Just as Cullen had asked Black to serve as a laboratory assistant, Black gathered Robison, Watt, and Irvine around him to assist with experiments on heat. It was in this context that Watt, having been asked by Anderson to repair a model Newcomen steam engine, invented the separate condenser. When Black accepted the Edinburgh chair of chemistry in 1766, again replacing Cullen, Robison replaced Black at Glasgow, on the latter’s recommendation. Robison was replaced in 1769 by Irvine, who held the lectureship until his death in 1787. Irvine’s disagreement with Black’s understanding of latent heat helps make the point that the word discoveries underestimates Black’s accomplishments. His “discoveries” were actually far-reaching theoretical conclusions, that of latent heat being placed with Newtonian gravitation by James Hutton as the finest of scientific insights (Donovan, Philosophical Chemistry; Simpson, Black; Hutton, Dissertations). Black’s methodology followed Newton’s 31st Query in the Opticks. This query was his manifesto for chemistry, in which his rules of reasoning in philosophy became rules of reasoning in chemistry. Appearing in the second edition of the Principia in 1713, Newton’s rules proceeded from nature’s simplicity to its uniformity (stones fell the same way in Europe and in America) to its universality. If conclusions inferred from available phenomena were not universally valid, then nature would be neither uniform nor simple. Hence, one could argue from experience via the “analogy” of a nature that was “always consonant to itself” to a mutual gravitation between all bodies and to the universality of extension, hardness, impenetrability, mobility, and inertia of the “least particles of all bodies.” Such inductive conclusions contrasted with non-inductive “dreams,” “vain fictions,” and “hypotheses.” Inductive propositions should be revised only because of contrary phenomena, not contrary hypotheses (Newton, Principles, II 398–400). In Query 31, nature was again “very consonant and conformable to her self,” and, avoiding hypotheses, one made experiments and observations, “drawing general Conclusions from them by Induction” (Newton, Opticks, 376, 397, 404). In this way, the analogy of nature confirmed the hardness and impenetrability of nature’s smallest particles and the existence of attractions and repulsions between them. There was no “feigning” hypotheses of hooked or springy particles which would only “beg the question” (ibid., 388, 396). Consequently, without pretending to know the causes of short-­ range attractions and repulsions themselves, Newton employed them in explaining a plethora of chemical phenomena: the mixture of chemicals generally, the different actions of aqua fortis and aqua regia on silver and gold, the taste of acids, and the dissolving of metals in acids. Mixing chemicals, for example, produced heat – the increased motion of material particles due to their clashing violently because of mutual attractions (ibid., 378). Black cited and read from Query 31 at the conclusion of his lectures on the “general effects of mixtures.” Though invoked at this specific point in his course, Query 31 coincided with Black’s general conception of chemistry. Chemistry was “a

8  Scotland’s Philosophico-Chemical Physics

181

branch of Natural Philosophy,” (Black, Notes 2, I 8)2 and particles and forces were the reality underlying chemical phenomena. Different strengths of attraction of substances for one another caused, for example, what chemists called “elective attraction” and “double elective attraction” (ibid., I 121–123). Generally, Black lectured, “when we Explain any thing we endeavour to Make it more Simple, by Comparing it with something more familiar and obvious to our Senses” (ibid., I 110). Thus at times he argued explicitly by analogy. Even though gold and silver were immune to calcination, for example, they were still known to contain phlogiston, because of their other similarities to other metals, which contained phlogiston. Though Black’s lectures dwelt upon the observable “effects of heat” and the observable qualities of observable chemical bodies, the realism of Query 31 formed the overall context of the lectures, and occasionally appeared in direct statements. This was most obvious and most significant in what Black said (and implied) about heat and phlogiston. There were two, competing theories of heat. That of Newton and others stated that heat was the motion of material particles of bodies. Mainly a Continental theory, the second claimed “that Heat is a Tremor or vibration of an Elastic Fluid, w[hic]h pervades all bodies” (Black, Notes 2, I 14). The vibrating fluid was equated with Newton’s aether, which also caused the phenomena of electricity, magnetism, and perhaps gravity. Though Black’s lectures very much focused on the effects of heat, whatever its nature, Black did reject Newton’s theory. Experiments that established the concept of specific heat also showed that Newton’s theory of heat conflicted with the laws of motion (ibid., I 39). The Continental theory of heat, therefore, explained “many more of its effects” (Black, Notes 3, 2). The more likely theory was that heat was vibrating aether, evidently involving some kind of interaction between aether and matter that would explain the phenomena of specific heat. If sensible heat were vibrating aether, latent heat would presumably be aether with such vibrations suppressed – perhaps an extreme example of that influence of matter on aether suggested by the phenomena of specific heat. In the form of aethereal tensions awaiting release, latent heat was thus potentially sensible heat. Phlogiston, with both its existence and widespread role in chemistry well established, was also a kind of potential, sensible heat. If there were a Newtonian aether, “there is no doubt that this principle of Inflammability is this very matter;” and if aether did cause gravity, “it would be absurd to suppose that this fluid is a ponderous Body” (Black, Notes 4, I 167).3 To explain observed weight relations during combustion, Black concluded that phlogiston was a positively light substance. Posing a problem for chemistry at one level, these weight relations, at a deeper level, thus formed a theoretical link between phlogiston theory and gravitational theory. Moreover, “from what appears to our Senses we would say that this principle is Heat and Light, or some modification of Matter upon which Heat and Light depend” (ibid., III 616). Consequently, phlogiston seemed to be the aether whose vibrations  See also Black, Notes 1. Harris’ notes are more complete and less obscure than Cochrane’s.  Internal evidence suggests that these notes were copied from a “master” copy dating from the late 1760s. A similar set of notes is Black, Notes 5. For example, the same point is made in Dk.3.42308. See Perrin, Joseph Black. 2 3

182

D. B. Wilson

constituted sensible heat. In combustion, some phlogiston/aether must have escaped the inflammable, in order to explain its gain in weight. However, to explain the great quantity of heat produced during combustion, phlogiston/aether must also have contained suppressed vibrations which were freed during combustion. Such aethereal tensions linked to combustion would have been much stronger than those tied to latent heat, and inflammables, unlike other bodies, would have contained both kinds of tension. I am proposing, therefore, that Black’s chemical phlogiston (equated with Newton’s aether) was the most firmly established component of his far-reaching, speculative natural philosophy of chemistry. His vision seemed to rely on an aether which pervaded the universe (as shown by the phenomena of heat and light), whose motion produced some phenomena (phlogiston escaping during combustion, possibly sparks and electrical conduction), whose vibrations produced others (sensible heat, light), whose internal tensions were responsible for the most dramatic (latent heat, inflammabiltiy), and whose pressure gradients caused even more (gravitational attractions, possibly electrical and magnetic attractions and repulsions). This interpretation of Black is consistent with his experimental results, his theoretical statements, his speculative disposition, and his admiration for Newton’s 31st Query.4 If Black were the pre-eminent man of science, Reid was the pre-eminent man of philosophy in mid-1760s Glasgow. Born near Aberdeen, he took his M.A. at Marischal College, Aberdeen, in 1726, serving as librarian there in the mid-1730s and as minister at New Machar from 1737 to 1752. While at New Machar, he published a paper in the Philosophical Transactions of the Royal Society of London which entered the vis viva controversy (Laudan, Vis viva) and criticised attempts by the Glasgow professor of moral philosophy, Francis Hutcheson, to quantify human qualities (Reid, Essay). In 1752, he accepted the chair of moral philosophy at King’s College, Aberdeen. Having read, pondered, and deplored David Hume’s Treatise on Human Nature (1739), Reid published his Inquiry in 1764. Later that year, he replaced Adam Smith as professor of moral philosophy at Glasgow. Overlapping for two sessions in Glasgow with Black, Reid attended his chemistry lectures, being highly impressed by Black’s concept of latent heat. Reid was also close to Anderson and Robison. He and Anderson were allies in university affairs for years before eventually falling out. It was Reid (and Patrick Wilson, son of the professor of astronomy, Alexander Wilson) to whom Robison confided his ingenious idea about phlogiston in the late 1760s. Reid was a generation older than Black, Anderson, and Robison, but he and his Inquiry came to Glasgow only after those three had already been contemplating knowledge and nature for some time. Reid’s Inquiry responded to the spectre of scepticism emerging from the “theory of ideas” as developed by philosophers from Descartes to David Hume. Dependent  My view of Black and speculation is more like that of Thackray, Atoms and Powers, 147–148, than that of some other commentators on Black. 4

8  Scotland’s Philosophico-Chemical Physics

183

on the analogy that ideas were like impressions made in wax by a seal, the theory of ideas, Reid wrote, claimed that the mind contemplated images that pictorially resembled the external objects that they represented. These images or thoughts had been taken as the starting point for reasoning about human knowledge. In the century since Descartes, philosophers had demonstrated that reason, if it began with images, could not actually demonstrate the existence of either the natural world or the human mind. This second result had been present in the “womb” of Cartesianism and was the “monster” given birth by Hume’s Treatise in 1739 (Reid, Inquiry, 384–385). Reid slew this monster with the pure, brute recognition of the human faculties of reason and perception. That is, though Reid had obvious, theological motives for his battle against scepticism and though he followed the inductive method in sorting out the “furniture” of the mind, knowledge of these two human faculties was ultimately independent of both induction and theology. These faculties were, in fact, what justified the method of induction and allowed an inductive proof of the existence of God. The faculty of perception included both the act of sensing an external object and belief in its existence. In the single most important sentence in the Inquiry, Reid proclaimed: I am not conscious of any pictures of external objects in my sensorium any more than in my stomack: the things which I perceive by my senses, appear to be external, and not in any part of the brain; and my sensations, properly so called, have no resemblance of external objects. (Reid, Inquiry, 302)

Contrary to the theory of ideas, there was no perception of an internal image. “This belief is not the effect of argumentation and reasoning,” Reid explained, “it is the immediate effect of my constitution” (ibid., 307). Likewise, the faculty of reason was a pre-logical entity that existed within man prior to reasoning and that remained beyond reasoning’s scrutiny. It included a thirst for knowledge and an undeniable belief in the existence of mind. It also included the conviction that the future would resemble the past. That is, it included belief in the “continuance” of the inductively identified “constant conjunctions” of phenomena into the future (Reid, Inquiry, 358–361). Moreover, the faculties of reason and perception were of equal standing. Whereas Descartes had used reason to analyse perception, Reid declared perception, too, beyond examination by reason. Including no reasoning within it, perception instead provided the faculty of reason with things to think about. Just as analogy had led philosophy down the misguided path of the theory of ideas, it was also an important obstacle to accurate natural philosophy. Newton’s rules of reasoning were “maxims of common sense” and the best guide to an inductive study of nature (Reid, Inquiry, 19). In reality, however, men had been seduced into error by their own genius, by slipshod induction, and by careless analogy. The most egregious example was Descartes’ vortex theory of planetary motion. Even the incomparable Newton had mistakenly viewed all of nature as being like that part

184

D. B. Wilson

which included attractive and repulsive forces. Reid’s Inquiry did not completely exclude such theories, accepting theories of odoriferous particles as the cause of smell and aerial vibrations as the cause of sound. However, Reid usually linked such conjectures to words like vanity, folly, laughable, dreams, and ravings (ibid., 19, 297). A word like heat, for example, could easily mislead. Because the word could refer both to the sensation of heat and to its underlying cause, knowledge of the first could be mistaken for knowledge of the second as well. Usually, natural philosophy’s proper goal was discovering the laws of nature or, as Reid put it, “general facts”– the constant conjunction of events rather than their underlying causes (ibid., 27–28, 74–76, 212–213, 380–387). Reid concluded by contrasting the erroneous “way of analogy” with his own “way of reflection” (ibid., 371–372). His “way” embraced a few necessary truths about mind and nature, led to the discovery of nature’s “general facts,” and strongly rejected most causal explanations. His conception of natural philosophy, that is to say, combined extreme certainty with a version of deep scepticism.5 Black and Reid were thus two methodological Newtonians who disagreed with each other. To be sure, both accepted Newton’s rules of reasoning, both blasted unwarranted conjecture, and both affirmed a realism with respect to unseen nature, though without explicitly presenting a complete theory of it. However, Black’s lectures, but not Reid’s Inquiry, contained statements appearing actually to reflect such a deep theory of nature. Black’s comments on the nature of heat contrasted with Reid’s brief warning that the word heat could mislead. Black’s use of analogy contrasted with Reid’s condemnation of that approach. Phlogiston’s centrality in Black’s chemistry was unmatched by any unobservable’s role in Reid’s philosophy. As Black judged the situation, a Newtonian realism naturally blended with the state of chemistry in the 1760s. As Reid judged the situation, philosophy in the 1760s required a Newtonian scepticism, combined with common-sense certainties. For Black, unwarranted conjectures seemed to be non-inductive conclusions about nature. With Black’s new experiments (and in accordance with Newton’s fourth rule of reasoning), Newton’s theory of heat became such a non-inductive conclusion. For Reid, on the other hand, unwarranted conjectures seemed to be analogical conclusions about hidden nature. The question now is what influence did these competing views, based respectively in the subjects of chemistry and moral philosophy, exert on the natural philosophy courses of John Anderson and John Robison?

 Given the discussion of Robison below, I am arguing that this presentation of the Inquiry is how both Reid and Robison understood the book. There exists a large literature on Reid, but Beaublossom, Introduction, discusses Reid’s view of faculties; Daniels, Reids ‘Inquiry’, focusses on vision and geometry in the Inquiry; and Wood, Reid, considers Reid’s view of hypotheses more widely than in the Inquiry. I think Robison relied on the Inquiry. 5

8  Scotland’s Philosophico-Chemical Physics

185

8.2 John Anderson and John Robison, Circa 1780 For all their similarities, Anderson and Robison were not confidants. Anderson took his M.A. at Glasgow in 1745 and was professor of Oriental languages there in the mid-1750s, before replacing Dr. Robert Dick as professor of natural philosophy in 1757. He thus commenced his professorship at about the time Black did his lectureship. Robison took his M.A. at Glasgow in 1756 but, though supported by Adam Smith, was evidently deemed too young for the vacant professorship in natural philosophy. A decade later, Black recommended Robison for his Glasgow lectureship in chemistry. In 1774, Black recommended him for the Edinburgh chair of natural philosophy. Both Anderson and Robison were Glasgow-educated and in proximity to Black and Reid during the 1760s. Their natural philosophy professorships overlapped from the mid-1770s to the mid-1790s. But Robison regarded Anderson as an inferior natural philosopher to Dr. Dick (his own teacher), and Anderson was not part of the Black-Watt-Robison collaborative existence. There are, therefore, reasons to expect that their respective courses might have been similar and reasons to think that they might have been different. This section concentrates on their courses around 1780. Anderson divided his course into two series of lectures, one mathematical the other experimental. The experimental lectures excluded mathematics and provided experimental results that were taken for granted in the mathematical lectures. In the early years at least, Anderson used John Keill’s Introduction to Natural Philosophy as the basis for his mathematical lectures. His own textbook for the experimental lectures, his Institutes of Physics, grew to more than 500 pages by its last edition in 1795. Most relevant here are the editions of the Institutes from 1777 and 1786, his annotations to them, and other manuscript evidence.6 Anderson’s theory of knowledge was a Newtonian realism. His lectures emphasised Newton’s rules of reasoning and quoted long passages from the Principia and Opticks on induction, laws, causes, and God. Anderson’s Newtonianism also drew on Joseph Butler’s Newtonian defence of religion in his Analogy of Religion of 1736 and on ‘sGravesande’s “Oration Concerning Evidence” in the 1747 edition of his Mathematical Elements of Natural Philosophy. Anderson distinguished among levels of knowledge that he called ideal, demonstrative, probable, analogical, medium, and chance. Ideal knowledge was that of mathematics and metaphysics, which depended solely on “the relations of our ideas.” The remaining categories were ones of decreasing degrees of probability. Exceedingly probable, demonstrative knowledge included conclusions like “fire will burn a man’s hand” and “the sun will rise tomorrow.” Demonstrative evidence for the Copernican system included “the aberration of fixed stars” and “the oblate figure of the earth.” A probable argument for the Copernican system was “the  The principal collection of Anderson’s manuscripts is in Strathclyde University, The Andersonian, Special Collections, which also holds his personal library, including Keill’s Introduction to Natural Philosophy and ‘sGravesande’s Mathematical Elements. 6

186

D. B. Wilson

likelihood of the same causes being extended to the heavens, which exist upon the Earth.” Descartes’ vortex theory of planetary motion was positively improbable, because of its disagreement with experience. With these various probabilities in mind, let us turn to Anderson’s assessment of natural philosophical knowledge.7 Inert and infinitely divisible matter plus Newton’s laws of motion were among Anderson’s most secure, demonstrative truths about nature. Annotations to his 1777 Institutes indicate the experiments to be performed to demonstrate each law of motion. Anderson’s introductory discussion of Newton’s third rule of reasoning included inert and divisible matter. In fact, along with the existence of void space, the infinite divisibility of matter always resided prominently in the opening sections of Anderson’s experimental course. One grain of gold, for example, could be divided into two million, still-visible bits of gold. These barely visible bits that were obviously subject to further division provided a perfect bridge from macroscopic to microscopic to sub-microscopic nature (Anderson, Institutes (1777), III 3–4; Introductory lecture). Smell and sound were areas of highly probable knowledge, whether demonstrative or not. Anderson cited invisible odoriferous particles only 38 trillionths of an inch in size as evidence for matter’s divisibility. He also accepted the long-held theory that sound was caused by vibrations in the air (Anderson, Institutes (1786), 330). From the outset, fire was crucial to Anderson’s concept of nature. Probably influenced by Hermann Boerhaave, he presented fire as one of nature’s four elements. He speculated that nature’s many substances might be reduced to only two elements, earth and fire, or perhaps to only one. Accepting Black’s discoveries, he began lecturing about “latent, or imbibed, fire.” Fire consisted of “particles of matter extremely subtile.” The particles could be in a fixed state as latent fire. Their motions caused the sensations of heat and light – sometimes one or the other, sometimes both. Moving in straight lines, fire particles caused light; moving in all directions, they caused heat. Phlogiston might be “quiescent fire,” since neither phlogiston nor latent fire visibly affected the body within which it resided or caused the sensations of heat and light. Around 1770, Anderson had speculated that fire constituted electrical matter, too.8 Anderson’s concept of light as moving fire particles evidently combined ideas from Boerhaave and Newton. Like other material corpuscles, those of light could be attracted, repelled, and absorbed. Anderson emphasised the smallness of light corpuscles in countering standard objections to the corpuscular theory of light. Yet, the corpuscular theory of light was only probable, Anderson said, and he therefore did not use it in support of the theory of matter’s divisibility. To have done so would

 Anderson, Institutes (1786), 397–399; For what reason, 14–15; Lecture First, 30–35, 41–43; Introductory lecture. 8  Anderson, Compend, 36–37; Institutes (1777), I 36, 44, 47, 68, 77, 79, 90–91, 236; Institutes (1786), 22, 37, 51–52, 64, 66, 78. The Anderson Collection includes a copy of Enquiry. 7

8  Scotland’s Philosophico-Chemical Physics

187

evidently have committed the error of trying to support a demonstrable conclusion with one that was only probable.9 Anderson accepted Benjamin Franklin’s electrical theory with its notion of “electric matter [that] consists of particles extremely subtil, which mutually repell each other and are strongly attracted by all other matter.” Electric matter could be seen, heard, smelled, and tasted. Fire and electric matter could “subsist together in the same body” as distinct entities. Heat influenced the conduction of electricity and produced in tourmaline a curious distribution of electric matter.10 Anderson accepted Descartes’ theory of magnetism with its notion of magnetic matter moving from one pole of a magnet to the other, in the process causing attractions and repulsions. Electric and magnetic matter could usually exist together without affecting each other, but an electric shock could create or destroy magnetic polarity or reverse the poles of a magnet. Fire and magnetic matter, on the other hand, evidently could not reside together unaffected, for that mixture diminished a magnet’s strength and strong heat destroyed it. Anderson reported no influences of magnetism on fire or electric matter, nor did magnetism produce heat, as did an electric spark.11 Significantly, Anderson defended the existence of magnetic matter by comparing it to other, better-known forms of matter. Magnetic matter was invisible, but so were odoriferous “Effluvia” and “the Particles of electric Matter.” Magnetic matter often caused no effects, but the same was true for fire and electric matter in the cases of latent fire and of electric matter in non-electrified electric bodies.12 Magnetic matter seemed the least probable of these various hidden entities. Anderson argued from smell, fire, and electricity to magnetism, for example, but not in the reverse direction. He reduced light to fire and contemplated the same for electricity  – but apparently not for magnetism. Magnetism lacked the appearance of interchangeableness possessed by the other forms of hidden matter. In a prize-­ winning essay in natural philosophy in 1770, Archibald Arthur, later Reid’s assistant and successor, declared that causes like the Cartesian magnetic fluid could be “adopted without any proof,” so long as they did not disagree with experience. “It is more satisfactory to imagine such a fluid producing the effect than no cause at all,” Arthur wrote (Arthur, Essay, 10). Whether these were exactly Anderson’s sentiments or not, he did sound a similar note as he defended the existence of magnetic matter.

 Anderson, Institutes (1777), I 75; Institutes (1786), 51, 62, 343. Annotated copy of Anderson, Institutes (1786), vol. I, “lecture on divisibility of matter.” Cantor, Optics, a standard study of British theories of light in the eighteenth century, includes Robison but not Anderson. 10  Anderson, Institutes (1777), I 99–100, 102, 106, 108–110, 120–123; Institutes (1786), 192, 194, 197–202, 211–214. Heilbron, Electricity, the standard study of eighteenth-century electricity, discusses Robison but not Anderson. 11  Anderson, Institutes (1777), I 118, 134; Institutes (1786), 210, 228. Yost, Lodestone and Earth, is an extended examination of British magnetism during this period. It discusses Robison at some length and Anderson briefly. See also Yost, Robison. 12  Annotated copy of Anderson, Institutes (1786), vol. III, “Sect. XIV. Of the cause of the magnetic virtue.” 9

188

D. B. Wilson

The business therefore of true Philosophy is to extend our views, by unfolding the latent Causes, and by them explaining their manifold Effects. The Discovery of one such Cause is an advance in real and important knowledge. To undervalue such a discovery, as some have done, because the cause of that cause cannot perhaps be assigned is very absurd since the same objection must forever lye against all Causes except Primary ones, which are probably removed far beyond the reach of Human Inquiry.13

Similar degrees of probability permeated Anderson’s discussions of nature’s attractions and repulsions. He generally sought to quantify forces without identifying their causes, though he did offer an underlying, material cause for magnetic forces. Gravity was, of course, the best-known force. Anderson discussed many failures to find its underlying cause but judged it premature either to give up the search or simply to attribute gravity to God’s action.14 None of this sounds exactly like Thomas Reid’s Inquiry. At one point around 1770, Anderson had argued that belief in God was part of man’s nature and that matter’s inertia had been recognised by all men at all times (Anderson, Natural Theology). Both could have been Anderson’s version of Reid’s common-sense philosophy, but they could also show the influence of Joseph Butler. It seems, in fact, that Anderson had assimilated a Newtonian realism well before 1764 and that, at most, he drew only fragments of reinforcement from Reid. Instead, Anderson had combined Joseph Black’s chemistry and Isaac Newton’s natural philosophy. Anderson’s Newtonian realism embraced Black’s concept of latent fire which, in turn, became crucial to Anderson’s spectrum of probabilistic Newtonian theories of hidden nature. In contrast to Anderson, Robison performed fewer experiments, talked faster, was less generally popular, and considered Reid’s ideas more fully (Playfair, Robison; Wood, Science). Robison did not divide his course into experimental and mathematical components. In 1780, he published his 128-page Outlines of Mechanical Philosophy, covering the astronomy and mechanics portions of his class. But his own lecture notes are the best source for the content of his natural philosophy course at Edinburgh around 1780.15 They display his deep engagement of Reid’s philosophy, but also indicate that a logical tension within Reid’s thought snapped into a different pattern of understanding for Robison. Let us begin, however, with Robison’s notes for his earlier lectures, those on chemistry at Glasgow.16

 Annotated copy of Anderson, Institutes (1786), vol. III, “Sect. XIV. Of the cause of the magnetic virtue.” 14  Anderson, Institutes (1777), I 146; Institutes (1786), 241; For what reason; annotated copy of Anderson, Institutes (1786), vol. III, “Gravitation Prop. VIII.” 15  Edinburgh University Library, Special Collections, Dc.7.1 to Dc.7.40. These forty volumes contain notes ranging from the mid-1770s to around 1800. Generally, each volume concerns one topic of the course, though sometimes more than one volume deals with the same topic, reflecting revisions during his long tenure. 16  St. Andrews University Library, Special Collections, QD 39.R8. Unlike the manuscript notes for Robison’s lectures on natural philosophy, these eight volumes of notes for his lectures on chemistry begin at the beginning of the course and go through to the end, without years of frequent revisions. Pasted within the first five volumes are twenty-two pages of Robison’s printed Plan of Chemical Lectures. This undated Plan is missing a few pages, including, for example, material on two of the effects of heat, ignition and inflammation. 13

8  Scotland’s Philosophico-Chemical Physics

189

Robison organised his chemical lectures similarly to Black’s and included discussions of latent heat, specific heat, theories of heat, and phlogiston. Robison described the same two current theories of heat and rejected them for the same reason, because they contradicted the principles of natural philosophy. As with a magnet and a moving piece of iron, so also with heat and its effects, it was their “constant conjunction,” not a mechanical theory, that established their relationship as cause and effect. However, Robison also proposed a third, better theory of heat. He speculated that heat was a fluid whose parts were attracted in different degrees by the parts of ordinary substances. By obvious analogy with the chemical idea of elective attraction, Robison argued that if the attraction between parts of matter were weaker than that between matter and fire, then unions between fire and matter would replace those between portions of matter. In this way, with no repulsions but with more and more fire, parts of matter would be separated from each other further and further, thus causing various effects of heat, including latent heat. Robison also emphasised Stahl’s theory of phlogiston, “by no means a mere conjecture.” Indeed, Stahl had “ascert[aine]d its exist[ence] bey[on]d contrad[iction].” It was a “general fact” that phlogiston never appeared by itself. Phlogiston was “extremely subtil,” positively light, and the source of fire in combustion. That is, phlogiston and fire were interconvertible. Occasionally employing some of the language of Reid, Robison could seem both more sceptical and more speculative than Black. Robison decisively rejected the two main theories of heat, not as follies, however, but because they disagreed with the laws of motion. Though he was also sceptical about his own theory of heat, its presence in his lectures indicated the validity of the search for a mechanical theory of heat. Robison seemed in closest agreement with Black in the 1760s on the reality of phlogiston. They both appeared to regard it as a kind of potential heat or fire – Black as an aether, somehow harbouring suppressed vibrations that could become the vibrations of sensible heat; Robison as a quiescent fluid, which was either fire greatly concentrated or a fluid that could be transformed into the fluid of fire (Robison, St.AUL, QD 39.R8 I 83, II 108–122, III 311–338, VII 2–9; Plan, 1–2). Robison’s introductory lectures in natural philosophy followed Reid in attacking the theory of ideas. Given Descartes, Hume was right. Descartes’ mistake had been simply to assume the existence of mind as the home of thoughts. Nevertheless, following Descartes, Berkeley had severed the connection between ideas and a natural world, and Hume had done the same for that between ideas and mind. The upshot of Hume’s philosophy was, Robison explained, that we can know only ideas of the moment. If valid, Hume’s views would undermine natural philosophy. “Let us think a little before we resolve to employ the Studies of a Winter in so fruitless a pursuit,” Robison lectured. Echoing Reid, Robison responded with declarations that the existence of thought and mind was “an opinion which is inevitable, a belief which is irresistable” and that “in the very same Manner, perception suggests to us the notion of external things with the belief of their existence” (Robison, EUL, Dc.7.29, lecture II). Having demonstrated the existence of nature, Robison could go on with the course. Natural philosophy combined necessary truths with more limited knowledge. Like the existence of mind and matter, nature’s regularity and Newton’s first two laws of motion were necessary truths rooted in man’s constitution. Robison

190

D. B. Wilson

emphasised the importance of “general facts” in natural philosophy. The complexity of the tides, for example, could be reduced to two general facts, “matter is heavy” and Newton’s first law of motion. General facts were laws, not theories of nature’s “hidden operations.” Gravitational force, for example, meant simply that “all matter tends to all matter.” Magnetism referred only to observed relations between magnets or magnets and iron. Analogy could lead one astray. If Robison used the concept of a magnetic fluid in his lectures, for example, “I should proceed unphilosophically.” However, if he said that the phenomena were merely analogous to what would be caused by such a fluid, he would “argue according to the rules of sound Logic” (Robison, EUL, Dc.7.29, lectures II and IV). Magnetism, electricity, and light constituted the latter part of Robison’s course. He approached them in similar ways but reached dissimilar findings. In each area, he identified the most general fact, and these resembled each other. But “curiosity,” he said, demanded further enquiry, and he accordingly did seek hidden operations in each area. Chemistry assisted all three searches, but they concluded differently. Robison had recognised the leading general fact of magnetism while an undergraduate in the 1750s and had alluded to it in his lectures on chemistry in the 1760s. The fact was that in the presence of a magnet a piece of iron was magnetised. This satisfactorily explained the familiar distribution of iron filings around a magnet, rendering mechanical theories of magnetism unnecessary, especially inconsistently mechanical ones like Descartes’ (Robison, EUL, Dc.7.32, section G). This general fact helped provide an orderly arrangement of more specific magnetic facts, while claiming, and needing to claim, nothing about the nature either of magnetism’s influence on iron or of magnetic attractions and repulsions. The case was similar in electricity and optics (ibid., Dc.7.36, 8–9; Dc.7.39, section A, 5). Electrified bodies electrified other bodies, and luminous objects illuminated objects around them. In neither case was there necessarily a material medium involved. Given these general facts, one could distinguish between different kinds of objects in each area. Some objects could be magnetised, most could not. Some objects were electrics, some non-electrics. Some objects were luminous, some opaque. Though these were satisfactory explanations, Robison said that curiosity forced him to consider possible hidden material causes in each area. In his lectures on natural philosophy, the chemistry of phlogiston and fixed air was significant. For Robison in 1780, phlogiston had long been established as a material substance, and fixed air, discovered by Black in the 1750s, was a standard part of chemistry. For various reasons, Robison concluded that an electric fluid actually existed. “I do not think […],” he lectured, “that the existence of a fluid substance, which is the cause of Electrical phenomena, is an hypothetical assertion.” (Robison, EUL, Dc.7.36, 18–20) Among his reasons was the electric spark which made the electric fluid more visible than a supposed magnetic fluid ever was. Moreover, the various movements of electricity within electrics and non-electrics seemed exactly like a fluid flowing among particles with varying degrees of viscosity. External heat

8  Scotland’s Philosophico-Chemical Physics

191

bringing a phlogisticated body to combustion was like an external influence electrifying an electric. In each case, an entity already within the body was activated by something external. Other similarities led Robison to speculate that the electric fluid might be the same thing as phlogiston – or the fluid of heat, which he now treated in a straightforwardly realistic manner, perhaps because the speculations of his chemical lectures had been reinforced by the work of William Cleghorn.17 Fixed air helped, too. In the one-fluid theory of electricity, material particles were attracted to particles of electric fluid but repelled each other. This explained the repulsion between two negatively charged bodies. Was it physically plausible, however, for particles of one thing to be attracted to those of another but to repel each other? Yes. Fixed air provided the perfect analogue (Robison, EUL, Dc.7.36, facing pp. 4–5, 18–20, 113–117). Robison lectured at length about physical theories of light, concluding that light was probably material because of its link to phlogiston. But he thought Newton had been correct in not unequivocally endorsing a specific physical theory of light (ibid., Dc.7.39, section A, 1–8). Although Robison also lectured enthusiastically about deriving a theory of the magnetic fluid, he concluded, in the end, that the theory was merely a conjecture (ibid., Dc.7.32, section S). How should we understand the ambiguous relation of Robison’s natural philosophy to Reid’s common-sense philosophy? Like Reid, Robison rejected Cartesian analogy and Humean scepticism and developed a natural philosophy that combined necessary and contingent truths. Unlike Reid’s Inquiry, however, Robison vigorously pursued nature’s hidden operations. This difference turns, I think, on the question of man’s inherent desire for knowledge. For Reid, ardent desire too often joined with careless analogy to produce nice-looking mistakes. For Robison, ardent desire, though still tempered by scepticism, led through cogent reasoning and relevant analogy to the unveiling of nature’s hidden causes. Reid’s Inquiry had balanced strong scepticism with both extreme certainty and inherent desire. Though his particular balance between scepticism and certainty may have been stable enough, that between scepticism and desire was always likely to be unstable. In Robison’s natural philosophy, that instability appeared in the disjunction between his quite sceptical introductory lectures and his less sceptical lectures enthusiastically seeking the hidden causes of magnetism, electricity, and light. In effect, in Robison’s search for the logic of nature, logical scepticism frequently yielded to a pre-logical craving for knowledge.

 Cleghorn, De Igne, argued that heat was a fluid whose particles repelled each other but attracted those of ordinary matter. Though this theory of heat was similar to Robison’s of the 1760s, Cleghorn also maintained that heat and phlogiston were quite distinct. Robison reported that Cleghorn’s theory of heat convinced Black, and I am suggesting that it probably also convinced Robison that his earlier theory of heat was not so conjectural after all. See Black, Lectures, I 33–34; McKie and Heathcote, Cleghorn’s De Igne, 7–8. 17

192

D. B. Wilson

8.3 Conclusion Students at Glasgow and Edinburgh around 1780 learned quite different versions of natural philosophy. Anderson accepted Descartes’ theory of magnetism, Robison derided it. Anderson presented Newton’s laws of motion as inductive truths, Robison said the first two were necessary truths. Giving little, if any, attention to Reid, Anderson’s straightforward Newtonian realism offered degrees of probable knowledge, declaring the reality of the element fire and corpuscles of light, as well as electric and magnetic matter. Modifying Reid’s common-sense philosophy, Robison profoundly contemplated the question of knowledge generally and intricately evaluated specific claims to knowledge of nature’s hidden operations, accepting unequivocally the reality of the electric fluid. Anderson and Robison agreed more about chemistry than about natural philosophy. Black’s latent heat impressed them both, and phlogiston convinced both of its reality. Both regarded the matter of fire as real and suggested that phlogiston might be a form of latent fire. Indeed, entities associated with chemistry seemed the surest realities of hidden nature, fire for Anderson and phlogiston for Robison. Anderson easily included these along with entities of natural philosophy in his realistic reading of Newton’s methodological statements. With more of a struggle, Robison ultimately used phlogiston to widen the reluctant realism of Reid’s common-sense philosophy. In the high period of the Scottish Enlightenment, Anderson and Robison, instead of avoiding theories of hidden nature, proclaimed their respective versions of a philosophico-chemical physics.18

References Addison, W. Innes. 1898. A Roll of the Graduates of the University of Glasgow. Glasgow: James MacLehose. Anderson, John. 1760. A Compend of Experimental Philosophy. Glasgow: Robert and Andrew Foulis. Though the title page says 1760, this volume appears to date from the late 1760s. ———. 1770. Natural Theology, The Christian Religion, A Proof that All the Knowledge in Natural Theology, which is to be found in the World, has arisen from Revelations and not from the natural Powers of Human Nature (ca. 1770). Anderson Collection, unnumbered MS. ———. 1775. For What Reason Did the ROYAL Society Send Mr Maskeline in Summer last to Sheehallan in Perthshire?. Anderson Collection, MS 18. ———. 1777. Institutes of Physics. Vol. 3 vols. Glasgow: Andrew Foulis. In Anderson Collection which holds vols. I and III. Annotated by Anderson. [Institutes 1777]. ———. 1786a. Institutes of Physics. 4th ed. Glasgow: Robert Chapman and Alexander Duncan. [Institutes 1786]. ———. 1786b. Lecture First at the Experiments (ca. 1786). Anderson Collection, MS 24.

 Editor’s note: Since the 1st edition of this volume in 2001, David Wilson published a comprehensive elaboration of the subject: David B. Wilson: Seeking Nature’s Logic – Natural Philosophy in the Scottish Enlightenment. University Park, PA: The Pennsylvania State University Press, 2009. 18

8  Scotland’s Philosophico-Chemical Physics

193

Anderson, John. “Introductory lecture.” 1786. Institutes, Anderson’s annotated copy divided into six volumes, vol. I, Anderson Collection. Arthur, Archibald. 1770. An Essay on the Inducements to the Study of Natural Philosophy. Anderson Collection, MS 2. Also in Discourses, 407–440. ———. 1803. Discourses on Theological & Literary Subjects. Glasgow: The University Press. Beaublossom, Ronald E. 1975. Introduction. In Thomas Reid’s inquiry and essays, ed. Keith Lehrer and Ronald E. Beaublossom, ix–li. Indianapolis: Bobbs-Merrill. Black, Joseph. 1803. In Lectures on the Elements of Chemistry, ed. John Robison, vol. 2 vols. Edinburgh: Murdell and Son. ———. 1770. An Enquiry into the General Effects of Heat; with Observations on the Theories of Mixture. London: J. Nourse. Taken from Joseph Black’s lectures and published anonymously. [Notes 3]. [Black, Joseph.] 1773. A Course of Lectures on Chemistry delivered in the University of Edenburgh [sic] by Dr. Black. Oct: ye 28th 1773. 4 vols. 1773–1774, Yale University, Beinecke Library, MS 118. [Notes 4]. ——— 1774. Lectures on Chemistry Delivered by Joseph Black M.D. Professor of Chem[istry] in the University [of] Edinburgh, 1774. 4 vols. 1774–75, Edinburgh University Library, Special Collections, MS Dk.3.42–45. [Notes 5]. ———. 1966. Notes from doctor Black’s lectures on chemistry [taken by Thomas Cochrane] 1767/8. Cheshire: Imperial Chemical Industries Limited. [Notes 1]. [Black, Joseph.] A Course of lectures on Chymistry delivered by Joseph Black M.D.  Professor of Chymistry in the University of Edinburgh. Taken by Tucker Harris 1768/9. 2 vols., Yale University, Beinecke Library, MS 113. [Notes 2]. Butler, Joseph. 1844. The Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature. New edition Oxford: Thomas Tegg. First published in 1736. Cantor, G.N. 1971. Henry Brougham and the Scottish Methodological Tradition. Studies in the History and Philosophy of Science 2: 69–89. ———. 1983. Optics after Newton: Theories of Light in Britain and Ireland, 1704–1840. Manchester: Manchester University Press. Cleghorn, William. 1958. De Igne. Annals of Science 14: 11–59. De Igne was first published in 1779. Coutts, James. 1909. A History of the University of Glasgow. Glasgow: James MacLehose. Daniels, Norman. 1989. Thomas Reid’s ‘Inquiry’: The Geometry of Visibles and the Case for Realism. Stanford: Stanford University Press. Donovan, A.L. 1975. Philosophical Chemistry in the Scottish Enlightenment: The Doctrines and Discoveries of William Cullen and Joseph Black. Edinburgh: Edinburgh University Press. Gravesande, W.  James. 1747. Mathematical Elements of Natural Philosophy, Confirm’d by Experiments: Or, an Introduction to Sir Isaac Newton’s Philosophy. Trans. J. T. Desaguliers. 6th edition, 2 vols., London: W. Innys, T. Longman and T. Shewell, C. Hitch, and M. Senex. In Anderson Collection. Heilbron, J.L. 1979. Electricity in the 17th and 18th Centuries, a Study of Early Modern Physics. Berkeley: University of California Press. Hutton, James. 1792. Dissertations on Different Subjects in Natural Philosophy. Edinburgh: A. Strahan; London: T. Cadell. Keill, John. 1741. Introductio ad Veram Physicam: Seu Lectiones Physicae Habitae in Schola Naturalis Philosophiae Academiae Oxoniensis, A.D. 1700. Cambridge: In Anderson Collection. Laudan, L.L. 1968. The Vis viva Controversy, a Post-Mortem. Isis 59: 131–143. ———. 1970. Thomas Reid and the Newtonian Turn of British Methodological Thought. In The Methodological Heritage of Newton, ed. R.E. Butts and J.W. Davis. Oxford: Blackwell. McKie, Douglas, and Niels H. De V. Heathcote. 1958. William Cleghorn’s De Igne (1779). Annals of Science 14: 1–82. Muir, James. 1950. John Anderson, Pioneer of Technical Education, and the College He Founded. Glasgow: John Smith & Son.

194

D. B. Wilson

Murray, David. 1927. Memories of the Old College of Glasgow: Some Chapters in the History of the University. Glasgow: Jackson, Wylie and Co. Newton, Isaac. 1934. Mathematical Principles of Natural Philosophy, Trans. Andrew Motte (1729), ed. Florian Cajori. 2 vols. Berkeley: University of California Press. ———. 1952. Opticks. 4th edition (1730), New York: Dover Publications. Olson, Richard. 1975. Scottish Philosophy and British Physics 1750–1880. Princeton: Princeton University Press. Perrin, Carleton E. 1983. Joseph Black and the Absolute Levity of Phlogiston. Annals of Science 40: 109–137. Playfair, John. 1815. Biographical Account of the Late John Robison, LL.D.  F.R.S.  Edin. and Professor of Natural Philosophy in the University of Edinburgh. Transactions of the Royal Society of Edinburgh 7: 495–539. Reid, Thomas. 1748. An Essay on Quantity. Philosophical Transactions of the Royal Society 45: 505–520. ———. 1819. An Inquiry into the Human Mind, on the Principles of Common Sense. Glasgow: James Cameron. Reprint of 1764 edition. Robinson, Eric, and Douglas McKie, eds. 1970. Partners in Science: Letters of James Watt and Joseph Black. Cambridge: Harvard University Press. Robison, John. 1780. Outlines of Mechanical Philosophy, Containing the Heads of a Course of Lectures. Edinburgh: William Creech. Robison, John. Lecture Notes: Natural Philosophy. Edinburgh University Library, Special Collections, Dc.7.1 to Dc.7.40. [EUL]. Robison, John. Lecture Notes: Chemistry. St. Andrews University Library, Special Collections, QD 39.R8. [St.AUL]. Robison, John. “Plan of Chemical Lectures.” Lecture notes: Chemistry. St.AUL. Simpson, A.D.C., ed. 1982. Joseph Black, 1728–1799: A Commemorative Symposium. The Royal Scottish Museum: Edinburgh. Smith, Crosbie, and M. Norton Wise. 1989. Energy and Empire: A Biographical Study of Lord Kelvin. Cambridge: Cambridge University Press. Thackray, Arnold. 1970. Atoms and Powers: An Essay on Newtonian Matter-Theory and the Development of Chemistry. Cambridge: Harvard University Press. Wood, Paul. 1989. Reid on Hypotheses and the Ether; A Reassessment. In The Philosophy of Thomas Reid, ed. Melvin Dalgarno and Eric Matthews, 433–446. Dordrecht: Kluwer Academic Publishers. ———. 1994. Science, the Universities, and the Public Sphere in Eighteenth-Century. History of Universities 13: 99–135. ———. 1995. ‘Jolly Jack Phosphorous’ in the Venice of the North; or, Who Was John Anderson? In The Glasgow Enlightenment, ed. Andrew Hook and Richard B. Sher, 111–132. East Linton: Tuckwell Press. Yost, Robinson M. 1997. Lodestone and Earth: The Study of Magnetism and Terrestrial Magnetism in Great Britain, c. 1750–1830. Ph.D. Dissertation, Iowa State University. ———. 1999. Pondering the Imponderable: John Robison and Magnetic Theory in Britain (c. 1775-1805). Annals of Science 56: 143–174.

Part IV

Can Matter Think?

Chapter 9

Materialistic Theories of Mind and Brain Ann Thomson

Abstract  The chapter discusses three main issues of the mind-body problem as discussed by materialistic physicians and philosophers in the seventeenth and eighteenth centuries: (1) The question of how to conceptualize matter that was capable of sensing, feeling, and thinking. Examining the positions of La Mettrie, Diderot and Maupertuis in France and of Priestley in Britain, the chapter shows the main alternatives that were considered. (2) The question of whether the human soul is a function of the body or an immaterial substance and, related to this, the ideologically highly charged question of whether the human soul is mortal or immortal. (3) The physiological and anatomical research undertaken in this period. The chapter shows in this way that the materialistic denial of the existence of an immaterial soul had an important general impact on the sciences (especially physiology and anatomy). At the same time, developments in the life sciences of the eighteenth century and the then emerging notion of organized matter allowed a far more subtle handling of the mind-body problem than before.

9.1 Introduction The question of eighteenth-century materialism – generally seen as a purely French phenomenon – has given rise to quite a large number of misconceptions, concerning its nature, its philosophical inspiration or its aims, to name but a few. One can even doubt whether such a label, despite being consecrated by usage, has any real meaning, as there are great differences between those who have been included in the group of eighteenth-century French materialists (usually Meslier, La Mettrie, Diderot, Helvétius, d’Holbach), and doubts have even been thrown on how far they can all be classified as ‘materialists’; in addition, materialistic ideas are not confined A. Thomson (*) European University Institute, Florence, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_9

197

198

A. Thomson

to these particular thinkers, and recent research has been more and more concerned to study lesser-known writers and works. No-one holds any more the misleading, but at one time very common, view which (totally ignoring dates of publication) saw it as a purely late eighteenth-century phenomenon, centred around the Système de la Nature, published in 1770, which did, it is true, lead to a great polemical debate and the republication of earlier materialistic works. What I would like to do in this article is not to give a general survey of eighteenth-century French materialism but, in order to throw some light on the relationship between philosophy and science in the case of eighteenth-century materialists, to look at the essential scientific question raised by materialistic thinkers, in particular in the early years of the century, namely the functioning of the brain. This will also enable us to see the extent to which scientific developments in other countries may have influenced them, for I maintain that to understand this type of thought, quite apart from the question of philosophical influences on it, it cannot be isolated from developments in other countries, particularly in England, at the turn of the seventeenth to the eighteenth century. To begin with, we need to have a clearer idea of what is meant by materialism, and what the word meant in the eighteenth century. In general terms, we could say that materialism is the assertion that all natural phenomena can be explained entirely in terms of matter without recourse to any sort of immaterial prime mover or intelligent structuring principle – which implies the denial of final causes (although we do find a sort of materialism coexisting with belief in a god, as we shall see). Materialism goes back of course to Antiquity with the thought of Democritus and Lucretius, and, as Olivier Bloch shows in his extremely stimulating and useful little book on materialism (Bloch, Materialisme), modern materialists were aware of belonging to this tradition, and affirmed their allegiance by means of references to the ancient atomists, even if they did not follow their theories very closely. Materialism is thus to some extent a self-conscious tradition and not a label stuck on afterwards to a certain number of disparate thinkers, even if the term itself, as Bloch also shows, appeared in a polemical context opposing materialists to idealists in the Platonic tradition. The term ‘materialist’ is attested in England in the seventeenth century, in 1668 (More, Dialogi Divini) but, as Miguel Benitez has recently shown, it had already been used at least once in French, in 1676 (Spanheim, L’Athée convaincu).1 Furetière’s Dictionary in 1727 defines materialists as: a type of philosopher who claims that only matter or body exists and that there is no other substance in the world, that it is eternal and that everything is formed from it.2

 Benitez, Philosophie clandestine, 355. Previously its first use in French was attributed to Leibniz in 1702. 2  “[…] sorte de philosophes qui soutiennent qu’il n’y a que la matière ou le corps qui existe, et qu’il n’y a point d’autre substance au monde; qu’elle est éternelle, et que c’est d’elle que tout est formé.” (Furetière, Materialiste) 1

9  Materialistic Theories of Mind and Brain

199

The word was more frequent in the works of the enemies of the materialists than in those of the materialists themselves, who for obvious reasons of prudence tended to avoid proclaiming such dangerous opinions. An exception was La Mettrie in the middle of the century, who repeatedly proclaimed that he was a materialist. The term referred not only to general statements about the explanation of the universe and the denial of the existence of an intelligent plan, but more vitally, from Hobbes onwards, to a desire to extend to humans the claim that matter is enough to explain all phenomena; thus all human faculties, intellectual as well as physical, can be explained in material terms without the need for an immaterial or immortal soul. Debates thus tended frequently, particularly in the late seventeenth and early part of the eighteenth century, to centre around the question of the existence of the soul and of what, if anything, distinguishes humans from animals. The defence of the soul’s immortality against “the somatists or Epicureans and other Pseudo philosophers” published by Baxter in 1667 (Baxter, Reasons) gave a detailed view of the arguments of the materialists, including Hobbes, but situated him in a longer tradition, and particularly discussed the claim that matter in motion could produce thought. Similarly Bentley, in his 1692 Boyle lectures, set out to attack the materialists by proving, against the Epicureans, that matter and motion cannot think (Bentley, Matter & Motion). It is, however, important to emphasise here that this purely material conception of human beings could take several different forms. A simple quotation from the definition given by the Encyclopédie article Matérialistes (vol. X, 1765), is enough to show the diversity, and even confusion that reigned on this subject: The name materialists is also given to those who claim either that man’s soul is matter, or that matter is eternal and is God, or that God is only a universal soul spread throughout matter, which moves and disposes it, in order either to produce beings or to form the different arrangements that we see in the universe. See Spinosistes.3

What is striking about this definition is the fact not only that a diversity of forms of materialism is given, but also that it is taken as more or less the equivalent of ‘Spinosism’, in the deformation of Spinoza’s philosophy that was current in the eighteenth century and that has been studied by Paul Vernière.4 Although this Encyclopédie article was published in the second half of the century, it corresponds to the view that predominated in the early eighteenth century, when the two terms of materialiste and spinosiste were frequently seen as interchangable. In addition, the different varieties of materialistic thought given here do not exhaust the possibilities. What is emphasised in the Encyclopédie article, alongside a sort of pantheism – which is how Spinozism has often been interpreted – is the existence of a material soul, which is one of the forms that materialism took,

 “On donne encore aujourd’hui le nom de matérialistes à ceux qui soutiennent ou que l’âme de l’homme est matière, ou que la matière est éternelle et qu’elle est Dieu; ou que Dieu n’est qu’une âme universelle répandue dans la matière, qui la meut et la dispose, soit pour produire les êtres, soit pour former les divers arrangemens que nous voyons dans l’univers. Voyez Spinosistes.” 4  See Vernière, Spinoza, esp. II 344ff. 3

200

A. Thomson

particularly in the clandestine philosophical works of the early part of the century. This was not however the only type of materialistic explanation for human faculties to be found in the eighteenth century: another theory, more common in the later part of the century (although it is by no means absent in the earlier part, and indeed the two interpretations sometimes coexist in the same works), denied the existence of any separate soul, material or otherwise; instead sensitivity, and by extension thought, were considered to be either inherent in matter, or alternatively the result of a particular arrangement of matter, this latter point being also a matter for speculation. It is these questions that I shall mainly be addressing in this article, but there are first of all certain other preliminary remarks that must be made. The Encyclopédie article Matérialistes, with its reference to ‘Spinosisme’ also points to another problem in relation to eighteenth-century materialism, which involves not only a question raised by those writers themselves but also an issue at debate amongst modern critics. The long-standing interpretation of eighteenth-­ century French materialism used to be that it could be divided into two strands: one in the tradition of Cartesian mechanism and the other in that of Lockean sensualism. Thus La Mettrie and his Homme machine are presented as the culmination of Cartesian mechanism; he is said to have done no more than extend Descartes’s animal-machines to human beings (which was in fact what he claimed to be doing), while Helvétius, with his insistence on the determination of human characteristics by external factors and education, is seen as the chief representative of the Lockean sensualist strand which was particularly emphasised in the nineteenth century. This is, by and large, the interpretation to be found in Marx’s description of eighteenth-­ century French materialism in The Holy Family, although, as Olivier Bloch has shown, he was simply adopting the interpretation of the French historian of philosophy, Renouvier.5 This over-simplified and rigid interpretation of eighteenth-century materialism, while still found here and there, is no longer taken seriously by critics, who emphasise, on the contrary, the much more diversified and eclectic inspiration for these ideas. In particular, the inheritance of the ‘libertin’ tradition of Epicureanism, as found in certain clandestine works such as Theophrastus redivivus and as revived by Gassendi amongst others, has particularly been emphasised by recent research.6 The diverse inspiration in the clandestine philosophical manuscripts of the late seventeenth and early eighteenth century, many of which were used by the leading materialistic figures and some of which were re-edited in the later eighteenth century, notably by d’Holbach, is an indication of the diverse sources on which the materialistic current drew. Recently, John Yolton has studied the fortunes of Locke’s hypothesis concerning thinking matter (Yolton, Locke and French Materialism), which was particularly popularised by Voltaire in his thirteenth Lettre philosophique (which also circulated separately in manuscript form); this too has contributed to a more diverse picture of materialism in this period. Despite these studies and the way

 See Marx and Engels, Heilige Familie VI3d (‘Kritische Schlacht gegen den französischen Materialismus’) (MEW II 131-141); Bloch, Marx, Renouvier. 6  For example, Bloch, L’héritage libertin. 5

9  Materialistic Theories of Mind and Brain

201

in which they show the need to be prudent when attempting to interpret eighteenth-­ century materialism, it is frequently classified, particularly in the form expounded by its most notorious representative, La Mettrie, as ‘mechanical materialism’, a label that I find unsatisfactory for several reasons, which will become clear below. The reference to La Mettrie also reminds us of the importance of the medical tradition in the inspiration for much of the materialistic writing in the eighteenth century, which is again an important aspect of what I shall be discussing.

9.2 Can Matter Think? I wish to concentrate here not on a materialistic cosmogony of the type found in Le Système de la Nature, but on the kind of materialism found earlier in the century, including in the writings of La Mettrie, and which represents a continuation of the concerns of the late seventeenth century.7 The main aim of this materialism was to demonstrate, in opposition to the teachings of the Catholic Church, that there is no need for an immaterial or immortal soul, and that the human faculties can be explained purely by matter. It therefore denies an afterlife and future punishments and rewards, a position which was seen as critically undermining not only the authority of the church but any basis for morality. These debates inevitably drew heavily on developments in physiology in order to attempt to explain how the brain could produce thought alone. Now obviously, those who attempted to explain the workings of the mind in purely material terms, or in other words to claim that the material brain thinks, needed to discuss the much vexed question of whether matter and motion could think (as it was put by Bentley). Thus, not surprisingly, an important question raised by materialists involves the nature of matter. How can matter explain all the workings of the human being, in particular the intellectual functions? John Toland, who was very influenced by Leibniz (despite Leibniz’ clearly expressed disapproval of any insinuation that matter alone exists8), affirms in his Letters to Serena (1704), that matter always possesses the capacity to move, distinguishing this motion from local movement from place to place, in order to claim that matter is sufficient to explain all phenomena; however, he (prudently?) attempts to reconcile this with belief in a God, claiming that chance meetings of atoms could never create a universe, and that God could just as well create matter endowed with motion as with extension. He claims only to exclude “an extended corporeal God, but not a pure spirit or immaterial being” (Toland, Letters to Serena, 236). D’Holbach, who translated the work into French in 1768 under the title of Lettres philosophiques,  I shall however not discuss J. Meslier’s Mémoire, as it is mainly an attack on the Church and the existing social order drawing mainly on Malebranche’s writings, and was written in isolation from the tradition I am here discussing, of attempts to provide a materialistic explanation of humans drawing on physiological data. 8  See Leibniz’s letter to Toland, April 30, 1709: https://earlymodernintellectualhistory.wordpress. com/2017/11/12/letter-from-leibniz-to-toland-dated-april-30-1709-bl-add-mss-4465-5-6/ 7

202

A. Thomson

drew heavily on Toland’s arguments in his Système de la Nature, despite important differences between their theories (Lurbe, Matière, nature, mouvement). It is not surprising that La Mettrie begins his first philosophical work with this question. The Histoire naturelle de l’âme (1745, which was reworked to become Le Traité de l’âme in 1750) opens with a discussion of matter and its properties, in which he rejects the Cartesian conception of matter as simply extension. However, this discussion, which attempts to use the scholastic categories of matter and form (and which he himself mocks in his main work L’Homme machine, published 2 years later), contains a certain confusion in the use of the words ‘matter’ and ‘substance’ and is rather inconclusive. T. Verbeek, in his critical edition of this work, has shown the variety of works and philosophies on which La Mettrie has drawn in these chapters, including Madame du Châtelet’s interpretation of Leibniz, and the extent to which it is a satire on number of them.9 The only conclusion which he does reach is that matter as it is observed in organised bodies always possesses a certain number of properties, including the faculty to move and to feel: In bodies, we have knowledge only of matter, and we observe the faculty of feeling only in these bodies: on what basis should we then set up an ideal being, disproved by all our knowledge?10

In fact he abandons any further attempt to understand the nature of matter as such, admitting his ignorance and preferring to stick to a discussion of organised matter, to show experimentally that it possesses these qualities. L’Homme machine therefore begins with a review of the main philosophical systems concerning the human soul, which he divides into those of the materialists and those of the spiritualists. He criticises in particular the Leibnizians and the Cartesians for trying to define matter, whose essence is unknowable, and he declares: To ask whether matter, considered only in itself, can think is like asking whether matter can indicate the time.11

Instead, he provides a series of examples of experiments on animals intended to show that the smallest parts of organised matter, or the fibres, possess the capacity to react and to move, even when separated from the whole body of the animal. Thus he is able to declare that: Given the slightest principle of movement, animate bodies will have everything they need to move, feel, think, repent and, in a word, behave in the physical sphere and in the moral sphere which depends on it.12

 See La Mettrie, Le Traité de l’Ame, esp. II ch. 3 and 4.  “Nous ne connaissons dans les corps que la matière, et nous n’observons la faculté de sentir que dans ces corps: sur quel fondement donc établir un être idéal désavoué par toutes nos connaissances?” (La Mettrie, Traité de l’âme, 24*; transl. From idem, Machine Man, 51) 11  “En effet, demander si la matière peut penser, sans la considérer autrement qu’en elle-même, c’est demander si la matière peut marquer les heures.” (La Mettrie, L’Homme machine, 149; transl. From idem, Machine Man, 3) 12  “Posé le moindre principe de mouvement, les corps animés auront tout ce qu’il leur faut pour se mouvoir, sentir, penser, se repentir, et se conduire en un mot dans le physique, et dans le moral qui 9

10

9  Materialistic Theories of Mind and Brain

203

The same questions were afterwards at the heart of Diderot’s discussion of materialism, particularly in his central work on the subject, Le Rêve de d’Alembert (1769). The first part, the Entretien entre d’Alembert et Diderot, begins with the nature of matter; rejecting, like La Mettrie, Descartes’ dualism, Diderot affirms that as a consequence of motive power in matter, it is capable of feeling and can therefore explain all intellectual as well as physical capacities (Diderot, DPV, XVII 89ff.). This question had already been touched on in Diderot’s Pensées sur l’interprétation de la nature (1753) in which, influenced by Buffon and by the first version of Maupertuis’s Essai sur la formation des corps organisés or Système de la nature (1751),13 he insisted on the energy of the living molecule. Maupertuis’s study of reproduction had attempted to extend Newton’s principles of attraction to the animal kingdom by postulating, instead of a “uniform and blind attraction spread throughout all the parts of matter”,14 something like what we call desire, aversion or memory, in the smallest parts of matter, which he calls ‘elements’ (Maupertuis, Formation des corps organisés, § XIV); these elements originating from the two parents join together in order to form the different parts of the body. Hence: the elements suitable for forming the foetus swim in the seminal fluids of the parent animals but when each one has been removed from the part similar to the one it is to form, it keeps a sort of memory of its former situation, and whenever it can, will go to take up that situation in order to form the same part in the foetus.15

Maupertuis, who was aware of the dangers inherent in according feelings to the smallest parts of matter, attempted to avoid accusations of irreligion by affirming his belief in an immortal soul (Maupertuis, Formation des corps organisés, § LVII) and by condemning the system which only allows the existence of “eternal atoms without feeling or intelligence, whose chance meetings have created everything”16 and he reaffirmed the need for a creating intelligence. Diderot, however, in his 1753 work, tried to push Maupertuis’s hypothesis as far as it could go and emphasised the ‘terrible consequences’ of the theory, in other words its materialistic or ‘Spinozistic’ conclusions. He declares in Pensées sur l’interprétation de la nature that if this universe is a whole then it has a soul, like a great animal, and this soul of the world is God (Diderot, DPV, IX 76, 82). Maupertuis reacted violently to Diderot’s interpretation, in a reply published as an addition to the new version of his work,17 but the dangers inherent in adapting Newtonianism to animals were clear. en dépend.” (La Mettrie, L’Homme machine, 180; transl. From idem, Machine Man, 26) 13  Dissertatio inauguralis metaphysica de universali naturæ systemate, Erlangen 1751, published in French in 1754, as Essai sur la formation des corps organisés. 14  “[…] attraction uniforme et aveugle, répandue dans toutes les parties de la matière […]” 15  “[…] les éléments propres à former le foetus nagent dans les semences des animaux père et mère; mais chacun extrait de la partie semblable à celle qu’il doit former, conserve une espèce de souvenir de son ancienne situation, et l’ira reprendre toutes les fois qu’il pourra, pour former dans le foetus la même partie.” (Maupertuis, Formation des corps organisés, § XXXIII) 16  “[…] des atomes éternels, sans sentiment et sans intelligence; dont les rencontres fortuites ont formé toutes choses […].” (Maupertuis, Formation des corps organisés, § LXIII) 17  Maupertuis, Oeuvres, II 165–70.

204

A. Thomson

However, like La Mettrie, Diderot hesitated to ascribe the faculty of feeling to the smallest parts of matter, or molecules, and in the Entretien entre d’Alembert et Diderot as well as in the Réfutation d’Helvétius he refers to “sensibility, a general quality of matter or product of organisation”.18 In his commentary on Hemsterhuis, he poses a series of questions: You say that humans and animals feel, but what is feeling? Is it a general property of matter? Is it a property which results from a particular combination? Is it the effect of a cause analogous to the effect? Is it the effect of a cause essentially different from the effect?19

And in the Réfutation d’Helvétius, he claims that the affirmation that the molecules of matter generally possess sensation is not certain but simply “a supposition which derives all its force from the difficulties it solves, which is not enough in good philosophy.”20 Despite his study of chemistry, Diderot then, like La Mettrie, comes to no very clear conclusion concerning the nature of matter and is unable to decide whether the faculty of feeling is the result of a particular organisation or inherent in its smallest parts. On this vital question of the nature of matter, the English scientist Joseph Priestley provides an original answer in his Disquisitions relating to Matter and Spirit (1777). Priestley, in addition to being a renowned chemist, was extremely active in many fields of intellectual life and a leading political radical, to the extent that he was finally forced to leave Britain for the USA due to public hostility to his open support for the French Revolution. He was also a leading Unitarian, a member of a sect which was finally emerging from clandestinity in the later eighteenth century, but his religious unorthodoxy went as far as espousing the mortalist heresy which had been influential in certain English circles in the seventeenth and early eighteenth centuries, and to which we shall return below. In order to substantiate his belief that there is no immortal soul but that the whole human being dies, to be resurrected completely only at the Last Judgement (which he believed to be the true teachings of Christianity, later corrupted by the Catholic Church under pagan influence), he undertook to demonstrate that the distinction of two substances was absurd and that it was possible to account for thought in terms of matter alone. His first reflections on this subject are to be found in his 1775 edition of David Hartley’s Observations on Man, his Frame, his Duty and his Expectations (first published in 1749), in which he replaces Hartley’s study of the workings of the brain and nerves by an Introductory Essay where he considers the question of whether matter can think, and affirms:

 “[…] la sensibilité, propriété générale de la matière ou produit de l’organisation […].” Diderot, DPV, XVII 105 (my underlining). 19  “Vous dîtes que l’homme et l’animal sentent; mais qu’est-ce que la sensibilité? Est-ce une propriété générale de la matière? Est-ce une propriété résultante d’une certaine combinaison? Est-ce l’effet d’une cause analogue à l’effet? Est-ce l’effet d’une cause essentiellement différente de l’effet?” (Diderot, LEW, XI 25) 20  “[…] une supposition, qui tire toute sa force des difficultés dont elle débarrasse, ce qui ne suffit pas en bonne philosophie.” (Diderot, LEW, XI 492) 18

9  Materialistic Theories of Mind and Brain

205

I rather think that the whole man is of some uniform composition, and that the property of perception, as well as the other powers that are termed mental, is the result (whether necessary or not) of such an organical structure as that of the brain. (Priestley, Introduction, xx)

Two years later, in his Disquisitions, Priestley enlarges on this initial supposition, refusing the usual definition of matter as a solid, impenetrable substance possessing merely a vis inertiae, and instead proposing a new conception of matter with which the faculties of feeling and thinking are not incompatible. He demonstrates that the smallest particles of matter, or atoms, possess a power of attraction and, drawing on experiments on electricity and light, he shows that matter is not impenetrable but that its resistance can be explained by its power of repulsion. And he adopts Boscovich’s definition of matter as composed only of physical points with space between them (Philosophiae naturalis theoria, 1759). Priestley’s matter is thus defined simply in terms of its powers of attraction and repulsion. The aim is to show that there is nothing therefore to oppose the ‘thinking matter’ hypothesis: Since the only reason why the principle of thought or sensation, has been imagined to be incompatible with matter, goes upon the supposition of impenetrability being the essential property of it, and consequently that solid extent is the foundation of all the properties that it can possibly sustain, the whole argument for an immaterial thinking principle in man, on this new supposition, falls to the ground; matter, destitute of what has hitherto been called solidity, being no more incompatible with sensation and thought, than that substance which, without knowing anything further about it, we have been used to call immaterial. (Priestley, Disquisitions, 18)

However, he seems to think that this capacity for thought is not possessed by the smallest particles of matter, but rather by a particular organisation of it: Unless we had a clearer idea than it appears to me that any person can pretend to have, of the nature of perception, it must be impossible to say a priori whether a single particle, or a system of matter be the proper seat of it. But judging from appearances, which alone ought to determine the judgement of philosophers, an organised system which requires a considerable mass of matter is requisite for the purpose. (Priestley, Disquisitions, 89)

Rather than attempting to go into details concerning the way in which this particular organisation in the brain produces thought, he prefers to emphasise the advantages for revealed religion of this system, which he himself calls materialistic. He defines it as follows: Man, according to this system, is no more than what we now see of him. His being commences at the time of his conception, or perhaps at an earlier period. The corporeal and mental faculties, inhering in the same substance, grow, ripen and decay together and whenever the system is dissolved, it shall continue in a state of dissolution, till it shall please that Almighty Being who called it into existence to restore it to life again. (Priestley, Disquisitions, 49)

As we can see, the initial basic question about the nature of matter led to a certain number of unresolved problems which could hardly be solved at the time; the unambiguous statement that matter was enough to explain all phenomena left several questions hanging in the air. In addition to the one we have just seen – whether the smallest particles of matter feel and think or whether a particular organisation of matter is needed – there were also difficulties concerning the transition from inert to

206

A. Thomson

feeling matter and that from sensation to thought. The first of these continued to present problems and likewise tended to be left unresolved. La Mettrie writes in L’Homme machine: Hence I am as reconciled to my ignorance about how inert simple matter becomes active and composed of organs, as I am to the fact that I can only look at the sun through a red lens.21

And Diderot, after having tried to show, in the Rêve, how a marble statue can become flesh, admits his ignorance in his Refutation of Helvétius: I can see clearly in the development of an egg and in some others of nature’s operations, apparently inert but organised matter passing, by means of purely physical agents, from a state of inertia to that of sensitivity and life; but the necessary link of this passage escapes me. Our notions of matter, organisation, movement, heat, flesh, sensitivity and life must still be very incomplete.22

Likewise, the question of the relationship between sensitivity and intelligence was problematic. Under the influence perhaps of Maupertius, Diderot seems at times tempted to believe that to say that molecules can feel is the same thing as saying that they can think, while for La Mettrie this would apparently run the risk of, as he says, spiritualising matter rather than materialising the soul, and would thus be inacceptable. But more frequently for Diderot, intelligence is the result of memory and the comparison of sense-impressions. Here again, he seems to prefer to admit ignorance, for in his criticism of Helvétius, he refuses the latter’s assimilation of thought to feeling and proclaims the difficulty of knowing how one moves from one to the other. (Diderot, LEW, XI 491).

9.3 The Question of the Soul As these problems were left unresolved, the essential question at issue therefore came to concern the workings of the brain, as it was clear that it is in this particular organisation of matter that intelligence is to be found. But it was impossible to discuss the workings of the brain without coming up against the vexed question of the soul. For it is obvious, as we have already seen, that the denial of an immaterial and immortal soul was at the heart of a material view of humans. The debate on the soul was of course extremely important in the seventeenth century, in the wake of that concerning the souls of animals and the Cartesian synthesis; this debate was not  “Je suis donc tout aussi consolé d’ignorer comment la matière d’inerte et simple devient active et composée d’organes, que de ne pouvoir regarder le soleil sans verre rouge.” (La Mettrie, L’Homme machine, 189; transl. From idem, Machine Man, 33) 22  “Je vois clairement dans le développement de l’oeuf et quelques autres opérations de la nature, la matière inerte en apparence mais organisée, passer par des agents purements physiques, de l’état d’inertie à l’état de la sensibilité et de vie, mais la liaison nécessaire de ce passage m’échappe. Il faut que les notions de matière, d’organisation, de mouvement, de chaleur, de chair, de sensibilité et de vie soient encore bien incomplètes.” (Diderot, LEW, XI 492) 21

9  Materialistic Theories of Mind and Brain

207

confined to France, but was particularly virulent in England, mainly in connection with the tradition of the Christian Mortalists. Their ideas were revived during the period of the Revolution in the middle years of the century, in particular by a pamphlet entitled Man’s Mortalitie, first published in 1643 and generally attributed to the Leveller R. Overton, and also by the republican J. Milton; Hobbes must also be situated as part of this debate.23 While it is true that during the Interregnum there were different varieties of Christian mortalists, ranging from those who insisted on the sleep of the soul until the Day of Judgement, to those who seemed to deny any soul (Burns, Christian Mortalism, esp. ch. 2 and 3), in the late seventeenth century, the debate centred essentially around the existence of the soul as a separate immaterial substance in the form propounded by Descartes and defended by Henry More. While claming to be Christians and affirming the existence of God, these materialists denied the existence of an immortal soul and of any life after death before the general resurrection at the Last Judgement, for they believed (or at least claimed) that this was the true Christian doctrine, which had been corrupted by the Catholic Church under the influence of paganism. There was an important debate on these opinions again in the early years of the eighteenth century, revolving particularly around the works of the medical doctor William Coward, which were condemned by the House of Commons. In them he denies the existence of an immortal soul and claims to prove that matter and motion can produce thought in humans as in animals; a particular organisation of matter produces thought in the brain by means of the animal spirits.24 John Toland’s Letters to Serena, already mentioned, were published at the same period, and Toland refers to Coward in the preface to the work. This attack on the doctrine of an immortal soul seems to have been part of a campaign against the established Church and a defence of freedom of thought and of the principles of the radical true Whigs against the Establishment during these years of ideological struggle.25 At the same time, one of the important themes of the clandestine anti-religious treatises in French, many of which date from the early eighteenth century, was the soul. Indeed, one of the most famous of them is called L’âme matérielle. It is impossible, in the context of the present article, to go in any detail into the different clandestine treatises of these years, which circulated frequently in manuscript form and which were directed against the doctrines of the Catholic Church. In recent years  See in particular Burns, Christian Mortalism.  See e.g. Coward, Second Thoughts, 105. Coward is referred to as one of the main English materialists by C. Wolff in Psychologia Rationalis, Francofurti, 1734: “§ 33. Materialistae dicuntur philosophi, qui tantummodo entia materialia, sive corpora existere affirmant. Materialista fuit Hobbesius, philosophus Anglus, qui plures ibidem asseclas hodienum habet. Eos inter eminent Tolandus & Cowardui. […] § 34. Quoniam Materialistae nonnisi corporum existentiam admittunt, immo nonnisi eadem possibilia esse contendunt (§. 33); nonnisi unum substantiarum genus existere affirmant, adeoque Monistae sunt (§. 32). § 35. Materialistae igitur animam pro ente materiali habent. Qui adeo demonstrat animam esse ens immateriale, Materialismus evertit […] ii quoque immaterialitatem animae negant & cogitationem per motum materiae cujusdam subtilis explicare conantur: id quod inferius accuratius examinatur, ubi de materialibus rerum ideis in cerebro agitur.” 25  I have discussed this in more detail in Religious heterodoxy. 23 24

208

A. Thomson

there has been an increase in interest in these treatises, and much work is being done on them, mainly in France and Italy. As I have already indicated, in the early eighteenth century, there were essentially two ways of denying the immortal soul. One was, as we have seen, to try to show how thought could be the result of a particular organisation of matter in the brain; this became the most fertile strand of reflection. But there were also those who posited the existence of a material soul, made up of a very subtle type of matter, like fire or light; this theory, part of the Epicurean tradition, was particularly taken from Italian Renaissance works (Vartanian, Quelques réflexions). One version of this theory was expounded by the French doctor Guillaume Lamy, in a famous passage that was taken over and inserted in the most notorious and widely-distributed of the clandestine treatises, L’Esprit de Spinosa or Traité des trois imposteurs, and it is likewise quoted by La Mettrie in L’Histoire naturelle de l’âme; La Mettrie however, despite some apparent hesitation, finally did not favour this older model. The more fertile hypothesis  – which has interested some modern neurobiologists, who see in these works the forerunners of modern theories – tried to look at the structure and functioning of the nerves and the brain in order to try to explain the production of thought, and it is on this debate that I would particularly like to concentrate. It is of course profoundly indebted to physiological study, in particular that of the brain, although physiologists attempted in the main to reconcile their studies with the teachings of the Church. Their reputation for heterodox thought came partly from the fact that Aristotelian and Galenic physiology presented a certain challenge to Church teaching, notably concerning the relationship between the spiritual and immortal soul and the faculties; there was also a strong materialistic tradition inherited from Atomism (Roger, Les Sciences de la vie, 95–96; Henry, Matter of souls, 88–89), as well as from the alchemical tradition and its speculation on thinking matter (Debus, Chemistry and the quest for a material spirit of life; Mothu, La pensée en cornue; and Mothu, Le mythe de la distillation). Thus medical doctors had a reputation for irreligion and doubts concerning the immortal soul, as for example, is claimed by Saint-Evremond.26 And indeed, the role played by medical doctors and their writings in the development of eighteenth-century materialism is vital. The most important figure in this connection – both for his research on the brain and the influence he had on all those who attempted to broach the question of the soul from a medical point of view in the late seventeenth and early eighteenth centuries – is the English doctor Thomas Willis; he was Professor of Natural Philosophy at Oxford in the 1660s and renowned as the author of, in particular, Cerebri anatome (1664) and De anima brutorum (1672), a work which resulted from the courses he gave at the university on physiology and the anatomy of the brain. He is generally considered to be the father of the localisation of brain functions and the inventor of the nervous system.27 Willis, who was strongly influenced by Gassendi, was hostile

26 27

 Letter reprinted by P.Bayle in Bibliothèque volante, quoted by Kirkinen, Les Origines, 222 n.5.  On Willis’s life and works, see Isler, Thomas Willis.

9  Materialistic Theories of Mind and Brain

209

to Scholastic philosophy and a promoter of the new science; he was a leading member of the important group of scientists, champions of observation and experiment, who were active at Oxford in the 1650s and 1660s. Medicine was a vital part of their study, in particular anatomy based on the work of Harvey, but also influenced by mechanical philosophy and chemistry.28 Willis’s extremely influential books provided a description of the workings of the brain and the nerves, accompanied by numerous illustrations of the dissection of animal brains (many of which were executed by the future architect Christopher Wren). Calling on atomism and chemistry, Willis describes the workings of the animal soul, which is an igneous, corporeal soul constituted by the animal spirits and present throughout the body; these spirits function not by contact or impact but by a sort of explosion.29 Although he carefully distinguishes the human soul which is rational and spiritual from the corporeal soul, he does accord a type of reason to animals. He was aware of the dangers inherent in this theory and defended himself in advance against all possible accusations of favouring irreligion. While such protestations were common, including from sceptics, it is clear that in Willis’s case they were sincere, for he was a devout and practising member of the established Church of England who even took part in secret celebrations of mass, sometimes in his own house, in Oxford during the Interregnum, an obviously dangerous activity (Isler, Thomas Willis, 13). Nevertheless, it is clear that he was attempting to reconcile political and theological positions which were to some extent incompatible. The dilemma facing him arose mainly from his emphasis on the similarities between human and animal brains and his extensive use of comparative anatomy. The differences between human and animal intellectual capacities can therefore only be explained by the workings of the immaterial immortal soul. But he situates this soul in a part of the brain and explains its malfunctioning by physical causes, while at the same time emphasising the superiority of the human nervous system as created by God.30 In view of these factors, it is hardly surprising that the English doctor’s works were used by all those in the early eighteenth century who attempted to extend the descriptions of the corporeal soul to humans and to explain all the intellectual functions by recourse to the material brain and the animal spirits. While, as we have seen, it is difficult to accuse Willis of secretly wishing to instill such ideas in the minds of his readers, it is clear that the problems raised by his works could easily be used in the service of materialistic arguments, together with Locke’s hypothesis on the possibility of thinking matter (Yolton, Thinking Matter and Locke and French Materialism). Indeed, some scholars have studied the influence of Willis’s cerebral anatomy on Locke and drawn parallels between Locke’s hypothesis and certain passages in Willis’s works (Isler, Thomas Willis, 178, and Wright, Locke). Thus for

 On scientific research in Oxford during this period, see Frank jr, Harvey.  On Willis’s explanation of the workings of the brain and the animal spirits, see in particular Canguilhem, La formation; Meyer and Hierons, Thomas Willis’s Concepts of Neurophysiology. 30  On this question, and in particular on the problems arising from Willis’s attempt to correlate structure and function, see Bynum, Anatomical Method. 28 29

210

A. Thomson

many materialists, including La Mettrie, Willis could be seen as a precursor, and their works often contain examples taken from his writings. Another important link in the development of materialistic interpretations of thought was Guillaume Lamy, the Epicurean ‘docteur-régent’ of the Paris Medical Faculty already mentioned, who expounded his ideas concerning the workings of the mind in his Discours anatomiques (1675) and Explication méchanique et physique des fonctions de l’âme sensitive (1677). The first work, published in Rouen, aroused such violent criticism from certain Cartesian doctors in his university that he brought out a second enlarged edition in Brussels in 1679, while the second work was published in Paris with the Faculty’s approval. The main characteristics of his philosophy are his antifinalism and an attempt to explain intellectual faculties in terms of matter without the need for an immaterial soul, but he presents his theories as only so many hypotheses and, like Willis, claims to be dealing only with the functions of the sensitive soul, common to humans and animals; he wisely claims to follow the teachings of the faith concerning the spiritual soul.31 But he nevertheless makes a clear distinction between the realms of faith and philosophy and seems to imply that philosophy does not teach the existence of an immaterial soul. He was clearly understood at the time to be providing an explanation of the mind in terms of a material soul, and his description of this material soul as a fine substance was absorbed into the tradition of clandestine antireligious thought. The passage in which he presents this hypothesis was, as has been indicated above, recopied word for word in works such as L’Ame matérielle and L’Esprit de Spinoza (see Lamy, Discours, 28). The English doctor William Coward wrote his works in very different conditions and they are very different in nature. After his medical studies at Oxford, where he then taught for 2 years as a Fellow of Merton College, he spent the rest of his life as a medical practitioner, first in Northampton and then in London; but he became famous for his polemical works denying the immaterial soul. The late seventeenth-­ century polemic was in fact started by a certain Henry Layton (1622–1705) who undertook to reply to Bentley’s famous Boyle lecture of 4 April 1692 in titled Matter and Motion cannot think.32 Layton’s attack on Bentley was continued in a work called A Search After Souls and Spiritual Operations in Man, which appeared with no indication of place or date of publication. Here Layton, who was not a doctor, explains that he arrived at his opinions after long meditations on the question during the summer of 1690 as a result of reading Willis’s De anima brutorum, and he even claims that Willis was convinced of the materiality of the human soul but dared not affirm it openly.33 Coward continued this campaign, firstly in Second Thoughts concerning Human Soul, published under the pseudonym of ‘Estibius Psychalethes’ in 1702, and burnt by order of the Parliament. He further developed his arguments in

 See for example Réponse aux raisons, par lesquelles le sieur Galatheau prétend établir l’empire de l’homme sur tout l’Univers, published with the 1678 edition of Lamy’s Explication. 32  Reproduced in Bentley, Matter and Motion, 35-50. 33  Layton, Second Part, 22. 31

9  Materialistic Theories of Mind and Brain

211

The Grand Essay, or a Vindication of Reason and Religion, against Impostures of Philosophy, 1704, written in reply to John Broughton’s Psychologia attacking Coward’s first book. The controversy raged on, with pamphlets and counter-­ pamphlets, until Coward’s departure from London around 1706. Although Coward dedicated his first work to the clergy of the Church of England and based his argument on numerous quotations from the Scriptures, a large part of his demonstration, particularly in the Grand Essay, relies on physiological examples showing how intellectual functions are dependent on the body. His theory is also expounded in a medical work in Latin on sight, intitled Ophthalmiatria (1706), which criticises the Cartesian doctrine of the pineal gland and affirms that thought is produced by the brain; here Willis is abundantly quoted. But Coward does not defend the theory of the material soul; for him, the soul is simply life. Nevertheless, like Lamy, when he comes to try to describe how ideas are produced, by the body or by a material soul, he adopts the theory of the animal spirits. While Lamy, following Willis, accepted the Cartesian description of traces made by these spirits in the brain (Lamy, Explication, 142ff.), for Coward it is not so clear. He states that the animal spirits, which are distilled from the blood, create thought by their motion in the brain; apparently they do not only leave imprints in the brain but also produce thought in a manner that is difficult to understand. In The Grand Essay, he defines thought as: the Result of certain Effluviums from the Brain, raised and continued by a perpetual Circulation or Rotation of Ideas thereon impressed, as by God originally so ordained, which last clause I have added because I think it impossible for any man in the world by mere Philosophy to explain How Material or Immaterial Substances either are able to think. (Coward, Grand Essay, 129)

The agitation of the spirits, which are compressed in the brain, thus produces both feelings and thought, and their motion is compared to the agitation of fire on highly rectified spirits of wine (ibid. 134). As we can see, there is no clear physiological description, but rather an explanation of the way the state of the spirits affects humans’ thoughts and feelings. Coward frequently insists on God’s power to make matter capable of thinking and judging the ideas impressed on “different small particles of Matter, called the Animal Spirits of the whole Man” (ibid. 142) or, as he writes in Second Thoughts, “to create an active power in dull heavy and unactive matter, by which it is enabled to perform all those noble operations it doth.” (Coward, Second Thoughts, 101). It is, I think, clear that Coward does not accept the idea of a material soul, as for him the animal spirits, which are a highly purified form of matter, do not constitute the soul, which is simply life. The spirits provide sense impressions or ideas, and the motion of the spirits produces thought; they are thus the ‘foundation of thought’ in humans (Coward, Grand Essay, preface). He seems to want to emphasise that thought is produced by a particular organisation of matter and he tries to avoid a conception of the soul as a particular material substance, even if he seems to be pushed in that direction by his reference to Willis. What does emerge is the difficulty for Coward, as for his contemporaries, to provide a materialistic explanation

212

A. Thomson

of humans, for these writers were apparently unable to go further than examples demonstrating the dependence of thought on the body and mainly intended to refute the theoretical arguments which attempted to prove that an immaterial soul must necessarily exist. What was apparently crucial was the affirmation that the brain could produce thought, even if it was unclear how this could happen. Thus in Letters to Serena, published in 1704, during the controversy surrounding Coward’s works, (which Toland refers to) Toland denies, in his ‘refutation’ of Spinoza, that there is one undifferentiated substance that always thinks; instead, he affirms: “Whatever is the principle of thinking in animals, yet it cannot be performed but by the means of the brain.”34 It is interesting to notice a similarity on this subject between Coward’s work and one by a French Protestant doctor called Abraham Gaultier, whose Réponse, published in 1714,35 includes several materialistic arguments, mainly in order to demonstrate, against the Cartesians, that matter can feel and that sensation (of animals and, by implication, of humans) can be explained by the workings of the body. Like Lamy, whose work he probably knew, Gaultier does not discuss humans, ostensibly sticking to animal soul, but he clearly insinuates that his analysis applies to humans as well.36 A version of this work, called La parité de la vie et de la mort, was absorbed into the century’s clandestine antireligious tradition. Like Coward, Gaultier does not favour the idea of a material soul, emphasising above all that a single substance is responsible for all phenomena and that everything can be explained by ‘modes’ of that substance. Thus there is no soul separate from the body, for the soul is simply the body and its workings: “The life of animals or their sensitive soul, which is the same thing, can thus only be the functions which emerge from their organs.”37 This affirmation that the soul is life is similar to the claim made by Coward; for Gaultier, the smallest parts of matter are not sensitive, for sensitivity is the result of numerous different causes (Gaultier, Réponse, 154), nor are the animal spirits (ibid. 158). But unlike Coward, he does not try to explain how thought is produced and only mentions Willis in order to criticise his localisation of brain function, denying that the source of the nerves is in the brain (ibid. 150-3). In fact his main purpose is polemical, to demonstrate, against the theologians, that life is the result of the organisation of matter.

 Toland, Letters to Serena, 139. See also Pantheisticon, quoted by Lurbe, Le spinozisme de John Toland, 42. 35  The complete title of the work is Réponse en forme de dissertation à un théologien qui demande ce que veulent dire les Sceptiques, qui cherchent la vérité par tout dans la Nature, comme dans les écrits des Philosophes; lors qu’ils pensent que la Vie & la Mort sont la même chose […]. It was published with official permission in Niort, chez Jean Elies. 36  On the subject, see O. Bloch’s introduction to Gaultier, Réponse, 106-109. He also considers that Gaultier must have known Lamy’s works, which inspired his own antifinalism. 37  “La vie des animaux, ou ce qui est la même chose, leur ame sensitive ne peut donc être que les fonctions qui naissent de leurs organes […]” (Gaultier, Réponse, 142). See also 170: “L’âme des bêtes est seulement les fonctions de leur corps.” 34

9  Materialistic Theories of Mind and Brain

213

9.4 The Workings of the Brain What is in fact remarkable in these early eighteenth-century attempts to dispense with an immaterial soul and explain thought in terms of matter alone, is that even though they refer to Willis, they do not provide a detailed description of the workings of the brain and, apart from Coward’s Ophthalmiatria, their use of Willis’s writings on the brain’s structure and workings is relatively limited; Lamy, for example, only has a couple of pages describing the structure of the brain in his Sixth Discours anatomiques, which use Willis’s description (Lamy, Discours, 96-8). After this description, and an explanation of how the spirits are distilled from the blood and circulated throughout the body, he concludes: “That, Gentlemen, is what I have to say concerning the brain, which is claimed to be the place where the soul principally lives, in other words where it exercises its noblest functions.”38 This leads him on to a much longer account of different opinions concerning the soul, ending with the passage already mentioned describing a material soul. It is really only with La Mettrie, in the middle of the century, that we find another attempt to explain how the brain can produce thought, and he came up against the same problems as Lamy, Coward or Gaultier, namely how to provide a clear explanation of the way in which matter produces thought, and whether there is a material soul or whether the soul is simply another word for life. La Mettrie tries to reply to these questions in his first philosophical work, L’Histoire naturelle de l’âme in 1745. In this work, as in his more famous Homme machine (1747), he undermines belief in an immaterial, immortal soul, which he calls ‘un être idéal’. In the earlier work, however, he ostensibly adopts the hypothesis of three souls and, like Lamy, claims to be only discussing the sensitive soul; but his protestations that he accepts the teachings of the Church concerning the intellectual soul are even less credible than those of Lamy. His discussion relies on physiological data to describe the workings of the nerves, and of the brain as the sensorium commune, using the descriptions already found in his translation of Herman Boerhaave’s Institutions.39 In this latter work, his translation of both Boerhaave’s course and Haller’s notes had brought out the materialistic implications of the master’s description of the brain and the nerves, and notably the siting of the sensorium commune. He even goes so far as to add, on this subject: It is clear that Mr Boerhaave places the seat of the soul, called sensorium, in the brain’s medulla; this is its essential part, whose imperceptible organic structure seems to differ from that of animals only in its effects. […] We should not be afraid of humiliating our self-­ esteem by the knowledge that mind is of such a corporeal nature.40

 “Voilà, Messieurs ce que j’avais à dire du cerveau, que l’on prétend estre le lieu où l’âme habite principalement, c’est à dire où elle exerce ses fonctions les plus nobles.” (Lamy, Discours, 98) 39  Boerhaave, Institutions, V (1747) 90ff. 40  “M.Boerhaave, comme on voit, met donc le siège de l’âme, sous le nom de sensorium, dans la moelle du cerveau; partie essentielle, dont la structure organique imperceptible, ne paraît différente du cerveau des animaux, que par ses effets […]. Qu’on ne craigne point qu’il soit trop humiliant 38

214

A. Thomson

Retaining the Cartesian model of brain traces brought by the animal spirits through the nerves by means of the impact of spherical globules on one another, rather than that of Willis, he shows that the seat of the soul or sensorium commune, situated in the nerve-endings in the brain, cannot be in a single spot; he therefore concludes that different parts of the brain are responsible for different sensations and that the sensorium commune is spread over the whole brain. His description of the different sensations brought by different nerves and different locations of the nerve-endings in the brain leads him to conclude: You can imagine, after all that has been said on the diverse origins of the nerves and the different seats of the soul, that there may well be some truth in all the different opinions of authors on this subject, however contradictory they may seem. And since diseases of the brain, according to the place they attack, destroy sometimes one sense and sometimes another, are those who place the seat of the soul in one of the pairs of optic lobes any more wrong than those who would like to limit it to the oval centre, the corpus collosum or even the pineal gland? We can therefore apply to the whole of the brain’s matter what Virgil says of the whole body, throughout which he claims, with the Stoics, that the soul is spread.41

But he is unable to go any further into the workings of this organ and is mainly interested in its role as the receiver of outside impressions. He hesitates as to which model of the soul to adopt; in his translation of Boerhaave, he simply referred to Locke’s hypothesis, “that God, who has given animals the faculty of perceiving, remembering, and having some ideas, may have given our more supple organs a much superior intelligence.”42 In L’Histoire naturelle de l’âme, although quoting favourably Lamy’s description of the soul of the world (La Mettrie, Traité de l’âme, 27-8), he prefers an explanation of thought as the product of a particular organisation of matter. As he is unable to explain the origin of feeling, he simply observes that it exists in bodies composed purely of matter, without deciding whether it is the result of their organisation:

pour l’amour propre de savoir que l’esprit est d’une nature si corporelle.” (Boerhaave, Institutions, V (1747) 111)—See Thomson, La Mettrie, lecteur et traducteur de Boerhaave, 23-9. 41  “Vous concevez enfin qu’après tout ce qui a été dit sur la diverse origine des nerfs et les différents sièges de l’âme, il se peut bien faire qu’il y ait quelque chose de vrai dans toutes les opinions des auteurs à ce sujet, quelqu’opposées qu’elles paraissent: et puisque les maladies du cerveau, selon l’endroit qu’elles attaquent suppriment tantôt un sens, tantôt un autre, ceux qui mettent le siège de l’âme dans les nates ou les testes, ont-ils plus de tort que ceux qui voudraient la cantonner dans le centre ovale, dans le corps calleux, ou même dans la glande pinéale? Nous pourrons donc appliquer à toute la moëlle du cerveau, ce que Virgile dit de tout le corps, où il prétend avec les Stoiciens que l’âme est répandue.” (La Mettrie, Traité de l’âme, 49*; transl. From idem, Machine Man, 64 f.) 42  “[…] que Dieu, qui a donné aux bêtes la faculté de s’apercevoir, de se souvenir, d’avoir quelques idées, ait pu comuniquer à nos organes plus déliées une intelligence bien supérieure […]” (Boerhaave, Institutions, I (1743) 104).

9  Materialistic Theories of Mind and Brain

215

we do not know whether matter has in itself the immediate faculty of feeling or only the power of acquiring it through the modification or forms of which it is susceptible. For it is true that this faculty only appears in organised bodies.43

He goes much further in L’Homme machine, where he abandons all precautions. He quotes a large number of experiments on animals to prove that the smallest parts of organised matter, namely the fibres, are capable of reacting and moving even when separated from the rest of the body, and he calls extensively on comparative anatomy. Any pretence of adopting the three-soul theory is abandoned and he explicitly denies the existence of any soul, material or immaterial, proclaiming: Thus the soul is merely a vain term of which we have no idea and which a good mind should only use to refer to that part of us which thinks. Given the slightest principle of movement, animate bodies will have everything they need to move, feel, think, repent and, in a word, behave in the physical sphere and in the moral sphere which depends on it.44

He no longer attempts, as he had done in L’Histoire naturelle de l’âme, to describe the structure and the functioning of the brain, preferring to stick to the results of experiments on animals which demonstrate, for example, the workings of the muscles, as we have indicated above. He undoubtedly knew the work of Baglivi and he had of course translated Haller’s annotated edtion of Boerhaave. But it is clear that La Mettrie did not grasp (or even less, as has been suggested, prefigure) Haller’s doctrine of irritability, as he discusses the reactions of all parts of the body, without understanding the particular properties attributed to muscle fibres. Although he continues to use the Cartesian terminology of animal spirits, the spirits he refers to no longer seem to play any real role in his system and are always depicted as violent, as a ‘torrent’, or in a state of fever. This goes with a much more ‘dynamic’ view not only of matter but also of the brain, and an emphasis on the ‘internal senses’ and the imagination, which he developed even further in his subsequent work, L’Anti-Sénèque (1748). The brain is no longer seen as simply a processor of external stimulation, but also as a producer of ideas of its own, which are influenced by its structure. Instead of describing, as in L’Histoire naturelle de l’âme, how the nerves transmit sensations to the brain, La Mettrie now provides numerous vivid descriptions of how the imagination affects the body, making the spirits galop and swell their tubes. To give an idea of the way the brain functions, La Mettrie uses a series of metaphors; it is compared to a musical instrument whose cords vibrate as a result of external stimulation (La Mettrie, L’Homme machine, 14) or a magic

 “[…] nous ignorons si la matière a en soi la faculté immédiate de sentir, ou seulement la puissance de l’acquérir par les modifications, ou par les formes dont elle est susceptible; car il est vrai que cette faculté ne se montre que dans les corps organisés.” (La Mettrie, Traité de l’âme, 24*; transl. From idem, Machine Man, 51) 44  “L’âme n’est donc qu’un vain terme dont on n’a point d’idée, et dont un bon esprit ne doit se servir que pour nommer la partie qui pense en nous. Posé le moindre principe de mouvement, les corps animés auront tout ce qu’il leur faut pour se mouvoir, sentir, penser, se reprentir, et se conduire en un mot dans le physique, et dans le moral qui en dépend.” (La Mettrie, L’Homme machine, 180; transl. From idem, Machine Man, 26) 43

216

A. Thomson

lantern on which images are projected (ibid. 15).45 There is no clear description of its workings, and no presentation of a mechanical model, despite the metaphor of clockwork and of wheels; this clockwork possesses its own innate force in all of its fibres and thus not only winds itself up, but also continues to function even when the main cogwheel has stopped. Its creative power is emphasised: “if the brain is both well organised and well educated, it is like a perfectly sown, fertile earth which produces a hundred-fold what it has received.”46 Likewise, the soul, “the part of us which thinks”, becomes a vague idea, defined as follows: the soul is only a principle of motion or a tangible material part of the brain that we can, without fear of error, consider as a mainspring of the whole machine […]47

La Mettrie is thus willing to show sympathy for any of his medical predecessors whose work could be used to explain thought in material terms, in particular Willis and Perrault, [who] seem to have preferred to posit a soul generally spread throughout the body rather than the principle which we are discussing. But in their hypothesis – which was Virgil’s and that of all the Epicureans […] – the movements which survive after the death of the subject in which they are found come from a remnant of the soul, preserved in the parts which contract although they are no longer irritated by the blood and the spirits. From which we can see that these writers, whose solid works easily eclipse all the fables of philosophy, were only mistaken in the same way as those who accorded matter the faculty of thought; I mean that they expressed themselves badly, using obscure and meaningless terms.48

What this significant passage shows, in my opinion, is that La Mettrie, in the tradition of the materialistic writers of the turn of the century, was willing to adopt any explanations, whatever the terminology they used, that could appear to be compatible with or provide support for his own materialism. While he was consistently hostile to Cartesian dualism, aspects of Cartesian physiology could be appropriated, combined with Epicureanism acquired via the followers of Gassendi. And he relies heavily on the data from physiology, particularly comparative anatomy, and animal experimentation. Indeed, he insists repeatedly on the importance of experimentation  See Thomson, L’homme machine, 374.  “[…] si le cerveau est à la fois bien organisé et bien instruit, c’est une terre féconde parfaitement ensemencée, qui produit le centuple de ce qu’elle a reçu […]” (La Mettrie, L’Homme machine, 167; transl. From idem, Machine Man, 16) 47  “[…] l’Ame n’est qu’un principe de mouvement, ou une partie matérielle sensible du cerveau, qu’on peut, sans craindre l’erreur, regarder comme un ressort principal de toute la machine […]” (La Mettrie, L’Homme machine, 186; transl. From idem, Machine Man, 31) 48  “[…] [qui] paraissent avoir mieux aimé supposer une âme généralement répandue par tout le corps, que le principe dont nous parlons. Mais dans cette hypothèse, qui fut celle de Virgile, et de tous les Epicuriens […], les mouvements qui survivent au sujet dans lequel ils sont inhérents, viennent d’un reste d’âme, que conservent encore les parties qui se contractent, sans être désormais irritées par les sens et les esprits. D’où l’on voit que ces écrivains, dont les ouvrages solides éclipsent aisément toutes les fables philosophiques, ne se sont trompés que sur le modèle de ceux qui ont donné à la matière la faculté de penser, je veux dire, pour s’être mal exprimés, en termes obscurs, et qui ne signifient rien.” (La Mettrie, L’Homme machine, 188; transl. From idem, Machine Man, 32) 45 46

9  Materialistic Theories of Mind and Brain

217

and observation rather than philosophical systems; for example, after having denounced both metaphysical systems and the recourse to revelation in the introductory section of L’Homme machine, he writes: “Thus, experience and observation alone should guide us here. They are found in abundance in the annals of physicians who were philosophers, not in those of philosophers who were not physicians.”49 It is not only the observations of medical doctors that are used, however, for the recent discovery by Trembley of the capacity of the freshwater polyp to regenerate itself was also seized on as providing further arguments in favour of the dynamic properties of matter and the lack of need for a soul (see Vartanian, Trembley’s Polyp). Indeed the problems posed by Trembley’s research were generally recognised, for Henry Baker, who presented this discovery to the British public, presented thus the objections of those who refused to accept that the polyp was a living creature: “If the animal soul or life, say they, be one indivisible essence, all in all, and all in every part, how comes it, in this creature, to endure being divided forty or fifty times, and still continue to exist and flourish?” (Baker, Attempt, 203). La Mettrie’s aim in L’Homme machine is not to construct a system but rather to show, by means of all available scientific evidence, that there is no need to have recourse to an incomprehensible hypothesis when the evidence shows that matter alone can produce thought. Despite the apparent impossibility of showing how this could come about, it is the plausibility of the proposition that is being demonstrated. In the same way, Diderot, particularly in the Rêve de d’Alembert, attempts to account for the production of intelligence by the brain, but can only do so in very general terms, again like La Mettrie, by the use of metaphors. ‘Bordeu’ discusses the functioning of “l’origine du réseau” and the source of consciousness and intelligence in the memory of sensations – without, however, entering into details, as he admits that it is impossible to observe how it works, as one can do with the nerves: Consciousness is in only one place. […] It can only be in one place, at the common centre of all sensations, where memory is, where comparisons take place. Each fibre is only capable of a certain fixed number of impressions, of successive, isolated, memoryless sensations. The centre is capable of all of them, it is the register which keeps a memory or a continuous sensation of them, and the animal is led, from its first formation, to refer itself to it, to reside there completely, to exist there. mademoiselle de l’espinasse: And if my finger could have memory? bordeu: Your finger would think. mademoiselle de l’espinasse: What is memory then? bordeu: The property of the centre, the specific sense belonging to the source of the network, like sight is a property of the eye. […] I am not avoiding anything. I am telling you what I know, and I would know more if the organisation of the source of the n­ etwork was as familiar to me as that of the fibres, if I had been able to observe them as easily.50

 “L’expérience et l’observation doivent donc seules nous guider ici. Elles se trouvent sans nombre dans les fastes des médecins qui ont été philosophes, et non dans les philosophes qui n’ont pas été médecins.” (La Mettrie, L’Homme machine, 151; transl. From idem, Machine Man, 4) 50  “C’est que la conscience n’est qu’en un endroit. […] C’est qu’elle ne peut être que dans un endroit, au centre commun de toutes les sensations, là où est la mémoire, là où se font les com49

218

A. Thomson

This passage is quoted in the neuroscientist Gerald Edelman’s work on the functioning of the brain; he refers to Diderot’s ‘remarkable surmise’ in view of the fact that no detailed information on the subject was known until the following century (Edelman, Bright Air, 19–21). What seems to me interesting in Diderot’s discussion is the attempt to provide a material explanation of humans, but one that is not simply ‘reductionist’, for the brain is seen as creative and dynamic, with its own energy, and not merely the sum of its parts or a passive receiver of external stimuli.51 This emphasis was already present in L’Homme machine, as we have seen, but it is much more pronounced in Diderot’s writings, which is why his materialism has been called ‘vitalistic’ (Belaval, Sur le matérialisme de Diderot). But this has led most commentators to contrast it with La Mettrie’s ‘mechanistic materialism’, whereas it is clear that they are much closer than has often been thought (Thomson, L’unité matérielle, 61–68). It was obviously impossible to go any further at the time, in view of the state of scientific knowledge, but these intuitions are very important. Diderot was aware of the difficulty, for in his Refutation d’Helvétius, he writes “the notions of matter, of organisation, of movement, of heat, of flesh, of sensitivity and life must still be very incomplete”52 and he considers that if Helvétius had shown how intelligence could result from physical sensitivity, “he would have done something new, difficult and fine.”53 For Helvétius’s works provided a very different model of human intelligence; for him, it is external sensation that is fundamental and “all the mind’s operations can be reduced to feeling”,54 the proposition criticised by Diderot in the above quotation. Helvétius considers that humans are all endowed with the same organisation and that the differences between them come from experience and education. Questions as to how the brain produces intelligence and how to account for human creativity and originality are therefore of little importance for him. This is a very different type of materialism, concerned with external determination and how it shapes ideas and behaviour, rather than the internal functioning of the material paraisons. Chaque brin n’est susceptible que d’un certain nombre déterminé d’impressions, de sensations successives, isolées, sans mémoire. L’origine est susceptible de toutes, elle en est le registre, elle en garde la mémoire ou une sensation continue, et l’animal est entraîné dès sa formation première à s’y rapporter soi, à s’y fixer tout entier, à y exister. mademoiselle de l’espinasse: Et si mon doigt pouvait avoir de la mémoire?… bordeu: Votre doigt penserait. mademoiselle de l’espinasse: Et qu’est-ce donc que la mémoire? bordeu: La propriété du centre, le sens spécifique de l’origine du réseau, comme la vue est la propriété de l’oeil; […] Je n’élude rien, je vous dis ce que je sais, et j’en saurais davantage, si l’organisation de l’origine du réseau m’était aussi connue que celle des brins, si j’avais eu la même facilité de l’observer.” (Diderot, DPV, XVII 175 f.) 51  On this subject, see Rey, Diderot et la médecine de l’esprit. 52  “[…] il faut que les notions de matière, d’organisation, de mouvement, de chaleur, de chair, de sensibilité et de vie soient encore bien incomplètes […]” (Diderot, LEW, XI 492) 53  “[…] il eût fait une chose neuve, difficile et belle […]” (Diderot, LEW, XI 491) 54  “[…] toutes les opérations de l’esprit se réduisent à sentir […]” (Helvetius, L’Homme, I.1; ‘Corpus’ edition 142)

9  Materialistic Theories of Mind and Brain

219

‘machine’. It is this type of materialism that was later criticised by Cabanis as being insufficient, due to the fact that its representatives lacked the necessary physiological knowledge (Cabanis, Rapports, 141); Cabanis himself attempted to provide a material explanation of human intelligence, without acknowledging his debt to those materialists who shared his preoccupations, like La Mettrie at least (for he could not have known Diderot’s materialistic works). He too, despite his detailed descriptions of sensations and nerves, is forced to admit his ignorance as to how the brain produces thought: We say […] that thought needs the complete brain; because without the brain we cannot think, and diseases of it produce similar and proportionate changes in the mind’s operations. But I must admit honestly that I am incapable of establishing exactly what constitutes this completeness.55

He admits that the intimate structure of the brain’s matter is little known, as the existing methods and instruments do not allow physiologists to study it (Cabanis, Rapports, 212). Cabanis could not have avoided knowing the notorious Système de la nature, which does, in the course of its exposition of its materialistic system, discuss the human being as a physical entity. It is remarkable that in the chapters devoted to humans, this work goes little further than La Mettrie, who is, however, violently attacked, on account of his amoralism. The first part of the work discusses nature, matter and movement, before coming on to ‘man’. Belief in a soul is of course attacked, and Chap. 8 discusses the intellectual faculties, with the primary purpose of showing that they are all derived from the faculty of feeling. The main discussion of the brain is intended to demonstrate that it is the seat of feeling, and a note refers to a certain number of experiments, in particular those of Willis (Holbach, Système de la nature, 134). The different senses are reviewed, in order to show how they affect the brain, but there is no more detailed analysis of the mechanism. The chapter concludes: In all that we can see only one substance acting differently in its different parts. If one complains that this mechanism is insufficient to explain the principle of movement or the faculties of our soul, we will reply that it is the same for all natural bodies, in which the simplest movements, the most ordinary phenomena, the commonest ways of acting are inexplicable mysteries of which we shall never know the first principles. […] It is enough for us to know that the soul moves and is modified by material causes which act on it. From which we are authorised to conclude that all its operations and faculties prove that it is material.56

 “Nous disons […] que la pensée exige l’intégrité du cerveau; parce que sans cerveau, l’on ne pense point, et que ses maladies apportent des altérations analogues et proportionnelles dans les opérations de l’esprit. Mais j’avoue ingénûment que je suis hors d’état d’établir avec exactitude en quoi consiste cette intégrité.” (Cabanis, Rapports, 212) 56  “En tout cela nous ne voyons qu’une même substance qui agit diversement dans ses différentes parties. Si l’on se plaint que ce mécanisme ne suffit pas pour expliquer le principe des mouvements ou des facultés de notre âme, nous dirons qu’elle est dans le même cas que tous les corps de la nature dans lesquels les mouvements les plus simples, les phénomènes les plus ordinaires, les façons d’agir les plus communes sont des mystères inexplicables, dont jamais nous ne connaîtrons les premiers principes. […] Qu’il nous suffise donc de savoir que l’âme se meut et qu’elle se modi55

220

A. Thomson

Once again, we see that the important point is to show that human intellectual faculties depend on the physical functioning of the organism, and that there is no need to have recourse to an incomprehensible immaterial substance. This conclusion results from the observation of nature, but it is impossible to go any further and to understand how this comes about. And like his predecessors, d’Holbach calls on different philosophical traditions and on previous works on the subject throughout the century to support his conclusions. After the sustained campaign in the earlier part of the century, the questioning of the existence of an immaterial soul was no longer as important as it had been, and the elaboration of a material explanation of the whole world plays a much greater role in Le Système de la nature. Priestley, whose Disquisitions followed in its wake, attempted to provide a theoretical basis to prove that matter could be capable of thought but, as we have seen, although he originally developed his ideas from David Hartley’s work Observations on Man, his Frame, his Duty and his Expectations (1749), he omitted all of Hartley’s description of the workings of the nerves and the brain, to concentrate on his theory of vibrations.

9.5 Conclusion The conclusion that one can, I think, draw from this survey of materialistic theories of the mind is that the interpretation of the human being as simply a more perfectly organised animal, and thus purely material, the structure of whose brain was sufficient to explain his superior intellectual functions, remained on the level of an intuition, a ‘surmise’ that seemed to be supported by the available evidence. This evidence showed that thought depended on the material brain, but how this brain could produce thought remained mysterious and inexplicable; greater knowledge of physiology would perhaps provide an explanation. This affirmation was therefore not a tenet of a dogmatic totalising system but the result of a desire to oppose the doctrines of the Church, seen as inhibiting and oppressive, and to place the human being at the centre of preoccupations. This preoccupation was particularly associated with medical study and evidence, and its philosophical basis was eclectic57; hostility to ‘systems’ is a permanent feature of the materialists of this period. The speculative nature of materialism can be seen most clearly in the writings of Diderot, with their open-ended form of dialogue and debate, but it is also present in La Mettrie’s writings. L’Homme machine, despite its title, which is all that most people know of the work, does not describe the workings of a mechanical man, but tries to convince the reader that this speculation is plausible, because it is compatible with the evidence. fie par les causes matérielles qui agissent sur elle. D’où nous sommes autorisés à conclure que toutes ses opérations et ses facultés prouvent qu’elle est matérielle.” (Holbach, Système de la nature, 146-7) 57  As was that of the medical writers on whom it drew; see for example King, The Philosophy of Medicine.

9  Materialistic Theories of Mind and Brain

221

Another factor to emerge from this study is the imbrication of speculation in France and Britain, despite the different religious situations. Atheistic materialism was only openly declared in France (despite the doubts frequently expressed about the true opinions of Hobbes or Toland, and one might also say, of Coward), whereas in Britain materialism remained linked to Christian mortalism, up to and including Priestley. But in both cases it was developed against the established Church, with the aim of freeing humans from the fear of Heaven and Hell, seen as a way for the priests to oppress the people. Materialism, at least in the late seventeenth and early to mid-eighteenth century was therefore not one system, or even several systems and was not even necessarily atheistic, but can more usefully be seen as a set of arguments and speculation, drawing on physiology and an eclectic philosophical tradition, attempting to show how humans could be explained purely in terms of matter in motion, it being clearly understood that this implied a dynamic conception of matter. It was a radical attempt to undermine religious orthodoxy and the authority of religious institutions, and its refusal of dogma also meant that it blurred the distinction between science and philosophy, in its attempt to provide a different understanding of humans.58

Afterword 2022 Since this article was published, I have written a book (Bodies of Thought, 2008), which discusses all these questions in much greater detail and in a longer-term perspective. In particular, instead of centring the study around the French eighteenth-­ century thinkers, it devotes much more attention to debates in England in the 17th and early 18th Centuries and the medical thinking around living matter, in particular the works of Francis Glisson, which are not discussed in this article. It also looks in much more detail at the works of Layton and Coward, situating them in the charged politico-theological polemics in the years following the “Glorious Revolution” of 1688-89 and the Socinian campaign. I also discuss the interventions of Henry Dodwell and Anthony Collins. I would therefore now nuance considerably the interpretation of writers like Coward, who were not opposed to Christianity but wanted a return to a purer form it. I also discuss the various routes by which knowledge of this debate reached France and took on a more clearly irreligious connotation in the French context. The present chapter should therefore be seen as a sketch of an argument which was subsequently refined and developed. There have also been quite a large number of publications, by myself and others, in the intervening years, not all of which I necessarily agree with, but which now need to be taken into account. These are listed below. The whole field has also been affected by the works of Jonathan I. Israel on the so-called ‘Radical Enlightenment’  [Annotation by the editor:] Since the first edition of this volume in 2001, Ann Thomson published a new book on the subject: Ann Thomson: Bodies of Thought – Science, Religion, and the Soul in the Early Enlightenment, Oxford: Oxford University Press, 2008 58

222

A. Thomson

(in particular Radical Enlightenment, 2000 Enlightenment Contested, 2006 and Democratic Enlightenment, 2011) which have muddied the waters considerably and attempted to impose a rigid and extremely questionable interpretation on intellectual developments in this period. While the scope is obviously much broader, several of the questions studied in this article are given extensive treatment. The literature around Israel’s interpretations and the many criticisms of it are too numerous to list here. Other relevant studies include: Champion, Justin. 2003. Republican learning: John Toland and the Crisis of Christian Culture, 1696–1722. Manchester: Manchester University Press. Crignon, Claire. 2017. How Animals May Help Us Understand Men. Thomas Willis’s Anatomy of the Brain (1664) & Two Discourses Concerning the Soules of Brutes (1672). In Human and Animal Cognition in Early Modern Philosophy & Medicine, eds. S. Buchenau and R. Lo Presti, 173–185. Pittsburgh: University of Pittsburgh Press. Dagron, Tristan. 2009. Toland et Leibniz. L’invention du néo-spinozisme. Paris: Vrin. Hecht, Hartmut (ed.) 2004. Julien Offray de La Mettrie. Ansichten und Einsichten. Berlin: Berliner Wissenschafts-Verlag. Niblett, M. 2009. Man, Morals and Matter: Epicurus and Materialist Thought in England from John Toland to Joseph Priestley. In Epicurus in the Enlightenment, ed. N. Leddy and A. S. Lifschitz, 137–59. Oxford: Voltaire Foundation. Saad, Mariana. 2016. Cabanis, comprendre l’homme pour changer le monde. Paris: Classiques Garnier. Thomson, Ann. 2003. Epicurisme et matérialisme en Angleterre au début du 18e siècle. Dix-huitième Siècle 35: 281–296. Thomson, Ann. 2007. Medicine and Materialism. In Littérature et médecine: approches et perspectives (XVIe–XIXe siècles), ed. A. Carlino and A. Wenger, 159–175. Geneva: Droz. Thomson, Ann. 2008. Bodies of Thought. Science, Religion and the Soul in the Early Enlightenment. Oxford: Oxford University Press. Thomson, Ann. 2010. Animals, Humans, Machines and Thinking Matter, 1690–1707. Early Science and Medicine 15: 3–37.

References Baker, Henry. 1743. An Attempt Towards a Natural History of the Polyp in a Letter to Martin Folkes, esq. London: Dodsley. Baxter, Richard. 1667. The Reasons of the Christian Religion. The First Part, of Godliness: proving by natural evidence the being of God, the necessity of holiness and a future life of retribution; the sinfulness of the world, the desert of Hell; and what hope of recovery mercies intimate. The Second Part, of Christianity: proving by evidence supernatural and natural, the certain truth of the christian belief: and answering the objections of unbelievers. First meditated for the well-settling of his own belief, and now published for the benefit of others, by Richard Baxter. It openeth also the true resolution of the Christian Faith. Also an Appendix, defending

9  Materialistic Theories of Mind and Brain

223

the Soul’s Immortality against the somatists or Epicureans and other Pseudo philosophers. London: R. White. Belaval, Y. 1967. Sur le matérialisme de Diderot. In Europäische Aufklärung, ed. H. Friedrich and F. Schalk, 9–21. Fink: Munich. Benitez, Miguel. 1998. Y a-t-il une philosophie clandestine? Le statuts des copies manuscrites de De rerum natura. La Lettre clandestine 7: 355–368. Bentley, Richard. 1971. Matter and Motion cannot think, or a Confutation of Atheism from the Faculties of the Soul (Sermon II, April 4th 1692). In Works, ed. A. Dyce. (London 1838), III 27–72. Hildesheim: Olms. Bloch, Olivier. 1997. Marx, Renouvier et l’histoire du matérialisme. La Pensée 191 (1977): 3–42, reprinted in Bloch, Olivier. Matière à histoires, 384–441. Paris: Vrin. ———. 1985. Le matérialisme. Paris: Presses Universitaires de France. ———. 1992. L’héritage libertin dans le matérialisme des Lumières. Dix-huitième Siècle 24: 73–82. Boerhaave, Herman. 1743/1750. Institutions de médecine de Mr Herman Boerhaave, traduites du latin en français par M. de La Mettrie. 2nd ed. Paris: Huart. Boscovich, Roger Joseph. 1759. Philosophiae naturalis theoria redacta ad unicam legem virium in natura existentium. Vienna: A. Bernardi. Burns, Norman T. 1972. Christian Mortalism from Tyndale to Milton. Cambridge MA: Harvard Univerity Press. Bynum, William F. 1973. Anatomical Method, Natural Theology, and the Functions of the Brain. Isis LXIV/5-6: 445–468. Cabanis, Pierre-Jean-Georges. 1956. Rapports du physique et du moral de l’homme (1796). In Oeuvres philosophiques, vol. I. Paris: Presses Universitaires de France. Canguilhem, Georges. 1955. La Formation du concepte de réflexe. Paris: Vrin. [Coward, William] Estibius Psychalethes. 1702. Second Thoughts concerning Human soul, demonstrating the notion of human soul as believed to be a spiritual immortal substance, united to human body, to be a plain heathenish invention, and not consonant to the principles of philosophy, reason or religion, but the ground only of many absurd, and superstitious opinions, abominable to the reformed churches and derogatory in general to true christianity. London: R. Basset. [Coward, William]. W.C.M.D.C.M.L.C. 1704. The Grand Essay, or a vindication of reason and religion, against impostures of philosophy. Proving according to those ideas and conceptions of things human understanding is capable of forming to it self, 1. That the existence of any immaterial substance is a philosophic imposture, & impossible to be conceived 2. That all matter has originally created in it, a principle of internal self-motion 3. That matter & motion must be the foundation of thought in men & brutes. To which is added A Brief Answer to Mr. Broughton’s Psycologia […]. London: John Chantry. Coward, William. 1706. Ophthialmiatria: quae accurata & integra Oculorum male affectorum instituitur Medela: nova methodo aphoristico concinnata. London: J.Chantry and T. Atkinson. Debus, Allen G. 1987. Chemistry and the Quest for a Material Spirit of Life in the 17th Century. In Chemistry, Alchemy and the New Philosophy, 1550–1700. Studies in the History of Science and Medicine. London: Variorum reprints. Diderot, Denis. 1975. In Œuvres complètes, ed. Herbert Dieckmann et  al. Paris: Hermann. 1975ff. (DPV). ———. 1969-73. Œuvres complètes, ed. R. Lewinter. Paris: Club Français du Livre. (LEW) Edelman, Gerald M., Bright Air, and Brilliant Fire. 1992. On the Matter of the Mind. London: Allen Lane. Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers. Paris: Briasson et al., 1751–1780 Frank, Robert G. jr. 1980. Harvey and the Oxford Physiologists. Berkeley: University of California Press.

224

A. Thomson

Furetière, Antoine. 1972. Materialiste. In Dictionnaire universel: contenant généralement tous les mots françois (1727), vol. III. Hildesheim: Olms. Gaultier, Abraham. 1993. Parité de la vie et de la mort. La Réponse du médecin Gaultier, ed. O. Bloch. Paris: Universitas. Oxford: Voltaire Foundation. Hartley, David. 1967. Observations on Man, his Frame, his Duty and his Expectations (1749). Hildesheim: Olms. Helvetius, Claude A. 1989. L’Homme (1773), Corpus des oeuvres de philosophie en langue française. Paris: Fayard. Henry, John. 1989. The matter of souls: medical theory and theology in seventeenth-century England. In The Medical Revolution of the Seventeenth Century, ed. Roger French and Andrew Wear, 87–113. Cambridge: Cambridge University Press. Holbach, Paul Henri Thiry d. 1990. Système de la nature (1770), Corpus des oeuvres de philosophie en langue française. Vol. I. Paris: Fayard. Isler, Hansruedi. 1968. Thomas Willis 1621–1675. New York: Hafner. King, Lester S. 1978. The Philosophy of Medicine. The Early 18th Century. Cambridge: Harvard University Press. Kirkinen, Heikki. 1960. Les Origines de la conception moderne de l’homme machine. Helsinki: Academiae scientiarum Fennicae. La Mettrie, Julien Offray de. 1745. Histoire naturelle de l’âme. La Haye: J. Neaulme. ———. 1960. In L’Homme machine (1748), ed. A. Vartanian. Princeton: Princeton University Press. ———. 1988. In Traité de l’âme (1750), ed. Th. Verbeek. Utrecht: OMI-­Grafisch Bedrijf. ———. 1996. In Machine Man and Other Writings, ed. A.  Thomson. Cambridge: Cambridge University Press. Lamy, Guillaume. 1996. Discours anatomiques (1675); Explication méchanique et physique des fonctions de l’âme sensitive (1677), ed. Anna Minerbi Belgrado. Paris: Universitas; Oxford: Voltaire Foundation. [Layton, Henry]. A Search After Souls and Spiritual Operations in Man. Second Part of a Treatise intitled a Search After Souls. (A single volume but pages numbered separately) N.p. and n.d. Lurbe, Pierre. 1990. Le spinozisme de John Toland. In Spinoza au XVIIIe siècle, ed. O. Bloch, 33–47. Paris: Méridiens Klincksieck. ———. 1992. Matière, nature, mouvement chez d’Holbach et Toland. Dix-huitième Siècle 24: 53–62. Marx, Karl, and Friedrich Engels. 1957. Die Heilige Familie (1845), Werke (MEW) II. Berlin: Dietz. Maupertuis, Pierre Louis Moreau de. 1754. Essai sur la formation des corps organisés. Paris: Prault. ———. 1756. Oeuvres. Lyon: Bruyset. Meyer, Alfred, and Raymond Hierons. 1968. On Thomas Willis’s Concepts of Neurophysiology. Medical History 9 (1–15): 142–155. More, Henry. 1668. Divine Dialoges. London: James Flesher. Mothu, A. 1990/1991. La pensée en cornue: considérations sur le matérialisme et la ‘chymie’ en France à la fin de l’âge classique. Chrysopœia IV: 307–445. ———. 1993. Le mythe de la distillation de l’âme au XVIIe siècle en France. In Alchimie et philosophie à la Renaissance, ed. Jean-Claude Margolin and Sylvain Matton, 435–461. Paris: Vrin. [Overton, Richard]. 1968. In Mans Mortalitie (1643), ed. Harold Fisch. Liverpool: Liverpool University Press. Priestley, Joseph. 1775. Introduction. In Hartley’s Theory of the Human Mind, on the Principle of the Association of Ideas, with Essays relating to the Subject of it, ed. Joseph Priestley. London: J. Johnson. ———. 1777. Disquisitions relating to matter and spirit: to which is added the history of the philosophical doctrine concerning the origin of the soul, and the nature of matter: with its influence on Christianity, especially with respect to the doctrine of the pre-existence of Christ. London: J. Johnson.

9  Materialistic Theories of Mind and Brain

225

Rey, Roselyne. 2000. Diderot et la médecine de l’esprit. Colloque international Diderot, 287–296. Paris: Aux Amateurs de livres, 1985. Republished as Diderot and the Medicine of the Mind. Graduate Faculty Philosophy Journal 22 (1): 149–159. Roger, Jacques. 1971. Les Sciences de la vie dans la pensée française du XVIIIe siècle. 2nd ed. Paris: A.Colin. Spanheim, Friedrich. 1676. L’Athée convaincu. Leiden: Daniel van Gaasbeeck. Thomson, Ann. 1985. L’unité matérielle de l’homme chez La Mettrie et Diderot. In Colloque international Diderot, 61–68. Paris: Aux Amateurs de livres. ———. 1988. L’homme machine, mythe ou métaphore? Dix-huitième Siècle 20: 367–376. ———. 1991. La Mettrie, lecteur et traducteur de Boerhaave. Dix-huitième Siècle 23: 23–29. ———. 2000. In “Religious heterodoxy and political radicalism in the late 17th and early 18th Century”. Republicanism anglais et l‘idée de tolérance, ed. E.  Tuttle, 129–147. Nanterre: Université de Paris X. Toland, John. 1704. Letters to Serena. London: B. Lintot. Vartanian, A. 1950. Trembley’s Polyp, La Mettrie and Eighteenth-century French Materialism. Journal of the History of Ideas XI: 259–286. ———. 1982. Quelques réflexions sur le concept d’âme dans la littérature clandestine. In Le matérialisme du XVIIIe siècle et la littérature clandestine, ed. O. Bloch, 149–163. Paris: Vrin. Vernière, Paul. 1954. Spinoza et la pensée française avant la Révolution. Paris: Presses Universitaires de France. Wright, John P. 1991. Locke, Willis and the seventeenth-century Epicurean soul. In Atoms, Pneuma and Tranquillity, ed. Margaret J. Osler, 239–258. Cambridge: Cambridge University Press. Yolton, John W. 1984. Thinking Matter. Oxford: Blackwell. ———. 1991. Locke and French Materialism. Oxford: Clarendon Press.

Chapter 10

Kant’s Second Paralogism in Context: The Critique of Pure Reason on Whether Matter Can Think Falk Wunderlich

Abstract  The paper puts Kant’s second paralogism in the first edition of his Critique of Pure Reason into the context of eighteenth century debates on materialism. In the second paralogism, Kant argues that neither dualism nor materialism about the human mind can be established, while focusing on a received anti-­ materialist argument that he dubs the “Achilles argument”. The Achilles argument that Kant ultimately rejects is based on the assumption that the unity of thought requires a unified substratum and thus an immaterial soul. I argue (1) that the second paralogism is not a paralogism formally but (2) nonetheless provides an illuminating discussion of the shortcomings of the Achilles argument. In doing so, I attempt to identify the contemporary background for Kant’s reconstruction of this argument. It was Kant’s major aim to provide in his Critique of Pure Reason (CPR) a novel and systematic account of almost all fields of theoretical philosophy, and so he did not reveal much of the contemporary debates he was referring to. In the first edition (1781) of the CPR (A edition), in the chapter on the “Paralogisms of Pure Reason,” the second paralogism is, however, an important exception in this regard, and it seems that former commentators have not taken this into sufficient consideration. It is my main thesis that this chapter offers an opportunity to discuss Kant’s relation to contemporary debates in a more detailed way, even though it is not overt and thus also rests on reconstruction. In what follows, I will first give a detailed analysis of the second paralogism and then turn to the contemporary context. In the chapter on the “Paralogisms of Pure Reason” of his first Critique, Kant intends to provide an exhaustive criticism of dualist views of the soul that are expressed in rational psychology. This sub-discipline of special metaphysics, first introduced by Christian Wolff, deals with the general notions of the soul and the attributes deduced from them, while empirical psychology focuses on mental F. Wunderlich (*) Seminar für Philosophie, Martin-Luther-Universität Halle-Wittenberg, Halle, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_10

227

228

F. Wunderlich

experiences and their classification according to the faculties of the mind.1 On a general level, Kant’s criticism of rational psychology is that it hypostasizes the subjective conditions of thinking by turning them into supposed knowledge of the soul2; or, as he puts it, that the attributes rational psychology ascribes to the thinking being in itself turn out to be mere formal conditions of human thinking. Kant does not discuss the actual contemporary theories in the paralogism chapter, but rather presents their main assumptions in a formalized and systematized way. They are formalized by reducing them to four syllogisms and systematized by ordering these syllogisms according to the table of categories. The second paralogism this paper focuses on is connected to the category of reality (A 344 B 402 and A 403). While in the B edition, only one syllogism is treated in detail and taken as an example for the others, all four paralogisms are discussed in the A edition. Here, the main focus of the second paralogism lies on several supposed proofs for the simplicity of the soul. The questions of whether the thinking being is simple or not, and how its simplicity can be demonstrated, were discussed at large in the eighteenth century. It is part of the extended controversies about materialism, for materialism denies the existence of a simple soul. This question was discussed at large, as contemporary overviews of the controversy show.3 In this paper, I will first examine the formal structure of the second paralogism (Sect. 10.1). Then, I will take a look at how Kant’s criticism refers to the contemporary discussions (Part II).

10.1 The Paralogism: Its Formal Structure Kant lays out the second paralogism in an abbreviated form4: That thing whose action can never be regarded as the concurrence of many acting things, is simple. Now the soul, or the thinking I, is such a thing. Thus etc. (A 351)

 Cf. for this distinction Meier, Metaphysik, II 10 f., e.g.  “One can place all illusion in the taking of a subjective condition of thinking for the cognition of an object.” (A 396) 3  See for example Justus Christian Hennings Geschichte von den Seelen der Menschen und Thiere. Yet the simplicity of the soul did not only have to be defended against materialism, it was attacked based on the doctrine of trinity as well; cf. ibid. § 37. 4  G. F. Meier, Beweiss, § 24 gives his main argument for the simplicity of the soul as a syllogism. Klemme, Kants Philosophie des Subjekts, 331 has pointed out that on the contrary, personal identity, the issue of the third paralogism, has never been treated this way in the German metaphysical tradition. 1 2

10  Kant’s Second Paralogism in Context: The Critique of Pure Reason…

229

Reformulated as a complete syllogism: 1. That thing whose action can never be regarded as the concurrence of many acting things, is simple. 2. The soul or the thinking I is a thing that can never be regarded as the concurrence of many acting things. 3. Thus, the soul is simple. According to eighteenth century logic, a paralogism is a kind of logical fallacy that is fallacious for formal reasons only.5 Hence, the validity of the premises is irrelevant for the invalidity of the syllogism, although at A 402 Kant seems to argue that the premises of the four paralogisms are in fact valid. It was common to distinguish several types of paralogisms, among them the sophisma figurae dictionis. Kant argues that the fallacies he discusses in the Paralogism chapter are instances of this type of fallacy. A sophisma figurae dictionis is a syllogism in which the middle term has two different meanings, i.e., it is based on a quaternio terminorum (A 402).6 According to Kant, in the four paralogisms, the middle term is one of the categories. At A 403, he gives an example of the two different meanings in which a category is used as a middle term. However, the example is confusing because he claims to be dealing with the paralogism of simplicity but then in fact discusses the category of substance that is connected to the first paralogism.7 His general explanation of the fallacy of the paralogisms is more informative: Whereas in the major premise the category is applied transcendentally, viz. as “a pure intellectual concept, which in the absence of conditions of sensible intuition is merely of transcendental use” (A 403), it is applied empirically in the minor premise, viz. as “applied to the object of all inner experience” (ibid.). In addition, Kant argues that the category is improperly applied within the minor premise because it is applied “without previously establishing it in concreto and grounding the condition of its application, namely its persistence” (ibid.). He does not make it clear whether this is a problem for the other paralogisms as well. Apart from the last point, all these general remarks about the logical structure of the paralogisms appear to be quite clear. At closer inspection though, it is striking that none of the categories is present in the syllogism the second paralogism is based on. Kant has been aware of this potential confusion and mentions at A 404 that the “simple” corresponds to the category of reality, and further, that in the Antinomy chapter, he will show how this is possible. But granted that the category of reality can be substituted by the concept of simple – what strikes next is where in the syllogism simplicity appears. According to the definition of a syllogism, the  See the general definition of a paralogism in Jäsche Logic § 90 (AA IX 134) and A 397. Klemme, Kants Philosophie des Subjekts, 293ff. has dealt with the relation to contemporary textbooks on logic in more detail. 6  The same definition in Jäsche Logic, § 90 (AA IX 134). 7  This is why Adickes assumes that Kant deals with the first paralogism here in fact (see Raymund Schmidt’s edition of the first Critique, p. 433a.); indeed Kant’s later reference to persistence supports this view. 5

230

F. Wunderlich

middle term is present in the major and in the minor premise, while the major term is present in the major premise and in the conclusion, and the minor term in the minor premise and in the conclusion. Now, the category-substitute of simplicity is in the major premise and in the conclusion, and thus it is not the middle term at all. Rather, the category-substitute is the major term as it is present in the major premise and in the conclusion, whereas the actual middle term is the “thing whose action can never be regarded as the concurrence of many acting things.” A similar formal problem occurs in the first paralogism as well, where the category of substance is the major term, and the middle term is “to be the absolute subject of our judgements.” On the contrary, the category of unity (represented by “numerical identity”) does indeed appear as the middle term of the third paralogism, while the formal structure of the fourth paralogism is an issue in its own right. It is notable that Kant changed the formal structure of the second paralogism in the B edition. Here, the concept of thinking is the middle term, and Kant argues that this concept is applied in an empirical sense in the major premise while applied in a transcendental sense in the minor one (B 411 note). This is strikingly different from the A paralogism where the middle term is applied in a transcendental sense in the major premise and in an empirical one in the minor.8 Now, it is still possible that the actual middle term of the A paralogism, the “thing whose action can never be regarded as the concurrence of many acting things,” is subject to an equivocation instead of the category that turned out not to be the middle term. Of course one can speak about “things” in different senses, namely in the sense of a thing in general and in the sense of an object of experience (whereas things in themselves would not make sense here, as we cannot make any meaningful assertions about them). Then, the minor premise would state that experience shows that the soul is simple. But since Kant argues that there is no immediate experience of the soul, we would be unable to apply an empirical concept to it, and thus, the minor premise would be invalid in itself.9 When viewed from the result, it would also be possible that there is an equivocation in the outer terms, namely between the soul as a substance on the one hand and the mere representation I on the other. So it would be possible to reformulate the paralogism as: 1. That thing whose action can never be regarded as the concurrence of many acting things, is simple. 2. The mere representation I is a thing that can never be regarded as the concurrence of many acting things. 3. Thus the substantial soul is simple.10

 This formal difference between the two versions of the paralogisms is often not considered in the literature, see e.g. Gäbe, Paralogismen and Horstmann, Paralogismen. 9  Because of these obvious logical oddities, Ameriks, Kant’s theory, 50-2. argues that Kant in fact had a different version of the paralogism in mind. 10  In terms of G. F. Maier, this equivocation in the outer terms still fits with his definition of sophisma figurae dictionis, cf. Maier, Auszug, § 393, while Kant’s own definition in Jäsche logic would only allow an equivocation in the middle term (§ 90, AA IX 134). 8

10  Kant’s Second Paralogism in Context: The Critique of Pure Reason…

231

But here, of course, the category does not play the role it should. Yet there is another possibility: The syllogism could be valid formally, but invalid because of one or more wrong premises. There is indeed an indication for this possibility in the way Kant further pursues his criticism of the second paralogism that he calls the “Achilles of all the dialectical inferences of the pure doctrine of the soul” (A 351). Kant here provides an extended criticism of the minor premise, viz. the claim that the actions of the soul cannot be derived from  the concurrence of many acting things.11 A potential objection against this interpretation could proceed as follows: At A 341 B 399 Kant explains the difference between a logical paralogism and a transcendental paralogism, stating that while a logical paralogism “consists in the falsity of a syllogism due to its form, whatever its contents may otherwise be,” a transcendental one “has a transcendental ground for inferring falsely due to its form.” Now, one could argue that the transcendental paralogism is fallacious not for formal reasons but with regard to its contents, and thus it would be misleading to examine its logical structure at all. However, contrary to this, Kant leaves no doubt that all kinds of paralogism consist in logical fallacies.12 The main reason for his distinction between two types of paralogism is that the examples of sophismae figurae dictionis normally discussed in logic are self-evident in contrast to the transcendental ones, and thus Kant holds that this is so because the latter ones are based on the categories themselves.13 Before proceeding to an analysis of the minor premise as to its contents, a few further remarks on how the paralogisms are related to the categories. Each paralogism is based on an improper use of one of the categories, according to Kant, so the table of categories is supposed to provide a natural scheme of classification. This includes the following problems: First, each of the four paralogisms is associated with only one category of each group, and thus the question arises what Kant’s criteria for picking them are, since he does not give an explanation. According to A 404, the relevant categories are substance, reality, unity and existence. In the Antinomy chapter where the same problem occurs, Kant does explain his choice (A 411 B 438), but the categories involved there are different from the Paralogism chapter (with the exception of the second paralogism and the second antinomy). The general principle of choice Kant provides in the Antinomy chapter is that the categories must “necessarily carry with

 Against this, Ameriks argues that these passages deal with the conclusion of the paralogism, not its minor premise (Ameriks, Kant’s theory, 48). 12  “[...] the dialectical inference to the conditions of every thought in general, which is itself unconditioned, does not commit a mistake in content (for it abstracts from all content or objects), but rather that it is mistaken in form alone, and would have to be called a paralogism.” (A 397) 13  G. F. Meier (AA XVI 762) gives an example for a sophisma figurae dictionis: A philosopher is a kind of scholar—Leibniz is a philosopher—Hence Leibniz is a kind of scholar (i.e., Leibniz himself is the kind). W. T. Krug, Handwörterbuch, III 811 gives the following example: A donkey has long ears—This man is a donkey—Hence this man has long ears. In both the examples the fallacy is immediately clear. 11

232

F. Wunderlich

them a series in the synthesis of the manifold” (A 415 B 442). Now, while the four antinomies aim at the absolute completeness of the synthesis (A 415 B 443), the paralogisms aim at unconditioned unity (A 404). It seems plausible that e.g. the category of causality fits an antinomy, as it includes asking for the complete chain of causes of a given state of affairs. In contrast, the category of substance represents an entity that can subsist in itself and is therefore unconditioned. But it is hard to see how reality, the category of the second paralogism, implies unconditioned unity, and moreover, this category is applied in the second antinomy as well. Second, in the list of the categories that play a role in rational psychology, their succession (their “topics,” A 344 B 402) has been changed compared with the original table of categories: The Paralogism chapter begins with a category from the relation group and then turns to one each of the quality, quantity and modality group. Actually, Kant provides an argument for this change of succession (A 344 B 402): only since here first a thing, I as a thinking being, is given, we will not, to be sure, alter the above order of the categories to one another as represented in their table, but we will begin here with the category of substance, and thus go backwards through the series.

This seems to be at odds with the table of categories, however, for the last group there is the modality group, which is still the last in the topics of rational psychology. Moreover, the quantity group appears before the quality group in the table of categories, while here, the reverse is true. So in fact, there is only one correspondence with the table of categories, namely that the modality group is the last one. Indeed if modality were the first one, the order would be consistently reversed in comparison with the table of categories. Third, to show how the categories are meant to work exactly is controversial in Kant research. One aspect of this wide field is the question in which way further a priori concepts can be derived from the categories. Kant deals with this issue e.g. at A 82 B 108, where he introduces the predicables as pure but derivative concepts. Here, this question concerns the nature of the derivative concepts of rational psychology mentioned by Kant at A 345 B 403, namely immateriality, incorruptibility, personality and spirituality and further derivations from them. An investigation of how these concepts of rational psychology are related to each other and to the paralogisms could throw some light on the general building principles of the critical system as a whole, which Kant admittedly never tried to complete. But I can only mention this point here.

10.2 The Context: Kant and His Opponents At A 351, Kant reconstructs the argument for the minor premise as follows: The action of a composite substance is an aggregate of many actions, each of which is performed by one part of the composite substance. But composite actions can only

10  Kant’s Second Paralogism in Context: The Critique of Pure Reason…

233

explain external events such as the motion of bodies. Thoughts, by contrast, are “accidents belonging inwardly to a thinking being” (A 352). Therefore, to understand a thought as an aggregate of many partial thoughts inhering many subjects contradicts the very concept of thought. Obviously, this argument is based on a certain notion of thought. It is important that the German “Gedanke,” of which “thought” is the English equivalent, used to be a technical term in eighteenth-century German metaphysics. Christian Wolff defines it as a representation someone is conscious of.14 Accordingly, a thought is composed of two elements, its “contents” (the representation) and its consciousness. In Kant’s own classification scheme of representations this definition corresponds to the “representation with consciousness (perceptio)” (A 320 B 376), and indeed Christian Wolff translates the Latin “perceptio” with the German “Gedancke.” (Wolff, German Metaphysic, 674) This relationship between the representation and its consciousness was not conceived as one between a container and the contained, as later commentators sometimes have believed, but as that of a subject and its predicates.15 This contemporary view was explained in detail by G. F. Meier, among others (Meier, Beweiss, 36; Metaphysik, III 22). The major difference between the predication-view versus the container-view is that thoughts are dependent for their very existence on a thinking subject whose predicates they are, while things in a container may very well exist without it. This can also explain the distinction between external relations and accidents belonging inwardly to a thinking being (A 352): predicates belong inwardly to a thinking being in the sense that they cannot exist without that being. Hence, the materialist notion includes a contradiction when viewed from a rationalist perspective: For suppose that the composite were thinking; then every part of it would be a part of the thought only when taken together. Now this would be contradictory. For because the representations that are divided among different beings (e.g., the individual words of a verse) never constitute a whole thought (a verse), the thought can never inhere in a composite as such. (A 352)

The rationalist argument Kant reconstructs here is that to distribute one thought over many subjects amounts to a contradiction to the notion of thought. Accordingly, the definition of thought seems to demand a unitary subject. Now, since thought has been defined as a representation with consciousness, the concept of consciousness has to be taken into account. Christian Wolff coined the concept of consicousness that was almost universally adopted in the German context of the time:

 Christian Wolff, German Metaphysic, 108: We call “thoughts those modifications of the soul we are conscious of” (my translation). Cf. his German Logic, 124: “That effect of the soul by which we are conscious of ourselves we call a thought; because everybody says that he does not think anything at the time when he thinks to be conscious of nothing” (my translation). The same definition occurs e.g. in Meier, Beweiss, 35 and Knutzen, Abhandlung, 8. 15  Cf. as an example of the container-view the definition of apperception in Eisler, Kant-Lexikon, 34. 14

234

F. Wunderlich

Therefore we note that we are conscious of the things when we distinguish between them. (Wolff, German Metaphysic, 454, my translation)16

This definition sounds almost trivial, but is of consequence. If representations are conscious because they can be distinguished, then they need to be related.17 But how is this relation possible if the representations have no common medium, as would be the case if every partial thought were to inhere in a separate subject? Martin Knutzen, one of Kant’s academic teachers, points to this most clearly. He adopts the general, Wolffian definition of consciousness in his Philosophische Abhandlung von der immateriellen Natur der Seele and provides a more detailed account of the conditions that have to be fulfilled in order for a thought to be conscious. According to Knutzen, these conditions are the unity of the subject (Abhandlung, 16) and its identity (idb., 18), and in doing so he gives the main reason why unity of consciousness is necessary18: Therefore it is impossible to think of a distinction between things that are represented separately in different subjects. (Knutzen, Abhandlung, 18, my translation)

His own proof of the simplicity of the soul reads: Matter cannot think. Because what thinks must be aware of itself and of other things. (§ I) This consciousness of itself and of other things includes an idea [Anschauung] of the difference, and an activity in the distinguishing, without which it cannot take place, nor be done. (§ II) Now noticing this idea of the difference between the things is solely the work of a single subject, and in no way a thing that comes from several or many; because it demands partly that the representations of the different things must be represented in a single subject, partly that their holding together is accomplished by the same acting subject, or by the same first source and the same force. (§ III) Now, because matter is nothing else than a coherence of many substances and subjects, and consists of several such things which have their own special forces; (§ IV) nothing will be more insightful and obvious than that the idea [Anschauung] of the difference of the things, and thus of every thought as well, is not the work of a matter, and consequently it is impossible that this could be accomplished by a matter, if it be matter. (Knutzen, Abhandlung, 31f., my translation)

This passage includes all relevant aspects of the rationalist argument in the minor premise of Kant’s second paralogism. Knutzen’s argument can be reconstructed in seven steps: 1 . Thoughts are defined as representations of which a subject is conscious. 2. Because a thought belongs to its consciousness like a predicate to its subject, it cannot exist without its consciousness. Hence, it would contradict the notion of a thought if it were not related to consciousness.

 This definition was not only common to Wolffians like Meier, Beweiss, 35. Cf. Tetens, Versuche, I 262, Sulzer, Abhandlung, 200 or Platner, Anthropologie, 13 as examples of thinkers who were more distant from Wolff and used this definition as well. For an historical overview cf. Grau, Entwicklung, 181-230. 17  Wolff himself points this out on p. 457 of his German Metaphysic. 18  Actually, Knutzen speaks of “unity” in the second case as well, but it is clear from the context that he means what is normally called identity of the subject. 16

10  Kant’s Second Paralogism in Context: The Critique of Pure Reason…

235

3. Representations are conscious if they are distinguished from other representations. 4. Distinguishing representations requires that they are compared with and thus related to each other. 5. In order to be mutually related, representations must inhere a single consciousness, i.e., they must be predicates of one and the same subject (this is the point especially made by Knutzen). 6. Therefore consciousness cannot be distributed among many subjects but belongs to a simple being. 7. Matter is a composite substance. Hence matter cannot think. What is the nervus probandi of this argument, according to Kant? According to the argument of the minor premise, the impossibility of thinking matter can be proved by an analysis of the concept of thought that Kant deems unsatisfactory. He argues that the rationalist presents an analytic judgement based on the concept of thought, where instead a synthetic a priori judgement would be required. More precisely, Kant notes that there are two possible ways of understanding the unity of thought, but there is no criterion to chose between these possibilities by conceptual analysis: For the unity of a thought consisting of many representations is collective, and, as far as mere concepts are concerned, it can be related to the collective unity of the substances cooperating in it (as the movement of a body is the composite movement of all its parts) just as easily as to the absolute unity of the subject. Thus there can be no insight into the necessity of presupposing a simple substance for a composite thought according to the rule of identity. (A 353)

Kant thus claims that the rationalist argument turns out not to be an analytic judgement, because it is based on predicates that in fact do not belong to the concept of thought. Hence, at least one of the implications of thought mentioned above would not belong to Kant’s notion of it, if this reconstruction is appropriate. So which of the features ascribed to thoughts do not belong to their concept? The way Kant puts the argument at A 353 does suggest, in my opinion, that he adopts the first four characteristics, for he holds that a thought implies collective unity, and therefore a kind of relation between the several partial thoughts. By contrast he does not accept the fifth one according to which thoughts have to inhere in the same medium in order to be related. As to the mere concept of thought, it remains an open question how the representations are related: either by the activity of a single subject and hence related to its “absolute unity” or by the collective activity of several subjects and hence related to their “collective unity.” This seems to be the core of his argument. But of course, Kant does not hold that the simplicity of the soul can be proven by synthetic a priori judgements instead of analytic ones, because there is no intuition of the soul. On the other hand he indeed maintains that a principle of unity is essential for thought. All he denies is that it is possible to draw conclusions about the soul in itself from this unity. As he puts it at A 354:

236

F. Wunderlich

For although the whole of the thought could be divided and distributed among many subjects, the subjective I cannot be divided or distributed, and this I we presuppose in all thinking.

Moreover, Kant’s argument does not imply materialism, as mere conceptual analysis leaves it open whether the thinking self is based on an absolute or a collective unity. Thus Kant’s argument turns out to be quite intriguing, because it is effective against both the dualist and the materialist view. The conflict between materialism and dualism thus remains unsolved, as far as matter’s capability of thinking is concerned. Additionally, Kant notes at A 353 that of course simplicity cannot be derived from experience either. Summing up, Kant’s own position is a neutral one, neither materialist nor dualist, irrespective of how unity-of-consciousness arguments are applied in other contexts.19 The purpose of Kant’s paralogisms is quite ambitious. Kant maintains that his arguments strike at the core of the whole discussion about the simplicity of the soul. But does he really display the variety of arguments involved in this discussion? In his Geschichte der Seelen der Menschen und Thiere, published in 1774, Justus Christian Hennings lists no less than 24 different types of arguments for the simplicity of the soul. (Hennings, Geschichte)20 Several of them do not rely on considerations about the unity of thought as in Kant’s rationalist argument. I will look at just two influential ones here. Christian Wolff argues that matter cannot think because motion is the only way to cause change in matter, and thoughts cannot be explained as physical motions (Wolff, German Metaphysic, 460). Many others accepted his argument; an especially interesting case is Ludwig Martin Kahle (Kahle, Vergleichung, 100), for he uses exactly the first four considerations listed in the above reconstruction, but then continues with stating that motion cannot explain thought. Another type of argument rests on the assumption that voluntary motions cannot be explained based on mere matter; Karl Franz von Irwing (Irwing, Erfahrungen, II 41), Justus Christian Hennings himself (Hennings, Geschichte, 70, 109) and, according to Henning’s report, Erich Pontoppidan21 follow this line. However, quite a few philosophers support the argument Kant outlines, according to which the unity of thought demands a simple soul. This is for instance true of Pierre Bayle (Bayle, Leucippus, 100) and Johann Georg Feder (Feder, Logik, 352) and, according to the report of Hennings, similar views are held by Ralph Cudworth, Gottfried Plouquet and Willem s’Gravesande.22 So Kant does address a widely held

 This is doubted by Ameriks who holds that in the end Kant maintains an immaterialist view (cf. Ameriks, Kant’s theory and Ameriks, Kant and Mind). As far as the argument of the second paralogism is concerned, I think it is impossible to understand it that way, but I cannot go into that discussion at large, cf. instead Klemme, Kants Philosophie des Subjekts, 328. 20  It is notable that Hennings’ book was published slightly before a revival of materialism in the mid 1770s. 21  Cf. Hennings, Geschichte, 208. 22  Cf. Hennigs, Geschichte, 169 for Cudworth, 173 for Plouquet and 176 for s’Gravesande. 19

10  Kant’s Second Paralogism in Context: The Critique of Pure Reason…

237

view, and he indeed does not merely summarise positions of the Königsberg context.23 In his discussion of the second paralogism, Kant outlines some further counter-­ arguments against the simplicity proof, to which I will turn now. In the last passage of the second paralogism, beginning at A 356, Kant mentions two further aspects of the contemporary discussion. He argues that the main use made of the various proofs of the simplicity of the soul is that “through it I distinguish this subject from all matter, and consequently except it from the perishability to which matter is always subjected” (A 356). Some of his contemporaries have distinguished between the question of whether the soul is independent of matter and the question whether the soul is simple. But Kant does not seem to follow this, as he (like Descartes) treats incorruptibility as an immediate consequence of independence.24 For example, K.  F. von Irwing argues that the soul is independent of the body  – because otherwise voluntary motions could not be explained –, but that independence does not entail simplicity (Irwing, Erfahrungen, II 36–42). This argument is quite suggestive, because independence seems to be a necessary condition of simplicity, but that one entity is independent of the other is a less far-reaching assumption and does not require that they be substances of a different type. But this is not the point Kant makes here. Kant also explains that if matter is a mere appearance of the outer sense – as shown in the transcendental aesthetic – it is of course different from our thinking self, as this is only an object of the inner sense. But this only means that our thinking self cannot be an appearance of the outer senses, viz. an appearance in space, and does not allow conclusions concerning properties of the soul in itself. Kant further examines the possibility of whether the soul is substantially different from the substratum of matter, or matter in itself, even if one were to admit that only simple entities are capable of thinking. His considerations here (A 356–A 361) are quite complex, so they require a more detailed discussion: while the outer senses provide representations like those of extension, impenetrability, connexion and motion, the inner sense provides representations of a different kind, like thoughts, emotions, preferences or decisions. Nevertheless, it is possible that the substrate underlying outer appearances also underlies the thinking subject in itself. Of course, this noumenon is not extended, not impenetrable and not composite – but this merely means that predicates of outer appearances cannot be attributed to the noumenon.25 It does not provide any insight into the nature of this substrate. So if we do not know the nature of the substrate underlying matter, how could we exclude the possibility that it is the substrate of our thoughts as well? As Kant puts it:

 Johann Stephan Müller has argued against Knutzen that a complex of subjects could have a unitarian consciousness as well as a simple subject, Müller, Problema, 21 f. 24  At A 345 B 403 he treats incorruptibility as an immediate consequence of substantiality and simplicity as well. 25  Knutzen, Abhandlung, 63-78 gives an exhaustive discussion of several negative attributes of the soul, like invisibility, non-extension and incorruptibility. 23

238

F. Wunderlich

Yet these predicates of inner sense, representation and thought, do not contradict it [sc. the noumenon]. Accordingly, even through the conceded simplicity of its nature the human soul is not at all sufficiently distinguished from matter in regard to its substratum, if one considers matter (as one should) merely as appearance. (A 359)

If matter were a thing in itself and, as such, composite, then it could be distinguished clearly from the soul. But, as matter is only an outer appearance, it cannot be excluded that its substratum is simple. Hence, it cannot be ruled out that matter is capable of thinking as well. This would lead to a kind of identity thesis, where the outer, extended appearance of the body and the inner thoughts would be merely two aspects of the same thing: Thereby, the expression that only souls (as a particular species of substances) think would be dropped; and instead it would be said, as usual, that human beings think, i.e., that the same being that as outer appearance is extended is inwardly (in itself) a subject, which is not composite, but is simple and thinks. (A 359f.)

Here, Kant wants to show that it is impossible to distinguish matter and mind as two substances even if it were admitted that composite substances cannot think, and hence, that the simplicity proofs of the dualist tradition are in vain. Of course, this does not imply that Kant is tending towards a materialist position; he merely holds that we cannot exclude the possibility that matter in itself and the soul in itself are identical. It is not very likely that any of Kant’s contemporaries would have agreed to this line of argument, i.e. that only simple beings can think and at the same time that matter is capable of thinking. Hence in this passage, Kant rather seems to anticipate possible objections against his own view than discuss contemporary positions. The same seems to apply to the short passage at A 354 f., where Kant argues that the simplicity of my self (as a soul) is not really inferred from the proposition “I think,” but rather the former lies already in every thought itself. I am simple must be regarded as an immediate expression of apperception.

Indeed it is not Descartes’ view that the simplicity of the soul is inferred from the “I exist” in the sense of formal reasoning or a syllogism, but rather that it is an intuitive truth, whereas Wolff did argue that consciousness of our existence is established by a syllogism.26

10.3 Conclusion Kant seeks to provide an exhaustive discussion of the fundamentals of rational psychology by reducing them to formal fallacies and to an improper use of the categories. In both respects, Kant has not seemed to be very successful, at least as far as the second paralogism is concerned. On the other hand, it has turned out that Kant 26  Cf. Descartes’ sixth meditation, Writings, II 59ff. and Wolff, German Metaphysic, 4. Contrary to this, Bennett, Kant’s Dialectic, 82ff. and Düsing, Cogito, argue that the whole second paralogism discusses Descartes, see also Brook, Kant and the Mind, 168.

10  Kant’s Second Paralogism in Context: The Critique of Pure Reason…

239

provided a meaningful discussion of an important line of argument that is based on the assumption that the unity of thought requires a simple soul. Apart from Kant’s discussion of contemporary arguments, the question remains how his own position can be characterized. While he rejects both materialism and dualism about the nature of soul, he acknowledges most of them if they were merely understood as formal conditions of thought. As he puts it at A 356: This much is certain: through the I, I always think an absolute but logical unity of the subject (simplicity), but I do not cognize the real simplicity of my subject. Just as the ­proposition “I am a substance” signifies nothing but the pure category, of which I can make no (empirical) use in concreto, so is it permitted for me to say, “I am a simple substance,” i.e., a substance the representation of which never contains the synthesis of a manifold.

So would the paralogisms be valid if just understood as logical conditions of our thought instead of substances underlying it? This question is relevant not only for the Paralogism chapter, as formal aspects of mind are crucial for Kant’s own, positive theory in the transcendental deduction of the categories as well. Is there really a large distance between Kant and the rationalist tradition, then, if he essentially relies on formal aspects of mind extracted from that tradition? This question concerning the rationalist source of the formal aspects of mind goes even farther than that of whether Kant is neutral or a closet immaterialist concerning the soul in itself.

 ostscript (2022): Materialism and Anti-materialism P in the Eighteenth Century27 Critique and rejection of materialism was very common in early modern philosophy. As a consequence, materialism was a notable factor and present to a larger extent than the relatively small number of actual supporters would suggest.28 Kant was aware of the importance of materialism, even though it is not a direct threat for his transcendental idealism. Transcendental idealism includes that we have no cognitive access to the mind as a thing in itself, and thus we cannot establish whether the mind is material or immaterial. Nonetheless, Kant recognizes materialism as an at least indirect threat. He thus argues that even though the „psychological idea“, i.e. the paralogisms, provides little insight “into the pure nature of the human soul elevated beyond all concepts of experience”, it “at least reveals clearly enough the inadequacy of those concepts of experience, and thereby leads me away from materialism, as a psychological concept unsuited to any explanation of nature and one that, moreover, constricts reason with respect to the practical.” (AA IV 363) Kant concludes: “The transcendental ideas therefore serve, if not to instruct us positively, at least to negate the impudent assertions of materialism, naturalism, and fatalism”  I have left the 2001 paper mostly untouched as to contents but revised it linguistically.  Since 2001, quite a few monographs on early modern materialism have been published, most notably Thomson, Bodies of Thought, Rumore, Materia cogitans and Wolfe, Materialism. 27 28

240

F. Wunderlich

(ibd.). Likewise, he argues: “Why do we have need of a doctrine of the soul grounded merely on pure rational principles? Without doubt chiefly with the intent of securing our thinking Self from the danger of materialism.” (A 383).29 Hence, Kant obviously believes that it is important to confront materialism, partly because of potential moral ramifications. But rather than addressing Kant’s motivation, I want to take a step back here and ask what materialism in early modern philosophy is, thereby adding some more context to the 2001 paper that is mostly concerned with the immaterialist side of the debate. According to a more traditional view, early modern materialism is based on a mechanistic ontology that it gives a more radical shape. In brief, a mechanistic ontology is the view that all natural events are reduced to a small set of basic properties, such as extension, shape and mobility in the case of Descartes, often accompanied by solidity or impenetrability in others like Boyle and Locke. According to this ontology, motion is the only kind of physical event, and pressure and impact the only way in which motion is generated by transmission. Matter is thus viewed as fundamentally passive and unable to generate motion from its own resources. Mechanistic materialism, then, would consist in extending this view to the human being and explain thought and consciousness on the basis of matter and motion alone. However, recent scholarship, most notably by Ann Thomson, has demonstrated that hardly any materialist, with the potential exception of Hobbes, actually argued in this way.30 Instead of proposing that passive matter is the source of thought and consciousness, almost all early modern materialists argue that matter as such, or certain kinds or configurations of matter have a potential for activity. They unanimously rely on an extended notion of matter that is at odds with the mechanistic view of matter as fundamentally passive. This potential for self-activity is spelled out in different ways that I have discussed in more detail elsewhere.31 They are less relevant here because they do not concern the Achilles argument itself. Another important distinction is that between psychological and ontological materialism and can be traced back at least to Alexander Gottlieb Baumgarten and Georg Friedrich Meier.32 Whereas psychological materialism is a thesis about the thinking subject alone and seeks to establish an alternative to substance dualism, ontological materialism is a thesis about what kind of substances exist in the world. Psychological materialism does not necessarily deny that non-material substances exist, it only denies that the human mind is of such a kind. Some ontological materialists such as Margaret Cavendish make an exception for God; according to Cavendish, “(n)ature is material, or corporeal, and so are all her Creatures, and whatsoever is not material is no part of Nature, neither doth it belong any ways to

 On Kant’s view of materialism, cf. recently Watkins, Kant on materialism, and Thiel, Priestley and Kant. 30  Thomson, Mechanistic materialism, Bodies of thought; on the relation of dualism and mechanism, Osler, Divine will. Cf. also Wolfe, Materialism, and Wunderlich, Varieties. 31  Wunderlich, Varieties; Materialism. 32  Rumore, La réception. 29

10  Kant’s Second Paralogism in Context: The Critique of Pure Reason…

241

Nature”,33 whereas God is a “spiritual, supernatural and incomprehensible infinite” and “God is not material”.34 The atheistic materialist Baron D’Holbach, on the contrary, argues that “the universe, this vast sum of all that exists, offers us everywhere just matter and motion”, leaving no room for immaterial substances at all.35 The question of early modern materialism is thus not identical with that whether matter can think, as the title of the original paper suggests. It is, however, remarkable that Kant seems to be concerned with materialism about the human mind or psychological materialism only, also as a consequence of choosing the Achilles argument as reference point. It is also remarkable that none of his arguments addresses the question whether matter is fundamentally active or passive in the paralogism chapter, Cavendish, Margaret. 1664. Philosophical Letters, or Modest Reflections Upon Some Opinions in Natural Philosophy. London: Unknown publisher. Cavendish, Margaret. 2001. Observations Upon Experimental Philosophy (1668), ed. Eileen O’Neill. Cambridge: Cambridge University Press. D’Holbach Paul Henri Thiry. 1994. Système de la nature ou des lois du monde physique et du monde moral (1770), ed. Yvon Belaval. Hildesheim: Olms. La Mettrie, Julien Offray de. 1988. OEuvres Philosophiques (1744). Reprint Hildesheim: Olms. Osler, Margaret J. 1994. Divine Will and the Mechanical Philosophy: Gassendi and Descartes on Contingency and Necessity in the Created World. Cambridge: Cambridge University Press. Rumore, Paola. 2013. Materia Cogitans. L’Aufklärung di fronte al materialismo. Hildesheim: Olms. Rumore, Paola. 2018. La réception matérialiste de Spinoza et la literature clandestine à l’âge de la Frühaufklärung. La Lettre Clandestine 26:49–68. Thiel, Udo. 2020. Priestley and Kant on Materialism. Intellectual History Review 30(1): 129–143. Thomson, Ann. 2001.” Mechanistic Materialism vs Vitalistic Materialism?” La Lettre de la Maison française d’Oxford 14: 21–36. Thomson, Anne. 2008. Bodies of Thought. Oxford: Oxford University Press. Watkins, Eric. 2016. Kant on Materialism. British Journal for the History of Philosophy 24(5): 1035–1052. Wolfe, Charles T. 2016. Materialism. A Historico-philosophical Introduction. Dordrecht et al.: Springer. Wunderlich, Falk. 2016. Varieties of Early Modern Materialism. British Journal for the History of Philosophy 24/5: 797–813. Wunderlich, Falk. 2022 (forthcoming). Materialism. In Encyclopedia of Early Modern Philosophy and The Sciences, ed. by Dana Jalobeanu and Charles T. Wolfe, Dordrecht (Springer).  Cavendish, Philosophical Letters, 320-1.  Cavendish, Observations, 220; 215. 35  D’Holbach, Systeme, vol. 1, 12 (transl. FW). 33 34

242

F. Wunderlich

References36 Ameriks, Karl. 1982. Kant’s Theory of Mind. Oxford: Clarendon Press. ———. 1995. Kant and Mind: Mere Immaterialism. In Proceedings of the Eighth International Kant Congress, ed. Hoke Robinson, 675–668. Milwaukee: Marquette University Press. Bayle, Pierre. 1741/1744. Leucippus. In Historisches und critisches Wörterbuch, ed. Pierre Bayle , vol. 3, 98–102. Leipzig.trans. Gottsched, Bennett, Jonathan. 1974. Kant’s Dialectic. Cambridge: Cambridge University Press. Brook, Andrew. 1994. Kant and The Mind. Cambridge: Cambridge University Press. Descartes, René. 1984. The Philosophical Writings of Descartes, ed. Cottingham/Cambridge: Cambridge University Press. Düsing, Klaus. 1987. Cogito, ergo sum? Untersuchungen zu Descartes und Kant. Wiener Jahrbuch für Philosophie 19: 95–106. Eisler, Rudolf. 1984. Kant-Lexikon: Nachschlagewerk zu Kants sämtlichen Schriften, Briefen und handschriftlichem Nachlass (1930). Hildesheim: Olms. Feder, Johann Georg, and Heinrich. 1778. Logik und Metaphysik: nebst der philosophischen Geschichte im Grundrisse. Göttingen: Dieterich. Gäbe, Lüder. 1954. Die Paralogismen der reinen Vernunft in der ersten eund in der zweiten Auflage von Kants Kritik. Diss. Univ. Marburg. Grau, Kurt Joachim. 1916. Die Entwicklung des Bewußtseinsbegriffes im XVII. und XVIII. Jahrhundert. Halle: Niemeyer. Hennings, Justus Christian. 1774. Geschichte von den Seelen der Menschen und Thiere. Pragmatisch entworfen. Halle: Gebauer. Horstmann, Rolf Peter. 1993. Kants Paralogismen. Kant-Studien 83: 408–425. Irwing, Karl Franz von. 1777/1785. Erfahrungen und Untersuchungen über den Menschen. Berlin: Realschulbuchhandlung. Kahle, Ludwig Martin. 1741. Vergleichung der Leibnitzischen und Neutonischen Metaphysik wie auch verschiedener anderer philosophischer und mathematischer Lehren beyder Weltweisen angestellet und dem Herrn von Voltaire entgegen gesetzet. Göttingen: Königl. Universitäts-Buchhandlung. Klemme, Heiner F. 1996. Kants Philosophie des Subjekts: systematische und entwicklungsgeschichtliche Untersuchungen zum Verhältnis von Selbstbewußtsein und Selbsterkenntnis. Hamburg: Meiner. Knutzen, Martin. 1744. Philosophische Abhandlung von der immateriellen Natur der Seele, darinnen theils überhaupt erwiesen wird, daß die Materie nicht denken könne und daß die Seele überhaupt uncörperlich sey, theils die vornehmsten Einwürffe der Materialisten deutlich beantwortet werden. Königsberg: Hartung. Krug, Wilhelm Traugott. 1969. Allgemeines Handwörterbuch der philosophischen Wissenschaften nebst ihrer Literatur und Geschichte (21832–1838). Stuttgart: Frommann-Holzboog. Meier, Georg Friedrich. 1742. Beweiss, dass keine Materie dencken könne. Halle: Hemmerde. ———. 1752a. Vernunftlehre. Halle: Gebauer. ———. 1752b. Auszug aus der Vernunftlehre. Reprint in Kant AA XVI. ———. 1755/1765. Metaphysik. Halle: Gebauer. Müller, Johann Stephan. 1753. Problema utrum doctrina de mentis materialitate hypothesis philosophica possit vocari. Jena: Marggraf.  As usual, the Critique of Pure Reason is cited according to the A and B editions. “A 304,” for instance, refers to page 304 of the first edition (1781), and “B 304,” accordingly, to page 304 of the second edition (1787). Citations follow the translation by Paul Guyer and Allen Wood (Immanuel Kant. The critique of pure reason, ed. Paul Guyer and Allan Wood. Cambridge: Cambridge University Press, 1998); the edition of Raymund Schmidt (Hamburg: Meiner, 1976) is used additionally. Other references follow the Akademie edition (AA), Berlin: De Gruyter 1910ff. 36

10  Kant’s Second Paralogism in Context: The Critique of Pure Reason…

243

Platner, Ernst. 1998. Anthropologie für Ärzte und Weltweise (1772). Hildesheim: Olms. Sulzer, Johann Georg. 1773. Herrn Professor Sulzers Abhandlung von dem Bewußtseyn, und dessen Einflusse auf unsere Urtheile. In Vermischte Philosophische Schriften, ed. Johann Georg Sulzer, vol. 1, 199–224. Leipzig: Weidmann. Tetens, Johann Nicolaus. 1979. Philosophische Versuche über die menschliche Natur und ihre Entwicklung (1777). Hildesheim: Olms. Wolff, Christian. 1983. Vernünfftige Gedanken von Gott, der Welt und der Seele des Menschen, auch allen Dingen überhaupt (1720). (= German Metaphysic) Hildesheim: Olms. ———. 1965. Vernünfftige Gedancken von den Kräfften des menschlichen Verstandes und ihrem richtigen Gebrauche in Erkäntnis der Wahrheit: den Liebhabern der Wahrheit mitgetheilet (1713). (= German Logic) Hildesheim: Olms.

Part V

Metaphysics and Natural History

Chapter 11

Kant’s Universal Natural History and Analogical Reasoning in Cosmology Stephen Howard

Abstract  This chapter aims to shed new light on the arguments and philosophical significance of Kant’s Universal Natural History by examining the work’s natural-­ philosophical methodology. The 1755 cosmological treatise, Kant asserts, follows “the leading thread of analogy”. After introducing the work’s main cosmological analogy, I examine the historical context of Kant’s analogical method. The most relevant context, I argue, is not the prior tradition of cosmology and natural history but rather works of scientific methodology and logic. Next, to better understand and assess the principal analogy of the Universal Natural History, I outline Kant’s later theories of analogy. Kant distinguishes between analogies of similarity and fourfold analogies of proportion; the latter are concerned not with things but with relations. Analogies of proportion are further subdivided into inferential and non-inferential analogies. Based on these distinctions, I propose an interpretation of the kind of analogical reasoning that is employed in the Universal Natural History.

11.1 Introduction In 1755, the 31-year-old Immanuel Kant attempted to publish his second book, Universal Natural History and Theory of the Heavens. The book was an ambitious effort to explain the formation and structure of the entire physical universe “through mechanical laws alone”, namely through the “Newtonian” forces of attraction and repulsion (1:234–5).1 Beginning from a primordial chaos and a dispersed matter  The Academy edition of Kant’s writings (Kant 1902) is cited according to volume and page number. I follow the translations in the Cambridge edition. 1

S. Howard (*) Institute of Philosophy, KU Leuven, Leuven, Belgium e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_11

247

248

S. Howard

endowed only with these forces, Kant seeks to explain the organization of our solar system, the stars and their planetary systems, and even the mental capacities of the inhabitants of other planets. As Kant puts it in the title of a chapter, he is concerned with nothing less than “creation in the entire extent of its infinity both in space and in time” (1:306). Just as the book was due to be released its publisher went bankrupt, so very few copies reached the public. Six years later, Johann Heinrich Lambert published an account of the structure of the universe that bore similarities to Kant’s theory, although the latter was unknown to Lambert at the time.2 The Universal Natural History was not completely lost for Kant’s contemporaries. Kant included a summary of some of its main points in his Only Possible Argument (1763); he repeated the basics of the theory in a short popular essay about volcanos on the moon in the Berlinische Monatsschrift in 1785; and he authorized and supervised the inclusion of extracts of the 1775 work as an appendix to a 1791 German translation of three essays by William Herschel.3 Complete editions of the treatise finally appeared in 1797, 1798, and, after Kant’s death, in 1808, and were enthusiastically received by members of the new generation of speculative philosophers, including Schelling.4 All this is well known to historians of philosophy. What is less clear is how we should view the philosophical significance, if any, of the Universal Natural History. Understandably, the great majority of studies of Kant’s treatise have focused on its natural-scientific content. That is, readers usually consider how its claims compare to the scientific consensus of Kant’s day and ours, with particular attention to the work of Kant’s predecessors, contemporaries, and followers, such as Newton, Lambert, and Laplace.5 It is clear that the treatise is at once a cosmogony, an account of the initial formation of the universe, and a cosmology, in the broad sense of an attempt to describe and explain the structure of the physical universe. With regard to these two tasks, most commentators present the treatise as an eclectic and syncretic natural-philosophical work.6 As a cosmogony, the Universal Natural History intervenes in early modern debates over how the universe, solar system, and earth initially formed: Descartes, Leibniz, Burnet, Whiston, and Buffon were among the major contributors.7 As a cosmology, the treatise can be said to draw on and blend

 Lambert 1761. See Kant’s note in the Only Possible Argument about the alignment of his and Lambert’s theories and the impossibility of Lambert knowing his 1755 work (2:68–9). Lambert describes his independent discovery of his theory in a 1765 letter to Kant (10:53). 3  See, respectively: 2:137–51; 8:67–76; Herschel 1791, 163–204. On variations across these texts, see Ferrini 2000: 303–11 and Ferrini 2004. 4  On the editions, see Kant [1755] 1968, 180–3. On Schelling, see Blumenberg 1987, 573 and Cooper, 85. 5  Among many examples, see Jaki 1981, Kerszberg 1984, Lalla 2003, Schönfeld 2000, 96–127 and 2010, Massimi 2011. 6  I borrow the formulation “eclectic and syncretic” from Ferrini 2022, 261. 7  Descartes’ Le Monde (1632–1633, published 1664) and the Principia philosophiae (1644); Leibniz’s Protogaea (1691–1693, published 1749). On Burnet and Whiston, see Jaki 1977, 87–96. Buffon is discussed below. 2

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

249

Cartesian, Newtonian, and Wolffian currents.8 The list of sources that Kant can be said to be synthesizing can be easily multiplied.9 The more sensitive readings in this vein have shown that while Kant draws on various natural-philosophical projects, he adds a healthy dash of originality.10 Some interpretations have gone beyond discussions of the eclectic or syncretic character of Kant’s natural-philosophical claims, however. One line of interpretation reads the Universal Natural History in the light of physico-theology, a tradition that attempted to prove the existence of God on the basis of natural phenomena and debated the character and extent of divine intervention in nature. (Waschkies 1987, Theis 2011, Watkins 2013, 433–5, Prunea-Bretonnet 2019). Another, more recent line has considered the work as a contribution to natural history, following Newtonian naturalists like Haller and, particularly, Buffon, whose monumental Historie naturelle began to be published in French in 1749 and in German in 1751 (Cooper 2020, Ferrini 2022). The present chapter aims to further develop an aspect of the latter line of investigation by shifting the focus more squarely onto questions of natural-philosophical methodology. Specifically, I will examine the method of analogical reasoning employed by Kant in 1755. In Sect. 11.2, I introduce the main cosmological analogies in the Universal Natural History. Section 11.3 examines the historical context for Kant’s analogical method. We will move from cosmology and natural history to what I consider a more relevant context, namely works in scientific methodology and logic. In Sect. 11.4, with reference to later writings, I outline Kant’s theory of analogy. On this basis, Sect. 11.5 explores the kind of analogical reasoning that is employed in the Universal Natural History. A clearer understanding of the work’s principal analogy, I suggest, can illuminate the continuities and discontinuities, with regard to scientific methodology, between Kant’s early cosmology and his later writings.

11.2 Kant’s Analogical Method in the Universal Natural History The methodological wager of the Universal Natural History is to proceed by “adhering to the leading thread of analogy” (1:235). Kant describes the main analogy of the treatise as follows:  On Descartes and Newton, see Kerszberg 1984; on Newton and Wolff, see Falkenburg 2000. On the character and extent of Kant’s Newtonianism in 1755, see Falkenburg 2000, 34–5, 57, Schönfeld 2000, 96–127, Massimi 2011, Watkins 2013, 431–3, Prunea-Bretonnet 2017. 9  To mention some of the figures to whom Kant explicitly refers: the ancient atomists, Bradley, Brahe, Cassini, Derham, Flamsteed, Haller, Halley, Huygens, Kepler, Pope, Pound, and Mairan. Jaki’s edition (Kant [1755] 1981), despite its dismissive perspective and overly literal translation, provides a wealth of information on Kant’s sources, as does Waschkies 1987. 10  Adickes’ balanced assessment of Kant’s project in the Universal Natural History remains a good example of such a reading (Adickes 1925, 206–315). 8

250

S. Howard

we may use the analogy of what has been observed in the orbits of our solar system, namely that the same cause that has imparted centrifugal force to the planets, as a result of which they describe their orbits, has also arranged them in such a way that they all relate to one plane, which is therefore also the cause, whatever it may be, that what has given the power of rotation to the suns of the upper world, as so many moving stars of higher orders of worlds, has, at the same time, brought their orbits into one plane as much as possible and striven to limit deviations therefrom. (1:250)

Kant’s claim in this complex sentence can be initially reconstructed as follows. The analogy leads us from something we know to something we do not know. First, what we know: astronomical observation and Newtonian mechanics teach us that the planets of our solar system rotate around the sun. Moreover, not only do all the planets orbit in the same direction, but they deviate very little from a common plane (1:247). Many mid-eighteenth-century writers on cosmology highlighted the latter fact as remarkable. Both Buffon (1749, 134) and Maupertuis (1750, 16–17) try to calculate how hugely improbable it would be for this arrangement to be the result of chance. Kant, too, assumes that there must be a cause for the disk-like arrangement of the planetary orbits. The analogy contends that “the same cause” governs both the arrangement of the planets of our solar system and, now turning to what we do not know, the arrangement of the “moving stars of higher orders of worlds”, which we can call the stellar system. In the passage, Kant does not yet provide his account of this cause, and indeed signals it is not important at this point (“whatever it may be”).11 A few pages later, however, he proposes how the motion and arrangement of the solar system were caused. This is what came to be called the ‘nebular hypothesis’: the claim that celestial bodies first formed out of an original chaos through the fundamental forces of repulsion and attraction.12 In this hypothetical account of the primal formation of bodies, matter is initially distributed chaotically throughout the universe (1:263). But the “elements” of this matter possess “essential forces”, namely repulsion and attraction (1:264). Kant claims to have “borrowed” these basic forces “from Newtonian philosophy” (1:234–5). On the basis of only these two forces, matter starts to coalesce into clumps; these clumps attract each other and form “eddies”, as the repulsive and attractive forces cause matter to swirl (1:265). These eddies in the originally distributed matter become the orbits of planets around stars and, on a higher level, the orbits of these solar systems around their own central point.

 At 1:261, Kant repeats “whatever it may be”, again regarding the cause of the arrangement of the solar system. He seems to be evoking Newton’s famous agnosticism regarding the cause of gravity, although he will shortly claim to identify this cause in the fundamental forces of matter. We shall return to the role played by these forces in the work’s principal analogy. 12  At least by the beginning of the twentieth century, ‘nebular hypothesis’ had become a common designation for the theories of the formation of the universe propounded by Kant and, in the Exposition du systéme du monde (1796), by Laplace (Adickes 1925, 206, 297–8). Shea (1986, 96) notes that in the 1850s Schopenhauer and Helmholtz ascribe the nebular hypothesis to Kant and Laplace. 11

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

251

We therefore know how our solar system is organized and the forces that govern it. Following the thread of analogy, Kant suggests that the systematic organization of our solar system is reproduced on a higher level by the system of stars. That is, the stars circle in a common direction around a central point, deviating little from a shared plane, so the arrangement of the stellar system mirrors that of our solar system. In making this proposal, Kant is guided by two sources. Firstly, a short cosmological work by Thomas Wright of Durham, which was summarized in a Hamburg periodical, the Freye Urtheile, in 1751 (1:231). Secondly, simple observations he makes by looking up at “the sky full of stars on a clear night” (1:248). Both sources lead Kant to notice the dense band of stars, the Milky Way, and to propose that this band is a common plane of stars, on which our sun is situated, and which revolves around a central point. In a footnote later in the work, Kant conjectures that Sirius, the dog star, is the centre of the stellar system (1:328-9n). As Kant summarizes his principal analogy: The shape of the heavens of the fixed stars therefore has no other cause than being exactly the same systematic constitution on a large scale as the planetary system has on a small one, in that all suns make up one system, whose universal plane of reference is the Milky Way. (1:251)

The two things linked by the analogy – the known solar system and the unknown stellar system  – share the same “systematic constitution”. At the end of a short opening summary of Newtonian notions, Kant explains what this phrase means. In a broader sense, ‘system’ designates celestial bodies that orbit a central point. In a narrower sense, such orbiting bodies are systematic if they also deviate very little from a common plane (1:246). With both the broader and narrower senses of the term, Kant is here obviously using ‘system’ in a very particular way: the term refers only to the character of the orbits of heavenly bodies.13 Kant describes the Universal Natural History as “based on analogies and harmonies” in the plural, and indeed he employs other analogies alongside this principal one (1:235). He speculates through analogy about such topics as the reasons for the differing eccentricities of planetary orbits, the origin of the ring of Saturn, whether the earth once had a ring, the cause of the fire of the sun at the centre of each solar system, the periodic destruction and rebirth of planetary systems, and  – notoriously – the characteristics of the inhabitants of the other planets in our solar system. Minimally, we can say that in each case, Kant’s use of the analogical method allows him to extend what is known about our solar system in order to make what he takes to be credible hypotheses about things that are unknown to us. In the next three sections, we will flesh out Kant’s conception of analogical reasoning, firstly by examining the historical background.

 This particular sense of ‘system’ that Kant utilizes in the 1755 work is easily overlooked: for example, Ferrini (2000, 300) takes systematicity to designate “the common origin of the essential properties of things in the design of God’s infinite Understanding”, which is not how Kant defines ‘systematic constitution’ at 1:246. Burt and Sturm (forthcoming) discuss in detail Kant’s conception of systematic constitution in the Universal Natural History. 13

252

S. Howard

11.3 Analogical Reasoning: Some Historical Context This section will survey some of the major uses and discussions of analogical reasoning among Kant’s predecessors, beginning with the cosmological writings that were an obvious direct influence. I will argue that a more significant historical context for Kant’s claims in the Universal Natural History appears in earlier writings on scientific method, so my account will broadly move backwards through the history. It is generally assumed that Kant was not doing anything unusual when employing analogical reasoning in the Universal Natural History. But his approach is far from standard in eighteenth century cosmology. Neither Wolff, in his German physics or cosmological writings, nor Maupertuis, in his Essai de Cosmologie (1750), employ an analogical method.14 It does not form the methodological basis of Newton’s Principia, which applies cutting-edge mathematics to observational data (although we will return below to Newton’s discussion of analogical reasoning in the second edition of the Principia). There is a passing reference to something like an analogical method in the summary of Thomas Wright’s book in the Hamburg Freye Urtheile.15 In the summary of the second letter, Kant would have read: In this letter the author shows that with regard to things where no mathematical proof can be expected, one must be content with moral certainty, and where a demonstration through geometry [durch Linien] is lacking, there another method must serve for judging in order to prove the controversial point, namely the similarity [Aehnlichkeit] of known and natural things.16

This reference to “similarity” is the only methodological statement in the German summary of Wright’s book. It is moreover a vague reference: “known and natural

 The cosmology chapter of Wolff’s physics textbook, “Von dem Welt-Gebäude” in Wolff [1723] 1981, 150–268, is a compendium of contemporary astronomical knowledge in a relatively popular style. Analogical reasoning plays no role in the chapter, as far as I can tell, nor in Wolff’s rational (or general) cosmology in the fourth chapter of the German Metaphysics (1720) and the Cosmologia generalis (1731). Maupertuis (1750, 109) once refers to the “single analogy” between the earth and the other planets that “leads one to believe” that the planets are opaque like the earth; but he immediately adds that there are “more sure proofs that do not permit doubt”, so he is clearly sceptical of the value of analogical reasoning. 15  Shea (1986, 105) points to this, although he overlooks the translation issue I mention in the next note. Shea (1986, 105–15) provides a rare extended discussion of Kant’s analogical method. His account is however broadly dismissive. This conceivably stems from his limited engagement with the historical context: Shea (1986, 105–6) mentions only Descartes’s methodological advice and the views of Leibniz and Pope, which he takes to exemplify Lovejoy’s notion of the great chain of being. 16  My translation of the Hamburg Freye Urtheile text from Fritz Krafft’s edition (Kant [1755] 1971, 201). Hastie gives an English translation of the Freye Urtheile summary in Kant [1755] 1968, 166–79 and Kant [1755] 1969, 169–80, but this is not always accurate, in part because he gives Wright’s English verbatim when it is (or he takes it to be) quoted: he therefore translates Aehnlichkeit in this passage as ‘analogy’. Jaki (1981, 220-1n3) notes discrepancies between the manuscript version translated by Hastie and the printed text in the Freye Urtheile. 14

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

253

things” do not self-evidently form a disjunction that needs to be bridged through analogy. And Wright’s guiding thread of “moral certainty” was not taken up by Kant, whose analogical claims in 1755 are instead restricted to natural-scientific topics and mechanical explanation. Commentators have not often considered the possible sources for Kant’s analogical method, but where they have done so, Buffon has been identified as a notable predecessor (Cooper 2020, 80–1). Buffon considers analogies valuable for finding regularities in nature. He begins the Historie naturelle by noting two obstacles that stand in the way of our understanding of nature: the great multitude of objects and their diversity (Buffon 1749, 4–5). He then states that in natural history we should not “limit ourselves solely to making exact descriptions and apprehending only particular facts”; rather, we must attempt to raise ourselves to something greater and more worthy of our attention, that is to combine the observations, generalize the facts, tie them together on the strength of analogies, and attempt to reach the high degree of knowledge [connoissances] where we can judge that particular effects depend on more general effects, where we can compare nature with herself in her great operations … (Buffon 1749, 50–1)

Analogy, for Buffon, allows the scientist to move from the overwhelmingly complex level of the particular to the general. By drawing connections between phenomena through the method of analogy, the scientist can identify general laws. The scientist’s aim is to “compare nature with herself”. Underpinning Buffon’s methodological claims are the assumptions that nature is consistent and that this consistency manifests itself in the analogies, that is, similarities, that can be found between disparate domains or between particular things and general laws. We shall see that this assumption is also influentially affirmed by Newton. Kant makes explicit and implicit references to Buffon in the Universal Natural History.17 The significance of Buffon’s approach for Kant relates not only to analogical reasoning but also to the French naturalist’s historicized accounts of the development of natural phenomena. Buffon’s historical method leads him to try to account for the beginning of natural history, namely how the earth was formed, as well as to speculate about the origins of the movement of the planets around the sun, because “the physics of the earth holds for celestial physics” (Buffon 1749, 127). Buffon’s hypothesis is that the planets were formed by a comet hitting the sun and breaking off material that cooled to become bodies orbiting in the same direction and close to a common plane (Buffon 1749, 133).18 There are some broad similarities between Buffon’s speculations about the origin of the solar system and Kant’s 1755 theory. Both authors pursue a historical  See 1:277 and 1:345, and also 1:261–2, 1:272, and 1:273–4: Jaki (1981, 257n3, 261n15, n17) argues that, in the latter three passages, Kant borrows from Buffon’s Historie naturelle without citing it. The title of Kant’s work seems to allude to Buffon’s title and more closely to the title of Kästner’s German translation, Allgemeine Historie der Natur (see Jaki 1981, 13; Cooper 2020, 80). Ferrini (2022, 263–5) suggests that there is a relevant conceptual difference between Historie and Geschichte. 18  For discussions, see Adickes 1925, 296–7, Jaki 1981, 18–19, and Cooper 2020, 80–1. 17

254

S. Howard

account of the formation of the planets in our solar system. Both attempt to explain the peculiar uniformity of the orbits of the planets through a single cause. As Kant will, Buffon advocates a method of analogical reasoning. However, there are significant differences between Buffon’s approach in the Historie naturelle and Kant’s in the Universal Natural History. Buffon’s theory begins with a comet, not with the primordial chaos posited by Descartes in Le Monde and adopted by Kant. Buffon is concerned only with the solar system, not with the whole universe. This is the mainstream approach in the period, from which Kant diverges: aside from brief references to the fixed stars, Newton’s Principia, Wolff’s German physics, and Maupertuis’ Essai de cosmologie are all concerned with our solar system alone. More generally, although in his natural history proper Buffon advocates the use of analogies for systematizing and generalizing empirical data about particular things, he does not employ this analogical reasoning in his theory of the formation of the planets in our solar system. As he admits, his cosmological theory is a speculative hypothesis, albeit one that he believes has a high degree of probability (Buffon 1749, 129). Unlike Kant, Buffon does not claim that his specific cosmological proposals are guided by any particular method. Another possible influence on Kant’s analogical method identified in the literature is Newton (Marty 1980, 28–9, Cooper 2020, 79). In the third of the “Rules for the Study of Natural Philosophy” added to the second edition of the Principia, Newton states that “qualities that square with experiments universally are to be regarded as universal qualities” (Newton [1687] 1999, 795). That is, if experiments consistently find properties in bodies, these properties should be considered to be present in all bodies. While advising that this analogical method should be used with caution, Newton insists it is a general guiding thread for scientific investigation: “Certainly idle fancies ought not to be fabricated recklessly against the evidence of experiments, nor should we depart from the analogy of nature, since nature is always simple and ever consonant with itself” (Newton [1687] 1999, 795). The analogical inference that Newton recommends is made possible by the self-­ consistency of nature: we can infer from what we know to what we do not because nature is “ever consonant with itself”. At the end of his explanation of the third rule, Newton applies it to celestial bodies. Because we know that there is a gravitational effect proportional to the quantity of matter between bodies and the earth, the moon and the earth, the planets, and comets and the sun, “it will have to be concluded” according to the analogy of nature “that all bodies gravitate toward one another” (Newton [1687] 1999, 796). Analogical reasoning, on Newton’s conception, directs us to infer a universal gravitation between bodies. It is significant that Newton discusses analogical reasoning in the context of the “Rules”. Analogy appears as one of the general guidelines for scientific investigation. It plays no major role in Newton’s specific claims in the Principia: as noted above, Newton’s empirical-mathematical method has no place for analogical reasoning. Newton’s point in the third Rule is only a broad one: that nature is self-­ consistent. By the “analogy of nature”, Newton therefore means the ‘similarity of nature’, like Buffon and Wright in his wake. Analogy in the sense of ‘similarity’

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

255

justifies the scientist’s move from the particular to the general, making possible the generalization of laws. The location of Newton’s discussion of analogy in the Principia – in the “Rules” – suggests that the most relevant context for Kant’s use of analogy may not be cosmological treatises per se, but rather works of scientific method and logic. Indeed, we find analogical reasoning treated in one of the most influential early modern accounts of scientific methodology, Bacon’s Novum Organum (1620). “Substitution by analogy” is one of Bacon’s “privileged instances”, or methodological aids for the investigation of nature. Analogical reasoning has a lowly place in Bacon’s hierarchy of methods, in nineteenth place; Bacon calls it one of the “instances of last resort” to be used “when direct instances are lacking” (Bacon [1620] 2000, 180, 181). Nevertheless, analogical inference is “certainly useful”. It allows a “non-sensible thing”, that is, something we have not perceived, to be “brought before the senses” by observing a sensible body that is “related” to the non-sensible thing. But although analogical reasoning can thus benefit the investigator of nature, it is “less sure, and therefore must be used with some discretion” (Bacon [1620] 2000, 180). Locke similarly states in his Essay that analogy can help us to understand non-sensible things on the basis of sensible things, and that this method provides us with “grounds of probability”, and so not certainty (Locke [1689] 1976: 412–13).19 Bacon and Locke both caution that analogical reasoning cannot provide certainty, while asserting that it can help us to gain knowledge of things to which we have no direct sensory access. Similarly, Leibniz considered analogy to be a method of natural-scientific investigation. In a letter to Thévenot about a visit to the anatomist and naturalist Malpighi during his Italian journey, Leibniz writes, “I am completely convinced by this maxim: Naturam cognosci per Analogiam [nature is known through analogy]”.20 Bernhard Sticker has shown that Leibniz considered analogical reasoning to be helpful for ordering objects into series though the incremental comparisons of their characteristic marks. This presupposes that “one is convinced about the uninterrupted continuity” of the series, “even if by no means all members are known” (Sticker 1969, 179). For Leibniz, like Bacon and Locke, analogical reasoning allows the natural scientist to make inferences about unknown things. Like Newton and, later, Buffon, Leibniz considers the method to be warranted by the continuity of nature. Two interesting shifts are evident if we turn to a work closer to Kant in eighteenth-­century Prussia. First, considerations of the use of analogy in scientific method are shifted to the discipline of logic; second, a new skepticism about the validity of the method appears. From the beginning of his lecturing career, as far as we know, Kant lectured on logic using Meier’s Auszug aus der Vernunftlehre

 These passages from Bacon and Locke are discussed in relation to Kant’s theory of analogy by Callanan (2008, 749–50). 20  Letter to Thévenot of 24 August 1691, quoted Sticker 1969, 177. 19

256

S. Howard

(1752b) as his textbook.21 Section 401 of Meier’s book is about “mutilated inferences [verstümmelte Vernünftschlüsse]”. Two types of such inference are “inductions” and “inferences from example [Exempelschlüsse (exemplum in ratiociniis)]” (Meier 1752b, 110). Induction is commonly paired with analogy in Aristotelean logic, so Meier’s ‘inferences from example’ take the place traditionally occupied by analogical inferences. That this is the case is clearer in the full Vernunftlehre, of which the Auszug is a summary: Meier describes Exempelschlüsse as “when one concludes from one case to another because they are similar” (Meier 1752a §430, 595). Meier’s example of a flawed Exempelschluss, in both the Vernunftlehre and the Auszug, is “humans can sin; therefore the holy angels can also sin” (1752a, 595; 1752b, 110). Analogical reasoning can lead to vague and arbitrary claims about similarities, which may even be blasphemous  – a particular problem for Meier and his Pietist milieu. By classifying analogical reasoning as a type of ‘mutilated inference’ and referring to it not by its standard name but as ‘inference from example’ based only on similarity, Meier makes clear that he dismisses this kind of inference. The positions we have considered in this section suggest that the most important context for Kant’s analogical method in the Universal Natural History is not works of cosmology per se, but rather discussions of the value of analogy in scientific methodology. Bacon and Locke view analogy as a fallible but potentially helpful means for bringing unperceived things before the senses. Newton, Leibniz, Buffon, and Wright likewise consider analogical reasoning to be a valuable scientific method, enabling us to posit similarities between seen and unseen things, based on the assumption that nature is uniform. However, the seeds of Kant’s divergence from these predecessors  – to which we turn in the next section  – can be seen in Meier’s dismissal of analogical reasoning about similarities. He designates it a species of “mutilated inference” that typically yields logically (and theologically) erroneous conclusions.

11.4 Kant’s Theory of Analogy Building on the previous section’s sketch of the historical backdrop, we can now turn to Kant’s theory of analogy, which we will reconstruct from passages in the Prolegomena (1783), the student notes of Kant’s logic lectures, Kant’s annotations on his logic textbook, and the Critique of Judgement (1790). Most of these texts stem from Kant’s critical period. I do not wish to claim that Kant already held his mature theory of analogy in 1755 – nor that he did not. Rather, I leave aside questions about the development of Kant’s views on analogy (there seems to be little

 Both Young (Kant 1992, xxiii) and Naragon (2006) believe that Kant used Meier’s Auszug from the earliest of his lectures on logic in the winter semester 1755–56. 21

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

257

evidence one way or the other), at least until my concluding remarks.22 I nevertheless draw on Kant’s later distinctions because they make possible a more structured analysis of the principal analogy of the Universal Natural History. At the heart of Kant’s mature theory of analogy is the notion of a ‘proportion of concepts’.23 The Prolegomena contains the classic description of this proportional conception of analogy. The context for the description is the question of what can be analogically inferred about God’s relation to the world. Kant provides a series of analogies: with the relation of a clockmaker to a clock, a shipbuilder to a ship, or a commander to a regiment. He then states, This type of cognition is cognition according to analogy, which surely does not signify, as the word is usually taken, an imperfect similarity between two things, but rather a perfect similarity between two relations in wholly dissimilar things. (4:357)

Let us take one of Kant’s examples, the analogy between God and the clockmaker. The clockmaker constructs the clock flawlessly and sets it running with no need to subsequently intervene. We infer through analogy that God does the same with the world. From the relation between two known things, the clock (A) and clockmaker (B), we can make claims about the relation between a third known thing, the world (C), and an unknown thing, God (X).24 The basis of the analogy is that the relation of A to B is the same as C to X; we can write this A : B = C : X.25 The ‘things’ – on the one hand, the clockmaker and the clock; on the other hand, God and the world – are wholly dissimilar. Additionally, one of the relata of the second pairing cannot be cognized by us, namely

 Callanan (2008, 752n18, 762-3n40) claims that the proportional conception of analogy, which is explained below, first appears in the notes of Kant’s metaphysics lectures from the mid-1770s and can be found neither in the logic notes nor in Kant’s annotations on Meier (we should add: in notes that Adickes dates prior to the 1790s, because the proportional conception seems to be alluded to in R3292 and R3294, which Adickes dates to the period after the third Critique). This may be true but it does not reveal anything about Kant’s views, because his references to analogies of similarity in the logic notes tend to be critical, in line with his textbook author Meier, and so they do not reveal him affirming the similarity conception of analogy before the 1770s. I am not aware of evidence that shows that Kant held or did not hold some version of his proportionality theory (or rather, as we shall see, theories) of analogy in 1755. In what follows, I will suggest that certain claims in the Universal Natural History can be clarified if we read its principal analogy as an analogy of proportion. 23  See Callanan 2008, 750–1, and Matherne 2021, 217–18. This phrase appears in the metaphysics lecture notes (28:292), as Callanan points out. 24  Here and in what follows, I use ‘known’, ‘unknown’, ‘unknowable’ etc. in a non-technical sense, following Kant’s reference to the “Unbekannte” at stake in analogies of proportion (4:357). The loose sense of knowledge here is a case of neither Erkenntnis nor Wissen in Kant’s technical senses, which are discussed in Willaschek and Watkins 2020. 25  Kant uses A, B, C, and X with reference to a different analogy (between parental love and God’s love) at 4:358-9n. A discussion, in abstract terms, of the fourfold form of analogy appears in the Critique’s Analogies of Experience (A179-80/B222). There, Kant distinguishes between philosophical analogies, through which we can determine a relation to an unknown fourth thing, and mathematical analogies, in which the unknown X is constructed (see Shabel 1998, 611n37). 22

258

S. Howard

God. But the two relations – clockmaker to clock; God to world – are, according to the analogy, the same. In this case, the relation is that of (impeccable) construction. An important aspect of Kant’s theory, and one that has not always been adequately recognized by commentators, is that this kind of proportional analogy does not serve to determine the unknown thing (X, God) as it is in itself.26 The analogy concerns only its relation to the known thing (C, the world) and does not permit us to affirm that it possesses any particular non-relational properties. The wider context of Kant discussion in the Prolegomena is an argument levelled by Hume against an anthropomorphic conception of God in which properties of humans are naively transferred, through analogy, to the supreme being (see 4:356). Kant considers Hume’s attack to be valid, but he claims that his analogical method escapes it.27 Key for Kant is that, after the analogical reasoning that he describes, the concept of God remains indeterminate in itself; all we have determined is a relation, namely that God is the rational causal of the world. He writes that in his analogy, “we have omitted everything that could have determined this concept [of God] unconditionally and in itself; for we determine the concept only with respect to the world and hence with respect to us, and we have no need of more” (4:358). Further, “reason is not thereby transposed as a property onto the first being in itself, but only onto the relation of that being to the sensible world, and therefore anthropomorphism is completely avoided” (4:359). This entails that, once Kant has made his analogical claims, it remains the case that “the supreme being, as to what it may be in itself, is for us wholly inscrutable and is even unthinkable by us in a determinate manner” (4:359). Kant is thus very clear that analogical reasoning, as he employs it, does not determine the properties of an unknown thing but only specifies its relation to something that we can cognize. In the key passage quoted above from the Prolegomena, Kant distinguishes his ‘proportionality’ conception of analogy from a ‘similarity’ conception, where the latter is the way that “the word is usually taken” (4:357). Kant regularly mentions the similarity conception in the logic lectures.28 The Hechsel notes (1780–82) describe it as follows: “when two or more things from a genus agree with each other in as many marks as we have been able to discover, I infer that they will also agree with one another in the remaining marks that I have not been able to discover” (Kant 1992, 408,  ‘Determination’ in the critical period still has the meaning Kant gives it in the early New Elucidation (1755): “To determine is to posit a predicate while excluding its opposite” (1:391). 27  For more on the Humean context and the debate in natural theology, see Reichl (forthcoming). Reichl doubts the success of Kant’s response in the Prolegomena to Hume’s attack on analogical reasoning. He argues that only the more developed account in the Critique of Judgement adequately meets Hume’s challenge. 28  Matherne’s generally helpful discussion of Kant’s theory of analogy does not in my view adequately distinguish between the similarity conception of analogy, which Kant discusses in the logic lecture notes, and the proportionality conception, which he opposes to it. See particularly Matherne 2021, 220. Callanan (2008, 751–2) insists on the distinction, but he then blurs it by claiming that Kant’s analogies of proportion, like analogies of similarity, aim at “the inference of unknown properties” (Callanan 2008, 753). As I argued in the previous paragraph, analogies of proportion do not permit inferences about properties but only about relations. 26

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

259

Kant 1998, 447; see also 24:287, 24:772, 9:133). An analogy of similarity simply infers that, if two things (of the same genus) agree in many respects, they will agree in the others.29 Kant adds: “That really does not hold, but what else are we to do?” (Kant 1992, 409, Kant 1998, 448). Analogies of similarity are often sources of error, but they can help us to extend our cognition to things we do not perceive. Such analogies are thus a “crutch for the human understanding” (Kant 1992, 409, Kant 1998, 448, see also 24:777). They yield merely probable claims that must be validated empirically; the more properties we know, the more probable the analogical inference. But they never provide apodictic certainty.30 As the Jäsche Logik has it: “inferences of the power of judgement are useful and indispensable for the sake of extending our empirical cognition [Erfahrungserkenntniss]. But since they give only empirical certainty, we must make use of them with caution and care” (9:133, see also 24:287, 24:772). By affirming that analogies of similarity can be helpful for empirical investigation while warning that they are fallible, Kant echoes the traditional position of Bacon and Locke. Kant’s proportional conception of analogy, by contrast, differs from the Baconian and Lockean conceptions, as John Callanan points out (Callanan 2008, 750–1). In fact, as indicated by his reference to the way that “the word is usually taken”, Kant here diverges from the mainstream early modern view. As we have seen, Newton, Leibniz, and Buffon, like Bacon and Locke, consider ‘analogy’ to designate a similarity between two things. Meier does likewise, but considers analogy to be a source of error rather than a helpful scientific method. Kant rejects the similarity conception of analogy common to all these predecessors. It may be Meier’s kind of challenge to the similarity conception – which is also the conception that Kant takes Hume to have criticized in the Dialogues31 – that spurred Kant to advocate an alternative, proportional conception of analogy. Kant thus rejects analogies of similarity and affirms analogies of proportion in the critical period (if not before). But where does Kant’s proportional conception of analogy come from? Callanan provides a helpful guiding thread for further investigation when he points out that Kant’s proportionality interpretation of analogy closely resembles the ancient Greek account of analogy. Noting the “striking resemblance” between the Kantian and Greek theories, Callanan adds that “Kant’s knowledge of Aristotle, or indeed of many medieval philosophers (especially, perhaps, Aquinas), may well have made him familiar with this interpretation” of analogy as a proportionality of concepts (Callanan 2008, 752n18).32 Another route through

 We shall return to Kant’s point that the two things should be species of the same genus.  As this point is put in one of the logic lecture transcripts: “no proposition of experience gives us universitas simpliciter, but only secundum quid, as far as we are acquainted” (24:777). 31  On Hume’s critique and whether the standard interpretation – that Hume criticizes the similarity conception of analogy in the Dialogues – actually holds, see again Reichl (forthcoming). 32  Wood (1978, 86–8, 86-7n97) notes that the Thomistic tradition makes a distinction between the “analogy of attribution” and the “analogy of proportion”. 29 30

260

S. Howard

which the Aristotelean conception of proportional analogy could have reached Kant is via the use of proportion, or ratio, in mathematics.33 Mary Hesse has shown that we find in Aristotle both the similarity and the proportionality conceptions of analogy. The spine of a fish and the bone of an animal are analogous in the sense of similar, in that they share properties in common, namely an “osseus nature” (Post. An. 98a, quoted in Hesse 1965, 329). But Aristotle also uses the proportional sense of analogy when he asserts that the relation of Dionysus to his cup is the same as that of Ares to his shield (Poetics 1457b, quoted in Hesse 1965, 330). That is, the cup and the shield can be said to stand in the same functional relation to their bearers: for example, they offer protection, or they define or symbolize the bearer. In the Topics, Aristotle clearly states a conception of analogy as a four-fold proportion of concepts according to the formula, A : B = C : D.34 Hesse notes that both senses of analogy can apply at once, so we could take our example of an analogy of similarity and express it in proportional terms (spine : fish = bone : animal) (1965, 330–1). In this case, the equivalent relation would be, for example, the structural support that both the spine and the bone provide. This possibility of applying both kinds of analogies at once does not undermine their difference. We shall see that this dual applicability of the two kinds of analogy causes some difficulties in interpreting Kant’s principal analogy in the Universal Natural History. It is to these two Aristotelean senses of analogy that Kant apparently refers when he distinguishes between the similarity and proportionality conceptions. And it now becomes clearer that, whereas Kant’s early modern predecessors exclusively discussed analogies of similarity, Kant rehabilitates analogies of proportion, an aspect of Aristotle’s theory of analogy seemingly forgotten by many early moderns (or perhaps dismissed as a remnant of scholastic hair-splitting), except in mathematics. We might recall Kant’s famous comment about the science of logic: “since the time of Aristotle” it has neither taken a step back nor forward and it thus “seems to all appearance to be finished and complete” (Bviii). Kant’s theory of analogy goes back to its source in Aristotelean logic. Pavel Reichl has recently argued that Kant sets out a yet more nuanced theory of analogy in the Critique of Judgement (Reichl forthcoming). When discussing the moral argument for the existence of God late in the Critique of Teleological Judgement, Kant makes two new distinctions, Reichl shows: between legitimate and illegitimate inferences through analogy, and between inferential and non-inferential analogies. Both distinctions can be clarified through an example provided by Kant: an analogy between the activity of beavers when they construct dams and the activity of humans when we build (say, houses). We can legitimately infer through analogy that beavers, like humans, “act in accordance with representations” (5:464n).  As mentioned in note 25, above, Kant refers to this mathematical use of proportional analogy in the Critique (A179-80/B222). It appears in Wolff’s mathematical writings: see Shabel 1998, 611. I thank Fabian Burt for pressing me on this point. 34  Topics 108a7ff, 108b23ff in Aristotle 1941, 204, 206; see Hesse 1965, 330, and Lloyd 1966, 409. 33

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

261

This is because beavers and humans are species of the same genus, namely living beings. However, we cannot legitimately infer that beavers use reason in the way that humans do when constructing things. Why not? Because, Kant claims, rationality constitutes the “specific difference” (5:464) between animals and humans: beavers and humans are differentiated within the genus of living beings in that the former do not have reason and the latter do.35 Regardless of whether we find Kant’s claims about the difference between humans and beavers convincing, the relevant point is that, through this example, Kant proposes a way to distinguish between legitimate and illegitimate analogical inferences about species of a common genus. If the inference concerns the very feature that distinguishes the two species within the genus, it is illegitimate. It is notable that Kant is here using a fourfold analogy of proportion: house  : human = dam : beaver. The ‘unknown thing’ here is the beaver, but it is clearly not unknown in the way that God is, because we can observe it. It is rather the mental processes of the beaver that are unknown to us. As in the Prolegomena, it is not a property that is determined through the analogy, but a relation: we legitimately infer that the relation of beavers towards their dams is that of acting according to representations. In this case, the analogy allows us to infer something about a thing that we can cognise, in this case the beaver, even if we do not cognise the inferred relation of acting according to representations, hence the need for the analogy.36 Kant then adds his second new distinction: between inferential analogies, such the previous example, and non-inferential analogies, in which the unknown thing is supersensible. In the footnote in the third Critique, Kant insists that we cannot infer that God possesses human properties because humans and God are not species of a common genus (5:464n). As Kant puts it in a note in the Religion, cited by Reichl: we can “in no way infer that what pertains to the sensible must also be attributed to the supersensible” (6:65n). On Reichl’s reading, when we make analogical claims about supersensible things like God, we need to already know, through an independent proof, that the relation in question holds. In the case of God, the moral argument for the existence of God already warrants the claim that God is the ground of the world. The clockmaker analogy would thus provide no new determination, but merely a new sensible representation of a relation that we already know on different grounds.37  In Kant’s terminology, in the case of the legitimate inference there is par ratio (equal reason) for ascribing the property to the two species, whereas in the case of the illegitimate inference there is not par ratio (5:464n). 36  A cosmological rough equivalent of the beaver example appears in Kant’s annotations on Meier’s Auszug (see note 39) and the logic lecture notes: Kant suggests that we can infer through analogy, in line with the par ratio constraint, that the inhabitants of the moon are rational beings, but not that they are humans (R3292, 16:760; 9:133; see also R3285, 16:758). 37  Matherne (2021, 220, 230) calls such sensible representation the ‘aesthetic’ function of analogy. I take my account here (drawn from Reichl) to be broadly in agreement with Matherne’s. However, I would not follow her claim that the sensible representation in this kind of analogy “makes the idea of God more concrete to us” (Matherne 2021, 230). Rather, I think that Kant takes it to make the relation between God and the world more concrete to us: see again 4:359.

35

262

S. Howard

So, to conclude this section, we can distinguish three conceptions of analogy in Kant’s critical-period works and notes38: Similarity: If two things of the same genus agree in the determinations with which we are acquainted, we infer that they agree in all determinations. This use of analogy often leads to error and so the inferences must be validated empirically. ProportionalityE (empirical): A four-fold proportional analogy. From a known relation between two known things, we make an inference about an unknown relation between another two known things. The subjects on each side of the analogy are members of the same genus. For example: house : human = dam : beaver. ProportionalitySS (supersensible): A four-fold proportional analogy. From a known relation between two known things, we can have a new sensible representation of a previously known relation between a known thing and an unknowable thing. The subjects on each side of the analogy are members of different genera, because the unknowable thing is supersensible. For example: clock  : clockmaker = world : God.

11.5 Kant’s Cosmological Analogy We can now return to Kant’s principal analogy in the Universal Natural History in the light of the findings of the previous two sections. Recall Kant’s description of the analogy: we may use the analogy of what has been observed in the orbits of our solar system, namely that the same cause that has imparted centrifugal force to the planets, as a result of which they describe their orbits, has also arranged them in such a way that they all relate to one plane, which is therefore also the cause, whatever it may be, that what has given the power of rotation to the suns of the upper world, as so many moving stars of higher orders of worlds, has, at the same time, brought their orbits into one plane as much as possible and striven to limit deviations therefrom. (1:250)

Of the three conceptions of analogy just discussed, which is at work here? One could justifiably claim that Kant’s principal analogy in 1755 is an analogy of similarity. On the basis of an observed partial similarity between the solar system and the stellar system, we would infer that the systems are completely similar. There are different options for how this analogy could work. One option begins from the observations that suggest the Milky Way is, like our solar system, arranged on a common plane. From this partial similarity we infer that the two systems are completely similar and so the stellar system, like the solar system, rotates around a central point. A further inference could then be the nebular hypothesis: the stellar system, like the solar system, formed out of eddies in primordial matter. A second option would begin from, rather than arrive at, the nebular hypothesis. This reading  On my use of ‘knowledge’ in these definitions, see note 24 above. Matherne (2021, 218–19) also makes the distinction that I draw here between two types of analogy of proportion, calling them “qualitatively sensible” and “qualitatively mixed” analogies. 38

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

263

is encouraged by the reference to the “same cause” of both systems in the passage just cited (and see again 1:251). This cause, common to both the solar system and the stellar system, is described in Kant’s nebular hypothesis and is ultimately the fundamental forces of attraction and repulsion. The analogy would thus claim that, because our solar system and the stellar system have a common cause in the fundamental forces of matter that first formed bodies, both systems have the same structure: circular rotations of bodies on a common plane around a central point. Both of these interpretations are based on the uniformity of nature that we have seen affirmed by Newton, Leibniz and Buffon. This is particularly clear in the case of the second option. Support for this reading can be found in one of Kant’s annotations on Meier’s Auszug.39 A note that Adickes dates to the early to mid-1750s, the period of Kant’s work on the Universal Natural History, states: “The planets attract each other, therefore all heavenly bodies” (R3275, 16:753).40 The note echoes the example that Newton gives in his third rule, discussed above: if experiments and observations show that bodies on earth, the moon, the planets, and comets all gravitate towards one another, then we should infer that “all bodies gravitate toward one another” (Newton [1687] 1999, 796). This claim – that we can infer from the particular case of our solar system to the general case of the stellar system, through the analogous character of these different orders of nature – would be an analogy of similarity. The common property identified in the analogy, like the “osseus nature” of the fish’s spine and the animal’s bone in our example from Aristotle, would be the fundamental forces essential to matter throughout its different orders across the entire extension of creation. Kant does of course claim elsewhere in his pre-critical and critical writings that fundamental forces of attraction and repulsion are essential to matter (see 1:476, 4:500, 511, 512, 515). Kant’s presentation in the Universal Natural History certainly permits us to read the principal analogy as one of similarity. But there are also reasons to doubt this interpretation. As an analogy of similarity, Kant’s cosmological analogy would be open to objections that he was aware of and raised himself. As we saw in Sect. 11.4, Kant warns in the logic lectures that the move from partial to total similarity is unjustified if stated a priori; it can only provide a hypothesis to be checked empirically. It is true that Kant states in the Universal Natural History that his claims, because they are based on analogies, do not possess “geometrical acuity and mathematical infallibility” but rather aim only for credibility and internal consistency (1:235). It is left to the “unprejudiced reader” to judge whether its hypotheses are supported by observation (1:234). However, in numerous other passages Kant suggests that his analogical claims have a stronger epistemic status than mere probability (1:263, 277, 306, 334, 335, 339, 341).41 These passages cannot be squared with  Kant heavily annotated his interleaved copy of Meier’s Auszug over the four decades that he taught logic. His notes on the topics of induction and analogy, jotted around §401 and on the facing page, are reproduced in the Academy edition, 16:753–61. 40  Adickes dates the note to phase ‘β1’, between 1752 and the winter semester 1755/56. According to Adickes’ dating, this is the earliest of Kant’s annotations on Meier’s §401. 41  These statements concern his cosmogony: see Adickes 1925, 243. We can note in passing that the statements entail that ‘nebular hypothesis’ is, strictly speaking, a misnomer: Kant claims that his 39

264

S. Howard

an interpretation of the principal analogy as one of similarity and so a mere hypothesis. More importantly, if the analogy of similarity is supposed to be based on the uniformity of nature, it is open to strong objections. The difficulty is how to determine that the solar system and the stellar system are constituted of bodies that are species of the same genus, as would be necessary for the analogical inference. If we lack sure grounds to claim that the planets of the solar system and the stars of the stellar system fall under the same genus, the inference from the analogy of similarity would be open to Meier’s criticism that it illegitimately moves between different genera. The analogy of similarity would be like the inference criticized in Kant’s logic textbook: “humans can sin; therefore the holy angels can also sin”. Given these objections, we can consider whether Kant may be conceiving of his principal analogy in 1755 as one of proportion. In line with the definition in the Prolegomena, such an analogy would identify precisely similar relations between two entirely different things. If the analogy is of the type proportionalityE, then the solar and stellar systems are both known empirically. This is a feasible reading because, as seen in Sect. 11.2, Kant claims that the knowledge of the Milky Way with which he begins can be gained by looking up at “the sky full of stars on a clear night” (1:248). In this case, the analogy would permit an inference about a relation that we did not previously know. Following the fourfold form, the analogy would propose that planets : sun = stars : central point. The relation that we can newly infer between the stars and the central point of the stellar system, on analogy with the planets and the central point of the solar system, is that of orbiting on a common plane. This, we recall, is how Kant defines systematicity in the narrow sense (1:246). Three concerns come to mind about this proportionalityE interpretation of Kant’s analogy, although I do not think any undermine it. First, it is not a problem for the analogy that our sun appears in both the first and the second pairing, because, in the first, it is the central point of a system around which the planets orbit, whereas in the second it is one of the bodies orbiting a different central point. We are concerned with two different systems, but these share a common “systematic constitution”, in Kant’s terms, that is determined through the analogy. Second, it may seem that this analogy differs from Kant’s beaver example in that one of the items, the central point of the stellar system, can only be conjectured (as we saw above, Kant tentatively proposes this could be Sirius (1:328-9n)). But Kant could respond that the precise location of the central point is not important for his analogy, which of course only concerns the relations between the items. What matters is only that there is such a central point and that it would be located in the observable universe, and so it is of the same genus as the sun. Third, and related to the previous response, one could argue that the objection I raised against the similarity interpretation of Kant’s analogy can also be levelled against the proportionalityE interpretation: we have no guarantee that the planets

theory of the formation of the universe possesses “an excellent kind of approval that elevates it above the appearance of a hypothesis” (1:263).

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

265

and the stars are species of the same genus, as seemingly required in the proportionalityE analogy. I think that Kant could reply that genera-species relations play a different role in these two types of analogy: unlike the similarity interpretation, the proportionalityE interpretation is not grounded on the uniformity of nature (i.e., on the claim that all heavenly bodies belong to a single genus). Kant mentions genera-­ species relations in his discussion of proportionalityE analogies in order to provide a caveat: the equal relations inferred through the analogy must not pertain to the very feature that differentiates the species. Now, one could assert that the ‘specific difference’ between planets and stars is that planets orbit stars: the former are in motion and the latter are fixed, and so the proportionalityE analogy here leads to an illegitimate inference. But I do not believe that Kant would agree with this conception of the specific difference between these species of heavenly bodies. Rather, Kant’s notes in his copy of Meier suggest that he takes stars and planets to be differentiated by whether they emit light or are “dark bodies” (R3286, 16:758–9, R3290, 16:760). On the proportionalityE interpretation, then, Kant’s principal analogy concerns four empirically observable items (even if we cannot be sure we have observed one of them, the central point of the stellar system), and it permits an inference about two equivalent relations. The inference is, firstly, spatial: the planets and the stars alike are arranged in circular orbits on common planes around central points. Secondly, the inference is causal: the orbital motions in both the ‘lower’ and ‘higher’ systems are governed by the fundamental Newtonian forces of attraction and repulsion. This interpretation of the principal analogy can make sense of many of Kant’s claims in the Universal Natural History. It is also possible, however, to read the analogy as being of the type proportionalitySS. In this case, the subject of the relation that the analogy should clarify is not the visible stars but the entirety of the universe. This is no longer an object of possible experience but what Kant will later call an idea of reason: the world-whole or the totality of appearances as a completed synthesis. Here we wilfully introduce terminology and distinctions that Kant only introduces in the critical period. As is well known, the rigorous distinction between concepts of the understanding and ideas of reason is not even present in Kant’s 1770 Dissertation; it is a major innovation of the first Critique. This said, passages in the Universal Natural History do indicate a distinction between the observable universe and the unobservable infinite totality of the universe. In the seventh chapter of the treatise, Kant explicitly moves to the latter level. He notes the shift in the Preface: If, therefore, in the seventh chapter, enticed by the fruitfulness of the system and the attractiveness of the greatest and most admirable thing we are capable of imagining, and while adhering to the thread of analogy and a reasonable credibility, I extend the results of our doctrine as far as possible; if I represent the infinite nature of all creation, the formation of new worlds and the decline of the old ones and the unlimited realm of the chaos of the imagination: I hope the reader will grant the charming attractiveness of the object and the pleasure one experiences in seeing the agreement of a theory in its greatest extension, sufficient consideration so as not to judge it according to the greatest geometrical strictness, which does not in any case have any relevance in this type of consideration. (1:235–6)

266

S. Howard

Chapter 7 thus extends the analogical reasoning “as far as possible” to “the infinite nature of all creation”. In the chapter, Kant proposes, in a wonderfully mind-­ expanding image, that “We do not come any closer to the infinitude of God’s creative power if we enclose the space of its revelation within a sphere described by the radius of the Milky Way than if we were to limit it to a ball of one inch diameter” (1:309). Compared to the infinite extent of the universe, the Milky Way – the subject of the proportionalityE analogy – is as inadequate a measure as if it were a golf ball. In the above passage from the Preface and in chapter 7, Kant acknowledges that he is spurred by the “pleasure” of maximally extending his theory (1:315). He recognizes that it may be considered “reprehensible boldness” to put forward suggestions that are not immune from the “objection of unprovability [Unerweislichkeit]” (1:315). The assertions in chapter 7 are beyond empirical proof because they concern the universe in the infinity of time and space, which, as Kant seems to already hold in 1755, is no object of experience. He goes on to state that, regardless of these objections: I do, however, expect from those who are in a position to appreciate degrees of probability that such a map of infinity, even though it encompasses a proposal that appears to be determined to remain forever obscured from human understanding, will not immediately be regarded as a fantasy for this reason, especially if one appeals to analogy, which must always guide us in such cases where understanding lacks the thread of infallible proofs. (1:315)

Although cognition of the infinite extent of the universe seems to exceed our capacities, Kant suggests that analogy can guide us in these realms beyond perception. He thus appeals to the reader who can “appreciate degrees of probability”.42 Moreover, he adds, “analogy can also be supported by acceptable reasons” (1:315). I take Kant here to anticipate what will later be a key characteristic of proportionalitySS analogies. As with the example of God in Kant’s fully-fledged theory, discussed above, a proportionalitySS analogy allows one to picture, in a new way, a relation that (on independent grounds) one already knows, which pertains to a supersensible thing – here, the universe in its infinite extent. The ‘acceptable reasons’ that Kant mentions can be understood as such independent grounds that warrant accepting his analogical claims about the infinite entirety of the universe. Kant suggests that these independent ‘acceptable reasons’ relate to the “constancy [Beständigkeit] … of creation”. More specifically, one should take up the nebular hypothesis (“the concept of the formation of the celestial bodies out of the  In the extracts from the Universal Natural History published in 1791 by Gensichen as an appendix to a translation of essays by William Herschel, which Kant authorized, nothing from chapter 7 is included. Gensichen explains his omissions at the end of his extracts: “This is now the essential part of the Natural History and Theory of the Heavens, which Herr Professor Kant allowed himself to be induced to now present once more to the public. The rest, he says, contains too much mere hypothesis for him to now still be able to completely endorse it” (Herschel 1791, 201). Arguably, this does not indicate any change in Kant’s view since he wrote the 1755 Preface, because in the latter he begged the reader’s indulgence for the more speculative character of chapter 7. The 1791 selection may not indicate that Kant had come to definitively reject the parts that were not included, but only that he selected what he had long thought were the more credible parts. 42

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

267

dispersed elementary matter, as we have outlined above”), but as long as one “does not restrict it here to a particular system, but rather extends it over the whole of nature” (1:316). I propose that Kant is here indicating that his proportionalitySS analogy about the infinite extent of the universe is warranted by our knowledge of the uniformity of nature, which stems from the common origin of all matter in the scene described by the nebular hypothesis  – including matter that we can never perceive. The warrant for accepting the analogy could be said to be the view that underpins the analogical reasoning of Newton and Buffon: that nature is thoroughly self-consistent. Or, more specifically, the warrant would be the two fundamental forces of matter that, Kant writes, are “equally original and universal”, both of which have been “borrowed from Newtonian philosophy” (1:234). It is unlikely that in 1755 Kant thought that the Newtonians had provided the necessary independent argument that these forces are essential to matter, because in the Physical Monadology of the following year he sought to provide such an argument himself (see 1:476). The important point for our purposes is that there should be an independent warrant, so the proportionalitySS analogy provides merely a new way of viewing a relation that is known on other grounds. In its fourfold form, the proportionalitySS analogy would be planets : sun = infinite universe : central point.43 The analogy allows us to represent to ourselves this relation, even though it concerns an unperceivable thing, the entirety of the infinite universe. It is striking that the proportionalitySS interpretation of Kant’s cosmological analogy here converges with the similarity interpretation. Both presuppose the uniformity of nature. But the proportionalitySS interpretation avoids the kind of objection that Kant knew from Meier’s Auszug, because it is not grounded on the a priori assumption that all the celestial bodies are of the same genus. This is because the analogy would be a fourfold analogy of proportion that only provides a new way of viewing a relation between a supersensible thing (the world-whole) and a sensible thing (the central point of the system of all the higher orders of worlds). Our knowledge of this relation would be warranted not through the analogy but by an independent argument that the fundamental forces are essential to matter.

 The analogical claim is particularly clear in this passage: “Millions and whole mountain ranges of millions of centuries will pass within which ever new worlds and world-orders will form and attain completion one after another in the remote distances from the centre point of nature; regardless of the systematic constitution among its parts, they will attain a universal relationship to the centre point that has become the first point of formation and the centre of creation by the attractive capacity of its pre-eminent mass” (1:314). Two pages earlier, Kant acknowledges and tries to address the difficulty of the very notion of the central point of an infinite space: this central point could not be determined geometrically, as it were by measuring from the outer edges of the space (because the space extends infinitely); rather, it is the point of highest density in the initial formation of the universe, which continues to hold the strongest attractive force across the universe (1:312). 43

268

S. Howard

11.6 Conclusion Which conception of analogy is Kant employing in the principal analogy of the Universal Natural History? In my view, cases can be made for all three. It seems least likely, however, that Kant intended his analogy to be a straightforward analogy of similarity. In the mid-1750s, Kant would have been aware of his textbook author Meier’s criticisms of analogies that simply inferred from partial similarity between things to their complete similarity. Indeed, he repeated these criticisms in the logic lectures, and in the Prolegomena he carefully distinguished his proportional conception of analogy, rehabilitated from the Aristotelean tradition, from the similarity conception that prevailed among his early modern predecessors. It seems more likely, then, that in 1755 Kant already has in mind, even if vaguely, a fourfold analogy of proportion. I have proposed that the largest part of the Universal Natural History employs an analogy of proportionalityE, in which all the elements are known empirically and we can infer a relation between the system of stars constituted by the Milky Way and a posited central point around which they orbit. But Kant’s avowedly speculative seventh chapter seems to develop an analogy of proportionalitySS, in which one element is what Kant will later call supersensible: the universe in its infinite extent. I have aimed to show that it is possible to reconstruct this analogy in a way that is consistent with Kant’s analogical claims about another supersensible thing, God, in his fullyfledged later theory of analogy. On this reading, Kant’s analogy of proportionalitySS in the Universal Natural History is based on an independent argument for the uniformity of nature, which results from the fundamental forces that are essential to matter. Our interpretation indicates that there may be previously unnoticed continuities between Kant’s use of analogy in 1755 and in the critical period, even if he only articulates his theory of analogy in the later writings. It also suggests that, when Kant distinguishes his speculative seventh chapter from the rest of the Universal Natural History, we find an early iteration of the critical distinction between nature, the legitimate object of physical science, and the world-whole, the dialectical object of rational cosmology. Intriguingly, in 1755 Kant seems to have considered the analogical method to be capable of producing insights into the universe as an infinite whole, or what he would later call a supersensible thing. The development of Kant’s views on the status of analogical claims about different supersensible objects  – God, the world, and the soul  – is, I think, a topic worthy of further attention.44

 I thank Fabian Burt, Andrew Cooper, and Pavel Reichl for their insightful comments on earlier drafts of this chapter. Wolfgang Lefèvre provided helpful advice at an early stage. The research was conducted while I was a visiting scholar in the Early Modern Cosmology group at Ca′ Foscari University of Venice: my thanks to Pietro Omodeo and his group for their feedback. I gratefully acknowledge the support of the Research Foundation – Flanders (FWO). 44

11 Kant’s Universal Natural History and Analogical Reasoning in Cosmology

269

References Adickes, Erich. 1925. Kant als Naturforscher. Vol. 2. Berlin: de Gruyter. Aristotle. 1941. The Basic Works of Aristotle, ed. Richard McKeon. New York: Random House. Bacon, Francis. [1620] 2000. The New Organon. Ed. Lisa Jardine and Michael Silverthorne. Cambridge: Cambridge University Press. Blumenberg, Hans. 1987. The Genesis of the Copernican World. Trans. Robert M.  Wallace. Cambridge, MA.: MIT Press. Buffon, Georges. 1749. Historie Naturelle, Générale et Particuliere, Avec la Description du Cabinet du Roy. In Tome Premier. Paris: Imprimerie Royale. Burt, Fabian, and Thomas Sturm. Forthcoming. Kant’s Early Cosmology, Systematicity, and Changes in the Standpoint of the Observer. In Kant and the Systematicity of the Sciences, ed. Thomas Sturm, Gabriele Gava, and Achim Vesper. London: Routledge. Cooper, Andrew. 2020. Kant’s Universal Conception of Natural History. Studies in History and Philosophy of Science 79: 77–86. Falkenburg, Brigitte. 2000. Kants Kosmologie. Die wissenschaftliche Revolution der Naturphilosophie im 18. Jahrhundert. Frankfurt am Main: Klostermann. Ferrini, Cinzia. 2000. Testing the Limits of Mechanical Explanation in Kant’s Pre-critical Writings. Archiv für Geschichte der Philosophie 82 (3): 297–331. ———. 2004. Heavenly Bodies, Crystals, and Organisms: The Key Role of Chemical Affinity in Kant’s Critical Cosmogony. In Eredità kantiane (1804–2004): Questioni emergent e problemi irrisolti, ed. Cinzia Ferrini, 277–317. Naples: Bibliopolis. ———. 2022. A “Physiogony” of the Heavens: Kant’s Early View of Universal Natural History. HOPOS. The Journal of the International Society for the History of Philosophy of Science 12 (1): 261–285. Herschel, William. 1791. Über den Bau des Himmels. Drey Abhandlungen aus dem Englischen übersetzt. Nebst einem authentischen Auszug aus Kants allgemeiner Naturgeschichte und Theorie des Himmels, ed. and trans. Johann Friedrich Gensichen. Königsberg: Nicolovius. Hesse, Mary. 1965. Aristotle’s Logic of Analogy. The Philosophical Quarterly 15 (61): 328–340. Jaki, Stanley L. 1977. Planets and Planetarians: A History of Theories of the Origin of Planetary Systems. New York: Wiley. Jaki, Stanley L. 1981. Introduction and Notes in Kant [1755] 1981, 1–76, 209–297. Kant, Immanuel. 1902. Kants Gesammelte Schriften, herausgegeben von der Deutschen Akademie der Wissenschaften. Berlin: De Gruyter. ———. [1755] 1968. Kant’s Cosmogony. Trans. William Hastie, ed. Willy Ley. New  York: Greenwood. ———. [1755] 1969. Universal Natural History and Theory of the Heavens. Trans. William Hastie. Ann Arbor: University of Michigan Press. ———. [1755] 1971. Allgemeine Naturgeschichte und Theorie des Himmels, ed. Fritz Krafft. München: Kindler. ———. [1755] 1981. Universal Natural History and Theory of the Heavens, Trans. Stanley L. Jaki. Edinburgh: Scottish Academic Press. ———. [1755] 1984. Histoire générale de la nature et théorie du ciel, ed. and trans. Pierre Kerszberg, Anne-Marie Roviello and Jean Seidengart. Paris: Vrin. ———. 1992. Lectures on Logic, ed. J. Michael Young. Cambridge: Cambridge University Press. ———. 1998. Logik-Vorlesung. Unveröffentlichte Nachschriften II.  Logik Hechsel, Warschauer Logik, ed. Tillmann Pinder. Hamburg: Meiner. ———. [1755] 2012. Universal Natural History and Theory of the Heavens or Essay on the Constitution and the Mechanical Origin of the Whole Universe According to Newtonian Principles. In Kant, Natural Science, ed. Eric Watkins and trans. Olaf Reinhardt. Cambridge: Cambridge University Press. Kerszberg, Pierre. 1984. Post-face. In Kant [1755] 1984, 205–59. Lalla, Sebastian. 2003. Kants “Allgemeine Naturgeschichte und Theorie des Himmels” (1755). Kant-Studien 94: 426–453.

270

S. Howard

Lambert, Johann Heinrich. 1761. Cosmologische Briefe über die Einrichtung des Weltbaues. Augsburg: Eberhard Kletts Wittiv. Lloyd, G.E.R. 1966. Polarity and Analogy: Two Types of Argumentation in Early Greek Thought. Cambridge: Cambridge University Press. Locke, John. [1689] 1976. An Essay Concerning Human Understanding. A. D. Woozley. London: Fontana. Marty, François. 1980. La naissance de la métaphysique chez Kant. Une étude sur la notion kantienne d’analogie. Paris: Beauchesne. Massimi, Michela. 2011. Kant’s Dynamical Theory of Matter in 1755, and its Debt to Speculative Newtonian Experimentalism. Studies in History and Philosophy of Science 42: 525–543. Matherne, Samantha. 2021. Cognition by Analogy and the Possibility of Metaphysics. In Kant’s Prolegomena: A Critical Guide, ed. Peter Thielke, 215–234. Cambridge: Cambridge University Press. Maupertuis, Pierre Louis de. 1750. Essai de cosmologie. Berlin. Meier, Georg Friedrich. 1752a. Vernunftlehre. Halle: Johann Justinus Gebauer. ———. 1752b. Auszug aus der Vernunftlehre. Halle: Johann Justinus Gebauer. Naragon, Steve. 2006. Kant’s Lectures by Discipline: Logic. Kant in the Classroom. https://users. manchester.edu/facstaff/ssnaragon/kant/Lectures/lecturesListDiscipline.htm#logic. Accessed 15 April 2022. Newton, Isaac. [1687] 1999. The Principia: Mathematical Principles of Natural Philosophy: A New Translation, Trans. I. B. Cohen and Anne Whitman. Berkeley: University of California Press, 1999. Prunea-Bretonnet, Tinca. 2017. Newton et la cosmologie Kantienne en 1755. In Kant et les penseurs de langue anglaise, ed. Sophie Grapotte, Mai Lequan, and Lukas Sosoe, 83–94. Paris: Vrin. ———. 2019. From the Folds of the Rhino to the ‘Hand of Nature’: Maupertuis’s Essay on Cosmology and its Reception in the 1750s. Archivio di Filosofia 87 (1): 75–90. Reichl, Pavel. Forthcoming. Kant’s Response to Hume on Natural Theology: Dogmatic Anthropomorphism, Analogical Inference, and Symbolic Representation. Journal of the History of Philosophy. Schönfeld, Martin. 2000. The Philosophy of the Young Kant: The Precritical Project. Oxford: Oxford University Press. ———. 2010. Kant’s Early Cosmology. In A Companion to Kant, ed. Graham Bird, 47–62. Oxford: Blackwell. Shabel, Lisa. 1998. Kant on the ‘Symbolic Construction’ of Mathematical Concepts. Studies in History and Philosophy of Science 29 (4): 589–621. Shea, William R. 1986. Filled with Wonder: Kant’s Cosmological Essay, the Universal Natural History and Theory of the Heavens. In Kant’s Philosophy of Physical Science, ed. Robert E. Butts, 95–126. Dordrecht: D. Reidel. Sticker, Bernhard. 1969. Naturam cognosci per  analogiam. Das Prinzip der Analogie in der Naturforschung bei Leibniz. In Akten des Internationales Leibniz-Kongresses, Hannover, 14.–19. November 1966, vol. 2nd, 176–196. Wiesbaden: F. Steiner. Theis, Robert. 2011. La physico-théologie du jeune Kant. Avec Wolff, au-delà de Wolff. In Kant et Wolff: Héritages et ruptures, ed. Sophie Grapotte and Tinca Prunea-Bretonnet, 31–42. Paris: Vrin. Waschkies, Hans-Joachim. 1987. Physik und Physikotheologie des jungen Kant. Amsterdam: Grüner. Watkins, Eric. 2013. The Early Kant’s (Anti-) Newtonianism. Studies in History and Philosophy of Science 44: 429–437. Willaschek, Marcus, and Eric Watkins. 2020. Kant on Cognition and Knowledge. Synthese 197: 3195–3213. Wolff, Christian. [1723] 1981. Vernünfftige Gedancken von den Würckungen der Natur. In Gesammelte Werke. 1.6. Hildesheim: Olms. Wood, Allen W. 1978. Kant’s Rational Theology. Ithaca, N.Y: Cornell University Press.

Chapter 12

Natural or Artificial Systems? The Eighteenth-Century Controversy on Classification of Animals and Plants and Its Philosophical Contexts Wolfgang Lefèvre Abstract  Botanical and zoological systematics in the early modern period – from Cesalpino in the sixteenth century to Linnaeus and Jussieu in the eighteenth century – was a two-faced and latently contradictory enterprise: It was, on the one hand, an empirical naturalistic science and, on the other hand, aligned with metaphysical principles concerning the order of natural things which form, according to these principles, a continuous chain of beings and a scala naturae, arranged according to degrees of their perfection. According to these principles, and especially according to that of continuity, no botanical or zoological classificatory system could establish anything but an artificial and unnatural order of plants and animals. The chapter illuminates these contradictions and tensions and traces the development of biological insights that eventually, at the turn of the eighteenth century, led systematists to renounce these metaphysical principles.

12.1 Eighteenth-Century Classification as a Double-Faced Enterprise Natural classification or how to devise a natural system of classification was a prominent subject of controversy among naturalists of the eighteenth century. Classificatory work itself was one of the most important occupations of the naturalists of the time among whom we encounter such famous figures as Carl Linnaeus (1707–1778), Georges-Louis Leclerc Buffon (1707–1788), Michel Adanson (1727–1806), Antoin Laurent Jussieu (1748–1836), and Jean Baptiste Lamarck (1744–1829). Though every new botanical and zoological system was dismissed W. Lefèvre (*) Wissenschaftsgeschichte, Max Planck Institute for the History of Science, Berlin, Berlin, Germany e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_12

271

272

W. Lefèvre

upon further biological1 insight, biologists and historians of biology take the classificatory efforts of these men to be crucial steps on the way towards modern taxonomy. How much eighteenth-century classificatory principles are still part of present thinking in biology is shown by the frequency with which eighteenth-­ century naturalists are invoked as forerunners of modern convictions or as original sources of combatted doctrines in today’s controversies on various topics of biological systematics.2 There are, however, also historians of biology who warn not to mistake naturalistic classification of the eighteenth century for taxonomy in the sense of modern biology. “I want to support the contention,” wrote for instance Vernon Pratt, that when historians regard eighteenth-century system-building as biology, or even taxonomy, in an early stage of development, they are guilty of anachronism, but not on the grounds that the eighteenth-century order of nature is different from our own. Their radical mistake, in my view, lies in their assumption that the interest taken in that order in the eighteenth century was the same as the interest we take in it today. The two perspectives are in fact quite different. For modern biology the order of nature is by no means the principal topic of study. We are today concerned primarily with understanding the workings of organisms, and how these relate to their environments. Taxonomy is a secondary discipline, subservient to these objectives. It is from this perspective that the classical concentration on taxonomy is seen as ‘obsessive’. (Pratt, System-Building, 429f.)

Many points of this statement deserve closer consideration, and I will come back to some of them at the end of this chapter. Presently I want to take up the last phrase – taxonomy as an obsession. Indeed, one can contend that the idea of classification dominated the thinking of the eighteenth century (or at least of its second half) like an obsession. Large amounts of energy were spent on classification and system-building, not only in botany and zoology, but also in mineralogy and crystallography, in chemistry, in astronomy, and even in the humanities (Lesch, Systematics). Behind this stood a spirit affected by an intense fondness for assessing the things around us by measure and number and for developing clear and consistent nomenclatures in order to give unambiguous and ever-lasting names to each individual item. Measure and number, classificatory systems, nomenclature – they all seem to be different aspects of the same principal custom to order and arrange the whole world according to logical principles, a custom characteristic of the late Enlightenment (ibid., 73).

 As is generally known, biology—the word as well as the discipline—was unfamiliar in the eighteenth century. Though exceptionally occurring also then—see, for instance, the title of (Wolff, Philosophiae naturalis)—it was not until the beginning of the nineteenth century that the word became a familiar label, and the discipline gradually emerged only in the second half of that century. For pragmatic reasons, however, I will use the term in this article for all kinds of scientific activities concerned with living beings. 2  To give only two examples without implying any assessment: Advocating a phenetic approach to systematics, Peter H.A.  Sneath discovered Michel Adanson as forerunner of this view (Sneath, Mathematics and classification) while Arthur J. Cain shows the heritage of Linnaeus to be a dangerous one (Cain, Logic and memory). – Of the literature on early modern systematics published after 2001 I would like to point to Wilkins and Ebach (2014), Dietz (2017), and Müller-Wille (2017). 1

12  Natural or Artificial Systems? The Eighteenth-Century Controversy…

273

Michel Foucault tried to understand and describe this ordering and arranging not only as a kind of behaviour peculiar to the “classical age” but as a specific kind of representation of the known and the knowable and expressible which engendered and structured a new type of historia naturalis clearly distinct from that of former times (Foucault, Order of things, ch. 5). True, scientific classification deeply transformed natural history in early modern times, especially by the standardisation of description and depiction associated with this activity (Ogilvie, Image and Text). But it may be doubted whether a portrayal of seventeenth- and eighteenth-century natural history as an embodiment and consequence of a characteristic representational order of the “classical age” enhances our understanding (which, by the way, reminds us of the “Gestalten des Geistes” in Hegel’s Phänomenologie des Geistes). The outcome is statements like this: We must therefore reverse what is usually said on this subject: it is not because there was a great interest in botany during the seventeenth and eighteenth centuries that so much investigation was undertaken into methods of classification. But because it was possible to know and to say only within a taxonomic area of visibility, the knowledge of plants was bound to prove more extensive than that of animals. (Foucault, Order of things, 137)3

What cannot be questioned, however, is the close link between botanical and zoological classifications and general, philosophical conceptions and convictions regarding the possibility of arranging all beings within one single and universal system. These convictions were still very much alive in the eighteenth century even though the Aristotelian theory of classification “which had, up until the eighteenth century, served as the conceptual foundation for all classificatory biology” (Sloan, Locke, 2) was already fading away. There were not only formal or logical conceptions of an universal order but also such that comprehended qualitative understandings of this order which had great bearings especially on natural history. As is well known, the eighteenth century experienced a renaissance of the old philosophical conception of the scala naturae according to which all beings of the universe are ordered in a hierarchical manner – a renaissance which, by laying emphasis on the related and no less old ideas of the universe as a plenum or continuum, transformed the scale into a chain, the great chain of being.4 It is remarkable that these conceptions were revitalised at the turn from the seventeenth to the eighteenth century by both the empiristic and the rationalistic philosophical camps as if to make sure that nobody in the eighteenth century could escape them. There is no doubt that these philosophical ideas exerted deep influence on natural history. With regard to the significance of the principle of continuity for eighteenth-century natural history, Arthur Lovejoy went so far as to state:

 As to “visibility,” I will come briefly back to this topic later in this article.  See still Lovejoy, Great chain of Being. In 1987, the Journal of the History of Ideas published five papers (vol. XLVII/2, pp. 187–264) which reappraise Lovejoy’s work. See also Leathers Kuntz et al., Jacob’s Ladder. 3 4

274

W. Lefèvre

It [sc. the principle of continuity] set naturalists to looking for forms which would fill up the apparently ‘missing links’ in the chain. […] The metaphysical assumption thus furnished a program for scientific research. (Lovejoy, Great chain, 231f.)

But for this to be true, one may add that this scientific research was devoted to a program very different from a today’s scientific program, namely to one of proving that nature is a divine creation or – more secularly or philosophically expressed – that nature possesses a rational order. If the classificatory efforts of the eighteenth century could be taken as being not only embedded in but also being executions of those philosophical ideas, Vernon Pratt would be right in stating that the interest taken in the order of nature by eighteenth-­century system-builders was not the same as that of modern systematists. But it is not true that those botanical and zoological classifications were mere executions of these over-arching philosophical ideas. Otherwise it would be unintelligible why just these classifications led within an interval of less than hundred years to the complete destruction of the great chain of being, first of its linear form, then of the hierarchical meaning of its arrangement, and finally of its continuity (Lefèvre, Entstehung, 200ff.). Classification and system-building in classical natural history appear thus as a double-faced enterprise: on the one side belonging and adhering to philosophical doctrines of the age and, on the other, driven by different forces which finally divorced it from those orientations. Since I assume that the tensions between these two faces can be considered to be tensions between philosophy and science as appearing in eighteenth-century natural history, I will investigate some of their aspects in what follows, thereby focusing on the question of “natural” versus “artificial” classificatory systems.

12.2 Are Systems as Such Unnatural? In 1708, in his Eulogy on the great French botanist and systematist Joseph Pitton de Tournefort (1656–1708), Bernard Fontenelle wrote: This order [sc. of botanical systems] which is so necessary was not established by Nature, who preferred magnificent confusion to the convenience of Physicists, and it is incumbent on them to form, almost despite Nature, an arrangement and a System in Plants. (Fontenelle, Eloge, 11)5

To form a system almost despite Nature – this is how Fontenelle expressed a tension felt by many philosophers and naturalists throughout the eighteenth century. If nature is essentially continuous, if between any two of her forms there are always

 Cet ordre si nécessaire n’a point été établi par la nature, qui | a préféré une confusion magnifique à la commodité des physiciens; et c’est à eux à mettre presque malgré elle de l’arrangement et un système dans les plants. Fontenelle (1825), 188 f. – English translation by Betty E. Spillmann from Jacob, Logic of Life, 47. 5

12  Natural or Artificial Systems? The Eighteenth-Century Controversy…

275

intermediates, how is it then possible for systems with clear-cut borderlines between the taxonomic units to be natural? What here appears to be at variance is the enterprise of natural historical classification and the general natural philosophical idea of the continuous great chain of being which nevertheless belongs to the world of ideas in which this enterprise was embedded in the eighteenth century. Initially, when philosophers like John Locke gave new vigour to the great chain of being, nothing seemed to indicate such a latent conflict. Locke wrote ingenuously that the several Species are linked together, and differ but in almost insensible degrees. (Locke, Essay, III.4.12 447)

And a letter which became famous in the middle of the eighteenth century, because of a dispute whether or not it was a letter of Leibniz,6 shows that one could include even higher taxonomic ranks in the great chain of being picture: All the different classes of beings [différentes classes des Etres] which taken together make up the universe are, in the ideas of God who knows distinctly their essential gradations, only so many ordinates of a single curve so closely united that it would be impossible to place others between any two of them, since that would imply disorder and imperfection. Thus men are linked with the animals, these with the plants and these with the fossils, which in turn merge with those bodies which our senses and our imagination represent to us as absolutely inanimate. And, since the law of continuity requires that when the essential attributes of one being approximate those of another all the properties of the one must likewise gradually approximate those of the other, it is necessary that all the orders of natural beings [tous les ordres des Etres naturels] form but a single chain, in which the various classes [les différentes classes], like so many rings, are so closely linked one to another that it is impossible for the senses or the imagination to determine precisely the point at which one ends and the next begins – all the species [les espèces] which, so to say, lie near to or upon the borderlands being equivocal, and endowed with characters which might equally well be assigned to either of the neighbouring species [espèces voisines].7

But forty years after Fontenelle’s first allusion to a discrepancy between the idea of a continuous nature and classification, Buffon wrote in the opening discourse of his Histoire naturelle: It is necessary to divide the whole under consideration into different classes, apportion these classes into genera, subdivide these genera into species, and to do all this following a principle of arrangement in which there is of necessity an element of arbitrariness. But nature proceeds by unknown gradations, and, consequently, it is impossible to describe her with full accuracy by such divisions, since she passes from one species to another, and often

 The publication of the undated and until then unknown letter in 1753—Appel au public du jugement de l’Académie royale de Berlin sur un fragment de M. de Leibnitz cité par M. Koenig. Leiden 1753—triggered a severe quarrel and even a crisis at the Prussian Academy of Science. See, for instance, Breger, Samuel König and Sect. 2.8 of Hartmut Hecht’s Chap. 2, in this volume. In 1906, the letter was again edited by Ernst Cassirer (Leibniz, HS, II 556ff.—the fourth ed. (1996, I 327ff.) has only the German translation). Though Leibniz himself did not endorse the great chain of being idea—see his critique of Locke’s favor of this idea (Leibniz, GP, V 455)—, actually this idea was going well together with his principle of continuity. It is, therefore, not very surprising that eighteenth-­century philosophers erroneously ascribed this idea to Leibniz—see, for instance, Kant, Kritik der reinen Vernunft, B 696; the passage will be quoted below. 7  Leibniz, HS, II 556ff.; English translation from Lovejoy, Great chain, 144 f. 6

276

W. Lefèvre

from one genus to another, by imperceptible nuances. (Buffon, Manier, 13; Engl. transl. 150)8

What so far perhaps could be considered an inconvenient discrepancy between a practical need and a theoretical conviction was transformed into an open contradiction by Buffon in the same opening discourse: For, in general, the more one augments the number of divisions of the productions of nature [sc. in classification], the more one approaches the truth, since in nature only individuals exist, while genera, orders, and classes only exist in our imagination. (ibid, 38; English transl. 164)9

If only individuals exist in nature, it follows inevitably that no distribution of these individuals into taxonomic units can claim to be natural, or to be anything other than a pragmatic aid and means for our orientation. In the sentence quoted, Buffon, with rhetorical cleverness, literally left open the question of whether species, too, exist only in our imagination – which he didn’t think10 – and suggested at the same time that all taxonomic units without exception are artificial. Charles Bonnet (1720–1793), however, who already had distinguished himself as an naturalist authority on insects in the 1740s (Anderson, Charles Bonnet, 4 f.), didn’t hesitate to draw the obvious conclusion and to utter unequivocally: If there are no cleavages in nature, it is evident that our classifications are not hers. Those which we form are purely nominal, and we should regard them as means relative to our needs and to the limitations of our knowledge. Intelligences higher than ours perhaps recognise between two individuals which we place in the same species more varieties than we discover between two individuals of widely separate genera. Thus these intelligences see in the scale of our world as many steps as there are individuals. (Bonnet, Contemplation, 29)11

The conflict is clear-cut: Classificatory systems cannot do otherwise but represent the realm of beings as consisting of discrete units. Hence their violation of the principle of continuity which was one of the constitutive features of the great chain of being. This notion, on the other hand, when pushed to the extremes, was forced to  […] pour faire un système […] il faut diviser ce tout en différentes classes, partager ces classes en genres, sous-diviser ces genres en espèces, & tout cela suivant un ordre dans lequel il entre nécessairement de l’arbitraire. Mais la Nature marche par des gradations inconnues, & par conséquent elle ne peut pas se prêter totalement à ces divisions, puisqu’elle passe d’une espèce à une autre espèce, & souvent d’un genre à un autre genre, par des nuances imperceptibles […]. Buffon, Manier 150. 9  […] car en général plus on augmentera le nombre des divisions des productions naturelles, plus on approchera du vrai, puisqu’il n’existe réellement dans la nature que des individus, & que les genres, les ordres & les classes n’existent que dans notre imagination. Buffon, Manier 38. 10  Below, I will go into his significant contribution to the development of the concept of species. 11  Mais, si rien ne tranche dans la Nature, il est évident que nos Distributions ne sont pas les siennes. Celles que nous formons sont purement nominales, & nous ne devons les regarder que comme des moyens relatifs à nos besoins & aux bornes de nos connoissances. Des Intelligences qui nous sont supérieures découvrent peut-être entre deux Individus que nous rangeons dans la même Espèce, plus de variétés que nous n’en découvrons entre deux Individus de Genres éloignés. Ainsi ces Intelligences voyent dans l’Echelle de notre Monde autant d’Echellons qu’il y a d’Individus. Bonnet, Contemplation I, 29. English translation from Lovejoy, Great chain, 231. 8

12  Natural or Artificial Systems? The Eighteenth-Century Controversy…

277

deny the existence of units other than individuals in nature and thus also the possibility of systems which can claim to be natural. It is unclear, however, what the opposing forces were: Was it two different philosophical principles taken to be equally necessary for sound natural philosophy – the one being the distinction of all beings according to genus and differentia specifica which formed the basis of naturalistic classification and which can be traced back to antiquity, while the other was the principle of plenitas and continuitas, also of ancient origin? But what was latently or openly at variance with the latter principle was not only another principle but a scientific practice of botanical and zoological classification which preceded the rebirth of the great chain of being by more than a century; that is, if we take, as is usually done, Andrea Cesalpino (1519–1603) to be the founder of biological taxonomy of the early modern period. Whether or not one considers this taxonomy an early stage of our scientific biological taxonomy, it was at any rate a scientific enterprise, a collective, socially supported, and even to some extent already institutionalised activity of gaining knowledge, which cannot be reduced to one of its philosophical principles. This distinction between such socially established practices of systematically gaining knowledge in a specific field and philosophical ideas seems to me to have important bearing on the general question of how to distinguish between philosophy and science or, within a given field of knowledge, between its philosophical and scientific elements. The point is here neither the distinction between an activity and a theory nor between a specific and hence comparatively narrow and a general and therefore overarching kind of thinking. Rather, by keeping in mind that there are not only different ideas and theories but also collectively performed research practices, we gain, at least on principle, the possibility of investigating philosophical ideas themselves in terms of their own consequences. We may ask whether they actually function as working principles in or at least as heuristic principles for a given specific research activity or whether their status is that of a personal conviction with little, if any, consequence for the research enterprise. Relating this to the two philosophical principles considered so far, it is a likely expectation that the great chain of being rather played the role of a heuristic principle in naturalist classification, whereas the Aristotelian principles of classification actually functioned as working principles. But if so, did the latter function in this way as principles of natural philosophy or merely as logical means of classification?

12.3 Method and Form I – Is the Tree of Porphyry Natural? As is well known, in the tradition of Aristotelian philosophies, genus and differentia specifica were not merely logical terms but were also embedded in an epistemological and metaphysical philosophy of the essences. Since there is no doubt that the Aristotelian principles of classification, at least in the beginning of early modern naturalistic classification, namely by Cesalpino, were resumed in this full

278

W. Lefèvre

essentialistic sense (Sloan, Locke, 9ff.), one can expect that these principles were taken by the historical actors to be principles which engendered natural systems. But was that true? The so-called Aristotelian logic of classification consists essentially of a series of dichotomous divisions (dihairesis) into sub-units (tertium non datur). The outcome is the so-called tree of Porphyry with a stem splitting into two, four, and eight branches, etc. This arrangement is that of a nested hierarchy ensuring that no taxon can belong to two different taxa of equal rank. Such systems of complete inclusions are now called encaptic systems. Now the surprising fact is that according to today’s biology a natural system of the kingdoms of plants and animals always has to be encaptic. This is not at all trivial but for two reasons quite remarkable. First, because this is not a consequence of logical structure on classification in principle (other classifications are possible like, for instance, the periodical table of chemical elements). It is remarkable, second, because it is Darwin’s theory of descendance which provides a rationale for why only an encaptic system can be considered a natural one for biological taxa: this system is unique in its ability to represent the phylogenetic relations among them which are today taken to be the natural ones.12 But why then should one have considered the encaptic mode of classification the natural one in the time before Darwin? It seems therefore reasonable to assume that indeed Aristotelian principles might have been decisive for the fact that all camps in the eighteenth-century struggle about a natural system agreed upon its encaptic form. This can be concluded from the almost universal and very swift acceptance of Linnaeus’ binominal system of nomenclature which contains an encaptic structure.13 But how can we bring this seemingly so Aristotelian accord among the camps into harmony with the non-­ Aristotelian view, upon which they also agreed unanimously, namely that the procedure of dichotomous divisions (dihairesis) leads inevitably to artificial classifications? In a certain sense, the latter view may also be called an Aristotelian one. Aristotle was too knowledgeable a naturalist not to see that dihairesis cannot be applied successfully to the realm of living beings. He rejected its application explicitly (Aristotle, Parts of animals, I.2642 b 5ff., esp. 643 b 9ff.). The crucial point, known under the name of Aristotle’s problem, is that one simply cannot select uniformly a single character or structure among plants or animals without producing a highly arbitrary and unnatural dichotomous subdivision that would lump unrelated and tear apart closely related taxa. Full awareness and attention to this crucial problem accompanied the very beginnings of early modern naturalistic classification: it was exactly the claim of Cesalpino to have a solution for Aristotle’s problem. But despite  That does not mean that today’s biologists consider a classificatory system already natural if it represents exactly lineages of descendance of taxa, i.e., if it is a cladistic system—see, for instance, Mayr, Biological Thought, 226ff. 13  To the connection between binominal nomenclature and an encaptic form of systematics in Linnaeus see Müller-Wille, Botanik, part I. 12

12  Natural or Artificial Systems? The Eighteenth-Century Controversy…

279

this contention and similar assertions by other naturalists following Cesalpino, the usual procedure up to the time of Linnaeus was to use more than one single character as fundamentum divisionis and, accordingly, to carry out more than only one dihairesis so that systems of a combinatorial instead of an encaptic structure came about.

12.4 Method and Form II – Method Versus System By contrasting “method” and “system,” in 1789 Antoine-Laurent de Jussieu invented the catchwords of the expert debate on natural and artificial system-building after Linnaeus (Jussieu, Genera plantarum, ii). “System” alluded of course to the famous or notorious sexual system of Linnaeus which then was taken as paradigm for an unnatural, artificial taxonomic system. But as contrasted with “method,” it stood first of all for a method of building taxonomic systems which was considered erroneous and misleading. The procedure implied by “system” was nothing other than the method of constructing taxonomic systems by dichotomous subdivision  – by dihairesis. “Method,” on the other hand, stood for the procedure of grouping taxa into taxa of a higher rank, not by subdivision of already given taxa of higher rank, but rather inversely by starting from the lowest level, comparing the species with regard to many aspects, assembling them according to their affinities, thus establishing genera just by this assembling, then reiterating this procedure on the level of genera, establishing families, and so on. What was contrasted in this way was – in today’s terms – “downward classification by logical division” and “upward classification by empirical grouping” (Mayr, Biological Thought, 158, 190). Catchwords are usually telling and misleading at the same time. “Method versus system” is no exception. If taken to stand for two clear-cut camps of naturalists, this conception would simply be at variance with the historical facts: there were no such camps. One has to look through the rhetoric trimmings of the seemingly methodical controversy in order to see what actually changed in the second half of the eighteenth century compared with the time when Linnaeus published his works. The sexual system which Linnaeus set up for botany in his Systema naturae (1735) (Linnaeus, Systema) is a characteristic example of a combinatorial system produced by two dichotomous subdivisions using different structures as fundamentum divisionis. The first subdivision led to the classification into classes, and the second into ordines whereby each of the latter can form a sub-unit of more than only one class – which would be excluded by an encaptic system (Müller-Wille, Botanik, 55ff.). What should be noted is, however, that Linnaeus himself didn’t consider this system a natural one. Taking his system to be advantageous in comparison to the most influential systems of the first third of the eighteenth century, that of John Ray (1686) (Ray, Historia plantarum) and that of Tournefort (1694) (Tournefort, Elémens), he recommended it only as an useful and indispensable means for studying the kingdom of plants, but did not claim it to be a representation of the natural order of this kingdom. But this did not mean that Linnaeus limited himself to merely

280

W. Lefèvre

constructing a useful diagnostic, though artificial system for botany. Just 2  years after the Systema naturae he published in his Genera plantarum (Linaeus, Genera) a botanical system which he claimed to be natural. This system was, however, restricted to the taxonomic ranks of species and genus. The form of this limited system was encaptic and – what should be stressed – its units were not set up by either-or-divisions along one or two characters but by grouping the plants or the species into species or genera, respectively, according to many  – albeit not arbitrarily chosen – features. The situation of botanical classification at the middle of the century thus appears as follows: For the two upper ranks of taxonomic systems, viz. classes and ordines, there existed different systems, all of them combinatorial in form, achieved by combined dichotomous divisions – systems which nobody considered to be natural. For the two lower ranks, viz. genera and species,14 there existed systems which contended to represent the natural order among the plant taxa of these ranks – systems which were achieved not by dihairesis but by comparison of many different features even though the structures of the reproductive organs played a prominent role. Two alternative options arose from this situation. The one was to accept that the result achieved by Linnaeus is in accordance with the order of things, i.e., that, even in a system much more perfect than that of Linnaeus only the lower classificatory ranks are entitled to represent the natural order of plants whereas the higher ones are of necessity artificial divisions (for diagnostic purposes, etc.). The second option was to find ways of naturalising the ordines and classes. The most prominent champion who held that all higher classificatory ranks are merely artificial ones was Buffon (Sloan, Buffon-Linnaeus; Larson, Linné’s French critics). As seen above, Buffon adhered in a rather extreme manner to the great chain of being and dismissed therefore the entire idea of a natural system. In his famous Histoire naturelle, in particular in the first volumes, he chose the degree of benefit and familiarity to man as criterion for the order in which to treat the different species of animals, not refraining from adding the provocative remark: […] there is not one of them [sc. classificatory systems], whether of those which have been constructed, or of all those which might be constructed, which would not have more of an arbitrary element in them than our method. (Buffon, Maniere, 38; English transl. 162)15

But perhaps because of its radical and principled character, this opposition against the enterprise of natural classification was not very successful among naturalists of the age. Only a few subscribed to it, among these the young Lamarck (Stevens, Development, ch. 2), and its impact on the rest was rather insignificant.16 For the  The rank of familia, first introduced by Pierre Magnol (1638–1715) and today placed between ordines and genera, was not used by Linnaeus. 15  […] parce qu’il n’y en a pas une, & de celles [sc. méthodes] qui sont faites, & de toutes celles que l’on peut faire, où il N’y ait plus d’arbitraire que dans celle-ci […] Buffon, Manier 34. 16  It is probably superfluous to stress that this qualification of the influence of radically critical attitudes towards classification does not mean that the champions of this opposition, above all Bonnet, Buffon, or Lamarck, were second-rate figures of eighteenth-century biology or, as Lamarck proves, even of eighteenth-century classificatory botany as well as zoology. 14

12  Natural or Artificial Systems? The Eighteenth-Century Controversy…

281

majority of naturalists, the pressing question was not whether or not natural systems are possible at all but how to attain a natural system – natural not only with respect to its low ranks but to its high ones as well. The debate on natural versus artificial systems in the second half of the eighteenth century was thus precisely about how to arrive at a grouping of genera into ordines and/or classes that could be considered a natural one. It was this particular question which formed the background of Jussieu’s “method versus system,” and this should also form the background of our interpretation. Raising the whole matter above technical (botanical) particulars and divested of its rhetoric, the contrast between “system” and “method” appears no longer as one between alternative methods of competing schools of naturalists. Rather, it becomes a matter of choice between two alternatives, the respective legitimacy of which depends solely on which ranks of classification are at issue. Both of which are therefore adopted on different occasions by almost every single botanist involved in taxonomic work. Moreover, the debate was not about which of the two methods was more appropriate for building a natural system – everybody agreed that downward classification produces only artificial systems. The controversial element was rather whether the systems built by empirical grouping were in fact convincing. This is true not only with regard to Michel Adanson’s Famillies des plants (1763/64), which was considered a rather idiosyncratic system and had almost no impact, but also with regard to Antoine-Laurent de Jussieu’s Genera plantarum (1789), which was practically dismissed by even those French naturalists of the next generation who celebrated it (Stevens, Development, ch. 4). By focussing in this way on the shared convictions of the majority of the systematists of the age, the impression might be conveyed that no really new developments took place in these debates (except for practical efforts like that of Adanson and Jussieu) or that the conceptions on classification remained essentially the same after Linnaeus. All that happened, then, seems to have been a slight change of emphasis – from admitting that a system like Linnaeus’ sexual system is unnatural to the assertion that no system produced by dihairesis can be natural; from the practice of establishing genera by empirical grouping to the claim that a natural system can only result from such empirical grouping, a claim which eventually led to a new meaning of “natural,” namely “empirical” as contrasted with “artificial” (Mayr, Biological Thought, 200). But these slight changes entailed a big one which easily is overlooked when one takes the debate to be merely a methodological one about upward versus downward classification. What tacitly became reshaped through all these oscillations was the meaning of the task of building a natural classification. The task was no longer to find the place occupied by a plant or animal in the great chain of being, or – more generally – in a given order of nature. The task was now rather to subject this order to investigation by the empirical study of plants and animals. In the course of the debate this order was taken increasingly less as something known and deducible from principles, and it was realised that it, too, constituted the subject matter of empirical investigation by science. However unaffected the belief still was that there was an intrinsic order of nature, traditional ideas of this order gradually lost their former status as preconditions of scientific research, and the

282

W. Lefèvre

question of the make-up of this order, whether or not this order constituted, for instance, a continuous whole, began to become an empirical question.

12.5 Biological Content I – Resemblance of Structure So far, I have evaded focussing on the question of what is meant by calling a system of classification natural or, more precisely, what the historical actors intention was when speaking of natural systems. Now this question deserves special attention. As opposed to “artificial,” a “natural” classification implied arrangement of things concerned according to their intrinsic relations rather than according to the relations important to man. In this sense one could say that systems are natural ones if they represent, or are considered to represent, the objective relations among the beings classified by them. By using the adjective “objective” I am pointing to the strongly and perhaps embarrassingly realistic basic convictions held by the naturalists. No matter what they thought about the knowability of the essence of things, i.e., independent of whether they shared the epistemological scepticism of Locke, they all believed objective relations to exist among natural beings and that it is the task of scientists to uncover them. But this belief is not limited to naturalists of the eighteenth century. When today’s biologists discuss natural systems they also presuppose that a system which deserves to be called natural is an objective one in this sense – irrespective of the opinion of modern philosophers. This objectivity was, however, not only a universal theoretical claim but also intended as a criterion for distinguishing naturalistic classifications from other inventories of natural things which were used in the realm of trades and crafts. It was a conscious assertion as well as a fact that naturalistic classifications did not arrange natural things subjectively, i.e., according to the use and practical significance these things had for man. This abstraction from the usus of the classified beings, practised since the days of Cesalpino and unquestioned in the eighteenth century,17 assigned generality to naturalistic classifications in that it rendered their outcomes independent of human purposes. The subjective element left consisted in divisions and arrangements which were justified only by their diagnostic or mnemonic value. And it was above all because of this not yet removed subjectivity that systems were called artificial in the eighteenth century. Now, to take a natural classification of entities to be an objective arrangement is not a peculiarly biological idea. This is common practice across different fields of knowledge. And this is also true of the criterion according to which the affinity of plants and animals was judged, namely the criterion of resemblance which can be found also in mineralogical or chemical classification. But it is obvious as well that the qualities with respect to which resemblance was confirmed or denied could not be the same in the different fields of knowledge.

17

 With the exception of Buffon, as we have seen above.

12  Natural or Artificial Systems? The Eighteenth-Century Controversy…

283

The features of plants and animals which naturalists took almost exclusively into consideration when studying their resemblance were the shape of the parts and their arrangement, i.e., the structure of the body of plants or animals. In this restriction we encounter once more the abstraction from the use men can make of these bodies and their parts. But we also note deliberate exclusions of relations between plants and animals which doubtlessly belong to the objective relationships among living beings, for instance their relations within ecological systems and biotopes. It is necessary, wrote Tournefort, to collect, as if in bouquets, plants that resemble one another and to separate them from those that do not. As to resemblance, only their near ones are to be taken into consideration, i.e., that of the structure of any of their parts; remote relations occurring among certain plants have to be disregarded, for instance relations of their virtues or of their natural places. (Tournefort, Elémens, I 60, English transl. Jacob, Logic, 47)

Obviously, this concentration on the structure of plants and animals as the decisive property for their resemblance is not an expression of a naive or pre-scientific point of view. On the contrary, it shows the selective, experienced, and deliberate mode of thought of an expert. Similarly, it cannot be taken to be simply an instance of privileging the sense of sight. Colouration, for example, was excluded just like smell or taste (Foucault, Order of things, 132 f.) and, besides, structure, even if all its parts are visible to the naked eye, is not reducible to visual perception. Pragmatic aspects, however, were without doubt important for this concentration on structure. Classification as a collective enterprise must build on features which are easily identifiable, constant, accessible, unambiguously communicable, etc. And structure, in the case of plants and animals, does in fact provide many of those assets. In this way the eminent concentration on structure was based on rich experience of the specific nature of plants and animals gained not at least in the then evolving international system of natural historical collections, botanical gardens, and menageries. This dimension of naturalist classification of the eighteenth century thus reveals an element of specifically biological thinking and affirms the common notion that scientific classifications always depend on theories about the classified entities. Moreover, the conviction that resemblance of structure provides the key to objective and natural relationships among plants and animals has to be taken as one of the characteristic features of this thinking. The importance of resemblance of structure is by no means evident (Rheinberger, Bedeutungswandel). In hindsight, it is rather obvious that a natural system in botany and zoology cannot be based on this resemblance.18 And it could be added that structure, as understood by botanical and zoological naturalists in the middle of the eighteenth century, contained a pattern of thought which, once more in hindsight, hardly could be called specifically biological. I will come back to this at the end of the following section.

 Perhaps, advocates of phenetic systematics wouldn’t subscribe this statement. In the context of this article, it may suffice to refer to Pratt, Biological Classification, and Mayr, Biological Thought, 221ff. 18

284

W. Lefèvre

12.6 Biological Content II – Growing Tensions Classification by resemblance of structure harmonised in many respects extremely well with the notion of the great chain of being. This agreement was, however, only accidental. Neither was the concentration on such resemblance prompted by this notion nor vice versa. Because in such a situation friction is to be expected more often than not, it is worthwhile to take a short glance at how the biological assumptions involved in building a natural system affected the way natural history was embedded in those philosophical ideas.

12.6.1 Natural Groups There were specifically biological presumptions with a bearing on classification which appear neutral on first inspection. The idea of “natural groups” is a case in point – genera as well as groups of genera. With respect to the European flora, the botanists were convinced of having a sound knowledge of such “natural groups.” Though not totally uncontroversial in the details, these groups constituted a shared stock of botanical knowledge the viability of which served as a credibility test for newly proposed systems. Additionally, they formed stepping-stones for upward classification and came to serve, by and large, as building-blocks for system-building. But this custom also rendered these “natural groups” incompatible with one important feature of the great chain of being, namely with its linearity. It proved an impossibility to arrange these groups by degree of resemblance, given that each group has to be the intermediate in relation to exactly two other groups. By the middle of the eighteenth century it had become a widely shared opinion that this constraint had to be lifted. Linnaeus, for instance, replaced in his Philosophia botanica (1751) the image of a line by that of a map: All plants show affinities towards two dimensions (utrinque affinitatem) like a territory on a geographic map. (Linnaeus, Philosophia botanica, 27)19

As these words indicate, the conflict with a linear arrangement wasn’t prompted by the specific choice of “natural groups” but was inherent in the very practice of comparing plants by the resemblance of structures. Thus even this case of a generally harmonious interaction between the idea of resemblance of structure and that of an overarching chain of being was beset by an important element of discord.

19

 See Müller-Wille, Botanik, ch. 3.

12  Natural or Artificial Systems? The Eighteenth-Century Controversy…

285

12.6.2 Buffon’s Species Concept Above, in Sect. 12.2, I already discussed the latent tension between the idea of a continuous nature and an enterprise of classification which presupposes discreteness, a tension which finally became manifest through the work of naturalists like Buffon and Bonnet who consistently called into question the feasibility of non-­ artificial systems. But ironically, it was also Buffon who established a specifically biological notion which rendered discreteness a fundamental feature in the realm of living beings for the next hundred years. This was a notion involved in his species concept.20 No longer did he base the species concept primarily on the resemblance among individuals. Rather, procreation of fertile offspring became the yardstick.21 Portraying a species as a reproductive community is also equal to defining it in relation to other species, i.e., − in today’s words – as a reproductively isolated group. What is important in our context is that, according to this concept, it is not the naturalist who draws the dividing lines which separate species; it is the plants and the animals themselves which discriminate between mates and non-mates and exclude the latter. Species acquired thereby a specifically biological meaning as basic units of biological classification and came to be considered natural units. Hence, the notion of naturalness of classifications acquired a completely new dimension. Among those who realised the implications of this species concept for the notion of natural and artificial systems was Immanuel Kant, who wrote in 1775: Buffon’s rule that animals belong to the same genus if they produce fertile offspring together can be considered as constituting the definition of a natural genus, as distinct from a school genus. The school divisions concern classes based on external similarities, the natural divisions concern stocks based on kinships. The school system brings creatures under headings or titles, the natural system under laws. (Kant, Racen, 429)22

Even though limited in the beginning to the ranking of species, the whole idea of considering the naturalness of a taxonomic unit as a feature which is independent of  In the context of this chapters, I can leave open the question of whether actually Buffon merits the honour of being the father of this species concept or whether this concept can be found already in the writings of John Ray. See, for instance, Lovejoy, Buffon, and Farber, Buffon. 21  See the article “L’Asne” in Buffon, Histoire, IV 377ff. 22  “Daher muß die büffonsche Regel, daß Thiere, die mit einander fruchtbare Jungen erzeugen, (von welcher Verschiedenheit der Gestalt sie auch sein mögen) doch zu einer und derselben physischen Gattung gehören, eigentlich nur als die Definition einer Naturgattung der Thiere überhaupt zum Unterschiede von allen Schulgattungen derselben angesehen werden. Die Schuleintheilung geht auf Klassen, welche nach Ähnlichkeiten, die Natureintheilung aber auf Stämme, welche die Thiere nach Verwandtschaften in Ansehung der Erzeugung eintheilt. Jene verschafft ein Schulsystem für das Gedächtniß; diese ein Natursystem für den Verstand: die erstere hat nur zur Absicht, die Geschöpfe unter Titel, die zweite, sie unter Gesetze zu bringen.” English translation from (Rabel, Kant, 98).—In eighteenth-century German both the term for species (Art) and the term for genus (Gattung) were frequently used synonymously and then meant species.—A possible reason why Kant restricted himself in his statement to the kingdom of animals might be found in the fact that the theory of the sexual reproduction of plants were then new and not yet universally accepted. 20

286

W. Lefèvre

any given classificatory system contains the germ of a new understanding of natural classification. The naturalness of classification is no longer seen as the straightforward outcome of the system’s inherent naturalness but has to be established by independent means, i.e., by independent investigation of the taxonomic unit in question. Such a unit does not acquire naturalness by considering its place in the system a natural one but only by systematic investigation of this unit. This is another proof of what was discussed above, at the end of Sect. 12.4, i.e., that the general order of nature (for instance, whether it constituted a continuous whole) gradually lost its status as precondition of scientific research and was increasingly subjected to assumptions and theories arising by the empirical sciences.

12.6.3 From Structure to Organisation François Jacob wrote in his Logique du vivant (1970): Throughout the eighteenth century, organisation still described only the combination of structures and the mosaic of elements that characterised a living being. At the end of the century, however, organisation acquired a different role and status. By progressively replacing visible structure, organisation provided a hidden foundation for the bare data of description, for the being as a whole and for its functioning. (Jacob, Logic of life, 82f.) Thus at the end of the eighteenth century there was a change in the relations between the exterior and the interior, between the surface and the depth, and between organs and functions of a living being. What became accessible to comparative investigation was a system of relationships in the depth of a living organism, designed to make it function. Behind the visible forms could be glimpsed the profile of a secret architecture imposed by the necessity of living. This second-order structure was organisation, which brought together into one coherent whole both what was seen and what was hidden. (ibid, 85)

At the end of the eighteenth century, naturalists had achieved a view of living beings as organised in a specific way, namely as a whole built of parts depending on each other and performing co-operatively in the life activities of this whole. This view had not only the status of a general assumption – in the way in which the famous § 65 of Kant’s Critique of Judgement from 1790 (Kant, AA, V 372ff.) might be (erroneously) interpreted – but was the summary of detailed studies of this mutual dependence of organs, of their subordination and correlation, studies carried out above all in zoology. To quote Georges Cuvier (1769–1832): Every organised being forms a whole, a unique and closed system, in which all parts correspond mutually, and contribute to the same definitive action by a reciprocal reaction. None of its parts can change without the others changing too; and consequently each of them, taken separately, indicates and gives all the others. (Cuvier, Recherches, I 58)23  Tout être organisé forme un ensemble, un système unique et clos, dont toutes les parties se correspondent mutuellement, et concourent à la même action définitive par une réaction réciproque. Aucune de ces parties ne peut changer sans que les autres changent aussi; et par conséquent chacune d’elles, prise séparément, indique et donne toutes les autres.  – English translation from Rudwick, Georges Cuvier, 217. 23

12  Natural or Artificial Systems? The Eighteenth-Century Controversy…

287

Looking back from this newly acquired concept of organisation, prior interpretations indeed amount to no more than “only the combination of structures and the mosaic of elements” (Jacob). What came into sight by virtue of Cuvier’s concept of organisation was the combinatory character of the hitherto prevailing view of living beings and, in consequence, of the whole of eighteenth-century classification – a characteristic which by now proved to miss totally the specifics of life. Not that eighteenth-century naturalists considered the structure of plants or animals as arbitrary combinations of parts. They knew, of course, that, for example, a flower could only function as reproductive organ if it were composed of certain parts. The knowledge that a higher organ like the flower comprises a whole of a series of indispensable lower organs was indeed one of the reasons why naturalists focused on such stable structures in their classifications.24 But what they did not realise before the last decades of the eighteenth century was the correlation of changes in each of those essential parts of an organ as well as in each organ. They had not yet discerned that any alteration of one part is necessarily accompanied by alterations of the others and that therefore a series of different forms of flowers which differ only in the shape of a single part without alterations of the rest is an impossibility.25 They could not have written: […] the form of the tooth entails the form of the condyle; the form of the shoulder blade and the claws, just like the equation of a curve, entail all their [sc. vertebrae] properties. (Cuvier, Recherches, 60)26

To no small degree did this combinatory thinking of the naturalists contribute to the linking together of the classificatory schemes of the “classical age” with the scala naturae idea. For combinatory imaginations unrestricted by rules of correlation were a common feature of all sorts of speculations involved in the great chain of being. Jean-Baptiste René Robinet (1735–1820), for instance, wrote in an essay from 1768: Nature could not realise the figure of men differently from combining all imaginable executions of each of the features which had to be inscribed in it. If she had left out only one single combination, the features would not had obtained that right measure of accordance they achieved through covering all gradations. (Robinet, Gradation naturelle, 4)27

 Staffan Müller-Wille (Müller-Wille, Botanik, ch. 9) shows how much morphological considerations played a role for Linnaeus. 25  In contrast with Foucault, it seems to me that not a restriction on “visibility” (Foucault, Order of things, 137, 226ff.) but exactly this combinatorial understanding marks the decisive difference which separates structure of living beings in the sense of the eighteenth century from organic structure or organisation in the sense of Cuvier’s morphology. 26  En un mot, la forme de la dent entraine la forme du condyle; celle de l’omoplate, celle des ongles, | tout comme l’équation d’une courbe, entraine toutes ses propriétés […]  – English translation from Rudwick, Georges Cuvier, 219. 27  La Nature ne pouvoir réaliser la forme humaine qu’en combinant de toutes les manières imaginables chacun des traits qui devoient [sic] y entre. Si elle eût fauté une seule combinaison, ils n’auroient [sic] point eu ce juste degré de convenance qu’ils ont acquis en passant par toutes les nuances. 24

288

W. Lefèvre

It is therefore hardly surprising that the dismissal of this combinatory view of living beings brought about the definitive end of the influence of these natural philosophical ideas upon biological thinking. “I do not have the pretension or the desire,” wrote Cuvier in the introduction to his Le règne animal, to classify the beings either in such a way that they form a single line or according to graduations of relative superiority, nor do I conceive such a plan to be practicable. […] The pretended scale of life, being nothing else than an erroneous application of some partial observations to the whole of the creation […] has impeded the progress of natural history in the past to an extent hardly imaginable. (Cuvier, Le regne, I xxf.)28

The general ideas connected with the great chain of being, viz. that of a linear order, that of a hierarchical graduation among the beings of the universe, and last but not least that of a continuity in nature, were eventually dismissed, at least by the majority in the community of professional naturalists, when classical morphology reached its first height at the beginning of the nineteenth century with Cuvier.

12.7 Prospects: A Meaningless Nature “Natural groups,” the species concept of Buffon, and the new view of organisms established by morphology – all of these items displayed a common feature: It was the low degree of insight into the intricacies of living beings that made overarching ideas like that of the great chain of being attractive for naturalists, and it was the growth of such insights by which naturalists realised step by step how little adequate these ideas were for understanding life. The dwindling of these ideas and the rise of a more specific biological thinking thus appear as two sides of the same coin, namely of a process in which the former balance of scientific and philosophical elements in biological thinking was disturbed but a new one had yet to be acquired. A influential proposal for how to find a new balance of these elements was made by Immanuel Kant. In his Critique of Pure Reason (1781), he wrote: If merely regulative principles are considered as constitutive, then as objective principles they can be in conflict; but if one considers them merely as maxims, then it is not a true conflict, but it is merely a different interest of reason that causes a divorce between ways of thinking. Reason has in fact only a single unified interest, and the conflict between its maxims is only a variation and a reciprocal limitation of the methods satisfying this interest. (Kant, Kritik der reinen Vernunft, B 694) It is the same with the assertion of, or the attack on, the widely respected law of the ladder of continuity among creatures, made current by Leibniz and excellently supported by Bonnet, which is nothing but a pursuit of the principle of affinity resting on the interests of

 […] je n’ai eu ni la prétention, ni le désire de classer les êtres de manière à en former une seule ligne, ou à marquer leur supériorité réciproque. Je regarde même toute tentative de ce genre comme inexécutable […] L’échelle prétendue des êtres n’est qu’une application erronée à la totalité de la création de ces observations partielles […] et cette application, selon moi, a nui, à un degré que l’on aurait peine à imaginer, aux progrès de l’historie naturelle dans ces derniers tems. 28

12  Natural or Artificial Systems? The Eighteenth-Century Controversy…

289

reason; for observation and insight into the arrangements of nature could never provide it as something to be asserted objectively. The rungs of such a ladder, such as experience can give them to us, stand too far apart from one another, and what we presume to be small differences are commonly such wide gaps in nature itself that on the basis of such observations (chiefly of the great manifoldness of things, among which it must always be easy to find certain similarities and approximations) nothing can be figured out about the intentions of nature. The method for seeking out order in nature in accord with such a principle, on the contrary, and the maxim of regarding such an order as grounded in nature in general, even though it is undetermined where or to what extent, is a legitimate and excellent regulative principle of reason, which, however, as such, goes much too far for experience or observation ever to catch up with it; without determining anything, it only points the way toward systematic unity. (ibid., B 696)29

Kant’s distinction between regulative and constitutive principles must not be understood as distinction between philosophical and scientific principles. Rather, it refers to principles which are both philosophical and cannot be confirmed nor denied by experience. They do not spring from experience and are prior to experience. However, Kant handled these principles in a new way that gave rise to a new frame of relations between scientific and philosophical elements of scientific knowledge. As is known, he took these philosophical principles to be worthless for gaining knowledge if not applied to and restricted by experience. And this is true even of the constitutive principles to which Kant assigned a strong status as universal prerequisites of understanding  – a status for which the principles of the old metaphysics were known. The price to pay for the preservation of this status was the retraction of their former claim to yield truth and knowledge independently of experience. This was the way Kant transformed the set of principles of the former ontologia or metaphysica universalis known as categories. Metaphysical principles like that of continuity, however, could not be saved in this way. The only possibility was to transform their status into that of “maxims of reason,” i.e., into heuristic principles of scientific research. At this time, this proposal was largely an obvious conclusion to be drawn from the fact that these principles played at best such a heuristic role in sciences and even, as seen, in natural history. Proposals like this one consist, at first glance, merely in the substitution of new epistemological claims for old ones associated with interesting ideas. The ideas seem to live on untouched except for the new formal setting. But are they really still the same ideas? Is, for instance, the idea of plenitas or continuitas really unaffected by the transformation from metaphysics to heuristics? After all, this idea was not a mere proposition about supposed qualities of the universe which may be true or false. To remind of the words of the letter allegedly by Leibniz, quoted above: All the different classes of beings which taken together make up the universe are, in the ideas of God who knows distinctly their essential gradations, only so many ordinates of a

29

 English translation from Kant, Critique of Pure Reason.

290

W. Lefèvre

single curve so closely united that it would be impossible to place others between any two of them, since that would imply disorder and imperfection. (Leibniz, HS, II 558)30

“Disorder and imperfection” – as a metaphysical principle of early modern times, the idea of plenitas or continuitas was involved in a perception of nature as a revelation of God’s own ideas, as not only a rationally ordered whole but also a meaningful and even normative cosmos which could claim moral authority. By transforming this idea into a heuristic principle, an entire view of nature was challenged, namely the view that nature as such a cosmos can be subjected to rational and scientific discourse. This transformation thus proves to be an element within a broader series of transformations (Lefèvre, Zwei Naturen) which eventually led to a view of nature as she is the subject of science today, namely as a meaningless.

References Anderson, Lorin. 1982. Charles Bonnet and the Order of the Known. Dordrecht: Reidel. Aristotle. Parts of Animals. Bekker pagination. Bonnet, Charles. 1764. Contemplation de la nature: Tome premier. Amsterdam: Rey. Breger, Herbert. 1999. Über den von Samuel König veröffentlichten Brief zum Prinzip der kleinsten Wirkung. In Pierre Louis Moreau de Maupertuis. Eine Bilanz nach 300 Jahren, ed. Hartmut Hecht, 363–381. Berlin: Berlin Verlag. Buffon, Georges-Louis Leclerc Comte de. 1749-1789. Histoire naturelle, générale et particulière. Paris: Imp. royale. ———. 1976. De la maniere d’etudier et de traiter l’histoire naturelle. In Histoire naturelle, générale et particulière, vol. I, 145–178. Paris: Impr. Royale., 13.  – First complete English translation by John Lyon in Journal of the History of Biology IX/1. Cain, Arthur J. 1958. Logic and memory in Linnaeus’s system of taxonomy. Proceedings of the Linnean Society of London CLXIX: 144–163. Cuvier, Georges. 1812. Recherches sur les ossemens fossiles des Quadrupèdes. Paris: Deterville. ———. 1817. Le règne animal: distribué d’aprés son organisation: pour servir de base a l’histoire naturelle des animaux et d’introduction à l’anatomie comparée. Paris: Deterville. Dietz, Bettina. 2017. Das System der Natur: Die kollaborative Wissenskultur der Botanik im 18. Jahrhundert. Köln, Weimar und Wien: Böhlau. Farber, Paul F. 1972. Buffon and the Concept of Species. Journal of the History of Biology V/2: 259–284. Fontenelle, Bernard Le Bovier. 1797. Eloge de Tournefort. In Elémens de botanique (1694), ed. Joseph Pitton de Tournefort, vol. I, 3rd ed. P. Bernuset: Lyon. Le Fontenelle, Bernard, and Bovier. 1825. Oeuvres de Fontenelle: 1 Éloges, T I. Paris: Salmon. Foucault, Michel. 1997. The order of things: an archaeology of the human sciences. Translation of Les mots et les choses: une archéologie des sciences humaines (1966). London: Routledge. Jacob, François. 1973. The Logic of Life. Princeton, NJ: Princeton Univ Press.

 […] que toutes les différentes classes des Etres, dont l’assemblage forme l’Univers, ne sont dans les idées de Dieu, qui connoit distinctement leurs gradations essentielles, que comme autant d’Ordonnées d’une même Courbe, dont l’union ne souffre pas qu’on en place d’autres entre deux, à cause que cela marqueroit du desordre & de l’imperfection. – English translation from Lovejoy, Great chain, 144. 30

12  Natural or Artificial Systems? The Eighteenth-Century Controversy…

291

Jussieu, Antoine-Laurent de. 1789. Genera plantarum / secundum ordines naturales disposita. Paris: Hérissant. Kant, Immanuel. 1910-1938. Von den verschiedenen Racen der Menschen: zur Ankuendigung der Vorlesungen der physischen Geographie im Sommerhalbenjahre 1775. In Kant’s gesammelte Schriften [AA], ed. Preussische Akademie der Wissenschaften, vol. II, 427–443. Berlin: de Gruyter. ———. 1787. Kritik der reinen Vernunft (1781). 2nd ed. Riga: Hartknoch. cited as B. ———. 1998. In Critique of Pure Reason, The Cambridge Edition of the Works of Immanuel Kant, ed. Paul Guyer and Allen W. Wood. Cambridge: Cambridge University Press. Larson, James L. 1980. Linné’s French critics. In Linnaeus: Progress and Prospects in Linnaean Research, ed. Gunnar Broberg, 67–79. Stockholm: Almquist & Wiksell. Leathers Kuntz, Marion. 1987. In Jacob’s Ladder and the Tree of Life: Concepts of Hierarchy and the Great Chain of Being, ed. Paul Grimley Kuntz. New York: Lang. Lefèvre, Wolfgang. 1984. Die Entstehung der biologischen Evolutionstheorie. Frankfurt/M/ Berlin/Wien: Ullstein. ———. 1992. Zwischen zwei Naturen. In Der Comenius-Garten – Eine Leseprobe aus dem Buch der Natur, ed. H. Vierck. Berlin: Hentrich. Leibniz, Gottfried Wilhelm. 1875–1890. Die philosophischen Schriften, ed. Carl Immanuel Gerhardt. Hildesheim: Olms, 1960–61. [GP] ———. 1966. In Hauptschriften zur Grundlegung der Philosophie, ed. Ernst Cassirer, 3rd ed. Hamburg: Meiner. [HS]. Lesch, John E. 1990. Systematics and the Geometrical Spirit. In The Quantifying Spirit in the 18th Century, ed. Tore Frängsmyr, J.L. Heilbron, and Robin E. Rider, 73–111. Berkeley/Los Angeles/Oxford: Universtiy of California Press. Linnaeus, Carl. 1735. Systema naturae, sive Regna Tria Naturae systematice proposita per classes, ordines, genera, & species. Leiden: Haak. ———. 1737. Genera plantarum Eorumque characteres Secundum numerum, figuram, situm, proportionum Omnium fructificationis Partium. Leiden: Conrad Wishoff. ———. 1751. Philosophia botanica: in qua explicantur fundamenta botanica. Stockholm: G. Kiesewetter. Locke, John. 1979. In An Essay concerning Human Understanding, ed. Peter Nidditch. (based on 4th edition of 1700). Oxford: Clarendon Press. Lovejoy, Arthur O. 1959. Buffon and the Problem of Species. In Forerunners of Darwin: 1745–1859, ed. Bentley Glass, Owsei Temkin, and William L. Straus, jr, 84–113. Baltimore: Johns Hopkins Press. ———. 1964. The Great Chain of Being: A Study of the History of an Idea (1933). Cambridge: Harvard University Press. Mayr, Ernst. 1982. The Growth of Biological Thought. Cambridge MA: Belknap Press. Müller-Wille, Staffan. 1999. Botanik und weltweiter Handel: Zur Begründung eines natürlichen Systems der Pflanzen durch Carl von Linné (1707–78). Berlin: VWB. ———. 2017. Names and Numbers: ‘Data’ in Classical Natural History. Osiris XXXII: 109–128. Ogilvie, Brian W. 2003. Image and Text in Natural History, 1500-1700. In The Power of Images in Early Modern Science, ed. Wolfgang Lefèvre, Jürgen Renn, and Urs Schöpflin, 141–166. Basel: Birkhäuser. Pratt, Vernon. 1972. Biological Classification. British Journal for the Philosophy of Science XXIII: 305–327. ———. 1985. System-Building in the Eighteenth Century. In The Light of Nature, ed. J.D. North and J.J. Roche. Dordrecht: Nijhoff. Rabel, Gabriele. 1963. Kant. Oxford: Clarendon Press. Ray, John. 1686. Historia plantarum. London: typis Mariae Clark, prostant apud Henricum Faithorne.

292

W. Lefèvre

Rheinberger, Hans-Jörg. 1986. Aspekte des Bedeutungswandels im Begriff organismischer Ähnlichkeit vom 18. zum 19. Jahrhundert. History and philosophy of the life sciences VIII: 237–250. Robinet, Jean-Baptiste René. 1768. Vue philosophique de la gradation naturelle des formes de l’etre. Amsterdam: E. van Harrevelt. Rudwick, Martin J.S., ed. 1997. Georges Cuvier, Fossil Bones, and Geological Catastrophes. Chicago/London: University of Chicago Press. Sloan, Philip R. 1972. John Locke, John Ray, and the Problem of the Natural System. Journal of the History of Biology V/1: 1–53. ———. 1976. The Buffon-Linnaeus Controversy. Isis LXVII: 356–375. Sneath, Peter H.A. 1964. Mathematics and classification from Adanson to the present. Adanson: the bicentennial of Michel Adanson’s Familles des plantes. Part 2, 471–498. Pittsburgh: Hunt Botanical Library, Carnegie Institute of Technology. Stevens, Peter F. 1994. The Development of Biological Systematics: Antoine-Laurent de Jussieu, Nature, and the Natural System. New York: Columbia Universtiy Press. Tournefort, Joseph Pitton, and de. 1694. Elémens de botanique. Paris: IMP royale. Wilkins, John S., and Malte C.  Ebach. 2014. The Nature of Classification. London: Palgrave Macmillan. Wolff, Christian. 1997. Philosophiae naturalis sive physicae dogmaticae tomus III continens Geologiam, biologiam […] (1766). Hildesheim: Olms.

Part VI

Looking Back and Ahead

Chapter 13

Beyond Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786 Marius Stan

Abstract  Early modern foundations for mechanics came in two kinds, nomic and material. I examine here the dynamical laws and pictures of matter given respectively by Newton, Leibniz, and Kant. I argue that they fall short of their foundational task, viz. to represent enough kinematic behavior; or at least to explain it. In effect, for the true foundations of classical mechanics we must look beyond Newton, Leibniz, and Kant.

13.1 Introduction My aim below is to examine critically whether Newton’s, Leibniz’s, and Kant’s respective doctrines of body and motion are sufficient foundations for classical mechanics. I argue that they are not. Each comes up short in various respects and to various extents. In consequence, I urge that, to discover the true foundations of mechanics, we must look beyond the figures  above. And also that, because their respective foundations are insufficient, we ought to debate exactly what we historians and philosophers may hope to get from looking at them. To make my case, I begin with an analytic preamble that elucidates the various senses of sufficiency and mechanical foundations I assume in this chapter (Sect. 13.2). Next, I dispel some old prejudices and misunderstandings about mechanics after Newton (Sect. 13.3). Further, I give a synopsis of its structure and scope, based on newer research (Sect. 13.4). Then I check whether the foundations above are sufficient for that mechanics. In particular, I show that Newton’s, Leibniz’s, and Kant’s laws of motion are too narrow for it (Sect. 13.5). And, that their respective pictures

M. Stan (*) Boston College, Chestnut Hill, MA, USA © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7_13

295

296

M. Stan

of matter are likewise insufficient foundations (Sect. 13.6). I end with some morals and suggestions for future research.1 This paper is summative: it relies on, and connects, work I have done elsewhere. Thus, it really ought to be read in conjunction with that work, for my point to sink in.

13.2 Background Distinctions To preempt confusion, and to help the reader see the force of my concerns, I must explain my charge of insufficiency above. A mechanical foundation F can be sufficient in two senses.2 Weak F entails a theory of mechanics M, and all of physics can be reduced to M.3 Strong F is enough to represent all mechanical phenomena. Namely, it entails equilibrium conditions and equations of motion for all possible bodies. I will explain these matters further as the need arises. Next, I must elucidate the particular foundations I have in mind for my case in this paper. Labeled for efficient use, they are as follows: N Newton’s Definitions I through VII, his three laws of motion (including f = ma), and their six corollaries in Principia. The law of universal gravitation. Optional: the matter theory in Query 31 of his Opticks. L Leibniz’s taxonomy of forces in Specimen dynamicum. Conservation of Vis Viva. Matter regarded as a deformable continuum. K Kant’s primitive concepts, their explications, his derived theorems, and the three laws of mechanics in his MAN. These preliminaries now enable me to state my thesis more precisely: Neither N, nor L, nor K are strongly sufficient foundations. None has the resources to represent the mechanical behavior of all bodies.

 For Newton, I use his Principia. For Leibniz, I use his Specimen dynamicum, and associated texts (see nos. 14, 16, 22–3, 31, A3–4 and E3–4 in Leibniz, Essays). For Kant, I rely on his 1786 tract, Metaphysical Foundations of Natural Science (henceforth MAN). 2  Broadly speaking, F is a set that contains concepts, laws, mathematical theorems, and perhaps heuristics for problem-solving and theory buildup. 3  This sense might seem idle, but it was long influential. Descartes’ 1644 Principles of Philosophy advocated for reducing physics (optics, magnetism, heat flow, even physiology and earth science) to a mechanics of matter in motion (specifically, of action by contact via collision and ether pressure). And so did Hobbes, in De Corpore of 1655. Centuries later, Hertz urged: “All physicists agree that the problem of physics consists in tracing the phenomena of nature back to the simple laws of mechanics” (Hertz, Mechanics, xxi). Halfway between these termini was Fischer’s program of a mechanische Physik, whose influence extended to France (see his Physique mécanique). 1

13  Beyond Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786

297

Most of my case below marshals evidence for the thesis above. Before I do so, however, I need to cast more light on two aspects above, viz. ‘representing’ and ‘mechanical behavior.’

13.3 The Shape of Mechanics After 1730 It is seductive, and has long been entrenched, to use Newton as the best vantage point for grasping the structure and foundations of mechanics after him (up to 1905–18, when Einstein supposedly displaced Newtonian theory). Here I will explain briefly why that is wrong. The Principia contains a rational mechanics of ‘centripetal’ forces— the mathematics of particle orbits in fields of central acceleration—and then an application of this apparatus to one particular species of centripetal force in nature, viz. gravity. Knowing that he had discovered just one species of impressed force, Newton in a famous exordium to his Principia urged future generations to continue his program of discovery: If only we could derive the other phenomena of nature from mechanical principles by the same kind of reasoning! For many things lead me to have a suspicion that all phenomena may depend on certain forces by which the particles of bodies, by causes not yet known, either are impelled towards one another and cohere in regular figures, or are repelled from one another and recede. As these forces are unknown, philosophers have hitherto made trial of nature in vain. But I hope that the principles set down here will shed some light on either this mode of philosophizing or some truer one. (Newton, Philosophical Writings, 60f.; my italics)

Now combine his exhortation with two pieces of received wisdom. One is Mach’s old chestnut that Newton’s laws of motion are a sufficient basis for all classical mechanics. The other is Kuhn’s old image of mechanics after Newton being ‘normal science.’4 Together, these elements can strongly seduce the reader into thinking that, from 1687 to Einstein, mechanics was in the business of discovering more forces—and their specific laws—by following Newton’s recipe and by building on his foundation N above.5

 “Newton’s principles suffice for solving every mechanical problem we encounter in practice, whether in statics or dynamics. We need not appeal to any new principle for that. If we run into obstacles, they are always just mathematical. Not difficulties with the principles” (Mach, Mechanik, 239; my emphasis). Kuhn counted Newton’s Principia as a paradigm—the exemplary achievement of classical mechanics—and claimed that it “served for a time implicitly to define the legitimate problems and methods of a research field for succeeding generations of practitioners” (Kuhn, Structure, 10; my emphasis). 5  Note that, if these framing assumptions were true, they would make short work of Leibniz, Kant, and anyone who diverged from the Newtonian program above. If mechanics post 1700 was in fact as the Mach-Kuhn has it, then attempts to supplant it (as Leibniz tried, with vis viva) or to correct 4

298

M. Stan

However, the Mach-Kuhn framing is wrong, on conceptual and empirical grounds; hence so is the historical picture that falls out of it. It is not true that mechanics after Newton was in the business of discovering more forces and their laws, by emulating his success with gravity. And, it is not true that mechanics post Principia built on his foundation N. In fact, mechanics then had a different agenda, pursued with very different tools, and evaluated from very different criteria of success. Here is why and how. To treat behaviors from theory—to incorporate them into mechanics—requires an indispensable thing, viz. obtaining the equation of motion for that particular type of behavior. For instance, the wave equation: the differential formula that quantifies how every point in a flexible string (more generally, in any harmonic oscillator) moves in an instant once the string is made to vibrate. By the way, that formula was discovered in 1747, by d’Alembert. This requirement is crucial for understanding my claim that post-Newtonian mechanics is drastically different from Newton’s approach and results in Principia. First, there are no equations of motion in his book.6 Pursuing them became the chief priority after 1730, at first with the Bernoullis and their associates, then collectively in continental Europe. Second, equations of motion must be derived from dynamical laws: from principles that relate mechanical agency (be it force, power, work, energy, or action) to kinematic change in space and time. That requires the laws themselves to be stated as differential equations. Third, post-Newtonian theorists seek dynamical laws shown to be general. That is, some one or two principles that entail equations of motion for all species of extended body. In sum: the old prejudice was that post-Newtonian mechanics aimed to discover more forces and their laws, by emulating Newton’s heuristics, and by starting from his principles. In contrast, recent research entails the key objective of mechanics was different—namely, to derive equations of motion for a very broad spectrum of bodies, from dynamical laws thereby shown to be general. This radically novel and extremely demanding objective is sine qua non for understanding the true shape and growth of mechanics after 1700. It has no precedent in the theories and research programs of the 1600s; and it is easy to miss if one looks at mechanics with Newton’s achievement as our lens for history.

it (as Kant tried, with foundation K) must appear as doomed to fail, or at least seriously misguided. I thank Katherine Brading for enlightening discussion of these broader points. 6  Decades ago Truesdell had pointed out that differential equations—the key representational device of modern mechanics—are absent from Newton’s tract (Truesdell, Essays, 90). We may wonder if Newton would have even recognized the need for them in mechanics. I thank George E. Smith for stimulating discussion on this topic.

13  Beyond Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786

299

13.4 Sufficient Foundations, 1760–1830 For a century after 1730, mechanics sought to mathematize two very broad classes of kinematic behavior: the motion of extended bodies; and motion with external constraints, viz. obstacles to free translation. It was all slow work—a testimony to how difficult these classes were.7 Mechanics came close enough to conquering these two areas in the 1820s. By the end of the Old Regime, it had already made enormous advances at the hands of Euler and Lagrange; later progress was due to Navier and Cauchy. Thanks to them and a few others, toward the mid-nineteenth century it became clear that only two candidates had any realistic chance to be foundations in the strong sense. I present them here. Euler-Cauchy Laws  The motion of extended bodies was conquered stepwise, one species at a time. First they mathematized low-dimensional elastics, then rigid bodies, then ideal fluids, then elastic solids, and then at last viscous fluids.8 After a century of effort, theorists learned that one dynamical law is indispensable for all these species. Namely, it is a required premise for deriving the equations of motion for every species. That law is9:



b + ( − ∇T ) = ρ x¨



(13.1a)

Expressed in words, it says: at every point of an extended object in motion, the net body force plus the gradient of the local contact forces (i.e. stresses) equals the point’s change of linear momentum in an instant. Bur for some motions (namely, for rigid bodies and elastic solids) the expression is not quite enough to represent their every quantitative aspect. Rather, it must be combined with another law; only together do they completely represent the change at a point. That second law is10:

H = dL / dt

(13.1b)

Again in words: the net torque on a body forces equals the change of angular momentum (at a point, in an instant).

 The claims in this section depend on research carried out in Brading & Stan, Philosophical Mechanics, chapters 8–12. For verification, the reader is invited to consult them. 8  Other types of extended-body motion (e.g. plasticity, fracture, hysteresis, creep, and brittleness) had to wait until the twentieth century for their mathematization. 9  b is the net body force, T the stress, or internal force, 𝜌 the mass density, and the acceleration (the second derivative of the position vector X). An early version of this law is in Cauchy, “Sur les equations.” 10  H is the net impressed torque, and L the angular momentum. The earliest expression of this law is Euler, “De motu in superficiebus,” § 48. 7

300

M. Stan

The figures who did most to showcase the descriptive power of these laws—their vast descriptive reach—were Euler and Cauchy. Thus, following recent tradition, I named the laws after them.11 Lagrange’s Law  Another area of intense research after Newton was constrained motion.12 It was an arduous domain in which the 1600s had bequeathed no useful principle or heuristic for problem solving. In particular, Newton’s second law was of no help.13 And so, theorists in effect had to create this area of mechanics from the ground up. Clairaut and d’Alembert made very important advances, but only Lagrange in 1788 would obtain a general solution. Namely, a dynamical law that governs all species of motion, free or constrained; plus a method for quantifying the action—the motion changes it induces—of any constraint, no matter its particular makeup. I call his principle ‘Lagrange’s law,’ in line with some latter-day authors who have explained the merits of his demarche.14 The law is a statement about the virtual work done in a mechanical system. It reads15:

∑ F⋅ δ f + ∑ − m x¨ ⋅ δ x + ∑ λ ⋅ δ L = 0

(13.2)

It says that when a set of bodies move, we may regard it as the target of three mechanical agencies: actual forces applied to it; certain fictitious forces; and the action of constraints on its motion. Each agency does virtual work, viz. it could displace its target mass by an amount 𝛿r. The law says that the net virtual work of all these agencies (forces and constraints) vanishes across the system as a whole.16

 See especially Truesdell, Rational Continuum Mechanics, 64ff.  Generally, a constraint is a limit on how a particle or a body is allowed to move. Some constraints are external to the body. E.g. an inclined plane, which prevents the body from moving straight down (under the force of gravity). Other constraints are internal to the body. E.g. rigidity, which prevents the body’s component points from changing their relative distances. 13  The reason is that, in general, the physical basis that secures the constraints—e.g., forces (if they are forces), their specific laws, and mechanisms of action—is not known in advance. It is not given at the outset of building the theory of mechanics. However, to apply Newton’s second law, that required knowledge must be available at the outset. The law really says that ∑f = ma, viz. the actual acceleration is the result of all the forces acting at that point. Absent knowledge of some forces, the law becomes inapplicable. “[T]he most widespread mistake about Newton’s three laws of motion is that they alone sufficed for all problems in classical mechanics.”—Smith, “Newton’s Principia,” § 5. 14  For the origin of the idea that this is really Lagrange’s law, together with a lucid explanation of its role in solving constraints, see Papastavridis, Analytical Mechanics. 15  See, for instance, Lagrange, Mechanique, 53ff. F is any actual, impressed force on a mass i in the system; 𝛿f is a virtual displacement that F would cause in i. And, −miẍi are so-called ‘reverse effective forces’ (or also ‘kinetic reactions’), viz. fictitious forces supposed equal and opposite to the particle’s effective acceleration ẍi; and 𝛿x a virtual displacement in their direction. Finally, 𝝀i is a Lagrange multiplier, and 𝛿L a virtual displacement compatible with the constraint given by 𝝀i. 16  By a mechanical system I mean one or more masses, point sized or extended. 11 12

13  Beyond Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786

301

Incidentally, the law includes Lagrange’s great breakthrough—his general treatment of constraints, which Newton’s laws cannot handle. Lagrange reasoned as follows. Let the action of any constraint in the system—the amount whereby it changes the motion of the mass it prevents from moving—be some amount 𝝀.17 And, let 𝛿L be a virtual displacement (of the target mass) compatible with that constraint. Lagrange’s insight was that, across the system as a whole,

∑ λ ⋅δ L = 0

namely, the virtual work of all the constraints, together, cancels out.18 I end with an important note. Of the two laws above, Lagrange’s is the most powerful. Namely, it can be used to quantify as well the kinds of motion that Euler-­ Cauchy principles can represent. The converse does not hold: Euler-Cauchy laws are not strong enough to describe the motion of masses with external constraints (which Lagrange’s law was designed to treat). Recall, that was a blind spot of Newton’s second law as well. In effect, Lagrange’s is really the only principle sufficient in the strong sense.19

13.5 Insufficient Foundations: Laws Central to the respective foundations of Newton, Leibniz, and Kant are their laws of motion. Below, I explain why those laws are insufficient. There are two ways to do that, long and short. Here is the short one. Neither N nor L nor K are the same (in terms of physical content and mathematical structure) as the Euler-Cauchy laws or Lagrange’s law. But, only these laws have been shown—they alone have the track record—to be sufficient foundations, or very nearly sufficient. Hence, Newton, Leibniz and Kant did not give us enough basis for mechanics. So, we must move beyond them. This explanation is brief and hard to impeach, but is not as illuminating as it gets. Accordingly, next I review the three candidates, and point out precisely what they lack. Newton  The foundation N is deficient in three respects: it lacks enough concepts of force, enough laws, and enough expressive power. From the Bernoullis to Cauchy, it took a century of struggles to gain the hard-won insight that, in order to mathematize the motion of extended bodies—fluids, elastics, plastic solids, and the like—we

 The modern name for this quantity is a ‘Lagrange multiplier.’  This capsule of Lagrange’s result is perforce terse, hence hard to follow, understandably. For a longer, more lucid explanation, see Brading & Stan, Philosophical Mechanics, chapter 11. 19  The evidence for my claim is Hamel’s extensive treatise Theoretische Mechanik, which, from Lagrange’s law above, derives equilibrium conditions and equations of motion for all the species of body treated by then (viz. rigid, flexible, fluid, and elastic). 17 18

302

M. Stan

must distinguish between internal and external forces.20 To describe exactly how matter moves at any point in an extended body, we must add up the actions of both kinds of force. However, these two kinds are mathematically unlike: external forces are vectors, internal forces are tensors.21 To find out how the net internal force at a point (in an extended body) contributes to moving that point over an instant, we must use the gradient of that force. Not the quantity of the force itself.22 That gradient then combines with the net external force to cause in that point a momentum increment 𝜌ẍ, just as the Euler-Cauchy law has it. Against this background, here is how N is insufficient. First, Newton did not have the distinction internal vs external force. It is neither explicit in his definitions, nor implicit in his practice of building the rational mechanics of Principia. Second, because he lacked that distinction, his most important principle—the second law above—is too weak to apply to most bodies. It is really quite narrow: the law can describe just two species of object, namely, a free mass point and one special point in a rigid body, in very special situations.23 This fact was known at the time: In a vacuum, a material point in projectile motion describes a parabola. From that, we can understand why a body too will cross a parabola, if we throw it. But, that point motion alone will not teach us the laws governing the motion of individual parts in a finite body. […] What Newton has proved about motion under centripetal forces applies just to a single point. (Euler, Mechanica, v-vi; added emphasis)

They just did not know how to overcome that major limitation of Newton’s second law. It took a century to overcome it.24 Third, the foundation N lacks the mathematical resources to even represent the action of internal forces. That task requires the calculus of partial derivatives. Newton did not have it, and the concepts he did have are too weak to make up for that lacuna.25

 External forces originate—they are exerted by sources—outside the bounding surface S of an extended body. Examples: gravity and magnetic forces. Internal forces are exerted below S (inside the extended body), due to the body’s parts acting on one another. Examples: pressure in a fluid, and stress in an elastic solid. 21  Interpreted geometrically, a vector is an arrow-like object with a length (size) and a direction. It was used to represent the action of an impressed force on a mass point; e.g. the velocity increment (acceleration) in f = ma. A tensor is analogous to a bundle of 9 arrows, or vectors; see next footnote. 22  A tensor-like force acts on a small volume of matter to compress, stretch, or twist it. Cauchy called it ‘pressure or tension,’ to indicate that it does more than just translate a point over a small distance (which vectorial forces do). We call is ‘stress.’ 23  Namely, only when the net resultant (of all the external forces) pass through the body’s mass center. If it does not, the resultant induces motion effects (e.g. precession) that Newton’s second law cannot predict. 24  Again, for a fuller account and history, cf. Brading & Stan, Philosophical Mechanics, chapter 10. 25  Newton did not have the term ‘derivative. He just had a proto-version of it, which he called a ‘fluxion.’ That Newtonian concept overlaps with our modern notion of rate of change (of a variable quantity in respect to another, e.g. dx/dt or even dr/dx). But, it cannot capture the idea of a partial rate of change, which a derivative like 𝜕f/𝜕x expresses. 20

13  Beyond Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786

303

Leibniz  The chief law of L is not sufficient for the strong task either. My evidence for this comes from the growth of mechanics after 1700. Historically, Conservation of Vis Viva played two roles, and neither role counts as a fundamental law for all mechanics. Some used it as a premise for deriving a narrow range of results, but none of these results was an equation of motion. Rather, each counts as an effective parameter, namely, a quantity specific to the whole motion (the path crossed in a finite time) of a special point in an extended body; or by a small part of a mechanical system. For instance, the maximum height to which a body’s center of mass can rise under gravity. For instance, the characteristic frequency for the oscillating motion of the midpoint in a string made to vibrate. For instance, the sum of speed and pressure for a thin slice of fluid moving in a tube of variable width.26 And, some proved that, in certain cases, Conservation of Vis Viva was a consequence of the equations of motion. In particular, that when certain mechanical systems are left alone—if no exogenous force acts on them—they will move such that their total vis viva remains constant over time. That is the class of systems made of masses interacting by ‘conservative’ forces, viz. derivable from a function V that depends only on the relative distances between these masses. Clairaut in the1740s and Lagrange in 1788 were the chief figures for this line of thought about the fundamental law of foundation L.27 In sum, Conservation of Vis Viva sometimes entailed some special quantitative aspect of a whole motion, or path integral; and sometimes it was a corollary of the equations of motion. Not a premise for them, which a fundamental law of mechanics must be. Kant  The set K is even less sufficient as a descriptive basis for a broad theory of mechanics. Two laws in it (conservation of mass, and the equality of action and reaction) do useful work, but for a limited range of motions, and only as auxiliary premises. By themselves, neither suffices to determine any motion. Specifically, Conservation of Mass is a co-premise in fluid dynamics. Euler derived a version of it—he called it the ‘continuity equation,’ as do we. From a species of the Euler-Cauchy law (13.1a) above, in 1755 the Swiss mathematician derived the equation of motion for the instantaneous change at any point in a frictionless fluid.28 With his formula in place, Euler then explained that, to determine the fluid’s motion completely, his formula is not quite enough. Rather, it must be supplemented with Conservation of Mass (which Kant has), but stated in the exact  For the first example, cf. Propositions 39–41 of Newton’s Principia. For the second, see the final section of Daniel Bernoulli’s Hydrodynamica (1738). 27  In our terms, they showed that, if interaction forces in a system are given by (monogenic) potentials, then Conservation of Vis Viva is a ‘first integral of motion,’ i.e. a quantity conserved over a finite stretch of time. For additional discussion and historical details, see Brading & Stan, Philosophical Mechanics, chapters 8 and 11. 28  That formula is known as the Euler Equation for a perfect fluid. For details of its derivation, see Darrigol, Worlds of Flow, chapter 1; and Brading & Stan, Philosophical Mechanics, chapter 10. 26

304

M. Stan

form that is the Continuity Equation above.29 Then Navier in 1821 extended Euler’s success, but for the more complicated case of viscous fluids. Navier first inferred the strength of the friction-like effect (the viscosity tensor) that two adjacent volume elements in a fluid exert on each other. Which he then added to the dynamical part— the left-side half that sums the local actions at a point—in Euler’s Equation for a perfect fluid. Thereby, he obtained the famous Navier-Stokes equation, a more ­realistic description of how fluids in our world move. Navier too knows that his equation alone is not enough to describe the fluid’s behavior (at a point) completely. It needs supplementation: “we must add the equation of continuity.”30 In sum, Kant’s law (conservation of mass) works as an auxiliary premise, for the case of fluid motion alone, provided we state it carefully and exactly, viz. as the Continuity Equation. What about Kant’s law of action and reaction, the other non-trivial principle in K? It is even weaker than his first law above, I submit. It too does work merely as a co-premise for a narrow class of motions, viz. the exit speed of a special point (the mass center) in extended bodies undergoing impact, or collision. That is the only quantitative use to which Kant ever put it, even though that law spans three decades in his career as a natural philosopher.31 Even so, that law by itself is unable to entail any determinate content about motion changes (in impact). It too needs supplementation with other premises, or laws, depending on the type of collision at issue. Only in conjunction with them does it yield a description of motion changes for that process.32 Beyond Kant’s narrow focus on impact—for instance, in the course of the gravitation theory articulated in Principia—the law of action and reaction likewise  remains insufficient. Newton there used it in two contexts. In one, the law allows Newton to redescribe a particle’s motion (e.g. the Kepler orbit it crosses under a centripetal force) from one reference point to another.33 But that presupposes the motion has been determined already, before he gets to appeal to the third

 Why it is not enough: Euler’s Equation determines just the change of velocity at a point; but when a fluid moves, there is mass flow as well—the density at that point changes over time. This latter change is what the Continuity Equation (or Conservation of Mass) describes exactly: 𝜕𝜌/𝜕t + 𝜕𝜌v/𝜕xi = 0. In words, in a volume element, the mass density at an instant equals the mass in it at the previous instant, plus the rate of mass flow across the volume’s bounding surface. 30  Navier, “Lois des fluids,” 252. 31  In Kant, the Equality of Action and Reaction first shows up in a 1758 paper on collision theory. In MAN, he again applies it to impact, and extends its range (without explanation) to action-at-a-­ distance forces too; cf. Stan, “Kant’s third law” and Friedman, Kant’s Construction. 32  Outcomes of collision range between two limit cases. One is inelastic impact, the other is elastic collision. To infer the outcome of each case, another premise (beside the law of action-reaction) is needed. For inelastic collision, that premise is Zero Relative Speed (viz. that the two bodies move together after impact). For elastic collision, it is the conservation of kinetic energy, or vis viva. 33  Newton models first the orbit that results if the force on a particle P is directed to a point fixed in space. Then he supposes that force to emanate from another particle that is itself in motion. He proves that, relative to the mass center of these two particles, then the orbit of P is likewise elliptical. 29

13  Beyond Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786

305

law. In the other context, Newton uses the law of action-reaction so as to infer— from the existence of force (gravity) on a body—to the existence of another force, on a different body. No equation of motion is at issue there. To sum up, the other law in K is likewise not enough. It does some regional work—it shows up in the inference to the mathematical description of two particular types of motion—but just as an auxiliary premise. By itself it is insufficient, even for that narrow domain. I end with the most serious issue. There is a lacuna in Kant’s foundation that makes it quite weak—really, the least sufficient among the three candidates N, L, and K. It is this: Kant lacks any principle that allows us to infer how the motion changes if a material point is disturbed: if an exogenous mechanical agency causes that point to change its state. There is nothing in K to let us infer any determinate answer to that generic question. But that is exactly what dynamical laws are for. It is the chief virtue of the laws of Euler-Cauchy and Lagrange. That is what makes them necessary foundations for all mechanics, not just sufficient. Kant lacks even the weakest species of this sort of indispensable foundation.34

13.6 Insufficient Foundations: Matter Early modern doctrines contained another thing (beside laws and principles) designed to work as a foundation for mechanics. That thing was a picture of matter—an account of bodies qua material objects. Rational mechanics was the study of that generic object: the motion of bodies. N, L, and K contain each a picture of material objects. In this section, I argue that these pictures are also insufficient for a general mechanics. Just like the laws I examined above. That completes my overall case that N, L, and K are not complete mechanical foundations. Here too, some analytic clarification at the outset is in order. ‘Matter theory,’ or ‘picture of body,’ can mean one of two things: Content A list of attributes (viz. properties and causal powers) that all bodies have universally. Architecture An account of the geometry of mass distribution at basic scales. Examples: the mass point; the rigid body; the deformable continuum. With this distinction in hand, my claim in this section is that—whether we read them as Content or as Architecture—the matter theories in N, L, and K are each insufficient in the strong sense. For three reasons, in this section I discuss Kant at length, with little attention to the other two figures. For one, the picture of matter in N is easy to dispatch as  Separately, Watkins, Kant on Laws, and Stan, “Evidence and explanation,” have noted that not even Newton’s second law—the basis for the equation of motion of all free mass points, though not extended bodies—is to be found in Kant’s foundation. Here I am just explaining the force of that alarming conclusion. 34

306

M. Stan

insufficient; and it was not really part of Newton’s considered view.35 For another, the picture L is a rudimentary version of K, and so my verdict about Kant will carry over to Leibniz, mutatis mutandis. Last but most important, the matter theory in K is the most explicit and detailed—it takes up a good deal of Kant’s MAN —and so it repays sustained discussion. Accordingly, I move on to examine K from the point of view of content. Content  To decide if a matter theory is sufficient, let us begin by asking: given a proposed matter theory, what is it for—what does Content do for rational ­mechanics? At least among Kant scholars, a frequent answer is that Content is explanatory: it explains why bodies obey the fundamental laws of that science.36 Then let us assess how well K discharges this task. Assembled from his MAN, the Content view of a Kant body is: Matter is mobile, impenetrable, and carries momentum. A body is a finite volume of matter. For it to be a sufficient explanatory basis, two things are needed. First, Kant’s matter theory must help us understand how or why bodies (as he defines them) move as dictated by the truly general laws: the Euler-Cauchy or Lagrange laws. Not by the laws he gave in MAN, because those are not sufficiently general. Second, his Content must explain every feature of the general laws—every quantitative aspect of the motion behavior it represents—or else it is explanatorily insufficient. But here is a reason for concern: K does not even explain the common minimum of the general laws, i.e. the mechanical behavior that the two laws above, otherwise distinct as they are, have in common. (Each law—because it is more determinate and specific than the common minimum—then places further explanatory demands on Content.) Now that common minimum is: matter exerts, and responds to, impressed forces. Both laws above explicitly contain the notion of impressed force; and neither can be stated without it.37 If K has no matter-based explanation for it, then K is insufficient in that respect. Architecture  The packages N, L, and K include as well a view about the distribution of mass at basic scales. Is that a sufficient foundation? I doubt it. To see why, here too I begin by asking what Architecture is for—what work does it do, within rational mechanics? It plays two related roles. One is metaphysical: it is a sharper picture—a more precise, determinate description—of the fundamental object that mechanics is a  In natural philosophy, Newton’s standard of evidence was ‘deduction from phenomena.’ The above theory of matter did not clear his standard, and so he offered it (in Query 31 of his Opticks) not as considered doctrine, but as an (initially plausible) proposal for further research. 36  Often, they couch this answer in terms of grounding as explanation. For examples and critical discussion, see Stan, “Evidence and explanation.” 37  Stresses are a more general species of impressed force, and their gradients (as in the first Euler-­ Cauchy law) are impressed forces, like gravity. In Lagrange’s law, both the applied and also the reverse effective forces are kinds of impressed force. 35

13  Beyond Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786

307

theory of: rational mechanics quantifies the motions of those objects.38 The other role is semantic: an architecture models the reference of the fundamental laws. It pictures the objects to which the laws (qua the most general equations of mechanics) refer. At this point, it becomes easier to see why the material foundations of N, L, and K are insufficient. I begin with Newton. His architecture of matter was the rigid body—tiny but finite, inflexible volumes of mass: All these things being considered, it seems probable to me, that God in the beginning formed matter in solid, massy, hard, impenetrable, moveable particles, of such sizes and figures, and with such other properties, and in such proportion to space, as most conduced to the end for which he formed them; and that these primitive particles being solids, are incomparably harder than any porous bodies compounded of them; even so very hard, as never to wear or break in pieces: no ordinary power being able to divide what God himself made one in the first creation. (Newton, Philosophical Writings, 184; my italics)

Here is why this picture falls short. Newton’s rigid atoms are discrete: there are small yet finite distances between them. But there are vast classes of extended-body motion that presuppose matter to be continuous. Paradigmatically, that is the motion of fluids, elastic solids, and plastic bodies. The equations of motion for these body types suppose that matter is continuous and deformable, not discrete and rigid.39 Now let us examine K. For the domains above where N fails, K is just right. It is precisely the architecture of matter that those parts of mechanics presuppose. Kant’s picture fails elsewhere, however. That picture models matter as deformable, but some areas of mechanics require us to model it as rigid. For instance, the statics and dynamics of bodies with constraints. Or the domain then called ‘the mechanics of machines,’ nowadays known as engineering dynamics and the statics of rigid structures.40 To insist, as Kant and Leibniz did, that all matter is deformable, at all scales, is to deprive the subfields above of an object domain. It turns their equations of motion into illicit fictions devoid of reference. Alternatively, we may conclude (as I am inclined to do) that L and K are insufficient foundations for a truly general mechanics. Objection: mechanics does not have a single ontology, or architecture—after all, that is an upshot of my discussion above, and of recent work as well.41 So, it is unfair to ask that Kant should provide what mechanics lacks to this day, viz. a preferred ontology.  Kant in fact called his treatise a “metaphysics of corporeal nature” (see MAN, 13). A study of early-modern matter theories from this vantage point is Holden, Architecture. 39  Look again at the Euler-Cauchy (13.1a) law above. On the kinematic side, it relies on the quantity 𝜌, viz. mass density. That property obtains only in continuous matter. Discrete particles do not have mass density; they have just mass, m. But m does not show up in the for fluids and elastics (e.g., it is not in the Navier-Stokes equation). 40  Already ancient statics—the science of the five ‘simple machines,’ later with the inclined plane as a sixth—was a theory of rigid bodies: those ‘machines’ were all supposed undeformable. On the ‘science of machines’ in the eighteenth century, especially in France, see Chatzis, “Mécanique rationnelle.” 41  See, for instance, Wilson, Physics Avoidance. 38

308

M. Stan

I respond: this objection ricochets against Kant’s doctrine, for two reasons. First, he insisted that his picture of matter in MAN amounts to a “general doctrine of body.”42 A natural reading of that phrase is that his matter theory there supports a general mechanics: the mathematical description of any body’s motion. Either that, or a key aspect of his doctrine becomes mysterious: what does he mean by a ‘general doctrine of body,’ and what makes it a foundation? Second, if Kant’s architecture of matter was not meant as an ontology for all mechanics, we ought to ask, what is it for? What partial role was it designed to play, and why did he think that a partial role was so philosophically important? Thus, I do not think Kant can escape the charge of insufficiency unscathed—and neither do Leibniz and Newton, for that matter.

13.7 Some Morals With Mach and the Marburg neo-Kantians, we have long been tempted to think that, between Newton, Leibniz, and Kant, enough foundations for all mechanics were given in the century after 1687. That thought is wrong, I have argued above. It seems plausible, but only because of some tacit beliefs that, as I explain next, are themselves wrong. First, the temptation ignores that classical mechanics is old and ongoing. Along the way, its logical structure, descriptive scope, and representational frameworks have changed dramatically. But so have its foundations. Then it is ill-advised to expect that complete foundations for science that is 400 years old were discovered and expressed in the first century of its long life. Second, it ignores that, between its Galilean birth and the death of Leibniz, mechanics was able to handle just the simplest kind of body— free particles, viz. unconstrained masses the size of a point—for that was all it had the resources to treat. Qua objects of rational mechanics, extended bodies that plausibly behave like things in our common experience (water flowing, trees swaying in the wind, fabric stretching, soil shifting under foot, etc.) were too hard for the seventeenth century. So, theorists avoided them until much later. But then it is unrealistic to expect that nomic and material foundations designed for the easiest, most rudimentary parts of mechanics will survive unscathed—with no need to massively change them—when mechanics has matured enough to handle real bodies in our world. Lessons  Then what benefit may we expect from engaging philosophically with Newton’s, Leibniz’s, or Kant’s foundations? I suggest that uncovering how they miss the mark can teach us three lessons. First, we often underestimate just how elusive and difficult classical mechanics is, for the philosopher of science. Seeing Newton, Leibniz, and Kant come up short

42

 Kant, MAN, 13 (4: 478).

13  Beyond Newton, Leibniz and Kant: Insufficient Foundations, 1687–1786

309

(in regard to its true basis) is a sobering experience. At the very least, it ought to cure us of the stubborn prejudice that classical mechanics is easy to figure out philosophically, and that it ended when Einstein allegedly supplanted Newton.43 Second, their problems remain our problems. We should not presume that our age has solved their two questions above, i.e. what laws of motion and picture of body suffice to ground a general theory. The several axiomatic presentations of mechanics that we have are partial (none have been shown to entail all of mechanics). And, it is not yet clear that classical mechanics can sufficiently rest on a single theory of matter.44 In fact, because the problem of a complete foundation has proven so hard—Newton, Leibniz, and Kant, three of the greatest early modern minds, could not solve it—perhaps we ought to be prepared for the prospect that the problem may be intractable. Third, a lesson for historians. For a century now, much scholarship on Newton, Leibniz and Kant has focused on their inertial-kinematic foundations. Namely, on which quantities of motion they counted as ‘absolute,’ or objective; and whether the true carriers of those quantities were material, mental, divine, or otherwise.45 Above I made an incipient case that proper foundations for mechanics require more than just space- and time structures. In particular, they require nomic foundations, and also matter-theoretic ones. It is high time that we look at these three major thinkers from this vantage point as well. Only then, I suggest, can we really hope to judge correctly the relative weight of their philosophical insight into early modern science.

References Brading, Katherine, Marius Stan. 2023. Philosophical Mechanics in the Age of Reason. New York: Oxford University Press. Bernoulli, Daniel. 1738. Hydrodynamica. Johann Reinhold Dulsecker: Strasbourg. Cassirer, Ernst. 1907. Das Erkenntnisproblem in der Philosophie und Wissenschaft der neueren Zeit. Vol. II. Berlin: Bruno Cassirer. Cauchy, Augustin Louis. Sur les équations qui expriment les conditions d’équilibre ou les lois du mouvement intérieur d’un corps solide élastique ou non élastique. In Oeuvres complètes d’Augustin Cauchy, Série II, Tome 2, 195–226. Paris: Gauthier-Villars. Chatzis, Konstantinos. 1994. Mécanique rationnelle et mécanique des machines. In La Formation Polytechnicienne 1794–1994, ed. B.  Belhoste, A.  Dahan Dalmedico, and A.  Picon, 95–108. Paris: Dunod. Cohen, Hermann. 1885. Kants Theorie der Erfahrung. Berlin: Dümmler. Darrigol, Olivier. 2005. Worlds of Flow. New York: Oxford University Press.

 My message here dovetails with lessons that Mark Wilson has long tried to teach us, e.g. in the perceptive and rewarding studies assembled in his Physics Avoidance. 44  On this point, see again Wilson, Physics Avoidance. 45  For Newton and Leibniz, the floodgates of research on that topic opened after Reichenbach, “Bewegungslehre.” For Kant, it began with Cohen, Kants Theorie, and Cassirer, Erkenntnisproblem; then it continued through Friedman, Kant’s Construction. 43

310

M. Stan

Euler, Leonhard. 1736. Mechanica. Vol. I. Ex Typographia Academiae Scientiarum: St. Petersburg. ———. 1746. De motu corporum in superficiebus mobilibus. In Opuscula varii argumenti, vol. I, 1–136. Berlin: Haude & Spener. Fischer, Ernst. 1806. Physique mécanique, transl. J.B. Biot. Paris: Bernard. Friedman, Michael. 2013. Kant’s Construction of Nature. Cambridge: Cambridge University Press. Hamel, Georg. 1949. Theoretische Mechanik. Berlin: Springer. Hertz, Heinrich. 1899. The Principles of Mechanics Presented in a New Form, transl. D.E. Jones and J.T. Walley. London: Macmillan. Holden, Thomas. 2004. The Architecture of Matter. Oxford: Clarendon. Kant, Immanuel.2004. Metaphysical Foundations of Natural Science, trans. M.  Friedman. Cambridge: Cambridge University Press. Kuhn, Thomas. 1996. The Structure of Scientific Revolutions. 3rd ed. Chicago: University of Chicago Press. Leibniz, Gottfried Wilhelm. Philosophical Essays, ed. and transl. D.  Garber and R.  Ariew. Indianapolis: Hackett. Lagrange, Joseph Louis. 1788. Mechanique analytique. Paris: Veuve Desaint. Mach, Ernst. 1883. Die Mechanik in ihrer Entwickelung. Leipzig: F.A. Brockhaus. Navier, Henri. 1821. Sur les lois des mouvements des fluides, en ayant régard à l’adhésion des molécules. Annales de Chimie et de Physique XIX: 244–260. Newton, Isaac. 1999. The Principia: Mathematical Principles of Natural Philosophy, ed. I.B. Cohen, trans. A. Whitman. Los Angeles: University of California Press. ———. 2014. Philosophical Writings, ed. A.  Janiak, 2nd edn. Cambridge: Cambridge University Press. Papastavridis, John G. 2014. Analytical Mechanics. London: World Scientific. Reichenbach, Hans. 1924. Die Bewegungslehre bei Newton, Leibniz und Huygens. Kant Studien XXIX: 416–438. Smith, George E. 2008. Newton’s Philosophiae Naturalis Principia Mathematica, The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), ed. Edward N. Zalta, URL = https://plato. stanford.edu/archives/win2008/entries/newton-­principia/. Stan, Marius. 2013. Kant’s third law of mechanics. Studies in History and Philosophy of Science XLVI: 493–504. ———. 2021. Evidence and explanation in Kant’s doctrine of laws. Studi Kantiani XXXIV: 141–149. ———. 2022. From metaphysical principles to dynamical laws. In The Cambridge History of Philosophy of the Scientific Revolution, ed. D.M.  Miller and D.  Jalobeanu. New  York: Cambridge University Press. Truesdell, Clifford. 1968. Essays in the History of Mechanics. Berlin: Springer. ———. 1991. A First Course in Rational Continuum Mechanics. 2nd ed. Boston: Academic. Watkins, Eric. 2019. Kant on Laws. Cambridge: Cambridge University Press. Wilson, Mark. 2018. Physics Avoidance. New York: Oxford University Press.

Appendices

 ppendix I: Newton’s Scholia from David Gregory’s Estate A on the Propositions IV Through IX Book III of His Principia edited, translated, and annotated by Volkmar Schüller James Craufurd Gregory indicated as early as 1832 that a number of important handwritten texts by Newton with drafts for several scholia were preserved in the estate of the Scottish mathematician and astronomer David Gregory (1659–1708). Newton originally meant to add these texts to Propositions IV through IX Book III in a later edition of his Principia, but an edition with these scholia was never published. These texts then were forgotten until Cohen (Quantum in se est p.  148) announced that he would release an edition of these texts; however, this edition never appeared. In the publication Newton and the ‘Pipes of Pan’ by J.E. McGuire and P.M. Rattansi (1966) these texts were analyzed and interpreted for the first time. This publication received much attention, especially as it showed that the contents of these drafts were known to a number of physicists and mathematicians who associated with Newton or belonged to the first two generations of Newtonians. As well Cohen as J.E. McGuire and P.M. Rattansi demonstrated that Newton wrote these texts at the beginning of the 1690s, but they were first published in full by Casini (Newton: The Classical Scholia, 1995) on the basis of the handwritten texts by Newton discovered in David Gregory’s estate. However, in the course of preparing a new German translation of Newton’s Principia, we unfortunate1y were forced to establish that the text edited by Casini contains quite a few misread errors and does not stand up to strict philological standards. Therefore, we had to consult Newton’s handwritten texts directly. Considering their extraordinary meaning for the history of science, a new, more precise edition of these drafts by Newton for the scholia on © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 W. Lefèvre (ed.), Between Leibniz, Newton, and Kant, Boston Studies in the Philosophy and History of Science 341, https://doi.org/10.1007/978-3-031-34340-7

311

312

Appendices

the Propositions IV through IX Book III proved urgent1y required. In the following we thus intend to edit these drafts by Newton again in what is hopefully a final, definitive form. Newton’s Philosophiae Naturalis Principia Mathematica first appeared on the book market in July of the year 1687, as we can infer from Edmond Halley’s letter of July 5, 1687 to Newton (Newton’s Correspondence II 481 No. 309). Halley, who, after all, really encouraged Newton to write the Principia and later was responsible for printing Newton’s Principia on behalf of the Royal Society, wrote in this letter to Newton that the printing of the Principia had finally been completed and that he hoped that Newton would be satisfied with the result. At the same time, he informed Newton that he would send him a few copies to Cambridge and moreover, as Newton requested, one copy of the Principia each to the Royal Society, Mr. Boyle, Mr. Pagit and Mr. Flamsteed. But it was not from them that Newton immediately received enthusiastic approval and thanks for his Principia, but from the young Scottish mathematician David Gregory. He was no longer a stranger to Newton since he had sent his Exercitatio geometrica de dimensione figurarum (Edinburgh 1684) to Newton with his letter of July 9, 1684 (Newton’s Correspondence II 396 No. 268). Newton, however, never responded to this letter, but David Gregory nevertheless continued to follow Newton’s activities closely. Thus, when the Principia finally appeared as a book, Gregory wrote on September 2, 1687 (Newton’s Correspondence II 484 No. 311) – less than two months after publication of the Principia – an enthusiastic letter to Newton, presumably with the intention of reminding Newton who he was. When Gregory and Newton met personally for the first time is unfortunately not known, but Newton’s letter of July 27, 1691 to Arthur Charlett, on the strength of which the Savilian chair for astronomy at Oxford was bestowed on David Gregory, suggest that Newton and Gregory may have encountered each other personally for the first time in the spring or summer of 1691. In his letter (Newton’s Correspondence III 154 No. 366), Newton writes on David Gregory: “He is very well skilled in Analysis & Geometry both new & Old. He has been conversant in the best writers about Astronomy & understands that science very well. He is not only acquainted with books but his invention in mathematical things is also good. [...] is respected the greatest Mathematician in Scotland.” When David Gregory visited Newton at Cambridge in May 1694, Gregory took notes on his conversations with Newton, in which he relates the following: “He will spread himself in exhibiting the agreement of this philosophy with that of the Ancients and principally with that of Thales. The philosophy of Epicurus and Lucretius is true and old, but was wrongly interpreted by the ancients as atheism .... It is clear from the names of the planets by Thoth (the Egyptian Mercury) – he gave them, in fact, the names of his predecessors whom he wished to be accepted as gods – that he was a believer in the Copernican system.” (Newton’s Correspondence III 334 No. 446). That Newton also wanted to include such thoughts in a later, edited version of his Principia is apparent from David Gregory’s memoranda of July 1694. Here Gregory describes in detail what Newton intended to change in the Principia and which new subjects he would include. Among others, Gregory writes, “By far

Appendices

313

the greatest changes will be made to Book III.  He will make a big change in Hypothesis III pag. 402. He will show that the most ancient philosophy is in agreement with this hypothesis of his as much because the Egyptians and others taught the Copernican system, as he shows from their religion and hieroglyphics and images of the Gods, as because Plato and others – Plutarch and Galileo refer to it – observed the gravitation of all bodies towards all” (Newton’s Correspondence III 384 No. 461). Through a stroke of luck, these manuscripts with Newton’s drafts for the scholia which were to be added to Propositions IV through IX in Book III fell to David Gregory’s estate. Although Gregory (Notice concerning an Autograph Manuscript by Newton) gave a quite comprehensive account of them, for a long time they unfortunately remained completely neglected. How these manuscripts by Newton came to be in David Gregory’s possession is not known. It cannot be determined whether Newton gave these manuscripts to Gregory as a gift or whether they became part of David Gregory’s estate although they were merely entrusted to him temporarily. David Gregory was doubtlessly one of the most thorough readers of Newton’s Principia, and as early as September 1687 he started writing a running commentary on Newton’s Principia. The manuscript of this commentary also offers a number of signs that Newton shared new scientific results with him directly. After several interruptions, David Gregory provisionally concluded work on this commentary in January 1693/4; in February 1697/8 he then continued and ultimately ended this commentary, including important remarks on Book III of the Principia, as Wightman (Gregory’s Commentary) substantiates in detail. At the end of his own manuscript, the Notae in Newtoni Principia Mathematica Phiosophiae Naturalis, now located in the Archive of the Royal Society in London, there is a transcript written by David Gregory of Newton’s manuscripts with the scholia which Newton wanted to add to Propositions IV through IX Book III. In formulating the foreword to his own Astronomiae Physicae et Geometricae Elementa (Oxford 1702), there is no doubt that David Gregory used Newton’s manuscript. Without directly referring to Newton, he cites nearly all of the same Ancient authors Newton mentions in his manuscript, but also includes several passages of Ancient authors not quoted by Newton. It is, however, quite doubtful that Newton was in fact as irritated about this as Thomas Hearne (Remarks and Collections I 123) relates in his comments on December 10, 1705, “Sir Isaac Newton has complain’d that Dr. Gregory, who borrow’d most of the best materials in his Book of Astronomy from Sir Isaac, has made little or no mention of him but just in his Preface”, for the passages quoted by David Gregory are not citations from Newton’s writings, but generally accessible Ancient sources. Besides which, Newton and David Gregory continued to correspond with each other after the Elementa was published. The scholia were to complement Newtons propositions IV through IX of Book III of the first edition (1687) of his Principia. In these scholia Newton endeavored to show, that the idea of universal gravitation was an ancient one and that the ancients even were acquainted with the law of universal gravitation. The propositions IV through IX were translated in Newton (Mathematical Principles of Natural Philosophy) as follows:

314

Appendices

Proposition IV Theorem IV The moon gravitates toward the earth and by the force of gravity is always drawn back from rectilinear motion and kept in its orbit.

Proposition V Theorem V The circumjovial planets gravitate toward Jupiter, and the circumsolar Planets gravitate toward the sun, and by the force of their gravity they are always drawn back from rectilinear motions and kept in curvilinear orbits.

Proposition VI Theorem VI All bodies gravitate toward each of the planets, and at any given distance from the center of any one planet the weight of anybody whatever toward that planet is proportional to the quantity of matter which the body contains.

Proposition VII Theorem VII Gravity exists in all bodies universally and is proportional to the quantity of matter in each.

Proposition VIII Theorem VIII If two globes gravitate toward each other, and their matter is homogeneous on all sides in regions that are equally distant from their centers, then the weight of either globe toward the other will be inversely as the square of the distance between the center.

Proposition IX Theorem IX In going inward from the surfaces of the planets, gravity decreases very nearly in the ratio of the distances from the center. The Sources for Our Edition Two versions of Newton’s scholia are included in the Gregory’s estate in the Archive of the Royal Society in London. One of these manuscripts (signature: MS 247 fol. 6–14) was written entirely by Newton himself and is in part extremely difficult to read because of the many corrections and deletions; unfortunately, a few passages are illegible and could not be deciphered, but these appear to be irrelevant to the contents. Since this manuscript is still the only known handwritten version of the scholia written by Newton, we used it as the basis for our edition of Newton’s scholia. On the last nine pages of the document handwritten by David Gregory himself, also preserved in the Archive of the Royal Society in London with its Notae in Newtoni Principia Mathematica Philosophiae Naturalis (signature: MS 2l0), is included a copy of Newton’s scholia without corrections but with the note: “Copied from the Ms. in Sir Isaac Newton’s own hand.” It is highly improbable that this note was written by David Gregory himself, in whose hand the bulk of Gregory’s Notae (MS 210) held in the Archive of the Royal Society in London were written. The undeniable similarity with the text of the drafts written by Newton himself for the

Appendices

315

scholia on Propositions IV through IX Book III suggests that this remark refers to the manuscripts written by Newton (MS 247 fol. 6–14), but see the remarks 10 and 88 on Newton’s scholia. The transcript in MS 210 largely corresponds with Newton’s manuscript (MS 247 fol. 6–14), but since it is a neat copy, of course it does not contain the corrections discarded by Newton. Great effort has been expended on their decipherment in our edition of MS 247 fol. 6–14. Through David Gregory’s transcript a number of completely corrupted passages in Newton’s manuscript (MS 247 fol. 6–14) could be emended. About the English Translation In the English translation of the authors cited directly or indirectly by Newton, we gratefully made use of the English translations of these authors listed in our [bibliography, whereby we occasionally altered these translations slightly where we believed that such changes would allow us better to express how Newton presumably translated or interpreted these authors, respectively. A German translation is available in Newton (Die mathematischen Prinzipien der Physik, 552–563). Abbreviations Used In Newton’s Latin text, pointed brackets < ..... > indicate the passages in the manuscript which were illegible due to damaged paper or similar factors, and which had to be completed under consideration of the context. In the English translation, pointed brackets < ..... > indicate completions which did not directly appear in Newton’s Latin text, but had to be added in order to obtain an understandable and readable English translation. The illegible passages in Newton’s text are indicated by XXX; the passages within a sentence which were deleted by Newton appear in the printed text as passages crossed out, and the underlined passages in Newton’s text are italicized. I thank the Archive of the Royal Society in London for providing the copies of RS. MS. 247. ff. 6–14 and RS. MS. 210. Newton’s texts are reproduced by kind permission of the President and Council of the Royal Society. I thank Susan E. Richter for valuable support of the translation into English.

316

Appendices

Newton’s Scholia folio 9r In Prop. IV Lib. III Princip. Math. p. 407.1

Propriâ manu D. Newtoni.2

Schol. Lunam esse corpus densum terrestre & grave & vi gravitatis in Terram nostram casuram esse nisi vi motus circularis cohiberetur et in orbe suo suspensa teneretur antiqua fuit opinio. Nam cum Philosophi aliqui Lunam esse Terram in sublimi suspensam docerent & alii Lunam aeris et ignis mixturam esse eontenderent, nec si corpus densum esse et terrestre esse negarent & aeris ac ignis mixturam esse maluerunt ne gravitate sua caderet in Terram nostram: a3Plutarchus introducit Lucium quendam pro priori opinione sic disputantem. Ne Terra cadat non metuit Pharnaces, miseretur autem Lunae conversioni suppositos Aethiopes & Taprobenos ne in eos tanta moles decidat sollicitus. Atqui Lunae auxilio est ne cadat, motus suus & revolutionis impetus: quomodo quae fundis imposita sunt & in orbem rotantur, per rotationem suam impediuntur ne delabi possint. Nam motus naturalis [sc. gravitatis] rem unamquamque agit si non ab alia aliqua re alio avertetur. Ea de causa Lunam gravitas non movet, cum a conversionis circularis etu descensus eius inhibeatur.

Καί τοι τῇ μὲν σελήνῃ βοήϑεια προς τὸ μὴ πεσεῖν ἡ κὶνησις αὐτὴ καὶ τὸ ῥοιζῶδες τῆς περιαγωγῆς, ὥσπερ ὅσα ταῖς σφενδόναις ἐντεϑέντα τῆς καταφορᾶς κώλυσιν ἴσχει τὴν κύκλῳ περιδίνησιν. ἄγει γὰρ ἕκαστον ἡ κατὰ φύσιν κίνησιν, ἂν ὑπ᾽ἄλλου μηδενὸς ἀποστρέφηται. διὸ τὴν σελήνην οὐκ ἄγει τὸ βάρος ὑπὸ τῆς περιφορᾶς τὴν ῥοπὴν ἐκκρουόμενον.

Desumpta videtur haec sententia a Philosophia Jonica. Haec enim a Thalete per Anaximandrum & Anaximenem ad Anaxagoram propagata fuit, & b4Anaxagoras aetherem igneum esse dixit & circumvolutionis vehementia abripuisse lapides e terra eosque adussisse & sic in stellas convertisse. c5Totum vero coelum lapidibus [i.e. corpora omnia coelestia] lapidibus constare, sed conversionis celeritate contineri cujus remissione casurum est. d6Lapidem quoque e Sole casuram esse finxit & Solem vocavit e7 μύδρον ἤ πέτρον διάπυρον lapidem igne candentem. Idem sensere f8 Archelaus a. Plutareh. de facie in orbe Lunae. b. Plutareh. Plaeit. Philos. X lib. 2. e. 13. e. Laertius in vita Anaxagorae. d. Laertius ib. e. Plato in Apolog. Socr., Plutarch Placit. Philos. I. 2 e. 20, Laertius ib., Cyrillus Alexandrinus I. 6., cont Jul. Suidas in Anaxa μύδρος Anaxagora f. Stobaeus Eel. phys. 20 vel 25

Appendices

317

folio 9r On Prop. IV Book. III Mathemat. Princip. p. 407.

In Mr. Newton’s own hand

Schol. That the earth’s moon is a dense body made of earth, and that it is heavy and would fall toward our earth due to the force of gravity if it were not prevented from doing so and held in suspension on its path of rotation due to the force of its circular motion, is an old view, since one school of philosophy taught namely that the earth’s moon is an earth floating up above, while another insisted that the moon is a mixture of air and fire, and, indeed, if not disputed that it is a dense body and made of earth, and thought that it be a mixture of air and fire, so that it would not fall to our earth due to gravity: Plutarcha introduced a certain Lucius, who espoused the former opinion in the following manner. And therefore Pharnaces is himself without any fear that the earth may fall but is sorry for the Ethiopians or Taprobanians, who are situated under the circuit of the moon, lest such a great weight fall upon them Yet the moon is saved from falling by its very motion and the rapidity of its revolution, just as missiles placed in slings are kept from falling by being whirled around in a circle. For each thing is governed by its natural motion [namely of the gravity] unless it be diverted by something else. That is why the moon is not moved by gravity: its des cent is prevented by the impetus of circular rotation.

Καί τοι τῇ μὲν σελήνῃ βοήϑεια προς τὸ μὴ πεσεῖν ἡ κὶνησις αὐτὴ καὶ τὸ ῥοιζῶδες τῆς περιαγωγῆς, ὥσπερ ὅσα ταῖς σφενδόναις ἐντεϑέντα τῆς καταφορᾶς κώλυσιν ἴσχει τὴν κύκλῳ περιδίνησιν. ἄγει γὰρ ἕκαστον ἡ κατὰ φύσιν κίνησιν, ἂν ὑπ᾽ἄλλου μηδενὸς ἀποστρέφηται. διὸ τὴν σελήνην οὐκ ἄγει τὸ βάρος ὑπὸ τῆς περιφορᾶς τὴν ῥοπὴν ἐκκρουόμενον.

This view appears to be taken from Ionic philosophy. This is what was passed on from Thales through Anaximander and Anaximenes to Anaxagoras, and Anaxagorasb said that the ether is made of fire and that it swept stones away from the earth with the intensity of its revolution, lit these on fire and thus transformed them into stars. Anaxagoras declared the whole firmament of stones [i.e., all heavenly bodies] to be made of stones, but that the rapidity of rotation caused it to cohere; and that if this abated it would fall.c It was his invention that a stone would fall from the sun as welld and called the sun a μύδρον ἤ πέτρον διάπυρον,e a stone glowing white with fire. This was also the view of the pupils of Anaxagoras, Archelausf a. Plutarch, The Face on the Moon b. Plutarch, Philosph. Teachings Book 2 Chap. 13 c. Laertius in Anaxagoras’ life d. Laertius ibid. e. Plato in Socrates’ Apology; Plutarch, Philosoph. Teachings Book 2 Chap. 20; Laertius ibid., Kyrill ofAlexandria Book 6 Against Julianus; Suidas to, Anaxa μύδρος Anaxagoras f. Stobaeus, Ecl. Phys. 20 or 25

318

Appendices

& g9Euripides Anaxagorae discipuli, ut et h10Democritus et Metrodorus & +11Diogenes Apolloniata qui dixit stellam saxeam ignis forma in Aegos fluvium decidisse. Per saxa vero nihil aliud intelligebant quam corpora gravia decidentia densa et fixa ad instar lapidum saxorum instar ut ignem sustinere possint. Nam et Solem k12glebam auream nonnunquam vocabant, hoc nomine tam fixitatem materiae quam densitatem & pondus designantes. Sed nec Lunam Anaxagoras nudum lapidem esse voluit at Terram gravem ac densam qualis est ea cui inambulamus. l13 In Luna enim habitari XXXX docuit & esse in ea colles & convalles & m14latam quandam regionem e qua Leo Nemeus deciderat. Per figmenta Leonis e Luna et lapidis e Sole cadentium docebat gravitatem corporum XXX Solis et Lunae in Terrarn, & per figmentum lapidum ascendentium docebat vim rotationis gravitati contrariam. m haec ad literam intelligenda non sunt. Philosophi mystici sub huiusmodi figmentis & sermonibus mysticis dogmata adumbrare solebant. Et haec Haec autem Philosophia tam late per Graeciam ad usque tempora Platonis propagata fuit ut n15Plato de ea sic conquestus sit. Cum Solem Lunam, Sidera et Terram quasi Deos et res divinas in medium folio 8r adducimus tunc juvenes ab istis qui [XX qui nuper in Graecia philosophati sunt] aliter persuasi, terram & lapides haec esse dicunt, nullamque rerum humanarum curam habere posse. p16Democritus autem sententias Anaxagorae de Sole & Luna ab ipso excogitatas esse negabat, antiquas enim esse dicebat, easque ipsum suffuratum esse. Proinde hae ad Philosophiam Jonicam merito referendae sunt. Nam et Thales Philosophiae illius q17Anaximenes Anaxagorae magister naturam siderum (fixorum scilicet) esse igneam censuit, tum corpora quaedam terrena sed inaspectabilia (id est Planetas terrestres XXXX ob distantiam invisibiles in sideris cuiusque systemate revolventes) commiscuit. Et r18Thales Philosophiae XX Jonicae fundator censuit γεώδη μὲν, ἔμπυρα δὲ τὰ ἄστρα, terrestres esse stellas fixas, sed ignitas interim. Eadem sententia obtinuit etiam in Philosophia Italica. Nam s19Pythagorei dicebant Solem esse ignem Lunam terrestrem esse, quia, sicut et nostra terra, circumhabitatur g. Plato in Apolog. h. Plutarch. Placit. Philos. 1. 2. c. 13,20 i. Plutarch k. Laertius XX in Anaxag. I. Laertius in Anaxag. m. Natalis Comes in Hercule p. 672 n. Plato de leg. lib. 10 sub initio p. Apud Laertium in Anaxagora. q. Stobaeus EcI. Phys. X 25 r. Plutarch. Placit. Philos. lib. 2 c s. Plutarch. ib. 1. 2. c. 30.

Appendices

319

and Euripidesg as did Democritus,h Metrodorus and Diogenes+ of Appollonia, who said that a star of rock fell in the form of fire in Aegospotami. Rock was understood to be nothing other than heavy falling dense and solid bodies just as stones much the same as boulders, so that they could endure fire. That is to say that they at times designated the sun as a golden clod,k whereby this designation alluded to both the solidity of the matter as well as its density and weight. But Anaxagoras was not of the opinion that the earth’s moon was just a stone, but rather a heavy, dense earth, like the one on which we walk around. That is, he taught that the earth’s moon was inhabited and that located there were mountains, valleys,l and a certain vast area from which the Nemean lion had fallen.rn Through the fiction of the lion falling from the earth’s moon and the stone falling from the sun he taught the gravity of the bodies of the sun and the earth’s moon; through the figment of ascending stones he taught the force opposite to gravity, that of rotation. This is not to be understood literally. The mystic philosophers usually hid their tenets behind such figments and mystical language. And these This philosophy was so widespread among the Greeks well into Plato’s era that Plato complained about it as folIows:n If we advance the sun, the earth’s moon, the stars and the earth as Gods and divine things, folio 8r then those young men who have been convinced otherwise by those [who in recent times have philosophized in Greece] say that these are earth and stones and that they are completely unable to take care of the affairs of mankind. Democritus,P however, disputed that Anaxagoras’ views about the sun and the earth’s moon were the product of his own thinking; that is, he said that they were old and that he had simply taken them over. Accordingly, these views must by all rights be attributed to the Ionic philosophy. For Thales of this philosophy Anaximes, q Anaxagoras’ teacher, also believed that the nature of the stars (the fixed stars, of course) is fire-­ like; furthermore he linked certain earth-like, but invisible bodies (i.e., planets or earth, which are invisible because of the distance and revolve in the system of the star in question). Even Thales,r the founder of Ionic Philosophy, believed γεώδη μὲν, ἔμπυρα δὲ τὰ ἄστρα, the fixed stars may be made of earth, but they are glowing. The same view was held in the Italic philosophy. It was the Pythagoranss who said that the Sun is a fire the earth’s moon is of earth, because it, like our own earth, is inhabited; g. Plato in the Apology h. Plutarch, Philosoph. Teachings Book 2 Chap. 13,20 i. Plutarch k. Laertius to Anaxagoras I. Laertius to Anaxagoras m. Natale Conti in Hercule p. 672 n. Plato, On the Laws Book 10 beginning p. In Laertius to Anaxagoras q. Stobaeus, Ecl. Phys. 25 r. Plutarch, Philosoph. Teachings Book 2 Chap. s. Plutarch, ibid., Book 2 Chap. 30

320

Appendices

a majoribus quidem & pulchrioribus animalibus ob dierum longitudinem. & Pythagoreorum aliqui fingebant stellmn XXXX gravitatem siderum docebant adumbrabant t20fingendo stellam tempore incendij a Phaetonte excitati de loco suo delapsam loca quae circulari cursu peragravit adussisse & in viam lacteam convertisse.21 Quinetiam Plato in eandem sententiam concessisse videtur. Hic enim u22statuit corpora mundana, etiam tum cum jam fabricata et omnino stabilita essent aliquamdiuXX motu recto agitata fuisse sed postquam ad certa determinataque loca pervenissent paulatim in gyrum revolvi coepisse motu recto commutato cum circulari in quo postea perstiterunt: et Galilaeus hoc refert ad gravitatem qua corpora illa primum motu recto accelerato caderent dein flecterentur in gyrum. folio 6r pag. 40823 Ad XXXX Prop. 5. adde Scholium. Gravitatem fieri in Solem ac Lunam aeque ac in Terram Plutarch de facie in fieri Plutarchus24 ex mente Veterum Philosophorum quo- orbe Lunae p. 92 rundam sic docet. Praejudicijs onusti 25eos dicunt inferiora superioribus adjungere26 qui Lunam quae Terra sit non in medio sed in sublimi collocant. At enim si omne corpus grave eodem fertur et ad centrum suum ab omnibus partibus vergit, Terra non ut centrum Universi potius quam totum quoddam] sibi omnia gravia ut suas partes vindicabit. et indicium erit corpora convergere non ut occupent medium mundi locum sed ob cognatione cum Terra, a qua vi repulsa rursum ad eam se conferunt. Sicut enim Sol omnes partes, ex quibus constat ad se convertit, sic et Terra lapidem ut ad se pertinentem accipit, & XX fert ad eum. Itaque horum unumquodque temporis progressu unitur cum ea & coalescit. Quod si quod est corpus ab initio Terrae XX non attributum, neque ab ea avulsum sed peculiari atura pro sese constat (qualem isti Lunam faciunt) quid obstat quin orsim id subsistat suis compactum ac constrictum partibus. Democritus autem cum diceret infinitos esse mundos cum diceret infinitos esse mundos et per mundos XXXXXX singulos non singulos Planetas sed singular Planetarum systemate intelligeret non solum Planetas qui in eodem sunt systemate in se mutuò graves esse XXXXX voluit sed XXXXX etiam gravitatem eorum in alia undique systemata XXXXX extendi. Docuit enim φϑείρεσϑαι ἀυτοὺς mundos alios generari, XX alio corrumpi deficere, φϑείρεσϑαι δὲ ἀυτοὺς ὑπ᾽ ἀλλήλων προσπίπτοντας corrumpi autem illos in se invicem cadendo. [Origenes in Philosophicis.]27 Ad quam sententiam Epic Lucretius28 sic alludit t. Plutarch. ibo 1. 3. c. 1. u. Galilaeus in Syst. cosm. sub initio.

Appendices

321

however, because of the length of the days, by larger and more beautiful creatures. And other philosophers of the Pythagorean school invented that the star said hid the gravity of the stars by inventingt that the star, which slid down from its location at the time of the fire kindled by the Phaethon, reached locations which executed a circular revolution and transformed itself into the Milky Way. Indeed, even Plato appears to have concurred with this view. That is, he maintainedu that even the bodies of the world, at the time that they had just been created and became completely solid, were put into motion for a certain period, but once they had reached certain determined locations, they began, one after the other, to revolve in a circle, as the straight motion had been substituted with a circular motion, with which they then stayed: and Galileo attributes this to gravity, due to which these bodies initially fell into a straight, accelerated motion and later were steered to a circle. folio 6r pag. 408 To Prop. V to be added Scholion That gravity arises toward the sun and toward the earth’s Plutarch, The Face moon as well as to the earth, Plutarch teaches based on the on the Moon p. 92 view of certain earlier philosophers as follows. Those who are subject to prejudice say that those who add below to above place the moon, though it is an “Earth,” on high and not where the center iso Yet if every heavy body is carried to the same point and tends toward the center, the earth can claim not to be the center of the universe, but rather to be a certain whole for itself of which all heavy are a part. An indication of this is that the bodies do not strive to converge to occupy the center position of the world, but rather, due to the kinship to the earth move back to her when they are removed from her by force. F or as the sun guides to itself all of the parts of which it consists, so the earth too accepts as stone as belonging to her and carries it to this . Consequently, every such ultimately unites and coheres with her. If some body was not originally allotted to the earth or detached from it, but due to its own peculiar nature exists on its own (as those would say of the earth’s moon), what is to hinder it from staying below, being compressed and bound together by its own parts. Democritus, however, when he said that there was an infinite number of worlds, when he said that there was an infinite number of worlds, and understood these individual worlds to be not individual planets, but individual systems of planets, thought that not only the planets which belong to the same system mutually are heavy toward each other, but that their gravity also extended all over toward the other systems. He taught that φϑείρεσϑαι ἀυτοὺς some worlds were produced while others are destroyed pass away, φϑείρεσϑαι δὲ ἀυτοὺς ὑπ᾽ ἀλλήλων προσπίπτοντας, those that fade away are destroyed by falling into each other. [Origines to the Philosophers] Epic Lucretius alludes to this sentence as follows: t. Plutarch, ibid., Book 3 Chap. I u. Galilei on the World Systems, beginning

322

Appendices

Lucret. 1. 5. sub initio.29 Quod superest, ne te in promissis plura moremur Principio maria ac terras caelumque tuere Horum naturam triplicem, tria corpora, memmi, Tris species tarn dissimilis, tria talia texta Una dies dabit exitio: multosque per annos Sustentata ruet moles et machina mundi. Nec me animi fallit quam res nova miraque menti Accidat, exitium caeli terraeque futurum Et paulo post30 - - - - dictis dabit ipsa fidem res Forsitan, & graviter terrarum et motibus ortis3l Omnia quassari in parvo tempore cernes: Quod procul a nobis flectat fortuna gubernans, Et ratio potius quam res persuadeat ipsa Succidere horrisono posse omnia victa fragore. folio 6v Ad Prop: VI32 Scholium Corpora omnia quae circa terrarn sunt tam aerem et ignem quam reliqua XXXX esse gravia esse in Terram et eorum gravitatem proportionalem esse quantitati materiae ex qua constant Veteribus etiam innotuit. Nam Lucretius pro vacuo sic disputae33 Denique cur alias alijs praestare videmus Pondere res rebus nihilo majore figura? Nam si tantundem est in lanae glomere quantum Corporis in plumbo est, tantundem pendere par est, Corporis officium est quoniam premere omnia deorsum: Contra autem natura manet sine pondere Inanis. Ergo quod magnum est eque leviusque videtur, Nimirum plus esse sibi declarat Inanis; At contra gravius plus in se corporis esse Dedicat, et multo vacui minus intus habere Est igitur nimirum id quod ratione sagaci Quaerimus, admistum rebus quod inane vocamus. Lucretius hic refert gravitatem ad corporis officium seu naturam qua ab inani non gravitante distinguitur et inde concludit pond corpori semper proportionale esse. Quo argumento corpora omnia tam insensibilia quam sensibilia comprehendit. Nam et atomis ipsis ex quibus alia omnia constant gravitatem hanc attribuit. Docet enim ignem et corpora alia quae levia dicuntur non spon sed vi subigente ascendere perinde ut lignum quod corpus grave est ascendit in aqua: corpora autem omnia per spatium inane deorsum ferri.

Appendices

323

Lucretius Book 5 at the beginning For the rest, that I may delay you no more with promises, first of all look upon seas, and lands, and sky; their threefold nature, their three bodies, Memmius, their three forms so diverse, their three textures, each in its kind, one single day shall hurl to ruin; and the massive form and fabric of the world, held up for many years, shall fall headlong. Nor does it escape me in my mind how strangely and wonderfully this strikes upon the understanding, the destruction of heaven and earth that is to be. And slightly later: - - - Maybe the very fact will give credence to my words, and within a little while you will behold earthquakes arise and all things shaken in mighty shock. But may fortune at the helm steer this far away from us, and may reasoning rather than the very fact make us believe that all things can fall in with a hideous rending crash. folio 6v To Prop. VI Scholion That all bodies located around the earth, air and fire as well as the others, are heavy toward the earth and that their gravity is proportional to the quantity of matter of which they consist, was known to the ancients. For Lucretius pleaded for the void as follows: Again, why do we see one thing surpass another in weight when its size is no whit bigger? For if there is as much body in a ball of wool as in lead, it is natural it should weigh as much, since it is the office of the body to press all things downwards, but on the other hand the nature of void remains without weight. So because it is just as big, yet is seen to be lighter, it tells us, we may be sure, that it has more void; but on the other hand the heavier thing avows that there is more body in it and that it contains far less empty space within. Therefore, we may be sure, that which we are seeking with keen reasoning, does exist mingled in things: that which we call void. Lucretius attributes the gravity to the “office of the body” or to nature, which differentiates itself from the non-gravitating void, and concludes from this that the weight is always proportional to the body. He includes all bodies in this argumentation, invisible as well as visible. Then he ascribes gravity to even the atoms themselves, of which all else consists: He teaches that fire and the other bodies which are called light bodies do not ascend of their own accord, but as a result of a force driving upwards, just as wood, which is a heavy body, rises in water: but all bodies are carried downward through empty space.

324

Appendices

Lucret. 1. 2. vers 183.34 Nunc locus est (ut opinor) in his illud quoque rebus Confirmare tibi, nullarn rem posse sua vi Corpoream sursum ferri, sursumque meare Nec tibi dent in eo flammarum corpora fraudem Sursus enim versus gignuntur et augmina sumunt Et sursum nitidae fruges arbustaque erescunt Pondera quantum in se est,35 cum deorsum cuneta ferantur Nec eum subsiliunt ignes ad tecta domorum Et celeri flamma degustant tigna trabesque, Sponte sua facere id sine vi subiecta putandum est. Quod genus e nostro missus cum missus corpore sanguis Emicat exultans alte spargitque cruorem. Nonne vides etiam, quanta vi tigna trabesque Respuat humor aquae? Nam quam magis ursimus altum Derceta, & magna vi multi pressimus aegre, folio 10r Tam cupide sursum revomit magis atque remittit, Plus ut parte foras emergant exsiliantque. Nec tamen hae quantum est in se, dubitamus, opinor, Quin vacuum per Inane cuneta ferantur. Sic igitur debent flammae quoque posse per auras Aeris expressae sursum succedere, quamquam Pondera quantum in se est deorsum deducere pugnent. Et quamvis res leviores quae aeris vel aquae resistentiam difficilius vincant in his fluidis descendant tardius, tamen in spatio vacuo ubi nulla est resistentia atomos omnes tam graviores quam minus graves propter gravitatem sibi proportionalem aequali celeritate descendere, docet Lueretius XXX sic docet Lueretius36 Quod Illud in his rebus quoque te rebus cognoscere avemus: Corpora eum deorsum rectum per Inane feruntur. Ponderibus proprijs, incerto tempore ferme, lncertisque locis spatio decedere paullum: .37 Quod nisi declinare solerent, ornnia deorsum, Imbris uti guttae caderent per Inane profundum: Nec foret offensus natus, nec plaga creata Principijs: ita nil umquam natura creasset. Quod si forte aliquis credit graviora potesse Corpora, quo citius rectum per Inane feruntur, Incidere e supero levioribus, atque ita plagas Gignere, quae possint genitalis reddere motus: A vius a vera longe ratione recedit. Nam per aquas quaecunque cadunt atque aera deorsum: Haec pro & ponderibus casus celerare necesse est,

Appendices

325

Lucretius Book 2 verse 183. Now is the place, I hold, herein to prove this also to you, that no bodily thing can of its own force be carried upwards or move upwards; lest the bodies of flames deceive you herein. For upwards indeed the smiling crops and trees are brought to birth and take their increase, upwards too they grow, albeit all things of weight, quantum in se est are borne downwards. Nor when fires leap up to the roofs of houses, and with swift flame like up beams and rafters, must we think that they do this of their own will, shot up without a driving force. Even as when blood shot out from our body spurts out leaping up on high, and scatters gore. Do you not see too with what force the moisture of water spews up beams and rafters? For the more we have pushed them straight down deep in the water, and with might and main have pressed them, striving with pain many of us together, folio 10r the more eagerly does it spew them up and send them back, so that they rise more than half out of the water and leap up. And yet we do not doubt, I believe, but that all these things, quantum in se est, are borne downwards through the empty void. Just so, therefore, flames too must be able when squeezed out to press on upwards through the breezes of air, albeit their weights are fighting, quantum in se est, to drag them downwards. Although the lighter things, which have more difficulty overcoming the resistance of the air or the water, descend in these fluids more slowly, Lucretius teaches Lucretius nevertheless teaches that in empty space, where there is no resistance, all atoms, both the heavier ones and those which are less heavy, descend at an equal speed because of the gravity proportional to these atoms, as follows: Herein I would fain that you should learn this too, that when first-bodies are being carried downwards straight through the void by their own weight, at times quite undetermined and at undetermined spots they push a little from their path: But if they were not used to swerve, all things would fall downwards through the deep void like drops of rain, nor could collision come to be, nor a blow brought to pass for the first-beginnings: so nature would never have brought to being. But if perchance anyone believes that heavier bodies, because they are carried more quickly straight through the void, can fall from above on the lighter, and so bring about the blows which can give creative motions, he wanders far away from true reason. For all things that fall through the water and thin air, these things must needs quicken their fall in proportion to their weights

326

Appendices

Propterea, quia corpus aquae, naturaque tenuis Aeris haud possunt aeque rem quamque morari: Sed citius cedunt gravioribus exsuperata. At contra nulli de nulla parte, neque ullo Tempore Inane potest vacuum subsistere reij, Quin, sua quod natura petit, concedere pergat. OMNIA QUAPROPTER DEBENT PER INANE QUIETUM AEQUE PONDERIBUS NON AEQUIS CONCITA FERRI38 Haud igitur poterunt levioribus incidere unquam Ex supero graviora, neque ictus gignere per se, Qui varient motus per quos natura gerat res. Quare etiam atque etiam paullum clinare necesse est Corpora. folio 10v Haec Lucretius ex mente Epicuri Epicurus ex mente Democriti et antiquiorum docuit nam quidam aequalitatem atomorum statuentes gravitatem corporum numero atomorum ex quibus constabant proportionalem esse volebant, alij autem quibus atomi inaequales erant,39 gravitatem non numero XXX solidorum sed qtitati solidi XXX proportionalem esse docebant. Id Aristoteles in libro qua de caelo capite secundo sic docet. Quidam, ait, de leviore & gravio sic XXX dicunt, ut in Timaeo est scriptum. Gravius quidem esse quod ex ijsdem pluribus constat [id est ex pluribus XXX solidis quae quoad magnitudinem & figuram XXXXX eadem sunt] levius autem quod ex ijsdem paucioribus, quemadmodum plumbum [plumbo] et aes aere majus gravius est  - -  - - . eodem modo e ligno plumbum gravius dicunt. Omnia corpora ex ijsdem quibusdam & una materia esse aiunt.40 Et paulo post recenset opinions aliorum (e quorum numero Simplicius, in commentario suo Ein) hunc locum dicit esse Leucippum et Demoritum) qui tribuunt gravitatem 41 numero solidorum sed quantitati solidi et levitatem quantitat vacui in singulis corporibus. Et ex horum philosophorum numero, Simplicius42 in hunc locum, dicit esse Leucippum et Democritum. Per vacui vero levitatem “vero Philosophi illi non positivam43 vacui qualitatem, XXX ut opinat est Aristoteles, sed defectum XXX tantum gravitates solummodo intellexerunt. Inter philosophos igitur qui corpora ex atomis composuere gravitatem tarn atomis corporibus quam corporibus compositis competere & quantitati materiae in singulis corporibus proportionalem esse recepta fuit opinio. Ex Atomis autem XXX corpora composuere XXXX philosophi tam Jonici Thales quam Italici. Thaletis et Pythagorae sectatores, inquam Italic Pythagorasquit Plutarchus, negant in infinitum pro in infinitum progredi sectionem eorum corporum quae motibus sunt obnoxia sed subsistere in ijs quae individua sunt & atomi dicunt< ur. > Plutarch. Placit. Philos. lib. XX 1 XX c. 16. p. 88144

Appendices

327

just because the body of water and the thin nature of air cannot check each thing equally, but give place more quickly when overcome by heavier bodies. But, on the other hand, the empty void cannot on any side or at any time support anything, but rather, as its own nature desires, it continues to give place; WHEREFORE ALL THINGS MUSTNEEDS BE BORNE ON THROUGH THE CALM VOID, MOVING AT EQUAL RATE DESPITE UNEQUAL WEIGHTS. The heavier will not then ever be able to fall on the lighter from above, nor of themselves bring about the blows, which make diverse the movements, by which nature carries things on. Wherefore, again and again, it must needs be that the first-bodies swerve a little. folio 10v Lucretius taught this based on the view of Epicurus, Epicurus based on the views of Democritus and older philosophers. For some, who asserted the equality of atoms, thought that the gravity of the bodies was proportional to the number of atoms of which they consist. The others, who believed atoms to be unequal, taught that the gravity was proportional not to the number of solid , but to the quantity of the solid . Aristotle taught this in the second chapter of the fourth book On the Heaven. Some explain relative lightness and weight, he said, in the manner which we find described in the Timaeus: the heavier is that which is made up of the greater number of identical , [i.e., of more massive [parts], which are identical in terms of size and form] the lighter that of fewer identical , e.g. of two pieces of lead or bronze the larger is the heavier ... in precisely the same way, they assert, lead is heavier than wood. F or all bodies, in spite of appearances, are composed of identical parts and of a single material. And shortly thereafter he discusses the view of the others (among them Letucippus and Democritus, according to Simplicius’s remarks on this passage) who attributed the gravity not to the number of the solid , but rather to the quantity of the solid and the lightness to the quantity of emptiness in the individual bodies. Among these philosophers would be Leucippus and Democritus, Simplicius says on this passage. These philosophers did not conceive of the lightness of the void as a positive quality of the void, as Aristotle did, but only merely the absence of weight. Thus among the philosophers who would have the body consist of atoms, the view is accepted again that gravity falls to the atoms as well as the constituted bodies and that it is proportional to the quantity of matter in the individual bodies. The Ionic Thales as well as the Italic philosophers would have the body consist of atoms, however. The disciples of Thales and Pythagoras, Plutarch says, dispute that the division of those bodies subject to the movements can be continued limitlessly, but rather that it stops at those which are indivisible and are called atoms. Plutarch, Philosophical Teachings Book I Chap. 16. p. 881

328

Appendices

The following passage is crossed out in its entirety Thales onmia ex aqua derivavit sed aquam ex corpusculis procul dubio composuit.45 Pythagoras unitatem Deum, infinitam autem binarij naturam, undeXX et multitudo materiae46 Plutarch ib. c. 7. Ex Thaletis discipulis Anaximander infnitatem [i.e. atomos solida47 numero infinita] initium atque elementum dicebat (non aerem aut aquam aut quidquam aliud XXX definiens) et partes illius immutari [i.e. ... in singulis corporibus]48 totam vero esse immutabilem.49 Laertius in ex hac autem gigni terram aquam aerem ignem XXX et ex alia onmia. Et id sensit Anaximenes50, Laertius XXXX atoms autem suos ab invicem dispersos infinitum aerem vocabat et ex eo aquam terram aquam et ignem gigni, ex his vero alia onmi51 ut Anaximader eosdem XX aethera vocabat XX (Laertius in eorum vitis)52 Et idem sensit Diogenes Apolloniates, Anaxagorae discipulus Anaximander vero infinitatem suam bat aethera (Galenus53 & Laertius in vita Diogenis54 et Clemens in admonitione ad gente55) Anaxagoras autem materiam infinitam, sed eas parti similes inter se, minutas; eas primum confusas postea in ordinem aducta mente divina (Cicero in quaest. Acad. lib. 2.)56 Nec dubium est quin XX discipuli hoc a magistris suis didicere. Certe Pythagoras statuit unitatem D infinitam autem binarij naturam, unde et multitudo materiae Plutarch ib. e. 7. End of the crossed-out passage Pythagoras XXX utique statuit unitatem Deum et infinitam bi naturam, unde et multitudo materiae. Plutarch XX ib. 1. 1. C. 7 Bus autem enim Pythagoreis materia est. Et hujusmodi infinitatem Thale discipuli etiam sectatores Anaximander, Anaximenes, Anaxagoras, Archelaus, Diogenes Apolloni atomos XXX innumelos intelligebant designabant pro rerum principio ha folio 11r Ad Prop. VII adde.57 Gravitatem non fieri per vim puncti alicujus in quod gravia undique tendunt, sed per vim materiae totius in Globo Terrae corpora onmia ad se trahentis Plutarchus ex mente Veterum sic docet. Si quicquid quocumque modo extra centrum Terrae est dici oportet supra esse, nulla pars mundi infra erit: sed supra fuerit et Terra & omnia quae ei incumbunt & simpliciter quodvis corpus centro circumpositum; infra autem unicum illud corporis expers punctum, atque hoc omni mundi naturae opponi necesse XXX erit quando superum et inferum naturae ratione invicem opponuntur. Neque hoc dumtaxat est in hac re absurdum; sed causam quoque gravia perdunt, ob quam deorsum vergant atque ferantur, cum nullum sit infra corpus ad quod moveantur. Nam quod corporeum non est, id neque probabile est, neque ipsi volunt tanta esse vi praeditum ut omnia ad se trahat & circa se contineat. Plutarch. de facie in Orbe Lunae. p. 926.58

Appendices

329

The following passage is crossed out in its entirety Thales derived everything from water, but without doubt he composed water of corpuscles. Pythagoras taught on the one hand that the monad god, but on the other hand the indeterminate dyad, to which the multitude of matter is related. Plutarch ibid. Chap. 7. Anaximander from the group of pupils of Thales asserted the apeiron as the principle and element [that is the atoms the infinitely many solid ] (without defining the apeiron to be air, water, or anything else). He taught that the particles might change, but that the whole is unchangeable [that is, .... ]. Laertius in from this however, are produced earth, water, air, fire XXX, and from these everything else. Anaximenes thought the same, Laertius XXXX calling his dissipated atoms infinite air, and believing that from this air water, earth, water and fire are created, and from these then everything else like Anaximander called this very same XX ether XX (Laertius in their biographies). The same belief was also held by Diogenes of Apollonia; however, Anaxagoras’ pupil Anaximander called his apeiron ether (Galen and Laertius in Diogenes’ biography and Clemens in his admonition to the heathen). Anaxagoras matter is infinite, but out of it minute particles entirely alike, which were at first in a state of medley but were afterwards reduced to order by a divine mind. (Cicero in his Academic Investigations Book 2). There can be no doubt that XX the pupils learned this from their teachers. Without doubt Pythagoras asserted on the one hand that the monad is God but on the other hand the indeterminate dyad, to which the multitude of matter is related. Plutarch ibid. book I Chap. 7. End of the crossed-out passage In any case Pythagoras asserted on the one hand that the monad God but on the other hand the indeterminate dyad, to which the multitude of matter is related. Plutarch ibid. Book I Chap. 7. It is the dyad which represents Pythagoras’ matter. And Thales’ pupils disciples Anaximander, Anaximenes, Anaxagoras, Archelaus, Diogenes of Apollonia and others designated understood as the principle of all things to be the countless XXX atoms a such an apeiron. folio 11r To be added to Prop. VII That gravity does not arise through the force of any point toward which the heavy tend from everywhere, but through the force of the entire matter in the sphere of the earth, which pulls all bodies to itself, Plutarch teaches based on the views of earlier as follows. If everything in any way at all off the center of the earth is “up”, no part of the cosmos is “down”; but it turns out that the earth and the things on the earth and absolutely every body surrounding the center is “up” and only one thing is “down”, that incorporeal point which must be in opposition to the entire nature of the cosmos, if in fact “down” and “up” are natural opposites. This, moreover, does not exhaust the absurdity. The cause of the descent of heavy and of their motion to this region is also abolished, for there is no body that is “down” towards which they are in motion. It is neither believable nor in accordance with the intention of these men that the incorporeal should have so much influence as to attract all these objects and keep them together around itself. Plutarch, The Face on the Moon p.926

330

Appendices

The following section is crossed out in its entirety: Igitur quemadmodum vis attractiva Thales Magnetis totius componitur ex viribus attractivis particularum singularum ex quibus Magnes componitur sic gravitas in Terram totam ex mente Veterum componitur ex gravitate in singulas Terrae particulas. XX Et qua ratione corpora omnia ab omnibus Terrae partibus ex mente Veterum trahuntur XXX corpora ad se debebunt omnia alia corporat a omnia ab alijs onmibus trahi materiam omnem ex qua globus Terrae constat. Et qnemadmodum Et qua ratio necgravitas XX in omnes Terrae particulas XXX ex mente veterum. End of the crossed-out section Igitur quemadmodum vis attractiva Magnetis totius componitur ex viribus attractivis particularum singularum ex quibus Magnes componitur constat sic XXX gravitatem in Terram totam ex gravitate in singulas ejus particulas oriri sententia fuit Veterum antiqua fuit opinio. XXXXXX Et propterea si Terra tota in globos complures divideretur deberet gravitas ex mente Veterum in globum unumquemque tendi, perinde atque XX attractio magnetica in singula magnetis fragmenta. XX Et par est ratio gravitatis in corpora universa. Pro Hinc docet Lucretius nullum esse universi centrum et & locum infinitum sed mundos infinitos esse mundos in spatio infinito mundos huic nostro similes, et XXX praeterea pro rerum infinitate sic disputat. Lucret. lib. l. sub finem59 Praeterea spatium summai totius omne Undique si inclusum certis consisteret oris Finitumque foret, jam copia materiai Undique ponderibus solidis confluxet ad imum; Nec res ulla geri sub caeli tegmine posset Nec foret omninò caelum, neque lumina solis: Quippe ubi materies omnis cumulata iaceret Ex infinito jam tempore subsidendo. At nunc nimirum requies data principiorum Corporibus nulla est: quia nil est funditus imum, Quo quasi confluere et sedes ubi ponere possint, folio 11v Semper in assiduo motu res quaeque geruntur Partibus in cunctis, aeternaque suppeditantur Ex infinito cita corpora materiai. Vis argumenti est quod si rerum natura alicubi finiretur, corpora extima, cum nulla haberent exteriora in quae gravia essent non starent in aequilibrio sed per gravitatem suam peterent interiora et undique ex infinito tempore confluendo jamdudum in medio

Appendices

331

The following section is crossed out in its entirety: Accordingly, as the attractive force Thales of an entire magnet is composed of the attractive forces of the individual particles composing the magnet, so is gravity toward the whole earth composed based on the view of the earlier of the gravity to the individual particles of the earth. And for this reason all bodies are attracted by all parts of the earth on the basis of the view of the earlier philosophers XXX the bodies must be attracted to themselves all other bodies by all the entire matter together of which the earth consists. And just as And this reason rather than gravity toward all parts of the earth based on the view of the earlier End of the crossed-out section Accordingly it was the opinion of the earlier it is an old view that gravity toward the entire earth originates from this gravity to its individual particles, just as the attractive force of an entire magnet is composed of the attractive forces of the individual particles of which the magnet is composed consists. Therefore if the entire earth were divided into several spheres, on the basis of the view of the ancients, gravity would have to tend toward each individual sphere, just as magnetic attraction tends toward the individual fragments of a magnet. The same is true for gravity toward all bodies. For Therefore Lucretius teaches that there is no center of the universe and no infinite place, but rather infinitely many worlds in infinite space, worlds similar to ours. Therefore he espoused the infinity of things as follows. Lucretius at the close of Book I Moreover, if all the space in the whole universe were shut in on all sides, and were created with borders determined, and had been bounded, then the store of matter would have flowed together with solid weight from all sides to the bottom, nor could anything be carried on beneath the canopy of the sky, nor would there be sky at all, nor the light of the sun, since in truth all matter would lie idle piled together by sinking down from limitless time. But as it is, no rest, we may be sure, has been granted to the bodies of the first-beginnings, because there is no bottom at all, whither they may, as it were, flow together, and make their resting-place. folio 11v All things are forever carried on in ceaseless movement from all sides, and bodies of matter are stirred up and supplied from beneath out of limitless space. The strength of the argument is that if the universe were bordered anywhere, then the outermost bodies would not be in equilibrium, because they have no outermost toward which they are heavy, but rather strive toward the inner through their own gravity. Because they have been flowing together forever, they long since would have accumulated in the center of the whole, so to speak at the lowest

332

Appendices

totius quasi in loco imo jacuissent. Igitur corpus unumquodque ex mente Lucretij grave est in rnateriam circumcirca positam et per gravitatem praepollentem fertur in regionem ubi materia copiosior est & mundi universi graves sunt in se mutuo & per gravitatem suam in mundos qui sunt ex una parte impediuntur ne cadant in mundos qui sunt ex altera. Cadent tamen aliquando vi praepollentis gravitatis ex mente Dernocriti, ut supra dictum est. folio 12r Ad Prop. VIII60 Qua proportione gravitas recedendo a Planetis decrescit Veteres non satis explicuerunt. Adumbrasse tamen videntur per harmoniam sphaerarum caelestium, designantes Solem & reliquos sex Planetas Mercurium, Venerem, Terram, Jovem, Martem, Jovem, Saturnum per Apollinem cum Lyra Chordarum septem & mensurantes intervalla sphaerarum per intervalla tonorum. Ita septem tonos effici voluerunt quam diapason harmoniam61 vocabant & Saturnum Dorio moveri phthongo hoc est gravi, caeteros Planetas acutioribus (ut Plinius lib. 1 c. 2262 ex mente Pythagoreorum refert) & solem chordas pulsare. Unde Macrobius (lib. 1 c. 19)63 ait Lyra Apollinis chordarum septem tot caelestium sphaerarum motus praestat intelligi quibus Solem Moderatorem natura constituit. Et Proclus in Timaeum Plat. l. 3. p.  200,64 Septinarium dedicarunt Apollini veluti ei qui concentus universos complectitur. Quapropter Deum vocabant Hebdomagetam, id est septinarij Principem. [∧ Έπτ. ἐπὶ ϑηβ. v. 739. a. Aeschylus: ὁ σεμνὸσ ἑβδομαγέτης Ἄναζ Άπόλλων. Venerandus Hebdomageta, Rex Apollo.]65 Similiter ab Oraculo Apollinis apud Eusebium Praep. Evangel. l. 5. C. 1466 Sol vocatur τῆς ἑπταφϑόγγου βασιλεὺς67 Rex harmoniae septisonae.68 Hoc autem symbolo significarunt Solem vi sua agere in Planetas in ratione illa harmonica distantiarum qua vis tensionis agit in chordas diversarum longitudinum, hoc est in ratione duplicata distantiarum reciproce. Nam vis et potentia quae tensio agit eadem agit in eandem chordarn diversarum longitudinum XXX est reciproce ut quadraXXtum longiXXtudinis chordae. Tensio eadem in chordam dupla breviorem quadruplo potentius agit: quam Octavam enim generat, et Octava per vim quadruplo majorem editur. Nam si chorda datae longitudinis dato pondere tensa datum tonum edit, eadem quadruplo pondere tensa Octavam edet. Et similiter eadem tensio in chordam triplo breviorem noncuplo plus agit. Nam duodecimam efficit, et chorda quae dato pondere tensa debet ut duodecimam tensa datum tonum edit efficit edit, noncuplo pondere tendi debet ut duodecimam edat efficiat. Et universaliter si chordae duae crassitudine aequales ponderibus appensis tendantur, hae chordae unisonae erunt ubi pondera sunt reciproce ut quadrata longitudinum chordarum. Subtilis quidern est haec

Appendices

333

point. Accordingly, based on Lucretius’ view, each body is heavy toward the matter surrounding it and is carried by the gravity with the superior force to regions where more matter is. All worlds gravitate toward each other and, are prevented by their gravity toward the worlds located on one side from falling toward the worlds located on the other. However, based on Democritus’ view, at some point in time they will fall due to the force of the superior gravity, as is explained above. folio 12r To Prop. VIII The ratio with which gravity decreases as the distance from the planet increases was not sufficiently explained by the ancients. They appear to have concealed this ratio using the harmony of the celestial spheres, whereby they portrayed the sun and the remaining six planets Mercury, Venus, Earth Jupiter, Mars, Jupiter, Saturn as Apollo with the seven-stringed lyre and measured the intervals between the spheres through the tone intervals. Accordingly, they believed that seven tones would bring forth what they called a complete scale, with Saturn moving with the Doric tone, i.e., the low tone in the scale, and the remaining planets with higher tones (as Plinius Book I Chap. 22 reports based on the views of the Pythagorans), and that the sun would stimulate the strings. Therefore Macrobius says (Book I Chap. 19) The lyre of Apollo with seven strings, as many as there are celestial spheres, enables us to understand their movements, for which nature has appointed the sun as ruler. Proclus, similarly, on Plato’s Timaeus Book 3 p. 200 The number seven was dedicated to Apollo, the one who possessed all harmonies together. Therefore they called the God Hebdomageta, the sovereign of the number seven. [∧ Έπτ. ἐπὶ ϑηβ. V. 739. Aeschylus: ὁ σεμνὸσ ἑβδομαγέτης Ἄναζ Άπόλλων. Venerable Hebdomageta, King Apollo] Similarly, by the oracle of Apollo in Eusebius Praep. Evangel. Book 5 Chap. 14 Sun is named τῆς ἑπταφϑόγγου βασιλεὺς King of the seven-tone harmony. Through this symbol they indicated that the sun acts on the planets with its force in the same harmonic ratio to the different distances as that of the tensile force to strings of different length, i.e., in a duplicate inverse ratio to the distances. For the force and the power with which this tension acts acts on the same string with different lengths, is inversely to the square of the string’s length. The same tension acts on a string half the length four times more strongly: which that is to say it produces the octave, and the octave is emitted with four times greater the force. For if a string of given length, stretched by a given weight, emits a certain tone, the same , when stretched by four times that weight, will emit the octave . Similarly, the same tension on a string one third the length acts on the string nine times more. That is to say it brings forth a duodecimal, and a string which, when stretched by a given weight, must stretched to a duodecimal, emits brings forth emits a certain tone must be stretched with nine times the weight to emit bring forth the duodecimal . And in general when two strings of equal thickness are stretched by weights hanging from them, these strings will sound in unison, as long as the weights are inversely to the squares of the strings’ lengths. This

334

Appendices

argumentatio, sed veteribus tamen innotuit. Nam Pythagoras, ut author est b69Macrobius, intestina ovium, vel boum nervos, varijs ponderibus XXX illigatis tetendit, & inde didicit rationem harmoniae caelestis. Igitur per talia experimenta cognovit quod pondera quibus toni omnes in chordis aequalibus audirentur essent reciproce ut quadrata longitudinum chordae unius et ejusdem quibus tonos eosdem XXX instrumentum musicum tonos eosdem emittit. Proportionem vero his experimentis inventam, teste Macrobio, applicuit ad caelos, ideoque folio 12v ideoque conferendo pondera XX illa cum ponderibus Planetarum & longitudines chordarum cum distantijs Planetarum, intellexit per harmoniam coelorum quod pondera Planetarum in solem essent reciproce ut quadrata distantiarum eorum a sole. Caeterum Philosophi sermones suos mysticos ita temperare amabant ut apud vulgus vulgaria inepte XX proponerent irrisionis ergo & sub hujusmodi sermonibus veritatem occultarent. Hoc sensu Pythagoras tonos suos musicos numerabat a Terra, quasi hinc ad Lunam tonus esset, inde ad Mercurium semitonum & inde ad reliquos Planetas intervalla alia musica; sonos autem edi docebat per motum et attritum sphaerarum solidarum quasi sphaera major graviorem tonum emitteret perinde ut fit in malleis ferreis percussis. Et hinc natum videtur systema Ptolemaicum orbium solidorum, cum interea XX Pythagoras sub hujusmodi Parabolis systema proprium & veram XX caelorum harmoniam occultaret. folio 11v (contains a variant of a part of the text from folio 12r) Nam Pythagoras, ut refert b70Macrobius, dum praeteriret officinam fabri ferrarij, reperit per experimenta ibidem facta quod soni, quos malle i ferrei emittunt acutiores essent vel graviores pro varijs ponderibus malleorum; deinde intestina Ovium vel Boum nervos, varijs etiam ponderibus illigatis tendendo didicit quod soni ponderibus appensis similiter responderent. Certum est igitur qttod Pythltgoras per huiusmodi experimentis cognovit veram rationem quae est in XXX ac tanti secreti compos deprehendit etiam numeros ex quibus soni sibi consoni nascerentur. Certum est igitur quod Pythagoras per experimenta illa cognovit veram rationem quae est inter sonos chordarum et pondera appensa, hoc est, quod pondera, quibus toni omnes in chordis aequalibus audiuntur sunt reciprocè ut quadrata longitudinum chordae quibus instrumentum musicum tonos eosdem emittit. Proportionem vero his experimentis inventam Pythagoras, cteste Macrobio, applicuit ad caelos et inde didicit harmoniam b Macrob. lib. 2 in Somn. Scip. c. 1. c. Macrob. ib.

Appendices

335

argumentation may seem subtle, but it was nevertheless known to the ancients. It was Pythagoras, as Macrobiusb relates, who stretched sheep intestines or ox tendons with different weights attached and ascertained from this the ratio of the celestial harmony. Consequently, through such experiments he knew that the weights with which all tones can be heard on the same strings are inversely to the squares of the lengths of the very same string, on which a musical instrument emits just these tones. However, according to Macrobius’ account, he applied the proportion discovered through these experiments to the heavens folio 12v and in that he consequently compared those weights with the weights of the planets and the lengths of the strings with the distances between the planets, he recognized through the harmony of the heavens that the weights of the planets toward the sun are inversely to the squares of their distances from the sun. By the way the philosophers loved to arrange their mystical language such that they offered the masses quite inappropriate general posts for the sake of derision and hid the truth behind such language. In this sense Pythagoras counted his musical tones outward from the earth, as if from there to the earth’s moon were one tone , from the moon to Mercury a semitone , and from there to the remaining planets the other musical intervals. Furthermore, he taught that a tone sounded through the movement and the friction of the solid spheres, as if a larger sphere would emit a deeper tone, as the sounds of iron hammers striking do. The Ptolemaic system of fixed shells appears to have originated from this, although Pythagoras hid his own system and the true harmony of the heavens behind such similes. folio 11v (contains a variant of a part of the text from folio 12r) Macrobiusb reports that Pythagoras, while passing the workshop of a smith, recognized through the experiments carried out there that the tones emitted by the iron hammers were higher or deeper corresponding to the different weights of the hammers. By consequently stretching sheep intestines or ox tendons with different weights attached, he also learned that the tones correspond to the attached weights in a similar manner. It is therefore certain that Pythagoras knew the true ratio from such experiments, which belongs to and, having acquired such as secret, he also found out the numbers from which the tones which harmonize with each other arise. Thus it is certain that Pythagoras knew from such experiments the true ratio which exists between the tones of the strings and the attached weights, i.e., that the weights with which the same strings emit all tones are inversely to the squares of the lengths of the strings with which a musical instrument emits these same tones. According to Macrobius’ account,c Pythagoras applied the proportion discovered through these experiments to the heavens and learned from it the harmony b Macrobius Book 2 On Scipio’s Dream Chap. I c. Macrobius ibid.

336

Appendices

sphaerarum. Ideoque conferendo pondera illa cum ponderibus Planetarum et intervalla tonorum cum intervallis sphaerarum, atque adeo longitudines chordarum cum distantijs Planetarum ab orbium centro, intellexit per harmoniarn caelorum quod pondera Planetarum in Solem (ad cujus utique Lyrarn omnes saltant) essent reciproce ut quadrata distantiarum eorum a Sole. Caeterum folio 13r Ad Prop. IX.71 Schol. Hactenus proprietates gravitatis explicui. Causam ejus minime expendo. Dicam tamen quid Veteres hac de re senserint. Thalesa72 corpora omnia pro animatis habuit, sicXXden id colligens ex attractionibus magneticis et electricis. Et multò magis attractionem gravitatis in vacuo quantitati materiae proportionalem ad animam materiae trahentis retulit. Et eodem argumento attractionem gravitatis ad animam materiae referre debuit. Hinc omnia Deorum plena esse docui73, per Deos intelligens corpora animata. Et eodem sensu Pythagoras dixit Solem pro Dijs habuit Solem et Planetas74 omnes & Solem propter ingentem ejus vim attractivam dixit esse τὴν τοῦ Διὸς φυλακή75 carcer Jovis, id est corpus vi maxima divina quarn maxima praeditum, quae Planetae in orbibus suis incarcerantur. Et mysticis Philosophis Pan erat Numen supremum hunc Mundum tarnquam instrumentum musicum ratione harmonica inspirans & modulate tractans, juxta illud Orphei, Ἁρμονίαν κόσμοιο κρέκων φιλοπαίγμονι μολπῇ.76 Indeque Deum et harmoniam nominabant et animam mundi ex numeris harmonicis compositam. Planetas autem vi animarum suarum moveri dicebant in orbibus suis moveri dicebant id est vi gravitatis ab actione animarum oriundae. Unde nata videtur opinio Peripateticorum de Intelligtijs XX orbes solidos rotantibus moventibus opinio. Animas autem Solis et Planetarum omnium pro eodem num Philosophi mystici antiquiores pro uno et eodem numine vires suas in corporibus universis exercente habuere, juxta illud Orphei in Cratere77 Nuncius interpres Cyllenius omnibus ipse est Nymphae aqua sunt frumenta Ceres, Vulcanus at ignis Est mare Neptunus canentia littora pulsans Mars bellum, Pax alma Venus, mortalibus ipse Taurigena & superis animi curaeque levamen Corniger est Bacchus convivia laeta frequentans Aurea justiciamque Themis rectumque tuetur: Sol est mox idem contorquens spicula Apollo Eminus et peragens et Divinator et Augur Morborum expulsor Deus est Epidaureus: ista Omnia sunt unum, sint plurima nomina quamvis. a. Aristoteles & Hippias apud Laertium in Thalete

Appendices

337

of the spheres. And by consequently comparing those weights with the weights of the planets, the intervals of the tones with the intervals of the spheres, and the lengths of the strings with the distances of the planets from the center of the shells, he recognized by means of the harmony of the heavens that the weights of the planets toward the sun (to whose lyre all of them dance) are inversely to the squares of their distances from the sun. By the way folio 13r To Prop. IX Schol. Up to this point I have explained the properties of gravity. I have not made the slightest consideration about its cause. However, I would like to relate what the ancients thought about this. Thales’ believed every body to be animate and concluded this from the magnetic and electrical attractions. Rather, he attributed the gravitational attraction in the void, which is proportional to the quantity of matter, to the soul of the matter that draws. And based on the same argumentation he had to attribute the attraction of gravity to the soul of the matter in question. Therefore he taught that everything is full of Gods, whereby with “Gods” he meant animate bodies. In the same sense Pythagoras said that the sun Pythagoras believed the sun and all of the planets to be Gods and said that the sun, because of its powerful force of attraction, is τὴν τοῦ Διὸς φυλακή, Jupiter’s jail, that is, a body endowed with the greatest possible divine force, with which the planets are locked inside their shells. For the mystic philosophers, Pan was the highest divine creature, who inflamed this world and melodically played it like a musical instrument with the harmonic ratio, in accordance with that by Orpheus Ἁρμονίαν κόσμοιο κρέκων φιλοπαίγμονι μολπῇ. Therefore they called both God and harmony the souls of the world composed by harmonic numbers. They also said, however, that the planets move within their shells due to the force of their souls, i.e. due to the force of the gravity originating from the influence of the souls. This appears to be the source of the view the view of the Peripatetics that they were created by the intellects which revolved moved the fixed shells. The older mystic philosophers, however, believed the souls of the sun and of all planets to be the same divine being the very same divine being which exerts its forces on all bodies, in accordance with that of Orpheus to Vulcan. Hermes is the messenger for all. The nymph is the water, Ceres the Grain, but Vulcan the fire. The ocean is Neptune, who sets the white-gray coasts shuddering, Mars war, peace Venus the gracious, mortals and the Gods in the world above are comforted by Bacchus, steer-born and horned, who frequently invites them to merry carousing. Themis the golden protects the right and the good. The sun is that arrow-slinging Apollo, who influences from afar and is a seer and sage. The banisher of diseases is the Epidaurean God: All of these are one and the same, although there are many names. a. Aristotle and Hippias in Laertius to Thales

338

Appendices

De ijsdem Hermesianax.78 Pluto Persephone, Ceres et Venus alma et Amores Tritones, Nereus, Thetis, Neptunus et ipse Mercurius, Juno, Vulcanus, Jupiter et Pan, Diana et Phaebus jaculator, sunt Deus unus. folio 14v (contains a variant of the preceding text from folio 13r)79 Ad Prop. IX Hactenus proprietates gravitatis explicui. Causas ejus minime expendo. Dicam tamen quid Veteres hac de re senserint. XXXX nimirum spiritum qnendam per caelos XXXX nempe caelos esse corporis prope vacuos XXXdemptis sed spiritu tamen quodam infinito quem Deum nominarunt ubique XXXXet plenos impleri: in quo astra infirma XXXXX corpora autem XXXX in spiritu illo libereme moveri XXXX ejus vi et virtute corpora naturali ad invicem impelli perpetuo impelli, idque magis vel minus pro ratione harrnonica distantiarum, & in hoc imsu gravitatem consistere. Hunc spiritum aliqui a Deo summo distinxerunt & animam mundi vocarunt. Et quemadmodum corpora animalium ex ma Spatia omnia coeletia quae XX quae corporibus spiritu infinito XX ex mente Veterum intpleri sic Planetarum desumpta sunt, sie animas eorum ab XXspiritu infinito oriri et anima mundi originem habere docuerunt & corpora quae in ipsis sunt secundum rationes harrnonicas perinde agitare. Sed et Planetas et corpora universa animatos esse nonnulli crediderunt et vi animarum suarum in se mutuo ad distantiam agere. XXX Nam Thales Jonicae Philosophiae fundator corpora omnia pro amatis habuit, id colligens ex attractionibus magneticis et electricis, ut Laertius refert, et edem argument magis attractionem gravitatis ad animam materiae refert retulit. XXX Nam et onmia Deorum plena esse docuit per Deos intelligens pora animata. Et eodem sensu Pythagoras pro Dijs habuit Sol et Planetas & solem propter ingentem ejus vim attractivam qua Planetas in orbibus suis retinet, dixit esse τὴν τοῦ Διὸς φυλακήν carcer Jovis, id est corpus a Deo quam maxime animatum seu vi divina quam maxima praeditum. Pla autem vi animarum suarum in orbibus moveri dicebant Philosophi veteres, id est vi gravitatis ab actione animarum oriundae. Et inde na videtur opinio Peripateticorum opinio de Intelligentijs orbes solidos moventAnimas autem solis et Planetarum omnium Philosophi antiquiores uno et eodem numine vires suas in corporibus universis exerc habuere juxta illud Orphei in Cratere Nuncius interpres Cyllenius &c

Appendices

339

Hermesianax on the same Pluto, Persephone, Ceres and Venus the gracious and love of Triton, Nereus, Thetis, Neptune and even Mercury, Juno, Vulcan, Jupiter and Pan, Diana and Phoebus the archer, are all one single God. folio 14v (contains a variant of the preceding text from folio 13r) To Prop. IX Up to this point I have explained the properties of gravity. I have not made the slightest consideration about its cause. However, I would like to relate what the ancients thought about this. Doubtlessly a certain spiritus through the heavens Quite apparently the heavens are nearly free of bodies, but nevertheless filled everywhere with a certain infinite spiritus, which they called God. The bodies, however, move around freely in this spiritus, as a consequence of its force and natural efficiency the bodies they are thrust constantly thrust toward each other, more or less in accordance with the harmonic ratio of the distances, and gravity consists in this impact. Some differentiated this spiritus from the highest God and called it the world soul. They taught that, just as the bodies of living creatures from matter All heavenly spaces, which XX which were filled by the bodies in the infinite spiritus based on the views of the ancients taken from the planets, they taught that their souls flow from that infinite spiritus have their origin in the world soul that the bodies which belong to them likewise drive along in accordance with the harmonic ratios. Some believed, however, not only the planets but all bodies to be animate and that they mutually influence each other even over distance due to the power of their souls. Thales, the founder of Ionic philosophy, believed bodies to be animate and concluded this from magnetic and electrical attractions, as Laertius reports, and with the same argument he attributes all the more did he attribute the attraction of gravity to the soul of matter. He also taught that everything is full of Gods, whereby with “Gods” he meant animate bodies. In the same sense, Pythagoras believed the sun and the planets to be Gods and said that the sun, because of its powerful force of attraction which holds the planets in their shells, is τὴν τοῦ Διὸς φυλακήν, Jupiter’s jail, that is, a body endowed by God with as much anima as possible and with the greatest possible divine force. The ancient philosophers said, however, that the planets move within their shells due to the power of their souls, i.e. due to the power of the gravity originating from the influence of the souls. This appears to be the source of the view the view of the Peripatetics that they were created by the intellects which revolved moved the fixed shells. The older philosophers, however, believed the souls of the sun and of all planets the very same divine being which exerts its forces on all bodies, in accordance with that of Orpheus to Vulcan. Hermes is the messenger etc.

340

Appendices

Hunc unum Deum in corporibus universis tamquam Templo suo XXX habitare voluerunt et inde Templa antiqua ad modum caelorum formabant ignem in medio templi pro Solarem Solem representate per ignem in medio XX Plantetas Atrij, et Planetas per homines circ euntes quos inde Microcosmos vocabant. Ad quam consuetudinem cum a Cicerone81 allusum esset, Macrobius Macrobius82 in ejus verba XX commemoratus sic scripsit Bene inquit universus mundus Dei templum XX vocatur; propter illos &c Eandem Philosophorum sententiam expressit Vergilius qui expressit: nam et mun animam dedit et ut puritati attestaretur mentem vocavit83 80

 ewton’s Excerpts from Macrobius’ Commentary on Clcero’s Dream N of Sclplo folio 7r Nullus sapientum animam ex symphonijs 84 musicis constitisse dubitavit. Macrob. Som. Scip. 1. 1. c. 6.85 Bene autem universus mundus Dei templum [a Cicerone ]86 vocatur propter illos qui existimant87 nihil esse aliud Deum quem nisi caelum ipsum et caelestia ista quae cernimus. ideo ut summi omnipotentiam Dei ostenderet posse vix intellegi, nunquam posse videri. quicquid humano subjicitur aspectui templum eius vocavit qui sola mente concipitur; ut qui haec veneratur88 ut templa cultum tamen maximum debeat conditori; XXX sciatque quisquis in usum hujus templi hujus inducitur ritu sibi vivendum sacerdotis. Macrob. Som. Scip. I. 1 c. 14.89 Hunc rerum ordinem 90 Vergilius expressit. nam et mundo animam dedit et ut puritati 91 attestaretur, mentem vocavit: Caelum enim, ait, et terras et maria & sydera92 spiritus intus alit93, id est anima, sicut alibi pro spiramento animam dicit Quantum ignes animaeque valent94 & ut illius mundanae animae assereret dignitatem, mentem esse testatur:95 Mens agitat molem.96 necnon ut ostenderet ex ipsa anima constare et animari universa quae vivunt, addidit: lnde hominum pecudumque genus.97 Macrob. ib. 1. 1. c. 14.98 Plato dixit animam essentiam se moventem, Xenocrates numerum se moventem, 99 Pythagoras et Philolaus Harmoniam, -100 Democritus spiritum insertum atomis, hac facilitate motus, ut corpus illi omne sit pervium Macrob. ib.1. 1. c. 14101

Appendices

341

They believed that this one God lives in all bodies as its temple, and thus they fashioned the old temples following the example of the heavens the fire in the center of the temple for the sun by portraying the sun as a fire in the center of the hall and the planets as the people walking around it, which they called the microcosm. Because this custom was referred to by Cicero, Macrobius, when he remarked upon Cicero’s words, wrote the following: “His designation of the universe as the temple of God was appropriate, too, and was for ... ” The same view of the philosophers was related by Virgil, who was related by Virgil: for he, too awarded the world a soul and, in order to attest to purity, he called it mind. Newton’s Excerpts from Macrobius’ Commentary on Cicero’s Dream folio 7r None of the wise men doubted that the soul was constituted by musical concords. Macrobius, The Dream of Scipio Book I Chap. 6 [Cicero’s] designation of the universe as the temple of God was appropriate, however, and was for the edification of those who think that there is no other God except the sky itself and the celestial bodies we are able to see. In order to show, therefore, that the omnipotence of the Supreme God can hardly ever be comprehended and never witnessed, he called whatever is visible to our eyes the temple of that God who is apprehended only in the mind, so that those who worship these objects as temples might still owe the greatest reverence to the Creator, and that whoever is inducted into the privileges of this temple might know that he has to live in the manner of a priest. Macrobius, The Dream of Scipio Book I Chap. 14 This c1assification was used by Virgil. He granted to the world a soul, and in order to bear witness to purity he also called it mind. He says that the sky, the lands, the seas, and the stars are internally sustained by spiritus, referring here to soul just as in another passage he uses the word soul to mean breath: Insofar as fire and breath avail. In order to affirm the excellence of the world-soul he offers the testimony that it is mind: Mind motivates the universe indeed, to show that everything that lives is derived from and is animated by soul he added Thence men and beasts. Macrobius, ibid. Book I Chap. 14 Plato said that the soul was an essence moving itself; Xenocrates, a number moving itself; ; Pythagoras and Philolaus, harmony;  – Democritus, a spirit implanted in the atoms having such freedom of movement that it permeated the body. Macrobius, ibid. Book I Chap. 14

342

Appendices

Hinc Plato postquam et Pythagoricae sucessione doctrinae et ingenij proprij divina profunditate 102 nullam esse posse sine his numeris [sc. musicis]103 jugabilem competentiam: in Timaeo suo mundi animam per istorum numerorum contextionem ineffabili providentia Dei fabricatoris instituit.104  - - Et paulo post. Ergo mundi anima quae ad motum hoc quod videmus universitatis corpus impellit, contexta numeris musicam de se conci creantibus concinentiam, necesse est ut sonos musicos de motu, quem proprio impulsu praestat efficiat, quorum originem in fabrica suae contextionis invenit. Macrob. Som. Scip. 1. 2. cap. 2.105 Inesse 106 mundanae animae causas musicae quibus est intexta praediximus. Ipsa autem mundi anima vitam viventibus omnibus vitam miXX ministrat, Hinc hominum pecudumque genus vitaeque volantum Et quae marmoreo fert monstra sub aequore pontus107 Jure igitur musica capitur omne quod vivit quia caelestis anima quae108 animatur universitas, originem sumpsit ex musica. Haec dum sphaeralem motum mundi corpus impellit sonum efficit quiXX intervallis est disjunctus imparibus. Macrob. Somn. Scip. 1. 2. c. 3.109 Et paulo post Porphyrius ait Platonicos110 credere ad imaginem contextionis animae 111 esse in corpore mundi intervalla quae epitritis, hemiolijs &112 epogdois hemitonijsque complentur & limmate; & ita provenire concentum cuius ratio in substantia animae contexta mundano quoque corpori quod ab anima movetur inserta est. ib.113 Versari caelum mundanae animae natura et vis et ratio docet, cuius aeternitas in motu est; quia nunquam motus relinquit quod vita non deserit nec ab eo vita discedit in quo viget semper agitatus. Igitur et caeleste corpus quod mundi anima futurum sibi immortalitatis particeps fabricata est, ne unquam vivendo deficiat semper in motu est et stare nescit, quia nec ipsa stat anima qua impellitur.114 Et paulo post, Quod autem [Cicero]115 extimum globum qui folio 7v qui ita volvitur summum Deum vocavit, non ita accipiendum est, ut ipse prima causa et Deus ille omnipotentissimus existimetur116 cum globus ipse quod caelum est animae sit fabrica; anima ex mente processerit, mens ex Deo qui vere summus est procreata sit. Sed summum quidem dixit ad ceterorum ordinem, qui subjecti sunt &c  - -117 ipsum denique Jovem veteres vocaverunt et apud Theologos Jupiter est anima mundi anima.118 hinc illud est Ab Jove principium Musae, Jovis omnia plena119 quod de Arato120 Poetae alij mutuati sunt, qui de sideribus locuturus, a caelo in quo sunt sidera, exordium sumendum esse decernens ab Jove incipiendum esse memoravit. Macrob. in Somn. Scip. lib. 1. c. 17121

Appendices

343

Therefore Plato, guided by Pythagoras’ teachings and thanks to the divine depth of his own genius, that there can be no star constellations brought together without these numbers [namely, the musical numbers], in his Timaeus he introduced the world-soul by interweaving these numbers, thanks to the ineffable providence of God the creator. --- And shortly thereafter: Thus the world-soul, which stirs to motion the body of the universe that we now witness, must be interwoven with those numbers which produce musical harmony, so that it can cause the harmonious sounds which it instills by its own impulse. He discovered the source of these in the structure of his combination. Macrobius, The Dream on Scipio Book 11 Chap. 2 We strongly emphasized that the causes of harmony are traced to the world-soul with which it is interwoven, but the world-soul itself grants life to everything that is alive. Thence come the race of man and beast, and the life of the birds And what creatures the ocean hides beneath its marble mirror Consequently everything that lives is captivated by music since the heavenly soul which animates the universe sprang from music. In impelling the bodies of the world to spherical motion, [the soul] produces tones which are separated from each other by unequal intervals. Macrobius, The Dream of Scipio Book 11 Chap. 3. And slightly later: Porphyrios says that the Platonics believe in the idea of the linking of this soul, that the intervals belong to the corporeal universe, which are filled with fourths, fifths, superoctaves and semitones and a leimma, and that harmony is thus produced, the proportional intervals of which were also injected into the corporeal universe which is animated by the soul. Ibid. That the heavens revolves is taught to us by the nature, force and quality of the worldsoul, whose eternity consists in motion, because motion never leaves what life has not abandoned, and life does not depart from that in which the instigator is still present. Therefore, the body of the celestial sphere, which the world-soul fashioned to participate in its immortality, in order that it should never cease living, is always in motion and does not know how to rest, since the soul itself, by which the sphere is impelled, is never at rest. And slightly later: Even when [Cicero] called the outermost sphere, folio 7v which so revolves, the supreme God, this does not imply that he believed it to be the first cause and all-powerful God. For the sphere itself, which is the sky, is the creation of the soul, and soul proceeded from the mind, and mind from God, who is truly the supreme: indeed, he called it supreme with respect to the other spheres lying beneath, - - - The ancients called it Jupiter, and to theologians Jupiter is the soul of the world. Therefore is written With Jove I begin, ye Muses; Of Jove all things are full which the other poets borrowed from Aratus, who, in introducing the subject of the stars, saw that he would have to begin with the celestial sphere, the abode of the stars; hence he said that he had to begin with Jupiter. Macrobius in The Dream of Scipio Book I Chap. 17

344

Appendices

Remarks on Newton’s Scholia 1. In the first edition (1687) of Newton’s Principia, Proposition IV, Book III was on the pages 406–407; the scholium was to be inserted immediately thereafter on page 407. 2. Propria manu D. Newtoni is noted on the manuscript (MS 247 fol. 6) in different handwriting, perhaps that of D. Gregory. In MS 210 top right is noted Copied from the Mss. in Sir Isaac Newton’s own hand. 3. Newton cites De facie in orbe lunae (The Face on the Moon) by Plutarch. In Plutarch (Omnia II 923 C–D) is written: καὶ διὰ τοῦτο Φαρνάκης αὐτὸς μὲν ἐν ἀδείᾳ τοῦ πεσεῖν τὴν γῆν ἐστιν οἰκτίρει δὲ τοὺς ὑποκειμένουσ τῇ περιφορᾷ τῆς σελήνης Αἰϑίοπας ἢ Ταπροβηνοὺς μὴ βάρος αὐτοῖς ἐμπέσῃ τοσοῦτον. καίτοι τῇν μὲν σελήνῃ βοήϑεια πρὸς τὸ μὴ πεσεῖν ἡ κίνησις αὐτὴ καὶ τὸ ῥοιζῶδες τῆς περιαγωγῆς, ὥσπερ ὅσα ταῖς σφενδόναις ἐντεϑέντα τῆς καταφορᾶς κώλυσιν ἴσχει τὴν κύκλῳ περιδίνησιν. ἄγει γὰρ ἕκαστον ἡ κατὰ φύσιν κίνησις, ἂν ὑπ᾽ἄλλου μηδενὸς ἀποστρέφηται. διὸ τὴν σελήνην οὐκ ἄγει τὸ βάρος ὑπὸ τῆς περιφορᾶς τὴν ἐκκρουόμενον.

ne terra cadat non metuit Pharnaces, miseratur autem Lunae conversion suppositos Aethiopes aut Taprobanos ne in eos tanta moles decidat solieitus. Atqui Lunae auxilio est ne cadat motus & eius impetus: quomodo quae fundis imposita in orbem rotata delabi non sinuntur. Nam motus naturae conveniens unamquanque rem agit, si non ab alia aliqua re alio avertatur. Itaque Lunam gravitas non movet, cum a conversione circulari eius motus profligetur.

Note that Newton changed the Latin translation given in Plutarch (Omnia) considerably. 4. Newton cites Plutarch’s De placitis philosophorum (Philosophical Teachings) Book II Chap. XIII 3, or Plutarch (Omnia II 888 D): Ἀναξαγόρας τὸν περικείμενον αἰϑέρα πύρινον μὲν εἶναι κατὰ τὴν οὐσίαν, τῇ δ᾽ εὐτονίᾳ τῆς περιδινήσεως ἀναρπάζοντα πέτρους ἐκ τῆς γῆς, καὶ καταφλέξαντα τούτους ἠστερικέναι.

Anaxagoras aetherem cireumsitum ignea quidem esse natura, cireumvolutionis autem vehementia abripuisse lapides e terra, eosque adussissse, et sic in stellas convertisse.

Newton changed the Latin translation given in Plutarch (Omnia) only slightly.

Appendices

345

5. Diogenes Laertius II 12 is cited by Newton in accordance with Diogenes Laertius (De vitis 1664,36 A), without changing the Latin translation given in this edition. There it reads: τὸνδὲ Ἀναξαγόραν εἰπεῖν ὡς ὅλος ὁ οὐρανὸς ἐκλίϑωνσυγκέοιτο· τῇ σφοδρᾷ περιδινήσει συνεστάναι καὶ ἀνεϑέντα κατενεχϑήσεσϑαι.

Anaxagoram autem, totum coelum lapidibus constare, dixisse, sed conversionis eeleritate contineri, cujus remissione casurum est.

Plutarch reports similarly in his Lysander biography (Λυσάνδος 12), see Plutarch (Omnia I 439 CD). 6. Newton quotes Diogenes Laertius II 10 as an authority, or Diogenes Laertius (De vitis 1664, 35 D). There it reads: φασὶ δ᾽αὐτὸν προειπεῖν τὴν περὶ Αἰγὸς ποταμοὺς γενομένην τοῦ λιϑου πτῶσιν, ὃν εἶπεν ἐκ τοῦ ἡλίου πεσεῖσϑαι. ὅϑεν καὶ Εὐριπίδην, μαϑητὴν ὄντα αὐτοῦ, χρυσέαν βῶλον εἰπεῖν τὸν ἥλιον ἐν τῷν Φαέϑοντι.

Ferunt eum lapidis, ad Aigos fluvium, ruinam praedixisse, quem a Sole casurum dixerit: quocirca Euripidem ejus discipulum in Phaethonte Solem auream glebam appellavisse

This means: There is a story that he predicted the fall of a meteoric stone at Aegospotami, which hesaid would fall from the sun. Hence Euripides, who was his pupil, in the Phaethon calls the sun itselfa “golden lump.” Newton also refers to Diogenes Laertius II 8, which corresponds to Diogenes Laertius (De vitis1664, 35 A), where is written: οὖτος ἔλεγε τὸν ἥλιον μύδρον εἶναι διάπυρον καὶ μείζω τῆσ Πελοποννήσου.

Is Solem ferrum candens atque ignitum esse aiebat, Peloponnesoque majorem.

This means: He declared the sun to be a mass of red-hot metal and to be larger than the Peloponnesus. Anaxagoras’ prediction that a stone would fall is also reported by Plutarch in his Lysander biography (Λυσάνδος 12). See Plutarch (Omnia I 439 C–D). 7. Newton refers to Plato’s Apology of Socrates (Stephanus 26 D): ἐπεὶ τὸν μὲν ἤλιον λίϑον φησὶν εἶναι, τὴν δὲ σελήνην γῆν

Nam solem quidem lapidem esse dicit, lunam vero terram

This means: He said that the sun is a stone, but the moon an earth. In Plato (Opera omnia 1590) the Greek text is found on page 362 F and the Latin on page 362 G.

346

Appendices

In Book II Chapter XX 5, Plutarch (Omnia II 900 A), of his De placitis philosophorum (Philosophical Teachings) Plutarch writes: Ἀναξαγόρας Δημόκριτος Μητρόδωρος μύδρον ἢ πέτρον διάπυρον

Anaxagor, Demokritus, Metrodorus, massam, aut lapidem, igni candentem

This means: Anaxagoras, Democritus, Metrodorus held the sun to be a mass or stone glowing with fire. Newton did not have an edition of the tracts of Kyrill of Alexandria, whose tract contra Julianum (Against Julianus) is contained in all of the large KyrilI editions and also was published many times asa single tract. In Cyrillus Alexandrinus (Opera VI 189 E) the passage in Book VI of Kyrill’s tractcontra Julianum reads: Καὶ γοῦν λίϑον εἶναι διάπυρον τὸν ἡλίου κύκλον Ἀναξαγόρου λέγοντος, κατεψηφοφόρουν αὐτοῦ τὸν ϑάνατον Ἀϑήνῃσιν οἱ δικάζοντες

Et certe quuum Anaxagoras solis orbem ignitum esse lapidem diceret. ab Atheniensibus damnatus est capitis.

This means: And certainly because Anaxagoras asserted that the disc of the sun is a stone glowing with fire (λίϑον διάπυρον), he was sentenced to death by the Athenians. Newton refers to Suidas (Lexicon) where under the keyword Ἀναξαγόρασ (Anaxagoras) is written: Οὖτός ἐστιν ὁ τὸν ἥλιον ειπὼν μύδρον διάπυρον, τουτέστι, πύριον λίϑον.

Hic est ille. qui Solem dixit esse globum. Vel lapidem ignitum.

This means: This is the one who said that the sun is a fiery sphere or stone. In the edition Suidas (Opera), which Newton also owned, the corresponding passage reads as folIows: Οὖτός ἐστιν ὁ τὸν ἥλιον ειπὼν μύδρον διάπυρον, τουτέστι, πύριον λίϑον.

Hic est ille, qui Solem dixit esse massam ignitam, vel igneam et candentem massam. hoc est igneum lapidem.

This Latin translation means: This is the one who said that the sun is a fiery mass or a glowing mass of fire, i.e., a glowing stone.

Appendices

347

8. Newton had no edition of the Eclogae Physicae et Ethicae by Stobaios. The chapter Newton names, Chapter 20, is apparently an error, but both in Stobaios (Eclogae 1575 Lib. I Cap. XXV 53 line 46, 47) and in Stobaios (Eclogae l609 Lib. I Cap. XXV 53 line 46, 47), this corresponds to Stobaios (Anthologia XXIV 202 line 23, 24), one reads: Ἀρχέλαος μύδους ἔφησεν εἶναι τοὺς ἀστέρας, διαπύρους δὲ

Archelaus ferreas luminas candentes dixit stellas

This means: Archelaus refers to the stars as glowing and shining lumps of metal (μύδρους διαπύρους). 9. Newton’s reference to Plato’s Apology of Socrates is incorrect, Euripides is not mentioned by name anywhere in the entire Apologia. Anaxagoras, on the other hand is named in the passage in which Meletos accuses Socrates of not believing in Gods and believing the sun to be a stone and the moon to be an earth (Stephanus 26 D). In Plato (Opera omnia 1590) the Greek text of this passage is located on page 362 F and the Latin on page 362 G. ἐπεὶ τὸν μὲν ἥλιον λίϑον φησὶν εἶναι, τὴν δὲ σελήνην γῆν

Nam solem quidem lapidem esse dicit, lunam vero terram

This means: He said that the sun is a stone, but the moon an earth. From Socrates’ answer to this accusation it is apparent that this is the generally known view of Anaxagoras. In naming Euripides Newton may have had the following passage from Diogenes Laertius II 10, or Diogenes Laertius (De vitis 1664, 35 D) in mind: ὅϑεν καὶ Εὐριπίδην, μαϑητὴν ὄντα αὐτου, χρυσέαν βῶλον εἰπεῖν τὸν ἥλιον ἐν τῷ Φαέϑοντι

quocirca Euripidem ejus discipulum in Phaetonte Solem auream glebam appellavisse

Which means: Hence Euripides, his pupil, also called the sun a golden clod in his Phaethon. The Phaethon by Euripides mentioned here is preserved only in fragments, see Nauck (Fragmenta No. 771 -786). 10. Newton’s reference to Chapter 13 Book II of Plutarch’s De placitis philosophorum (Philosophical Teachings) appears to be an error, as neither Democritus nor Metrodorus are mentioned by name in Chapter 13; apparently he meant Chapter 20. The reference to Chapter 13 apparently was added to the manuscript by Newton later and is not contained in the transcript of David Gregory’s Notae in Newtoni Principia Mathematica Philosophiae Naturalis (Royal Society London MS 210), which also contains a transcript of the Newtonian comments on the Propositions IV through IX Lib. III of his Principia, which are supposed to have been made directly from Newton’s own manuscript, as is apparent from a note on the transcript. We thus presume that the transcriber (i.e. David Gregory)

348

Appendices

used another Newtonian manuscript, which was probably a corrected version of the text prepared by Newton himself. The Newtonian manuscript from Gregory’s estate (Royal Society London MS 247 ff. 6 -14) which we used is thus quite apparently not this corrected version. See also the remark 88. In Chapter 20 Book II of De placitis philosophorum, i.e. Plutarch (Omnia II 890 D), is the passage: Ἀναξαγόρας Δημόκριτος Μητρόδωρος μύδρον ἢ πέτρον διάπυρον

Anaxagoras, Demokritus, Metrodorus, massam, aut lapidem, igni candentem

This means: Anaxagoras, Democritus, Metrodorus held the sun to be a mass or stone glowing with fire. 11. Newton crossed out the reference to Plutarch for reasons unknown to us, but in Plutarch’s De placitis philosophorum (Philosophical Teachings) Book II Chapter 13, i.e., Plutarch (1599) Tomus II page 888 D, is reported: Διογένης κισηρώδη τὰ ἄστρα, διαπνοὰς δὲ αὐτὰ νομιζει τοῦ κόσμου. Πάλιν δὲ ὁαὐτὸς ἀφανεῖς μὲν λίϑους, πίπτοντας δὲ πολλάκις ἐπὶ τὴν γῆν σβέννυσϑαι καϑάπερ τὸν ἐν Αἰγὸς ποταμοῖς πυροειδῶς κατενεχϑέντα ἀστέρα πέτρινον.

Diogenes pumicum instar esse stellas sensit exspirationes mundi exhalantis. idem, lapides quosdam esse, qui nusquam appareant, & saepe in terram delapsi exstinguantur: quomodo ad Aegos potamos sub ignis forma decidit stella saxea.

Which means: Diogenes believes that the stars are like pumice-stones, that they are evaporations of the world and that they glow. According to him, a number of invisible, and thus nameless stars more around the visible stars, often fall to earth and expire, just as the white-glowing star of stone which fell in Aegospotami. It is surprising that Newton wanted to name only Diogenes as the source for the matter of the stone which fell in Aegospotami and not Plutarch. It was, of course, Plutarch who reported in his Lysander biography (Λυσάνδος 12) that Anaxagoras predicted that one of the bodies fastened to the sky would break loose and fall as a result of a variation or vibration. 12. Here Newton confers this formulation which was handed down only from Anaxagoras’ pupil Euripides, to the other philosophers as weil. In Diogenes Laertius II 10, i.e. Diogenes Laertius (De vitis 1664, 35 D), is written merely: ὅϑεν καὶ Εὐριπίδην, μαϑητὴν ὄντα αὐτοῦ, χρυσέαν βῶλον εἰπεῖν τὸν ἥλιον ἐν τῷ Φαέϑοντι.

quocirca Euripidem ejus discipulum in Phaethonte Solem auream glebam Appellavisse.

Appendices

349

This means: Hence Euripides, his pupil, also called the sun a golden clod in his Phaethon. The Phaethon by Euripides mentioned here is preserved only in fragments, see Nauck (Fragmenta No. 771–786). 13. Diogenes Laertius II 8, i.e. Diogenes Laertius (De vitis 1664, 35 A), reports: τὴν δὲ σελήνην οἰκήσειςἔχειν, ἀλλὰ καὶ λόφους καὶ φάραγγας.

Habitarique in Luna, sed & esse in ea colles& convalles.

This means: He declared that the moon was inhabited, and that mountains and valleys were to be found there. 14. In Conti (Mythologia 673) is reported: Fabulatus est Anaxagoras in Luna fuisse latam quondam regionem e qua hic leo Nemeaeus deciderit ... This means: Anaxagoras reported that there was a certain vast area on the moon from which this Nemean lion had fallen. Conti provides no source for his report, which he probably based on the Scholia in ApolIonium Rhodium vetera. In the Scholia ApolI. (1935, I 496–498 p.  44) is reported: τὴν δὲ σελήνην ὁ αὐτὸς Ἀναξαγόρας χώραν πλατεῖαν ἀποφαίνει, ἐξ ἧς δοκεῖ ὁ Νεμεαῖος λέων πεπτωκέναι Which means: The earth’s moon is portrayed by Anaxagoras as a vast area, from which the Nemean lion appears to have fallen. 15. Newton here quotes the following passage (Stephanus 886 D) from Plato’s Laws, i.e. Plato (Opera omnia 1590, 665 A): ὄταν τεκμήρια λέγωμεν ὡς εἰσὶ ϑεοί, ταῦτα αὐτα προφέροντες, ἥλιόν τε καὶ σελήνην καὶ ἄστρα καὶ γῆν ὡς ϑεοὺς καὶ ϑεῖα ὄντα, ὑπὸ τῶν σοφῶν τούτων αναπεπεισμένοι ἂν λέγοιεν ὡς γῆν τε καὶ λίϑους ὄντα αὐτὰ καὶ οὐδὲν τῶν ἀνϑρωπείων πραγμάτων φροντίζειν δυνάμενα.

cum ego et tu haec ipsa signa esse, quod dij sint, asserimus, solemque ac lunam, sidera et terram, quasi deos et res divinas in medium adducimus, tunc iuvenes ab istis sapientibus aliter persuasi, terram et lapides haec esse dicant, nullamque humanarum rerum curam habere posse.

Which means: If you and I, as proof for the existence of the Gods, advance the sun, the earth’s moon, the stars and the earth as Gods and divine things, then those apostles who have been convinced otherwise by those sages say that these are earth and stones and that they are completely unable to take care of the affairs of mankind. Newton’s text is an abridged version of the Latin translation by M. Ficinus.

350

Appendices

16. Newton’s reference to Apud Laertium in Anaxagora is not correct; in fact, he means the beginning of the chapter about Democritus in Diogenes Laertius IX 34 -35, corresponding to Diogenes Laertius (De vitis 1664, 245 F–246 A): Φαβωρῖνος δέ φησιν ἐν παντοδαπῇ ἱστορίᾳ λέγειν Δημόκριτον περὶ Ἀναξαγόρου ὡς οὐκ εἴησαν αὐτοῦ αἱ δόξαι αἵ τε περὶ ἡλίου καὶ σελήνης, ἀλλα ἀρχαῖαι, τὸν δ᾽ὑφῃρῆσϑαι.

Phavorinus in historia variarum rerum ait, Democritum hostili in Anaxagoram animo, quod ab eo non sit receptus, de sole, ac luna sententias illius esse negare, antiquas autem esse dicere, easque ipsum furatum esse.

Which means: But Favorinus in his Miscellaneous History tells us that Democritus, filled with animosity against Anaxagoras because the latter would not accept him as a pupil, disputed that Anaxagoras’ views about the sun and the earth’s moon were his own conception. He said that these ideas were old and that he had only taken them over. 17. Newton had no edition of the Eclogae Physicae et Ethicae by Stobaios. Both in Stobaios (Eclogae 1575 Lib. I Cap. XXV p.  53 line 55, 56) and Stobaios (Eclogae 1609 Lib. I Cap. XXV p. 53 line 55, 56), corresponding to Stobaios (Eclogae 1884, 124 p. 203 line 13), one reads: Ἀναξιμένης πυρίνην μὲν τὴν φύσιν τῶν ἄστρων, περιὲχειν δέ τινα καὶ γεώδη σώματα συμπεριφερόμενα τούτοις ἀόρατα

Anaximenes ut igneam iudicavit esse stellarum naturam, ita permista quaedam ipsis terrena corpora non aspectabilia credidit

This means: Anaximenes said that the nature of the stars may indeed be firelike, but that bound tothem are certain invisible earth-like bodies revolving around them. Note that the Latin translation given in Stobaios (Eclogae 1575) and Stobaios (Eclogae 1609), which Newton may have used as a model for his text, does only partial justice to the Greek text. This Latin translation could be ­translated as follows: Anaximenes may have believed that the nature of stars is fire-­like, but he believed in certain invisible earth-like bodies linked to them. 18. Newton refers to Plutarch’s De placitis philosophorum (Philosophical Teachings) Book II Chap. 13, which corresponds to Plutarch (Omnia 1599 II 888 D), where is written: Θαλῆς γεώδη μὲν, ἔμπυρα δὲ τὰ ἄστρα

Thales censuit, terrestres quidem esse stellas, sed ignitas interim.

Which means: Thales believed that the stars were made of earth, but glowing.

Appendices

351

Newton slightly extended the Latin translation from Plutarch (Omnia 1599). Gregory indicates in the preface to his Astronomiae physicae et geometricae elementa that this sentence was also handed down from Stobaios. See the footnote h in his preface. 19. Newton cites Plutarch’s De placitis philosophorum (Philosophical Teachings) Book II Chap. 30, corresponding to Plutarch (Omnia 1599 II 892 A), where is written: Οἱ Πυϑαγόρειοι γεώδη φαίνεσϑαι τὴν σελήνην, διὰ τὸ περιοικεῖσϑαι αὐτὴν καϑάπερ τὴν παρ᾽ ἡμῖν γῆν μείζοσι ζῷοις καὶ φυτοῖς καλλίοσιν· εἶναι γὰρ πεντεκαιδεκαπλάσια τὰ ἐπ᾽ αὐτῆς ζῷα τῇ δυνάμει μηδὲν περιττωματικὸν ἀποκρίνοντα καὶ τὴν ἡμέραν τοσαύτην τῷ μὴκει

Pythagorei aiunt, terrestrem videri, quia, sicut & nostra terra, circumhabitur, a maioribus quidem & pulchrioribus animalibus, quinquies decies nostrorum quantitatem continentibus, neque ullum excrementum deiicientibus: tanta item diei longitudine.

This means: The Pythagorans believed that the earth’s moon appeared to be an earth because, like our own earth, it was inhabited, but by larger and more beautiful creatures, which, as a consequence of the length of the day, are fifteen times larger than our own and excrete no wastes. Newton used a slightly shortened and changed form of this Latin translation. 20. Newton cites Plutarch’s De placitis philosophorum (Philosophical Teachings) Book II Chap. 1, which corresponds to Plutarch (Omnia II 892 E): τῶν Πυϑαγορείων οἱ μὲν ἔφασαν ἀστέρος εἶναι διάκαυσιν, ἐκπεσόντος μὲν ἀπὸ τῆς ἰδίας ἕδρας, δι᾽ οὖ δὲ περιέδραμε χωρίου κυκλοτερῶς αὐτὸ καταφλέξαντος ἐπὶ τοῦ κατὰ Φαέϑοντα ἐμπρησμοῦ.

Pythagoreorum alij dixerunt stellae ardore effectum, quae suo loco delapsa tempore incendij a Phaethonte excitati, quidquid loci circulari decursu peragravit, adusserit.

This means: Other Pythagorans said that originated from the combustion of a star, which slid down from its location at the time of the fire kindled by the Phaethon and reached another location which executed a circular orbit. Note that Newton significantly changed the Latin translation given in Plutarch (Omnia).

352

Appendices

21. in viam lacteam convertisse is not included in Xylander’s translation in Plutarch (Omnia). Since Newton quite freely cites the Xylander translation of Plutarch here, he must have inserted this passage in the text so that the meaning of Plutarch’s text remains intact. 22. From Harrison (Library of Newton) can be inferred that Newton had a copy of Galileo’s Dialogue on the Two Systems of the World in the Latin translation the Systema cosmicum, albeit in the 1699 edition, Harrison (Library of Newton No. 648). Presumably Newton wrote the texts passed down to us from D. Gregory’s estate before 1699, however, such that Newton must have used an earlier edition of the Systema cosmicum for his nearly literal quoting. In Galileo (Systema cosmicum 17/18) there is the marginal note: Corpora Mundana initio motu recto, deinde circularimota, secundum Platonem, and the corresponding main text reads: Nisi tamen cum Platone statuere malimus, corpora Mundana etiam tum, cum jam fabricata et omnino stabilita essent, aliquandiu, sic ordinante cenditore, motu recto agitata fuisse, sed postquam ad certa determinataque loca pervenissent, paulatim in byrum revolvi coepisse, motu recto commutato cum circulari, in qua postea perstiterunt, semperque persistunt. Galileo’s original Italian text is Corpi mondani mossi da principio di moto retto e poi circolaremente, secondo Platone and, as the main text, se pero noi non volessimo dir con Platone, che anco i corpi monani, dopo /‘essere stati fabbricati e del tutto stability furon per alcun tempo dal suo Fattore mossi di moto retto, ma che dopo I’esser pervenuti in certi e determinati luoghi, furon rivolti a uno a uno in giro, passando dal moto retto al circolare, dove poi si son mantenuti e tuttavia si conservano. See Galileo (Dialogo I 20). From Harrison (1978) it is also evident that Newton did not own the English translation of Galileo’s Dialogs provided by Thomas Salusbury and published in London in 1661 under the title The Systeme of the world in four dialogues. It is not known whether Newton knew this translation, in which the marginal note on page 1l is translated as follows: Mundane bodies moved in the beginning in a right line, and afterwards circularly, according to Plato and the corresponding main text reads: Unless we will say with Plato, that these mundane bodies, after they had been made and finished, were for a certain time moved by their Maker, in a right motion, but that after their attainment to certain and determinate places, they were revolved one by one in Spheres, passing from the right to the circular motion, wherein they have been ever since kept and maintained. What is conspicuous about Newton’s quote is that he did not notice that Galileo is attributing to Plato a view which cannot be documented in Plato’s work and of which no other sources about Plato report in this form. In general one assumes that Galileo, when he assigned the above view to Plato, had in mind the following passage from Plato’s Timaeus (Stephanus 34 A): “For He granted to her the movement suited to her form ... and by leading her around, He caused her to revolve in a circle.” Perhaps it was the following passage instead which seduced Galileo into attributing the above view to Plato: “These initially moved irregularly and in a disorderly fashion, but when they began to

Appendices

353

let the world emerge, they were regulated and put into order to the extent possible by God.” See Diogenes Laertius III 76. 23. In the first edition (1687) of Newton’s Principia, Proposition V Book III is on pages 407–408, and after this Proposition V the Scholion was to be inserted on page 408. 24. The page reference in Newton’s reference to “Plutarch. de facie in orbe Lunae p. 92” is corrupted, as the page margin was presumably cut off such that the page number appears to be 92. Newton meant, however, Plutarch (Omnia II 926). 25. Up to the end of this paragraph, Newton cites with minor changes Xylander’s Latin translation fromPlutarch (Omnia II 924 D): … ἑτέρους φασὶ πελάζειν* ἄνω τὴν σελήνην, γῆν οὖσαν, ἐνιδρύοτας οὐχ ὅπου τὸ μέσον ἐστι. καίτοι γε εἰ πᾶν σῶμα ἐμβριϑὲς εἰς τὸ αὐτὸ συννεύει, καὶ πρὸς τὸ αὐτοῦ μέσον αντερείδει πᾶσι τοῖς μορίοις, οὐχ ὡς μέσον οὖσα τοῦ παντὸς ἡ γῆ μᾶλλον, ἢ ὡς ὅλον, οἰκειώσεται μέρη αὐτῆς ὄντα τὰ βάρη, καὶ τεκμήριον ἔσται τῶν ῥεπόντων, οὐ τῇ τῆς μεσότητος πρὸς τὸν κόσμον, ἀλλὰ πρὸς τῆν γῆν κοινωνίας τινὸς καὶ συμφυΐας τοῖς ἀπωσμένοις αὐτῆς, εἶτα πάλιν καταφερομένοις. ὡς γὰρ ὁ ἥλιος εἰς ἐαυτὸν ἐπιστρέφει τὰ μέρη ἐξ ὧν συνέστηκε, καὶ ἡ γῆ τὸν λίϑον, ὣσπερ προσήκοντα δέχεται, καὶ φέρει πως ἐκεῖνον, δ᾽ ϑεν ἑνοῦται τῷ χρόνῳ καὶ συμφύεται πρὸς αὐτὴν τῶν τοιούτων ἔκαστον. εἰ δέ τι τυγχάνει σῶμα τῇ γῇ μὴ προνενεμημένον ἀπ᾽ ἀρχῆς, μηδὲ ἀπεσπασμένον, ἀλλά που καϑ᾽ αὐτὸ σύστασιν ἔσχεν ἰδίαν καὶ φύσιν, ὡς φαῖεν ἂν ἐκεῖνοι τήν σελήνην τί κωλύει χωρὶς eἶναι καὶ μένειν περὶ αὐτὸ, τοῖς αὐτοῦπεπιεσμένον μέρεσι καὶ συμπεπεδημένον;

eos dicunt inferiora superioribus adiungere qui Lunam quae terra sit, non in medio sed in sublimi collocant. At enim si omne corpus grave eodem fertur, & ad centrum suum omnibus partibus vergit: terra non ut centrum Universi potius, quam totum, sibi omnia gravia ut suas partes vindicabit. Argumento est erit vergentium, quibus non medium mundi causa est suorum momentorum, sed cognatio cum terra, a qua vi repulsa, rursum ad eam se conferunt. Sicut enim Sol omnes partes, ex quibus constat, ad se convertit: & lapidem terra ut sibi convenientem accipit &fert ad eum. Itaque horum unumquodque temporis progressu unitur cum ea coalescit. Quid si quod est corpus ab initio terrae non attributum, neque ab ea avulsum, sed peculiari natura pro sese constat: (qualem isti Lunam faciunt) quid obstat quin seorsim id subsistat suis compactum propriis ac constrictum partibus?

* The newer Plutarch editions hold πελάζειν to be a corrupted reading and read at this position γελοιάζειν. Note that newer Plutarch editions in general have a text which diverges strongly from Plutarch (Omnia).

354

Appendices

26. With the translation “add below to above” we follow the Xylander translation cited by Newton, the Greek version of which uses πελάζειν, which Xylander translated as inferiora superioribus adjungere. Xylander’s Greek version could not be more aptly translated than “transplant below to above.” Almost all newer Plutarch editions hold πελάζειν to be a corrupted reading and read ελοιάζειν instead. Taking this reading as a basis (although it was unknown to Newton), one could translate as follows: “Those who are subject to prejudice say that those are joking who the earth’s moon ... ” 27. Newton’s literature reference “[Origenes in Philosophicis.]” could tempt the assumption that he was quoting from Origenes’ writings, of which he had several editions, see Harrison (Library of Newton No. 1208–1213). The quote φϑείρεσϑαι δὲ ἀυτοὺς ὑπ᾽ ἀλλήλων προσπίπτοντας, however, originates from Book I of the Refutatio omnium haeresium (Κατὰ παςῶν αἱρέσων ἔλεγχος), which falsely attributed the older handwritten copies to Origenes and is actually a tract by Hippolytus. Book I of the Refutatio contains an important doxography and bears the special title Philosophumena (Φιλοσοφούμενα), which at times is incorrectly used for the entire Refutatio. The Editio princeps of the Refutatio was not published until 1701 by Jacob Gronov (Thesaurus graecorum antiquitatum vol. X, Lugduni Batavorum 1701), however, sections of Book I had become known earlier, and as early as 1688 Pierre-Daniel Huet in Appendix § XI of his Origeniana in Huet (Commentaria) proved that Origenes cannot be the author of the Philosophumena. Certainty about Hippolytus’ authorship was not achieved until the middle of the nineteenth century, however. Until the Editio princeps appeared, Aegidius Menagius (Gilles Menage) had cited from the handwritten tracts of the Philosophumena at greatest length in his Observationes et emendationes in Diogenem Laertium. These Observationes were quite apparently known to Newton, for Diogenes Laertius (De vitis 1664), which Newton owned, contains the Observationes of Aegidius Menagius. In his Observationes in Laertii Lib. IX, see Diogenes Laertius (De vitis 239 E right column), Menagius cites the views of Democritus with the following passage from the Philosophumena, compare also Hippolytus (Refutatio 1916 Book I § 13 page 16/17); Hippolytus (Refutatio l986 Book I § 13, 2–4, page 72/73): ἀπείρους δὲ εἶναι κόσμους καὶ μεγέϑει διαφέροντας, ἐν τισὶ δὲ μὴ εἶναι ἥλιον μηδὲ σελήνην, ἐν τισὶ δὲ μείζω τῶν παρ᾽ἡμῖν καὶ ἐν τισὶ πλείω. εἶναι δὲ τῶν κόσμων ἄνισα τὰ διαστήματα, και τῇ μὲν πλείους, τῇ δὲ ἐλάττους, καὶ τοὺς μὲν αὔξεσϑαι, τοὺς δὲ ἀκμάζειν, τοὺς δὲ φϑίνειν, καὶ τῇ μὲν γίνεσϑαι, τῇ δ᾽ἐκ λείπειν. φϑείρεσϑαι δὲ αὐτοὺς ὑπ᾽ἀλλήλων προσπίπτοντας. εἶναι δὲ ἐνίους κόσμους ἐρήμους ζῴων καὶ φυτῶν καὶ πατὸς ὑγρου. τοῦ δὲ παρ᾽ἡμῖν κόσμου πρότερον τὴν γῆν τῶν ἄστρων γενέσϑαι, εἶναι δὲ τὴν μὲν σελήνην κάτω, ἔπειτα τὸν ἥλιον, εἶτα τοὺς ἀπλανεῖς ἀστέρας. τοὺς δὲ πλανήτας οὐδ᾽αὐτοὺς ἔχειν ἴσον ὕψος. ἀκμάζειν δὲ κόσμον, ἕως ἂν μη κέτι δύνηται ἔξωϑέν τι προσλαμβάνειν. This means: There are infinitely many worlds of different sizes, in some there is no sun and no moon either; in some they are larger, and some have multiple suns and moons. The distances of the worlds

Appendices

355

are different, and there are more worlds here and fewer there, and some are still situated in growth, others in full bloom and still others in disappearance, and at one location some are originating while at another location some are dying. They perish by falling toward each other. A number of worlds are devoid of living creatures and plants and completely devoid of moisture. In our world the earth came into being before the stars, the moon was located at the bottommost position, and then came the sun and finally the fixed stars. The planets, too, have different heights. A world is situated in full bloom until it can no longer assimilate anything from outside. Menagius still believed to have a text by Origenes before him, for he stated Origenes in Philosophicis as his source, which Newton appropriated into his text. The Latin translation given by Newton, corrumpi autem illos in se invicem cadendo for the passage φϑείρεσϑαι δὲ ἀυτοὺς ὑπ᾽ ἀλλήλων προσπίπτοντας appears to stem from Newton himself. We could not find any contemporary or older Latin translation of the corresponding passage from the Philosophumena. 28. In order to make the physical content of Lucretius’ verse as evident as possible, we give a prose translation in our English text from Lucretius (De rerum natura 1947), translated by Cyril Bailey. The verse numbering given in the following follows the verse numbering generally used today, as it was found in Lucretius (De rerum natura 1947, 1969), for example. 29. Lucretius Book V verse 91–98. 30. Lucretius Book V verse 104–09. 31. In Newton’s manuscript a transcription error occurred here: rather than ortis, as is found in Lucretius’ Book V verse 105, the word orbis is here in Newton’s copy. This error also occurs in the fair copy of David Gregory’s Notae in Newtoni Principia Mathematica Philosophiae Naturalis (Royal Society London MS 210). 32. The scholion was to expand on Proposition VI Book III and probably was to be inserted in the first edition (1687) of Newton’s Principia on page 411 after Corollary 4 of Proposition VI. 33. Lucretius Book I verse 358–369. 34. Lucretius Book II verse 184–205. 35. The meaning of the phrase quantum in se est is for the understanding of the law of inertia and the definition of the vis insita as it was formulated by Newton in his Principia, of crucial importance. Regardless of which meaning Lucretius links with this phrase, in our opinion the meaning which Newton links with this phrase in connection with his law of inertia is best expressed through the English translation “of its own accord, through its own force.” See also Cohen (Quantum in se est) and Schüller (Quantum in se est). In Lucretius (De rerum natura 1947) the translation of the phrase quantum in se est is “as far as in them lies.” 36. Lucretius Book II verse 216–244. 37. Verse 220 is missing in Newton’s manuscript; apparently this was a transcription error.

356

Appendices

38. Newton accentuated the two verses 238 and 239 in his manuscript by writing them in a particularly large hand. In our opinion, Newton appears to interpret this particular passage as confirmation that the antique authors were also of the opinion that all bodies would be accelerated at the same rate, which was a particularly important result of his theory of gravitation. 39. Instead of alii autem quibus atomi inaequales erant (this means: the others, however, for which the atoms were unequal) the original read alii inaequalitatem atomorum statuebant (this means: the others asserted the inequality of the atoms). 40. Since no Aristotle edition is named in Harrison (Library of Newton), it must be presumed that Newton did not own such an edition. From which edition Newton took his Aristotle quotation cannot be determined with any certainty. The translation he cites is by Johannes Argyropulos, and Newton’s deviations from Argyropolus’ translation in Aristoteles latine interpretibus variis are slight and probably can be traced to the edition used by Newton, whichever it may be. This edition probably contained a print error in that plumbo was left out, which Newton added to his text in pointed brackets. In Aristotle (Aristoteles latine interpretibus variis 162) this passage reads as folIows: quidam enim de leviore gravioreque sic dicunt ut in Timaeo est scriptum, gravius quidem id esse quod ex eisdem pluribus constet, levius autem id quod ex eisdem paucioribus constet, quemadmodum plumbo plumbum et aes aere maius gravius es . ... eodem modo lignum et plumbum dicunt. ex quibusdam enim eisdem omnia corpora et un maetia esse aiunt. This corresponds to Aristotle 308b 3ff.: λέγουσι γὰρ τὸ κουφότερον καὶ βαρύτερον οἱ μὲν ὥσπερ ἐν τῷ Τιμαίῳ τυγχάνει γεγραμμένον, βαρύτερον μὲν τὸ ἐκ πλειόνων τῶν αὐτῶν συνεστός, κουφότερον δὲ τὸ ἐξ ἐλαττόνων, ὥσπερ μολίβδου μόλιβδος ὁ πλείων βαρύτερος καὶ χαλκοῦ. ... τὸν αὐτὸν δὲ τρόπον καὶ ξύλου μόλιβδόν φασιν· ἔκ τινων γὰρ τῶν αὐτῶν εἶναι πάντα τὰ σώματα καὶ μιᾶς ὕλης. The supplement , which we have added in our English translation, can be justified with the remark that τῶν α᾽τῶν is the genitive plural of a masculine or neutral noun, i.e. it must designate several things. One could therefore supplement this with τὸ μέρος, τὸ μόριον (engl. part, portion, understood in contrast to the whole) or with τὸ μερίδον, τὸ μικρὸν (engl. particle). We decided on the supplement , as Newton obviously wanted this Aristotle passage to be understood in this sense. Aristotle’s remark about Plato’s Timaeus refers to Stephanus 63 C. 41. This non is only found in the fair copy of David Gregory’s Notae in Newtoni Principia Mathematica Philosophiae Naturalis (Royal Society London MS 210), as Newton’s manuscript from Gregory’s estate (Royal Society London MS 247 fols. 6–14) is so corrupted at this position that the non is no longer present in the manuscript. 42. Newton’s source reference “... Simplicius says about this passage” is imprecise, because it creates the impression for the reader that Simplicius communicated that Leucippus and Democritus would belong to these philosophers in

Appendices

357

the Aristotle passage 308b 3ff. (see remark 40). The Aristotle passage 308b 3ff is commented in the Latin translation of Simplicius (Commentaria 1584, 200–201 Comment. 3); the remark about Leucippus and Democritus referred to by Newton with his source reference “... Simplicius says about this passage” is in the next comment, Comment 4, see Simplicius (Commentaria 1584, 201), which refers to Aristotle 308b 30–309a 18 in accordance with this edition. Comment. 4 begins with the words: Post eos qui multitudine, et paucitate planorum grave, et leve determinant, transit ad eos qui circa Leucippem, et Democritum gravedinis quidem soliditatem atomorum causam ponentes. Levitatis autem vacui interceptionem ,* et dicit hos quamvis antiquiores extiterint magis noviter intellexisse de propositis quam eos quil multitudine et paucitate planorum gravis et levis differentia assignant. * interceptionem is obviously a misprint, it should be intercessionem for παρεμπλοκήν, as is evident from the following original Greek text, see Simplicius (Commentaria 1882, 684 line 19–25): Μετὰ τοὺς πλήϑει καὶ ὀλιγότητι τῶν ἐπιπέδων τὸ βαρὺ καὶ κοῦφον διορίζοντας μέτεισιν ἐπὶ τοὺς περὶ Λεύκιππον καὶ Δημόκριτον τοῦ μὲν βάρους τὴν τῶν ἀτόμων αἰτιωμένους ναστότητα τῆς δὲ κουφότητος τὴν τοῦ κενοῦ παρεμπλοκήν, καὶ λέγει τούτους καίτοι ταῖς ἡλικίαις ὀλιγότητι τῶν ἐπιπέδων τὴν τοῦ βαρέος καὶ κούφου διαφορὰν ἀποδιδόντας· This means: After those who determine the heavy and the light through a larger and smaller number of the surfaces, he proceeded to those associated with Leucippus and Democritus, who declare the reason for weight to be the solidity of the atoms and that for lightness the intervention of emptiness, and he says that these, although they were older, had more modern views on this topic than those who explained the difference between the heavy and the light through the greater and fewer number of surfaces. 43. Newton speaks of a positive quality, this is to be understood in the sense in which the concept ‘positive’ is explained in Zedler (Universal  – Lexikon XXVIII column 1732): “Positive wird etwas genommen, wenn der Grund der Benennung etwas reelles und in der That existierendes ist.” (This means: Something is taken to be positive when the reason for this designation is something real and something which in fact exists). 44. In Book I Chap. XVI, Plutarch (Omnia II 883 D), of his tract De placitis philosophorum (Philosophical Teachings) Plutarch writes: Οἱ ἀπο Θάλεω καὶ Πυϑαγόρου παϑητὰ Σώματα, καὶ τμητὰ εἰς ἄπειρον· ἢ τὰς ἀτόμους ἢ τὰ ἀμερῆ ἵστασϑαι, καὶ μὴ εἰς ἄπειρον εἶναι τὴν τομήν.

Thaletis et Pythagorae sectatores, negant in infinitum progredi sectionem eorum corporum, quae motibus sunt obnoxia, sed subsistere in iis quae individua sunt, et atomi dicuntur.

358

Appendices

This means: The disciples of ThaIes and Pythagoras dispute that the division of those bodies subject to the movements can be continued limitlessly, but rather that it stops at those which are indivisible and are called atoms. 45. That water was the principle of things for Thales was reported by Aristotle, for instance, in his Metaphysics Book I Chap. 3, 983b 20ff. and Diogenes Laertius I 27 in his Thales biography; no antique sources are known, however, from which could be inferred that Thales also held the view that water consists of corpuscles. 46. Newton cites passages from Plutarch’s De placitis philosophorum (Philosophical Teachings) Book I Chap. VII 14, Plutarch (Omnia II 888 D), where is written: Πυϑαγόρας, τῶν ἀρχῶν τὴν μὲν μονάδα ϑεὸν, καὶ τάγαϑὸν, ἥτις ἐστὶν ἡ τοῦ ἑνὸς φύσις, αὐτὸς ὁ νοῦς· τὴν δ᾽ἀόριστον δυάδα, δαίμονα καὶ τὸ κακὸν, περὶ ἥν ἐστι τὸὑλικὸν πλῆϑος, ἔστι δὲ καὶ ὁ ὁρατὸς κόσμος.

Pythagoras, de principiis unitatem Deum, ac bonum, quae sit Unius natura, ipsa mens: infinitam autem Binarii naturam, genium et malum, unde est multitudo materiae, et visui expositus mundus.

This means: Pythagoras taught on the one hand that the monad God and the good to the principles, for the monad is the essence of the unique, the spirit itself; on the other hand he asserted the indeterminate dyad as the demon and as the evil to which the multitude of matter and the visible world are bound. 47. Our translation “solid particles” for the Latin solida can be justified with the remark that the corresponding attribute numero infinita (Engl. The infinite with regard to number, infinitely many) must refer to something that can be enumerated. We interpret these enumeratable objects as particles, for Newton generally uses the Latin solidus in a physical context to mean “solid.” The atomos crossed out by Newton also suggests such a translation. 48. The text in [i.e ....] could not be deciphered. 49. Newton cites from the Anaximander biography by Diogenes Laertius II 1, that is, Diogenes Laertius (De vitis 1664, 33 A): Ἀναξίμανδρος Πραξιάδου Μιλήσιος, οὗτος ἔφασκεν ἀρχὴν καὶ στοιχεῖον τὸ ἄπειρον, οὐδιορίζων ἀέρα ἢ ὕδωρ ἢ ἄλλο τι. καὶ τὰ μὲν μέρη μεταβάλλειν, τὸ δὲ πᾶν ἀμετάβλητον εἶναι.

Anaximander, Praxiadis filius, Milesius fuit.Is infinitatem initium, atque elementum esse dicebat; non aerem, aut aquam, aut aliud quidpiam definiens. Et partes quidem illius immutari, totam vero esse immutabilem.

Appendices

359

Which means: Anaximander, son of Praxiades, was Milesian. He asserted the apeiron as a principle and element without defining it as air, water, or anything else. He taught that the particles might change, but that the whole is unchangeable. The Latin translator used infinitas (Eng. Infinity) to translate τὸ ἄπειρον (apeiron), as, for example Cicero did in his Academica (Academic Investigations) Book II Chap. XXXVII 118, where he reports about Anaximander: is enim infinitatem naturae dixit esse, e qua omnia gignerentur (i.e., he said that there exists an infinity of nature from which everything is engendered). The Greek τὸ ἄπειρον (apeiron) can only be approximated in English and means something both qualitatively indeterminate as well as quantitatively unlimited. Particularly noteworthy is the last sentence in the existing Latin translation used by Newton: Et partes quidem illius immutari, totam vero esse immutabiliem. In this translation the Latin totam refers to the Latin infinitatem in the previous sentence, i.e., the Latin translator related the Greek τὸ πᾶν in the last sentence to the Greek τὸ ἄπειρον in the previous sentence, such that totam must be translated as “the entire .” This final sentence has been interpreted quite differently by other Latin translators, however, who translated the passage instead as Partes quidem illius immutari, totum vero esse immutabile. While the Latin totum is the translation of the Greek τὸ πᾶν in the last sentence, totum cannot refer to the Latin infinitatem in the previous sentence, which means that the Greek τὸ πᾶν cannot refer to the previous τὸ ἄπειρον, but must be translated as “the whole” instead, whereby it is not possible to determine what “the whole” is. Such a grammatical analysis is also correct and would lead to the following English translation: The parts might change, but the whole is unchangeable. Such an interpretation of the sentence is found, for instance, in Diogenes Laertius (De vitis 1615, 88) and Diogenes Laertius (De vitis 1739, 133); in Diogenes Laertius (De vitis 1692, 78179) the body of the text gives the translation totum vero immutabile esse, but the corresponding remark shows the translation as totam vero esse immutabilem. In the German translations of Diogenes Laertius known to us (1921), (1990) and (1998), the Greek τὸ πᾶν in the last sentence is translated as “das Ganze” (the whole). 50. Newton is mistaken if he attributes to Anaximenes the same opinion as Anaximander; in particular, there is no evidence that Anaximenes was an atomist. Diogenes Laertius II 2 reports that air was the beginning of all things for Anaximenes. Plutarch’s De placitis philosophorum Book I Chap. 3 Proposition 4 also reports that Anaximenes believed air to be the principle for all things, from which all originates and into which all dissolves again. The report in Simplicius (Commentaria 1882, 24 line 26ff.) is quite detailed, reporting also that in the opinion of Anaximenes it is air from which everything comes and to which everything decomposes. When air is rarefied, fire is

360

Appendices

created; if air condenses instead, wind is created, then fog; should it condense even more, water is created. Further condensation would create earth and ultimately stone. 51. The passage ... infinitum aerem vocabat et ex eo aquam terram aquam et ignem gigni, ex his vero alia omni is reminiscent of Cicero’s Academia (Academic Investigations) Book II Chap. XXXVII 118, where is written of Anaximander: is enim infinitatem naturae dixit esse, e qua omnia gignerentur; post eius auditor Anaximenes infinitum aera, sed ea, quae ex eo orerentur, definita; gigni autem terram, aquam, ignem, tum ex his omnia. This means: he said that there exists an infinity of nature from which everything is engendered, later his pupil Anaximenes that air is infinite, but the things which emerge from it, finite; that is to say earth, water, fire would be engendered, and from these then all else. 52. The views which Newton attributes to Anaximander and Anaximenes are passed down through Diogenes Laertius only in part. In particular, there is no indication that they were atomists. 53. Presumably Newton meant Galeni de historia philosophica liber spurius, contained in Galen (Opera omnia XIX 221–345), however, Galen only says that the air is the apeiron for Anaximander and the element for Anaximenes and Diogenes of Apollonia. It is nowhere mentioned that Anaximander spoke of an ether. 54. Diogenes Laertius IX 57 merely reports that air is the element for Diogenes of Apollonia. In Diogenes Laertius there is also no indication that Anaximander called the apeiron ether. 55. Newton refers to the admonition to the heathen by Clemens of Alexandreia (admonitio ad graecos seu ad gentes). The edition Clemens Alexandrinus (Opera 1641) was unfortunately not available to us, so that we must cite from Clemens Alexandrinus (Opera 1688). In this edition the admonition (admonitio) is located on the pages 1 ff. Both of the following passages, which are doubtlessly those Newton had in mind, only partially support what Newton says about Anaximenes, Anaximander and Diogenes of Apollonia; in particular, there is nowhere any mention of an ether. In Chapter V, Clemens Alexandrinus (Opera 1688, 42 C) or Clemens Alexandrinus (Werke I page 48, line 34–page 49, line 2), is written: στοχεῖα μὲν οὖν ἀρχας ἀπέλιπον ἐξυμνήσαντες Θαλῆς ὁ Μιλήσιος τὸ ὕδρωρ καὶ Ἀναξιμένησος καὶ αὐτὸς Μιλήσιος τὸν ἀέρα, ᾧ Διογένης ὕστερον ὁ Ἀπολλωνιάτης κατηκολοὺϑησεν.

Principia itaque a se laudata reliquerunt Thales Melesius, Aquam: & Anaximenes, qui ipse quoque fuit Melesius, Aerem, quem Diogenes Apolloniates es postea consecutus.

Appendices

361

This means: Some left the elements as principles. Thales of Miletus extolled water as such a primary material, and Anaximenes, who also came from Miletus, in the same way extolled air, to which Diogenes of Apollonia subscribed later as well. In Chapter V, Clemens Alexandrinus (Opera 1688, 43 D) or Clemens Alexandrinus (Werke I page50, line 13–16), is written: Τῶν δὲ ἄλλων φιλοσόφων ὅσοι τὰ στοχεῖα ὑπερβάντες ἐπολυπραγμόνησάν τι ὑψηλότερον καὶ περιττότερον, οἵ μὲν αὐτων τὸ ἄπειρον καϑύμηνησαν, ὡς Ἀναξίμανδρος Μιλήσιος ἦν καὶ Ἀναξαγόρασ ὁ Κλαζομένος καὶ ὁ Ἀϑηναῖος Ἀρχέλαος.

Ex aliis autem philosophis, qui elemtis praeteritis, excesius aliquid & praestantius indagarunt: alii quidem ex ipsis laudarunt infinitum, ex quibus Anaximander Milesius, & Anxagoras Clazomenius, & Atheniensis Archelaus.

This means: Of the other philosophers who transcended the elements, searched laboriously for something higher and better. Some of them extolled the apeiron, as for instance Anaximander (he came from Miletus), the Klacomenian Anaxagoras and the Athenian Archelaos. 56. Newton cites Cicero’s Academica (Academic Investigations) Book II Chap. XXXVII 188 with one minor change, which is doubtlessly a transcription error. This citation corresponds to the Cicero edition probably used by Newton, Cicero (Opera omnia IV 25, line 36ff.), where this passage reads: Anaxagoras materiam infinitam, sed ex ea particulas simileis inter se minutas; eas primum confusas, postea in ordinem adductas a mente divina; in Cicero (Scripta 72) this passage reads: Anaxagoras materiam infinitam, sed ex ea particulas, similes inter se, minutas; eas primum confusas, postea in ordinem adductas mente divina. This means: Anaxagoras matter is infinite, but out of it minute particles entirely alike, which were at first in a state of medley but were afterwards reduced to order by a divine mind. 57. In the first edition (1687) of Newton’s Principia Proposition VII Book III is on pages 411–412. Unfortunately Newton does not indicate exactly where the text is to be inserted in the first edition. Possibly this text was to be inserted after Corollary 2 of Proposition VII, that is, on page 412 of the first edition. 58. Newton cites from Plutarch’s De facie in orbe Lunae (The Face on the Moon), Plutarch (Omnia II 926 AB):

362

Appendices

εἰ γὰρ τι ἂν καὶ ὁπωσοῦν ἐκτὸς γένηται τοῦ κέντρου τῆς, ἄνω ἐστὶν, οὐϑέν ἐστὶ τοῦ κόσμου κάτω μέρος, ἀλλ᾽ἄνω καὶ ἡ γῆ καὶ τὰ ἐπὶ γῆς, καὶ πᾶν ἁπλῶς σῶμα τὸ κέντρῳ περιεστηκὸς ἥ περικείμενον ἄνω γίγνεται κάτω δὲ μόνον ὂν ἕν, τὸ ἀσώματον σημεῖον ἐκεῖνο ὃ πρὸς πᾶσαν ἀντικεῖσϑαι τὴν τοῦ κόσμου φύσιν ἀναγκαῖον εἴ γε δὴ τὸ κάτω πρὸς τὸ ἄνω κατά φύσιν ἀντίκειται. καὶ οὐ τοῦτο μόνον τὸ ἄτοπον, ἀλλὰ καὶ τὴν αἰτίαν ἀπόλλυσι τὰ βάρηδι᾽ἢν δεῦρο καταρρέπει καὶ φέρεται·σῶμα μὲν γὰρ οὐδέν ἐστι κάτω πρὸς ὃ κινεῖται, τὸ δ ἀσώματονοὔτ᾽εἰκὸς οὔτε βούλονται τοσαύτην ἔχειν δύναμιν ὥστε πάντα κατατείνειν ἐφ᾽ ἑαυτὸ καὶ περὶ αὐτὸ συνέχειν.

Si enim quidquid quocumque modo extracentrum Terrae est dici oportet supra esse, nulla pars mundi infra erit: sed supra fuerit et Terra et omnia quae ei incumbent et simpliciter quodvis corpus centro circumpositum; infra autem unicum illud corporis expers punctum atque hoc omni mundi naturae opponi* quando superum et inferum naturae ratione invicem opponuntur. Neque hoc dumtaxat est in hac re absurdum; sed causam quoque gravia perdunt, ob quam deorsum vergant atque ferantur, cum nullum sit infra corpus ad quod moveantur. Nam quod corporeum non est, id neque probabile est, neque ipsi volunt tanta esse vi praeditum ut omnia ad se trahat et circa se continea.t

•  In Xylander’s translation in Plutarch (Omnia), necesse erit is missing, which is included in Newton’s text. In Plutarch (Opera IX 581), however, this necesse erit is included, but after atque hoc rather than where Newton cites it. We presume that Newton himself inserted into the Latin text this necesse erit, for which there is an analogy in the Greek text, rather than based on Plutarch (Opera), for in the latter case he would have inserted the necesse erit immediately following atque hoc. 59. Lucretius Book I verse 948–997. 60. In the first edition (1687) of Newton’s Principia, Proposition VIII Book III and its corollaries are located on pages 412–416; this text was probably to be inserted after Corollary 5 of this Proposition VIII, i.e. on page 416. 61. Harmonia (ἁρμονία) is translated as scale. Compare Waerden (Harmonielehre 276 footnote 2). 62. Newton’s reference is not entirely correct. Doubtlessly Newton meant not Book I of Plinus’ Historia naturalis (Natural History), but rather Book II, and refers to a passage located in Chapter XX of this book, De siderum musica (Musical Observations about the Stars), see Plinius (Historia 1866, 86) and Plinius (Naturkunde 83). This Chapter XX is Chapter XXII of De siderum musica in all older editions we were able to check, for instance Plinius (Historia 1553, 165), Plinius (Historia 1559, 9), Plinius (Historia 1582, 8), Plinius (Historia 1608, 78) and Plinius (Historia 1669, 33). Newton’s chapter reference thus is correct according to the old editions of Plinius. As can be

Appendices

363

concluded from Harrison (Library of Newton No. 1329), Newton owned only an edition with selections from Plinius’ Historia naturalis from the year 1725, which cannot have served Newton as a source, however, since he had already written his texts in the nineties of the seventeenth century. 63. The Macrobius citation listed by Newton comes from the Saturnalia by Macrobius. See Macrobius (Opera Lib. I Cap. XIX 250), Macrobius (Saturnalia I. 19. 15 page 111). 64. Newton refers to Proclus (Commentaria 1534, 200 line 28–30), see also Proclus (Commentaria 1903–1906  Vol. II page 197 line 28–32), where the following passage appears: ... τῷ Ἀπόλλωνι τὴν ἑπτάδα ἀνεῖσαν, ὡς συνέχοντι πάσας τὰς συμφωνίας· ἐν γὰρ μονάδι καὶ δυάδι καὶ τετράδι πρῶτον τὸ δὶς διὰ παςῶν, ἐξ ὧν ἡ ἑβδομάς. διὸ καὶ ἑβδομαγέταν ᾽κ῀άλουν τ`ν ϑεόν, καὶ τὴν ἑβδόμην ιερὰν ἔλεγον τοῦ ϑεοῦ· Which means: ... they devoted the heptad to Apollo, the one who possessed all harmonies together, for the double octave initially comprises a monad, a dyad and a tetrad, which yield the number seven. Therefore they also called the God Hebdomageta and dedicated the seventh day to him. According to Harrison (Library of Newton), Newton did not have an edition with Proclus Diadochus’ Commentary on Plato’s Timaeus. Newton’s Latin text is apparently an abridged translation of this passage; it is not possible to determine whether the Latin translation was undertaken by Newton himself or by another translator. 65. See remark 68. 66. Newton refers to Eusebius (Praeparatio Evangelica V 14 page 202 line 10–22), where the sun is referred to as τῆς ἑπταφϑόγγου βασιλεὺς: Καὶ πάλιν ὲν χρησμοἴς ἔφη τὸν Ἀπόλλωνα εἰπεἴν, Κληΐζειν Ἑρμῆν ἠδ᾽ Ἡέλιον κατὰ ταῦτα, Ἡμέρῃ Ἠλίου κατὰ ταῦτα, Ἡμέρῃ, ἠδὲ Κρόνον, ἠδ᾽ ἑξείς Ἀφροδίτην, Κλήσεσιν ἀφϑέγκτοις, ἅς εὖρε μάγων ὄχ᾽ ἅριστος Τῆς ἑπταφϑόγγου βασιλεύς, ὅν πάντεσ ἴσασιν.

Ac rursus Apollinem suis in responsis hunc in modum loqui testatur, Mercurium ac Solem simul appellare memento Luce sacra Soli: tum Lunam, ubi venerit ejus Nota dies, Saturnam exin, natamque Dione, Vocibus arcanis, quas maximus ille Magorum Septisonae Dominus reperit, notissimus idem Omnibus.

This could be translated into English as follows: And , for his part, said that Apollo proclaimed in his oracles: One calls Hermes and the sun in the same way on the day of the sun, the moon, when its day has come, with silent invocations discovered by the best of the magicians by far, the king of the seven-tone , known by all. The modern editions, like for instance Eusebius (Werke Book V Chap. 14, I page 248), diverge in part from the text in the Eusebius (Praeparatio Evangelica) edition given above.

364

Appendices

67. Note that Vigerus translates τῆς ἑπταφϑόγγου βασιλεὺς in Eusebius (Praeparatio Evangelica) as septisonae dominus, and leaves open to what septisonae refers. Newton, by contrast, changes Vigerus’ translation slightly, assuming with his translation of τῆς ἑπταφϑόγγου βασιλεὺς as Rex harmoniae septisonae that harmoniae must be added to the word septisonae by way of explanation. From the Greek literature about musical theory it can be inferred that the adjective ἑπταφϑόγγου, -ον refers to the musical instrument the lyre (ἡ λύρα) in musical theory. Newton’s translation or addition is grammatically correct, if he meant the Greek ἡ ἁρμονία with the Latin harmonia. For the translation of ἡ ἁρμονία, cf. Waerden (Harmonielehre 176 footnote 2). 68. At this position on fol. 12r, Casini (Newton: The Classical Scholia 31) reads “a” as a superseript, which in his opinion should refer to the note “a. Ἑπτ. ἐπι ϑηβ. v. 739. Aeschylus: ὁ σεμνὸς ἑβδομαγέτης Ἄναζ Ἀπόλλων Venerandus Hebdomageta, Rex Apollo” This note, however, is on fol. 11v and we were unable to find a superscript “a” on fol. 12r. In classifying this note we follow the transcription of David Gregory’s Notae in Newtoni Principia Mathematica Philosophiae Naturalis (Archive of the Royal Society London MS 210), where this note is placed in pointed brackets at the end of the previous sentence, whereby an insertion sign Λ immediately follows the first pointed bracket. It appears to us impossible to determine where Newton intended to place the note from fol. 11v. Newton refers to verse 739  in Aeschylus’ play “Seven against Thebes”, where the Greek or Latin text reads: venerable Hebdomageta, King Apollo. In older Aeschylus editions this passage sometimes is found in verse 785/786, but most often in verse 800/801, as is customary in modern editions. Newton’s reference to verse 739 is not incorrect, however, for there are a number of older editions where this passage is located in verse 739, for instance in Poetae graeci (Veteres tragici, lyrici, comici I 626) this passage has the address 739/740. Whether the Latin given here was translated by Newton himself or taken from another translation could not be determined. Aeschylus (Προυμηϑεὺς Δεσμώτης …) and Aeschylus (Tragoediae septem) contain only the Greek text; the translation given next to the Greek text in Poetae graeci (Veteres tragici, lyrici, comici) reads Septimam vero gravis Ebdomageta Rex Apollo. Hebdomageta (ἑβδομαγέτης) is an epithet for Apollo, because sacrifices were made to him on the seventh day of every month, see Herodot VI 57. In Sparta Apollo also had the epithet Hebdomagene (ἑβδομαγέτης), which means: he who was born on the seventh day, cf. Plutarch Symp. VIII 1,2. 69. On folio 12r there is a note, that b refers to Macrobius’ Book 2 on Scipio’s Dream Chap. 1, but such a note is missing on fol. 11v. 70. See the remark 69. 71. As Proposition IX Book III is on page 416  in the first edition (1687) of Newton’s Principia, this scholion was to be inserted on page 416.

Appendices

365

72. Newton refers to the life story of Thales in Diogenes Laertius (De vitis 1664, 6 D), which is Diogenes Laertius I 24: Ἀριστοτέλης δὲ καὶ Ἱππίας φασὶν αὐτὸν καὶ τοῖς ἀψύχοις μεταδιδόναι ψυχῆς, τεκμαιρόμενον ἐκ τῆς λίϑου τῆς μαγνήτιδος καὶ τοῦ ἠλέκτρου.

Aristoteles autem & Hippias aiuntinanimis etiam illum animas impartire, idipsum ex lapide magnete & electro conjicientem.

This means: Aristotle and Hippias report that he believes the lifeless to be animate, a view which led him to the observation of magnetic stone and of amber. Aristotle reports the same information in de anima (On the Soul) I 2, 405a 19f. as well. There is written: ἔοικε δὲ καὶ Θαλῆς, ἐξ ὧν ἀπουμνημονεύουσι, κινητικόν τι ψυχὴν ὑπολαβεῖν, εἴπερ τὴν λίϑου τῆς μαγνήτιδος καὶ τοῦ ἠλέκτρου. This means: It appears that Thales, too, according to that which is reported, believed the soul to be a cause of movement; in any case he said that magnetic stone is animate because it moves iron. 73. In the Thales’ life story, Diogenes Laertius (De vitis 1664, 7 B), that is Diogenes Laertius I 27, reports: καὶ τὸν κόσμον ἔμψυχον καὶ δαιμόνων πλήρη.

statuebat mundum animantem & laribus plenum.

This means: He believed the world to be animate and full of Gods. The same is reported by Aristotle in his tract de anima (On the Soul) I 5, 411a 8f., where is written: Θαλῆς ᾠήϑη πάντα πλήρη ϑεῶν εἶναι (this means: Thales believed that everything is full of Gods). Newton’s formulation is quite similar to the Latin translation of this passage by Johannes Argyropulos, who translated it as: Thales omnia plena deorum esse putavit. See Aristoteles latine interpretibus variis 214. Newton appears not to have owned an edition of Aristotle, however, as none is listed in Harrison (Library of Newton). In his tract de legibus (On the Laws) Book II Chap. XI 26, Cicero also reports: Thales ... homines existimare oportere, omnia quae cernerent deorum esse plena. This means: Thales ... asserted that people must believe that everything they see is full of Gods. It is quite probable that Newton knew this passage from de legibus, because Cicero was a widely-read author and the familiarity with his writings was part of the general canon of knowledge. In the edition Cicero (Opera omnia), which was in Newton’s possession as Harrison (Library of Newton No. 381) reports, this passage is located in Tomus IV, page 227, lines 26–29.

366

Appendices

74. In his Pythagoras biography, Diogenes Laertius (De vitis 1664, 220 C), or Diogenes Laertius VIII 27 writes: ἥλιον τε καὶ σελήνην καὶ τοὺς ῎λλους ἀστέρας εἶναι ϑεούς·

Solem, & lunam, & reliqua sidera deos esse.

This means: that the sun, the moon and the other stars are Gods. 75. There are two ancient sources which report of τὴν τοῦ Διὸς φυλακήν. Aristotle reports in de coelo (On the Heavens) Book II Chap. XIII 293a 20f. that, in the opinion of the Italic Pythagorans, a fire is at the center of the universe, the earth is a heavenly body, and day and night on the earth arise from the fact that the earth revolves in a circle around the center. Finally, in Aristotle’s de coelo Book II Chap. XIII 293b 1 is written: Ἔτιδ᾽ οἵ γε Πυϑαγόρειοι καὶ διὰ τὸ μάλιστα προσήκειν φυλάττεσϑαι τὸ κυριώτατον τοῦ παντὸς – τὸ δὲ μέσον εἶναι τοιοῦτον – ὃ Διὸς φυλακὴν ὀνομάζουσι τὸ ταύτην ἔχον τὴν χώραν πῦρ, ὥσπερ τὸ μέσον ἁπλῶς λεγόμενον, καὶ τὸ τοῦ μεγέϑους μέσον καὶ τοῦ πράγματος ὂν μέσον καὶ τῆς φύσεως. This means: Moreover, the Pythagorans also believed that it must be so because it is right that the most important thing of all – and this is the center – should be most protected. They call the fire which occupies this space the guard of Zeus, as if the concept of the center had only one single meaning and therefore the middle of the extended is at the same time the middle of the subject and of nature. Here Newton interprets Aristotle’s report about the views of the Pythagorans in Italy quite in his own way, and in a sense which serves his own interests, by interpreting the fire of which the Pythagorans speak, and which in their opinion should lie at the center of the universe, to be the sun. There can be no doubt that Newton refers to de coelo by Aristotle, for only here is reported that the fire in the center of the universe is τὴν τοῦ Διὸς φυλακήν for the Pythagorans. The translation of φυλακήν in this Aristotle quote as the Latin carcer goes back to Wilhelm Moerbeke; Johannes Argyropulos, for his part, translated φυλακήν as custodia in this Aristotle citation. Another source Newton may have used is the Simplicii Commentaria in quatuor libros Aristotelis de coelo. Newton’s remark about the great power of the sun suggests Simplicius as a source, for it was Simplicius who emphasized especially the highly significant meaning and power of the fire in the center of the universe. In Simplicius (Commentaria 1584) the above passage from Aristotle’s de coelo is discussed on pages 151 and 152 and Moerbeke translates Διὸς φυλακήν as carcer Jovis in Latin. 76. Newton took Ἁρμονίαν κόσμοιο κρέκων φιλοπαίγμονι from Conti (Mythologia), where the following Latin translation is given on page 453: Harmoniam mundi faciens dulcidine cantus. This means: a graceful song which creates the harmony of the world.

Appendices

367

This verse by Orpheus is also found in Orpheus (Argonautica 108), which is translated as follows on page 109: Vocibu’ flexanimis mundi concenta figuran. The translation in Conti (Mythologia), however, is closer to the Greek original. 77. The verses nuncius interpres .. plurima nomina quamvis are the Latin translation from Conti (Mythologia Lib. II Cap. IV 146/147) of the following Orphic verse: Ἑρμῆς δ᾽ ἑρμεὺς τῶν πάντων ἄγγελος ἐστι, Νύμφαι ὕδωρ, πῦρ Ἥφαιστος, σῖτος Δημήτηρ ἡ δὲ ϑάλασσα Ποσειδάων μέγς ἠδ᾽ Ἐνοσίχϑων· καὶ πόλεμος μὲν Ἄρης, εἰρήνη δ᾽ἔστ᾽ Ἀφροδίτη. οἶνος, τὸν φιλέουσι ϑεοὶ ϑνητοί τ᾽ ἄνϑρωποι, ὅν τε βροτοῖς εὗρεν λυπῶν κηλήτορα πασῶν ταυρογενὴς Διόνυσος ἐϋφροσύνην πόρε ϑνητοῖς ἡδίστην πάσηισί τ᾽ ἐπ᾽ εἰλαπίνηισι πάρεστι, καὶ Θέμις ἥπερ ἅπασι ϑεμιστεύει τὰ δίκαια, Ἥλιος ὃν καλέουσιν Ἀπόλλωνα κλυτότοξον, Φοῖβον ἑκηβελέτην μάντιν πάτων ἑκάεργον, ἰητῆρα νόσων Ἀσκληπιόν, ἔν τὰδε πάντα.

Next to the Latin translation, Natale Conti also cites these Orphic verses in the Greek original. This Greek text is also included in Kern (Orphicorum fragmenta 309–310). 78. The verses Pluto Persephone ... sunt Deus unus are the Latin translation in Conti (Mythologia 142) of the following verses: Πλούτων Περσεφόνη, Διμήτηρ, Κύπρις, Ἔρωτες, Τρίτωνες, Νηρεὺς, Τηϑὺς καὶ Κυάνοχαίτης, Ἑρμῆς ϑ᾽ Ἥφαιστός τε κλυτὸς, Πὰν Ζεύς τε καὶ Ἥρη, Ἄρτεμις ἠδ᾽ ἑκάεργος Ἀπόλλων εἶς ϑεὸς ἐστί.

Natale Conti writes that these Greek verses are by Hermesianax. However, these verses are contained in neither the Anthologia lyrica graeca nor in the Collectanea Alexandrina, which allows the presumption that these verses are not genuine and that Conti’s attribution is incorrect. 79. In David Gregory’s Notae in Newtoni Principia Mathematica Philosophiae Naturalis (Archive Royal Society London MS 210) there is no transcript for this variant, just a transcript of the text on fol. 13r. 80. This paragraph and the following paragraph are clearly set apart from the preceding text at the lower edge of MS Gregory fol. 14v, such that it is not possible to unambiguously determine whether these two paragraphs are a continuation of the preceding text or a text of its own. 81. Newton refers to Scipio’s dream in Cicero’s tract de re publica (On the republic), where is written in Book VI Chap. XV 15: Nisi enim deus is, cuius hoc templum est omne. quod conspicis. istis te corporis custodiis liberaverit. huc tibi aditus patere non potest. Homines enim sunt hac lege generati. Qui tuerentur illum globum. quem in hoc templo medium vides, quae terra dicitur. hisque animus datus est ex illis sempiternis ignibus, quae sidera et stellas vocatis,

368

Appendices

quae globosae et rotundae, divinis animatae mentibus. circulos suos orbesque conficiunt celeritate mirabili. This means: If it was not God, whose temple is all of this that you behold, who liberated you from the custody of the body, then the access to this liberation cannot be open to you. Men were created on the condition that they were to look after that sphere called Earth, which you see in the middle of the temple. Souls have been given to them out of the eternal fires you call fixed stars and planets, those spherical solids which, quickened with divine spirit, journey through their orbits and circuits with astonishing speed. Note that Cicero describes the heavenly spheres in Book VI 17. 82. Macrobius (Opera 55), Macrobius (Somnium Scipionis I.14.2 page 55) 83. See the remarks 93 through 97. 84. quoque is missing in Newton, but is included in both Macrobius (Opera) and Macrobius (Somnium Scipionis). 85. Macrobius (Opera 25), Macrobius (Somnium Scipionis 1.6.43 page 26) 86. [a Cicerone] is inserted into Macrobius’ text by Newton. See also the remark 81. 87. In Macrobius (Opera) and Macrobius (Somnium Scipionis), the word here is aestimant. 88. Originally, Newton wrote veratur but then changed it into veneratur and, later on he reverted to the original by crossing out ne.Veneratur is the word used in both editions of Macrobius (Opera and Somnium Scipionis). The reasons for Newton’s alternation are unknown. Veneratur and veratur have the same meaning. As Newton explicitely quotes from Macrobius’ Commentary on the Dream of Scipio, it is unlikely, that he should have introduced an unauthorized correction. Maybe some Macrobius edition(s) unknown to us vary on this point. The transcript of David Gregory’s Notae in Newtoni Principia Mathematica Philosophiae Naturalis (Royal Society London MS 210) contains the original veneratur. Therefore we believe that the transcriber (i.e. David Gregory) of Gregory’s Notae used a corrected version of the Newtonian manuscript from David Gregory’s estate (Royal Society London MS 247ff. 6–14). See also remark 10. 89. Macrobius (Opera 55/56), Macrobius (Somnium Scipionis 1.14.2 page 55) 90. In both Macrobius (Opera) and Macrobius (Somnium Scipionis) is written et, which Newton omitted in transcription. 91. Macrobius (Somnium Scipionis) reads eius, but in Macrobius (Opera) eius is missing. 92. Both Macrobius (Opera) and Macrobius (Somnium Scipionis) write sidera. 93. Macrobius cites Virgil, Aeneis VI 724–726. 94. Macrobius cites the beginning of the verse Virgil, Aeneis VIII 403. 95. Instead of assereret, in Macrobius (Somnium Scipionis) adsereret is written, but this has no meaning, and instead of testatur, testatus est. Macrobius (Opera) has the same as Newton in both positions. If one complies with the reading testatus est, in the English translation the passage he offers the testi-

Appendices

369

mony that it is mind would have to be changed to he offered the testimony that it was mind. 96. Macrobius cites the beginning of the verse Virgil, Aeneis VI 727. 97. Macrobius cites the beginning of the verse Virgil, Aeneis VI 728. 98. Macrobius (Opera 58), Macrobius (Somnium Scipionis 1.14.14 page 57) 99. Aristoteles ἐντελέχειαν is missing in Newton, but is included in both Macrobius (Opera) and Macrobius (Somnium Scipionis). 100. With “  – ” Newton indicates that he omits the following passage from the Macrobius text: Posidonius ideam, Asclepiades quinque sensuum exercitium sibi consonum, Hipprocrates spiritum tenuem per corpus omne dispersum, Heraclides Ponticus lucem, Heraclitus physicus scintillam stellaris essentiae, Zenon concretium copori spiritum. This means: Posidonius, an idea; Aesclepiades, the mutually harmonious exercise of the five senses, Hippocrates, a fine spirit distributed throughout each body; Heraclides Ponticus, the light; Heraclitus the physicist, a spark of stellar essence; Zeno, a spirit inherent to the body. 101. Macrobius (Opera 59), Macrobius (Somnium Scipionis 1.14.19 page 58/59) 102. cognovit is written in both Macrobius (Opera) and Macrobius (Somnium Scipionis), but was omitted by Newton during transcription. 103. [sc. Musicis] is not included in Macrobius (Opera) and not in Macrobius (Somnium Scipionis) either, but was inserted by Newton. 104. Hinc Plato postquam ... instituit is written in Macrobius (Opera 100/101), and Macrobius (Somnium Scipionis 2.2.1 page 99). 105. Macrobius (Opera 104), Macrobius (Somnium Scipionis 2.2.19 page 102/103) 106. enim is missing in Newton, but included in Macrobius (Opera) and Macrobius (Somnium Scipionis). 107. Macrobius cites Virgil, Aeneis VI 728–729. 108. The quae here is apparently a transcription error by Newton; Macrobius (Opera) and Macrobius (Somnium Scipionis) have qua. 109. Macrobius (Opera 107), Macrobius (Somnium Scipionis 2.3.11/12 page 106) 110. Porphyrius ait Platonicos is Newton’s forrnulation to replace the passage aitque eos in Macrobius. Macrobius refers here to Porphyrios’ Commentary on Plato’s Timaeus, which, however, has been lost, and was probably the main source for Macrobius’ commentary on Cicero’s The Dream of Scipio. 111. haec is missing in Newton and also in Macrobius (Opera), but is included in Macrobius (Somnium Scipionis). 112. “&” is not included in Macrobius (Somnium Scipionis), but in both Newton and Macrobius (Opera). 113. Macrobius (Opera 108), Macrobius (Somnium Scipionis 2.3.15 page 107) 114. Macrobius (Opera 68/69), Macrobius (Somnium Scipionis 1.17.8 page 68) 115. Instead of hunc istum, which is included here in both Macrobius (Opera), Newton’s Macrobius edition, and in Macrobius (Somnium Scipionis), Newton inserted “[Cicero]” into Macrobius’ text in reference to The Dream of Scipio

370

Appendices

in Cicero’s de re publica (On the republic) Book VI 17, where the model of spheres of the world is described. 116. Macrobius (Somnium Scipionis) has aestimetur, but Macrobius (Opera), Newton’s Macrobius edition, has existimetur. 117. With “& - - ” Newton indicates that he omitted the following passage from Macrobius’ text: unde mox subiecit arcens et continens ceteros, deum vero quod non modo immortale animal ac divinum sit et plenum inditae* ex illa purissima mente rationis, sed quod et virtutes omnes quae illam primae omnipotentiam summitatis sequuntur aut ipse faciat aut ipse contineat. This means: therefore he immediately followed with the words, “confining and containing all the other spheres.” “God” because it is not only an immortal and divine creature and full of the reason imparted to it by that purest mind, but also because it produces and itself contains all the effects which obey the omnipotence of the First and Most High. * Macrobius (Opera) reads inclytae, which makes no sense here and is probably a misprint, Macrobius (Somnium Scipionis), by contrast, has inditae. 118. At this position in Macrobius’ Commentarii in somnium Scipionis, one finds the following parallel passage in his Saturnalia (see Macrobius (Opera 246) and Macrobius (Saturnalia 1.18.15 page 104): physici Διόνυσον Διὸς, quia solem mundi mentem esse dixerunt. mundus autem vocatur caelum, quod appellant lovem. unde Aratus de caelo dicturus ait: ἐκ Διὸς ἀρχώμεστα. This means: For the physicists, Dionysius is the spirit of Zeus, because they say that the sun is the spirit of the world. The world, however, is understood to be the heavens, which they call Jupiter. Therefore, Aratus says when he speaks of the heavens: let us begin with Zeus. The fact that there is no reference to this parallel passage is not sufficient to conclude that Newton was not familiar with this passage in Macrobius’ Saturnalia. Verse 1 of Aratus’ Phainomena is cited. Compare with remark 120. 119. Macrobius cites Virgil, Bucolica III 60 120. Aratos, Phainomena verse 1 f., see Aratos (Phaenomena 7). In Harrison (Library of Newton) no Aratos edition is listed among Newton’s possessions. 121. Macrobius (Operae 69/70), Macrobius (Somnium Scipionis 1.17.12–14, page 68/69)

References Aeschyli. 1663. Tragoediae septem: cum scholiis Graecis omnibus; deperditorum dramatum fragmentis, vesione et commentario T. Stanleii. Londini. This is the edition Newton owned, cf. Harrison (Library of Newton No. 17). Aeschylus. 1552. Αίσχύλου Προμηϑεὺς Δεσμώτης, Ἕπτα ἐπὶ Θήβαις, Πέρσαι, Ἀγαμέμνων, Εὐμενίδεσ, Ἰκετίδες. Parisiis. This is the edition Newton owned, cf. Harrison (Library of Newton No. 16).

Appendices

371

Anthologia lyrica graeca, ed. Ernestus Diehl. Editio altera Vol. 1–11, Supplementum. Lipsia 1936–1943. Aratos. 1971. Phaenomena Sternbilder und Wetterzeichen, ed. Manfred Erren. München. Aristoteles latine interpretibus variis, ed. Academia Regia Borussia. Berlin 1834 (reprint: Humanistische Bibliothek Reihe 2 Texte, vol. 30, München 1995). Casini, Paolo. 1984. Newton: The Classical Scholia. History o/Science (Cambridge) 22: 1–54. Cicero, Marcus Tullius. 1618–1619. Opera omnia, quae exstant .... emendata studio atque industria J. Gulielmi et J. Gruteri .... Pars 1–IV. Hamburgensis. This is the edition Newton owned, cf. Harrison (Library of Newton No. 381). Cicero, Marcus Tullius. 1889. Scripta quae manserunt omnia, recognovit C.F.W. Mueller. Partis IV Vol. I. Lipsiae. Cicero, Marcus Tullius. 1988. De re publica, De legibus, ed. and transl. by C.W. C. Keyes. Loeb Classical Library 213. London. Cicero, Marcus Tullius. 1994. De natura deorum, Academica. ed. and transl. by H. Rackham. Loeb Classical Library 268. London. Clemens Alexandrinus. 1641. Opera Graece et Latine quae exstant .... Accedunt diversae lectiones & emendationes .... a F.  Sylburgio collectae. Lutetiae Parisorum. This is the edition Newton owned, cf. Harrison (Library of Newton No. 398). Clemens Alexandrinus. 1688. Opera Graece et Latine quae exstant post accuratam D.V.  Danielis Heinsii recensionem. Editio nova juxta Parisinam anni MDCXLI. Coloniae. Clemens Alexandrinus. 1905. “Protrepticus und Paedagogus.” Werke vol. I, ed. Otto Stählin (Die griechischen Schriftsteller der ersten drei Jahrhunderte Bd. 12). Leipzig. Cohen, I.B. 1963. Quantum in se est: Newtons Concept of inertia in Relation to Descartes and Lucretius. Notes and Records of the Royal Society of London 18: 131–155. Collectanea Alexandrina, ed. Iohannes U. Powell. Oxonii 1925. Conti, Natale (Comes, Natalis). 1653. Mythologiae sive explicationis fabularum libri X, in quibus omnia prope natura!is et mora!is philosophiae dogmata contenta foisse demonstratur. Genevae. Newton owned the edition Natalis Comes. Mythologiae sive exp!icationisfabularum libri X, in quibus omnia prope naturalis et moralis philosophiae dogmata contentafoisse demonstratur. Coloniae Allobrogum 1612, cf. Harrison (Library of Newton No. 439). Unfortunately, only the 1653 edition was available to us. Cyrillus Alexandrinus. 1638. Opera in VI Tomos tributa. Cura et studio Joannis Auberti, Lutetiae. Diogenes Laertius. 1615. De vitis dogmatibus et apophthegmatibus clarorum philosophorum libri X Omnia Graece et Latine ..... Is. Casauboni notae ad Lib. Diogenio, Coloniae Allobrogum. Diogenes Laertius. 1664. De vitis dogmatis et apophthegmatis ... libri X T.Aldobrandino interprete, cum annotationibus eiusdem. Quibus accesserunt

372

Appendices

annotationes H.  Stephani, & utriusque Causaboni; cum uberrimis Aegidii Menagii observationibus. Londini. This is the edition Newton owned, cf. Harrison (Library of Newton No. 519). Diogenes Laertius. 1692. De vitis dogmatibus et apophthegmatibus clarorum philosophorum !ibri X Graece et Latine .... ed. Marcus Meibonmius. Amstelaedami. Diogenes Laertius. 1739. De vitis dogmatibus et apophthegmatibus clarorum philosophorum !ibri X Graece et Latine ..., ed. Paullo Daniele Longolio. Curiae Regnitianae. Diogenes Laertius. 1921. Leben und Meinungen berühmter Philosophen, ed. and transl. by Otto Apelt. Leipzig. Diogenes Laertius. 1990. Leben und Meinungen berühmter Philosophen, transl. by Otto Apelt, ed. by Hans Günter Zekl. Hamburg. Diogenes Laertius. 1995. Lives of eminent philosophers, transl. by R.D Hicks. 2 vols., Loeb Classical Library 184, 185. London. Diogenes Laertius. 1998. Leben und Lehre der Philosophen, transl. and ed. by Fritz Jürß. Stuttgart. Eusebius Pamphili. 1688. Praeparatio Evange!ica, F. Vigerus ... recensuit, Latine vertit, notis illustravit. Ed. nova. Coloniae. This is the edition Newton owned, cf. Harrison (Library of Newton No. 591). Eusebius. 1982. Die Praeparatio Evangelica. Werke vol. VIII, part I, ed. by Karl Mras, 2nd edition. Berlin. Galen. 1977. Opera omnia, editionem curavit C.G. Kühn. Tomus XIX, Hildesheim, Zürich, New York. Galilei, Galileo. 1699. Systema cosmicum .... Accessit altera hac ed. praeter conciliationem locorum. S.  Scripturae cum terrae mobilitate, ejusdem Tractatus de motu, nunc primum ex Italico sermone in Latinum versus. Lugduni Batavorum. Galilei, Galileo. 1998. Dialogo sopra i duo massimi systemi dei mondo tolemaico e copernican. Edizione critica e commento a cura di O. Besomi e M. Helbing, 2 vols. Padova. Gregory, James Crauford. 1832. Notice concerning an Autograph Manuscript by Sir Isaac Newton, containing some Notes upon the Third Book of the Principia, and found among the Papers of Dr. David Gregory. Transactions of the Royal Society of Edinburgh 12: 66–76. Harrison, John. 1978. The Library of Isaac Newton. Cambridge. Hearne, Thomas. 1885. Remarks and Collections, ed. by C.E. Doble. Vol. I. Oxford. Hippolytos. 1916. Refutatio omnium haeresium. Hippolytos Werke vol. III ed. by Paul Wendland. Leipzig. Hippolytos. 1986. Refutatio omnium haeresium, ed. by Miroslav Marcovich. Berlin, New York. Huet, P.D. 1668. Origenis in Sacras Scripturas Commentaria, Quaecunque graece reperiri potuerunt. Petrus Daniel Huetius, Pars I Cui idem praefixit Origeniana. Rothomagi. Kern, Otto. 1963. Orphicorum fragmenta, collegit Otto Kern. 2nd edition. Berlin. Lucretius Carus. 1686. De rerum natura libri VI, Quibus additae sunt conjecturae et emendationes T. Fabri cum notulis perptuis .... Cantabrigiae. This is the edition

Appendices

373

Newton owned, cf. Harrison (Library of Newton No. 990). Because this edition had no verse numbering, Newton partially entered the verse numbers himself in his copy, as Harrison (Library of Newton) reports. Lucretius Carus. 1947. De rerum natura libri sex, ed. by Cyrill Bailey. Vol. I. Oxford. Lucretius Carus. 1969. De rerum natura libri sex, quintum recensuit Joseph Martin. Lipsiae. Macrobius, Ambrosius Aurelius Theodosius. 1628. Opera, loh. Isacius Pontanus secundo recensuit: adiectis ad libros singulos notis. Quibus accedunt I. Meursii breviores notae. Lugduni Batavorum. This is the edition Newton owned, cf. Harrison (Library o/Newton No. 1013). Macrobius, Ambrosius Theodosius. 1970. Saturnalia, apparatu critico instruxit Iacobus Willis. Lipsiae. Macrobius, Ambrosius Theodosius. 1970. Commentarii in Somnium Scipionis. edidit Iacobus Willis. Lipsiae. Macrobius. 1966. Commentary on the Dream of Scipio, transi. by W.H.  Stahl. New York, London. McGuire, J.E., and P.M. Rattansi. 1966. Newton and the Pipes of Pan. Notes and Records o/the Royal Society of London 21: 108–143. Nauck, August. 1889. Tragicorum Graecorum Fragmenta, reeensuit Augustus Nauck. 2nd edition. Lipsiae. Newton, Isaac. 1687. Philosophiae naturalis principia mathematica. Londini. Newton, Isaac. 1999. The Principia  – Mathematical Principles of Natural Philosophy, transI. by I.B. Cohen, A Whitman. Berkeley, Los Angeles, London. Newton, Isaae. 1999. Die mathematischen Prinzipien der Physik, transl. and ed. by V. Schüller. Berlin. Newton, Isaae. 1959–1977. The Correspondence of Isaac Newton, ed. by A.R. Hall, L. Tilling, H.W. Turnbull and J.F. Scott. Vol. I–VII. Cambridge. Orpheus. 1689. Argonautica, Hymni, et De lapidibus, curante A.C. Eschenbachio .... Accedunt H. Stephani in omnia et J. Scaligeri in Hyrnnos notae. Trajecti ad Rhenum. This is the edition Newton owned, cf. Harrison (Library of Newton No. 1214). Platon. 1590. Opera omnia quae exstant, M. Ficino interprete .... Lugduni. This edition was used in the place of the Plato (1602) edition. Platon. 1602. Opera omnia quae exstant, M. Ficino interprete ... Francofurti. This edition was owned by Newton and is registered under No. 1325  in Harrison (Library of Newton); because unfortunately this edition was not available to us, we had to use the Plato (1590) edition instead. Plato. 1994, 1984. Laws, transl. by R.G. Bury. 2 vols., Loeb Classical Library 187, 192. London. Plinius Secundus. 1553. Liber Secundus de mundi historia. Francofurti. Plinius Secundus. 1559. Historiae mundi libri XXXVII. Basileae. Plinius Secundus. 1582. Historia mundi naturalis. Francofurti. Plinius Secundus. 1608. Historiae mundi libri XXXVII. Francofurti. Plinius Secundus. 1669. Naturalis historia. 2 vols., Lugd. Batav. Roterodami.

374

Appendices

Plinius Seeundus. 1725. Histoire de la peinture ancienne, extraite de l’Hist. naturelle de Pline, liv. XXXV Avec le texte latin, corrige sur les Mss. de Vossius et sur la 1. ed. de Venise. Londres. Plinius Secundus. 1866. Naturalis historia, recensuit D. Detlefsen. Vol. I (Lib. I– VI). Berolini. Plinius Secundus d. Ä. 1997. Naturkunde Buch II, transl. and ed. by G. Winkler und R. König. Darmstadt. Plutarch. 1572. Quae exstant opera, cum Latina interpretatione. Ex vetustis codicibus plurima nunc primum emendata sunt, ut ex Stephani annotationibus intelliges .... Vol. I–XIII. Genevae. This is the edition Newton owned, cf. Harrison (Library of Newton No. 1330). Plutarch. 1599. Quae exstant omnia, cum Latina interpretatione H.  Cruserii, G. Xylandri .. 2 vols. Francofurti. This is the edition Newton owned, cf. Harrison (1978) No. 1331. Plutareh. 1995. Moralia (The face on the moon), transl. and ed. by H.  Cherniss, W.C. Helmbold. Vol. XII, Loeb Classical Library 406. London. Poetae graeci veteres tragici, lyrici, comici, epigrammtarii, additis fragmentis exprobatis authoribus collectis, nunc primum graece et latine in unum redacti corpus. 2 vols., Coloniae Allobrogum 16 I 4 Proklus, Diadochus. 1534. In Platonis Timaeum Commentaria. Contained in part II of Platonis omnia opera cum commentariis Procli in Timaeum et Politica thesauro veteris philosophiae maximo, Basileae. Proklus, Diadoehus. 1903, 1904, 1906. In Platonis Timaeum Commentaria, ed. Ernestus Diehl. 3 vols. Lipsiae. Scholia in ApolIonium Rhodium vetera, rec. Carolus Wendel. Berolini 1935. Schüller, Volkmar. 1990. Die Bedeutung von quantum in se est in Newtons Principia. NTM Schriftenr. Gesch. Naturw. Techn. Med. Leipzig 27: 11–23. Simplicius. 1584. Commentaria in quatuor libros Aristotelis de coelo. Venetiis. The translator of this Commentaria, Wilhe1m Moerbeke, was not listed on the title page. Simplicius. 1882. In Aristotelis physicorum libros quattuor priores commentaria, ed. Hermannus Diels. Commentaria in Aristotelem graeea Vol. IX. Berlin. Stobaios, Ioannis. 1575. Eclogarum libri duo: Quorum prior Physicas, posterior Ethicas complectitur; nunc primum Graece editi; Interprete Gulielmo Cantero. Antverpiae. Stobaios, Ioannis. 1609. Eclogarum libri duo: Quorum prior Physicas, posterior Ethicas complectitur; Graece editi; Interprete Gulielmo Cantero. Aureliae Allobrogum. Stobaios, Ioannis. 1884. Anthologii libri duo priores, qui inscribi solent Eclogae Physicae et Ethicae, recensuit Curtius Wachsmuth.Vol. I. Berolini. Suidas. 1705. Lexicon Graece et Latine. Textum ... purgavit, notisque perpetuis illustravit: versionem Latinam A. Porti ... correxit; indicesque ... adjecit L. Kusterus. 3 vols. Cantabrigiae. This is the edition Newton owned, cf. Harrison (Library of Newton No. 1580).

Appendices

375

Suidas. 1619. Nunc primum integer Latinitate donatus ... opera & studio A. Porti ... 2 vols., Coloniae Allobrogum. This is the edition Newton owned, cf. Harrison (Library of Newton No. 1581). van der Waerden, B.L. 1943. Die Harmonielehre der Pythagoräer. Hermes 78: 163–199. Wightman, W.P.D. 1957. David Gregory’s Commentary on Newton’s Principia. Nature 179: 393–394. Zedler, Johann Heinrich. 1741. Grosses vollständiges Universal- Lexikon. Band 28. Leipzig, Halle.

 ppendix II: The Concepts of Immanuel Kant’s Natural A Philosophy (1747–1780): A Database Rendering Their Explicit and Implicit Networks Wolfgang Lefèvre and Falk Wunderlich In 2000, the publishing house Walter De Gruyter published a database on Kant’s scientific concepts composed by us.1 The database addresses itself not only to Kant scholars but in particular to historians who know that the philosophy of early modern times cannot be adequately understood without understanding the science of the age and vice versa. There are two main reasons why we add a brief description of the database as an appendix to this volume. Firstly, since the database, resting essentially on the true wording of Kant’s writings, requires at least a passive command of the German language and was therefore entirely set up in German, it may easily escape the attention of even those English-­ speaking scholars who are highly interested in Kant’s natural philosophy, in the relations between science and philosophy, or generally in the history of science in the eighteenth century. Secondly, except for electronic editions of classical texts, dictionaries, and the like, the use of the electronic medium in the realm of the humanities is still rather under-developed. Accordingly, both the experience with this medium and the expectations of it are limited. In contrast with books, databases therefore still need introductions, explanations, and even protection against misunderstandings. In the first part of this presentation, we briefly explain why we are interested in the multiple explicit and implicit networks connecting Kant’s scientific concepts and then explain why a database rather than a book provides the most suitable medium for rendering these networks. In the second part, we try to convey an idea

 Lefèvre, Wolfgang and Falk Wunderlich. Kants naturtheoretische Begriffe (1747–1780) – Eine Datenbank zu ihren expliziten und impliziten Vernetzungen. Berlin and New  York: De Gruyter, 2000. The database is also accessible via the internet: http://knb.mpiwg-berlin.mpg.de/ 1

376

Appendices

of the performance of the database by tracing aspects of Kant’s dynamical theory of matter through several records. In the third part, we briefly describe the main features of the database. Networks of Concepts and Their Representation Kant’s Natural Philosophy Immanuel Kant’s natural philosophy attracts rather little attention today. If at all subject to scrutiny, what comes into focus is almost never his natural philosophy as a whole but only certain parts. Among philosophers, while Kant’s epistemological and moral writings are still lively discussed, his natural philosophical or scientific writings are all but neglected. Only Kant’s effort to establish the metaphysical foundations of mechanics is now and then addressed by philosophers of science. Among historians of science, his hypothesis about the origin of our planet system or his as-if-teleological concept of organity arouse occasional interest since these pieces of his natural philosophy are taken to be original and presentiments or even beginnings of later scientific achievements. Usually, however, Kant’s scientific work is regarded as uninteresting, i.e., as either amateurish or unoriginal. However, if one conceives of history of science as something other than a narrative of a success story, focusing on the heroes of the triumphal march of science, a different image of Kant’s scientific work emerges. It then appears as an extremely illuminating mirror image of the sciences of his age. Kant kept always in touch with the sciences. Being obliged, from the mid 1750s on, to lecture about the whole range of scientific subject matters at the university of Königsberg, he had to keep pace with scientific developments and was familiar with contemporary scientific knowledge, at least as it was rendered in textbooks. In some fields, however, he was even able to bring forth his own ideas – ideas, which a historically trained eye has to regard as being on an equal footing with the ideas of the famous scientists of his age. (By the way, Kant represents a typical eighteenth-century scientist even in that he did not keep abreast of the then emerging analytical mechanics driven forward by men like Euler, d’Alembert, and Lagrange.) The fact that universally educated persons, capable of surveying and competently judging the scientific knowledge of their age, were the norm rather than the exception in the eighteenth century was, of course, due to the comparatively small size of this knowledge. Notwithstanding its small size, however, it was also extraordinarily fragmented. It was characteristic that there existed well established and widely shared understandings with regard to single subjects of knowledge, but on the other hand, the scientists were not able to agree on overarching theories they could use to integrate this scattered knowledge into a comprehensive whole. As the famous, or notorious, vis viva controversy shows, which d’Alembert did not bring to an end, this holds even for a comparatively highly developed field of knowledge like mechanics. In physics, however, that a controversy could reduce the abundance of open questions to a few clear alternatives was inconceivable. Here, different

Appendices

377

theories on heat stood disconnectedly side by side with those on electricity and both again with those on magnetism. In chemistry, the earth and life sciences, there was a similar state of affairs. At the same time, different overarching theories were competing in the attempt to integrate these scattered pieces of knowledge – different kinds of atomism, partly conjoined with a reductionist mechanicism, partly with Newtonian forces, different physics of imponderabilia, hylozoistic assumptions with regard to the life sciences, etc. Although in hindsight all of these different theories proved to be little more than untenable speculations, they do not testify to a dark age full of wild speculations lacking methodical sobriety. Rather, they display a contradiction that is characteristic of sciences before the nineteenth century: While their methodically-gained empirical knowledge had successfully undermined speculative global theories in the tradition of Aristotle, the sciences had to resort to daring generalisations since the empirical knowledge acquired up to then did not provide a sufficient basis for overarching theories. Kant’s natural philosophy mirrors the fractured nature of the scientific knowledge of his age as well as the attempt to integrate this knowledge. His efforts are in no way inferior to those of famous contemporaries and deserve attention. Closer investigations of them promise discoveries of significance for history of science in general as well as for a better understanding of Kant as a scientist. It is, however, not easy to render Kant’s scientific work as a mirror image of the sciences of his age. First of all, his scientific work is not sufficiently displayed in his published writings. True, the thematic variety of these writings is impressive, even when we confine ourselves here to the pre-critical writings that include a discussion of the vis viva controversy, investigations of the earth’s rotation, a discussion of the ageing of the earth, a hypothesis about the emergence of the solar system, a theory on the states of aggregation, writings on earthquakes, a draft of a dynamical theory of matter, a theory of winds, a treatise on the relativity of motion and rest, a theory on negative magnitudes, a discussion of the different regions (Gegenden) of space as well as a treatise on human races. Nevertheless, this stately thematic spectrum appears as a very incomplete and unrelated collection of arbitrarily chosen pieces of his scientific work, compared with the wealth of topics with which Kant dealt in his private papers. In fact, with a few exceptions, it was rather accidental which occasions caused Kant to write and publish treatises just on the issues listed and not on others. Neither do the private papers display his scientific work. They consist mainly of short notes indicating rather than arguing a thought, and being “works in progress,” they cannot be read as traces of a coherent theory. Additionally, there are some extant student notes of his physics lectures. But, apart from the question of their reliability, one has to keep in mind that his lectures dealt with the subject matter not according to any system of Kant’s but according to the textbook on which he based his discussion. Given this state of affairs, on what basis can we render Kant’s scientific thoughts as a whole, and thus, as a mirror of the sciences in the second half of the eighteenth century? Now, we can resort to the concepts employed in Kant’s published writings as well as his private papers and even those in the lecture notes. His thoughts exhibit themselves in these concepts or, more precisely, in their networks. But they exhibit

378

Appendices

themselves only mutely as long as they remain unordered, i.e., as long as we are not able to render the networks among these concepts. The aim of this database is exactly to render the networks among the scientific concepts of Kant. Before discussing in more detail how the database accomplishes this task, a few clarifications about our understanding of such networks may be convenient. Explicit and Implicit Networks Among Concepts We commonly distinguish between explicit and implicit interrelations among the concepts used by a philosopher or scientist. Explicit interrelations are those which are expressis verbis used by an author – interrelations the author fixes by definitions or uses in proofs or less formal ways of reasoning. Interpreters establish such explicit interrelations by reconstructing the author’s trains of thought. Implicit interrelations among the concepts of an author originally come from the networks of concepts given in the culture to which the author belongs. As is well-­ known, individuals do not acquire such concepts as isolated bits. Though each individual acquires them in a peculiar way, he or she can only become familiar with these concepts along with the collectively established networks in which they are given. Moreover, these simultaneously found and assumed networks are to a considerable degree, if not even predominantly, employed tacitly – partly because the individual mind takes those interrelations to be obvious, partly because it is unconscious of them. Philosophers and scientists are no exceptions in this respect. These implicit networks cannot be properly established by applying the immanent procedures of interpreting documents alone, i.e., not just by analysing upon which tacit presuppositions certain definitions, proofs and derivations rest, or by studying in which range of application an author uses a certain concept, etc. Rather, one has to systematically connect such analyses with an investigation of the use and meaning of the concepts in the cultural context. The intricate network of interconnected concepts in a given culture does not constitute a consistent whole. It is even possible that certain parts are incompatible with others. One cannot presuppose that a completely consistent thought-world would emerge out of the implicit interconnections among the concepts of an author. This holds even for Kant in spite of his famous “Ich denke, muß alle meine Vorstellungen begleiten können.” But even though they are not completely consistent, the explicit and the implicit networks among the concepts of a scientist or a philosopher still constitute a unity. The explicit nets are embedded in the implicit ones, and the latter change with every development of the former. Thus, the explicit and implicit networks form a totality that undergoes change and development. These networks also form, furthermore, a unity for the interpreter. When trying to study the scientific work of Kant, one will not achieve an adequate understanding of the explicit interrelations among his concepts without having – not completely, that is impossible, but extensively – reconstructed the implicit ones. And vice versa.

Appendices

379

The Form of Representation The subject matter of the work introduced here is thus the totality of the explicit and implicit interrelations among the concepts of Kant’s natural philosophy. For pragmatic reasons, we have confined ourselves to a certain time span, namely to the time prior to the appearance of the Critique of Pure Reason. The natural philosophical concepts in all of Kant’s writings and letters through 1780 were systematically picked up and recorded in the database as well as the concepts in his unpublished papers (with the exception of the Opus postumum) and in the three extant student notes of his physics lectures. From what was said so far it follows that some specific requirements have to be met when rendering the totality of the explicit and implicit interrelations among the concepts of Kant’s natural philosophy. To name at least three of these requirements: –– Since the implicit interrelations among these concepts, notwithstanding the peculiar way in which Kant assumed them, are given in and received from his cultural setting, they cannot be rendered merely immanently. Rather, the interrelations as they appear in Kant have to be compared with the interrelations among these concepts within the contemporary sciences. Only against this background can these networks be rendered adequately. –– The totality of explicit and implicit networks among Kant’s scientific concepts must not be represented as though it were an enveloping theory on which, unwritten, but nevertheless formed in principle, the published writings on different subjects rest. Rather, the task is just to represent these networks without making them appear more consistent than they actually were. –– The representation is confronted with a particular challenge by the fact that the totality of these networks cannot be reconstructed conclusively. It is characteristic of the puzzling nature of implicit networks that they become comprehensible just as they are transformed into explicit ones, that is, when they cease to be implicit. At the same time, the totality of implicit interrelations reminds one of an infinite set, in that it does not become smaller when some of its elements are transformed into explicit ones. It was therefore the task to find a form for rendering the totality of the explicit and implicit interrelations among Kant’s scientific concepts that contains more interrelations than actually realised by the authors of the database, that is to say, to find a form for rendering these interrelations which also constitutes an instrument suitable for further investigation. –– To satisfy these requirements, the authors decided to render the networks among Kant’s scientific concepts in an electronic database rather than a book. The form of a book would not only add to the danger of representing these networks as more consistent than they really were, but is actually unsuitable for the purpose. As a linear text, a book would have to employ a lot of auxiliary tools in order to make the complexity of these networks accessible – countless cross-references, for instance, an arsenal of indexes, a large apparatus of footnotes, an elaborately classified table of contents, etc. What would be striven for with all these rather impractical tools, however, can be conveniently and incomparably effectively

380

Appendices

accomplished by an electronic database. Paradoxically, the atomistic segregation which the concepts undergo in a database creates the basis needed for a sufficiently complex and, above all, flexible rendering of their interrelations. Moreover, the facilities for searching and sorting of an electronic database provide incomparable possibilities of access to these interrelations. Aspects of Kant’s Theory of Matter as Rendered in the Database Before presenting the main features of the database in some detail, it may be convenient to convey an impression of how the central database “Begriffe” represents the concepts of Kant and what possibilities it provides for following the interrelations among them. In other words, it seems opportune first to demonstrate through some examples concerning the content how one can investigate networks of concepts of Kant’s natural philosophy by means of this database. The examples were of course chosen to convey an impression of the database. Everybody familiar with Kant’s natural philosophy will recognise, however, that the concepts chosen belong to the very heart of this philosophy and that they appear in some new light. As is well-known, Kant’s natural philosophy is distinguished by his dynamical concept of matter. Thus, we start this tour with the record of the term “Materie.” In the glossary field of this record we find historical information  – about atomistic conceptions of matter predominant at Kant’s time as well as the parallel between Boscovic’s and Kant’s dynamical conception of matter – as well as systematic information in the style of a concise lexicon. We read, that is, translate: Essential aspects of Kant’s dynamical theory of matter are: a) Extension and impenetrability are regarded as essential, even though not original and non-derivable properties of matter, but the effects of forces – see the term “Raum” with the specification “einnehmen / erfüllen” and the term “Undurchdringlichkeit.” b) These forces which, in a way, constitute matter, consist in an original repulsive force and an equally original attractive force  – see the term “Kraft” with the specification “Grundkraft.” c) The differences between different kinds of matter are not conceived of as resulting from being differently composed of an uniform basic matter. Rather, originally different basic matters are assumed – see the glossary entry to the term “Materien.” d) Whereas Kant in 1756 (Monadologia physica) assumed last simple units of matter by supposing physical monads (monades physicae) of a dynamical character – see the term “Monade” with the specification “physische” –, he later considered matter as infinitely divisible – see the term “Materie” with the specification “[Teilbarkeit].”

This is more or less a standard account of the principal features of Kant’s dynamical concept of matter, including the indication that Kant, having once framed this conception, never changed it substantially, with one exception: whereas he initially assumed ultimate units of matter (the physical monads), he later changed his mind and considered matter as infinitely divisible. This piece of systematic information indicates a network of conceptions related to “matter” by repeatedly pointing to the records of other terms where further and

Appendices

381

more elaborate information may be found. A lot of different investigative walks would be possible. To make things easier, we will trace only a few interrelationships among Kant’s concepts associated with that of matter. We follow the first reference given above – the reference to the term “Raum” with the specification “einnehmen / erfüllen” – and summon this term. The glossary field there informs us about Kant’s distinction between the terms “einnehmen” and “erfüllen” or “occupare” and “replere,” respectively. It is not necessary to translate that. The entry ends, however, by saying that Kant’s concept of how matter dynamically fills space makes it difficult to fix a definite extension of a piece of matter. A reference is attached pointing to the term “Ausdehnung” with the specification “bestimmte” (“definite extension”). On the record of this term, we find in the glossary field an entry which reads as follows: Within the framework of his dynamical theory of matter, Kant tried to prove that the opposed effects of the repulsive and the attractive force result in the filling (Erfüllung) of a definite space. In Monadologia physica, he assumed that the ratio between the original forces of repulsion and attraction which determines the extension of the monads is always the same, and that, hence, all monads fill an equal volume regardless of their respective quantitas materiae. […] Kant dismissed this assumption along with that of physical monads and assumed later that the basic matter (Grundmaterien) differs with regard to the – using a phrase from Metaphysische Anfangsgründe der Naturwissenschaften:  – “combination of the original forces of repulsion and attraction” (AA IV 532).2 [...] Regarding the principle that the ratio between the original forces determines a definite extension, no fluctuation can be observed in his published writings. [...] However, as some unpublished notes testify, in connection with his mechanistic explanation of cohesion by pressure of ether in the 1770s – see the glossary entry to the term “Zusammenhang”  – , Kant explored the idea that the dimension of space eventually filled by a certain matter results from its unlimited tendency of expansion and from the counteraction of other kinds of matter  – compare the quoted reflection (AA XIV 328f.) [...].

Following this last recommendation and consulting the quotation field of this record, we find a reflection from his unpublished papers: No matter is able to keep its force of expansion tied by its own attraction and to determine itself thereby space and shape.3

Erich Adickes dates this reflection to about 1775–77. The specification “eigene (own)” in the phrase “durch eigene Anziehung (by its own attraction)” seems to indicate that Kant was at that time pondering whether other forces of attraction might exist capable of checking the expansive tendency of the matter in question, that is, other matter compressing it because of mutual attraction. At any rate, this statement obviously contradicts what we know from the later Metaphysische

 “[…] Verbindung der ursprünglichen Kräfte der Zurückstoßung und Anziehung […]” (AA IV 532).  – [AA  =  Akademie Ausgabe: Kants Gesammelte Schriften. Hrsg. von der Königlich Preußischen Akademie der Wissenschaften. Berlin: Reimer (De Gruyter), 1902ff.] 3  “Keine Materie kann ihre [...] Kraft der [...] expansion durch eigene Anziehung gebunden erhalten und sich dadurch selbst Raum und Gestalt bestimmen.” (AA XIV 328f.) 2

382

Appendices

Anfangsgründe der Naturwissenschaften.4 Thus, we come across an alternative explanation of extension pondered by Kant. Maybe it is only a variant of his dynamical theory of matter, not a different theory – we will come back to this later. In any case, we learn that Kant’s dynamical theory of matter comprised two different explanations of extension and not only one as his published writings suggest. The appearance of his theory in his published writings can be called a facade and even a deceptive one as it conceals problems he could not handle satisfactorily. In addition and more important, this facade also hides alternative solutions he seriously deliberated which one would not have guessed and which shed new light on those published. What was the context of these transitional speculations that the extension of matter is determined by its original repulsive force and the counteraction exerted by different matter? Our last glossary entry already indicated a connection with a mechanistic conception of cohesion and gave a reference to the term “Zusammenhang.” The glossary entry of this record informs us about the two main approaches to cohesion in the eighteenth century: a mechanistic approach explaining cohesion by external pressure of the ether and a dynamical approach explaining it by attractive forces. Furthermore, we learn with respect to Germany that the mechanistic conception, which can be traced back to Malebranche, was represented by Wolff, Euler and Crusius, whereas the three authors of textbooks Kant used for his physics lectures, namely Eberhard, Erxleben, and Karsten, followed the dynamic conception which, though indicated by Newton himself, was developed first by Musschenbroek. Next, we read: Kant adhered in the 1750s and 1760s to the dynamical approach and assumed mutual attraction among the particles of a body assigning additionally, in the 1750s, a mediating function to the ether inside of the body. […] Kant changed his mind in the middle of the 1770s and subsequently followed the mechanistic conception  – compare Adickes [1924] II 117ff. Regarding the contradictions connected with this, see also idem [1925] 297f., 412ff. See also the glossary entry at the term “Äther” with the specification “elasticus.”

Here, we encounter Kant not only pondering alternatives within the framework of his dynamical theory but dismissing a Newtonian theory initially endorsed and adopting a mechanistic one which just avoids Newtonian forces. What does that mean for Kant’s Newtonianism, and for the consistency of his natural philosophy? Kant’s natural philosophy was often described as a compromise between Leibniz and Newton, although a compromise that was very complex and defies simple depiction. One of its features is nonetheless supposed to be certain, namely Kant’s adherence to a Newtonian dynamics which comprises forces acting at distance. Yet here, in the case of cohesion, seeing Kant replace a Newtonian theory by a mechanistic one, we recognise that he was capable of dismissing explanations of certain

 “Es erfordert also alle Materie zu ihrer Existenz Kräfte, die der ausdehnenden entgegengesetzt sind, d.i. zusammendrückende Kräfte. Diese können aber ursprünglich nicht wiederum in der Entgegenstrebung einer anderen Materie gesucht werden; denn diese bedarf, damit sie Materie sei, selbst einer zusammendrückenden Kraft.” (AA IV 508f.) 4

Appendices

383

phenomena in terms of Newtonian forces without generally questioning Newtonian dynamics. Contemplating this side of Kant’s natural philosophy which, perhaps, might be called a horizon of compromises between Newton and Euler, the question inevitably arises whether we come across an incoherent, eclectic bundle of theories in this horizon, or a kind of synthesis ruled by certain principles – despite the ease with which Kant crossed the borders of seemingly incompatible theoretical worlds. To get, at least, a preliminary answer it may be suitable to scrutinise how, according to Kant, the pressure of the ether caused cohesion. We follow the reference to the term “Äther” with the specification “elasticus” and read: Kant conceived of the ether as an originally elastic matter [...]. Moreover, the ether forms an “expansive medium” (AA XIV 316). As displayed by the quotation from his private papers (AA XIV 137f.), Kant derives this latter feature from the “compression” which the ether undergoes due to its gravity – see glossary entry for the term “Äther” with the specification “[Schwere].” As far as the elasticity of the ether is employed by Kant also for his apparently mechanistic explanations of light propagation – see the glossary entry for the term “light” – and of cohesion – see the glossary entry for the term “Zusammenhang” – , his dynamical concept of ether proves to be fundamental in these cases as well. The same is true for the ether conceived of as the matter of heat – see the term “Feuer” with the specification “Elementarfeuer” [...].

Admittedly, that sounds a little bit complicated. In particular, we are told that an “dynamical concept of ether” was fundamental for his explanation of how the ether causes cohesion, but do not immediately get information about what a dynamical concept of ether was. Thus, it may be helpful to go to the term “Äther” without any specification. There, in the glossary field, we get historical information on conceptions of ether in the eighteenth century and learn, in particular, that in this case, too, there were competing mechanistic and dynamical conceptions of ether. We read: The mechanistic one, coming from Descartes’ conception of matter (see Descartes [1644] part III §§ 48ff.) and having in the eighteenth century its classical champion in Euler, restricted the interactions among the particles of the ether and with the gross parts of macroscopic bodies to the transfer of motion by contact (impact and pressure). Within the framework of mechanistic theories, the ether served not only to explain of physical phenomena connected with heat, electricity, magnetism or propagation of light, but, above all, of classical mechanical phenomena connected with gravitation (falling and motion of the planets) – see, for instance, Euler [1768] letters LIVff. On the other hand, the dynamical conception of ether originating with Newton (see, above all, Opticks Queries 21 and 22 [1704/R] 350ff.) assumed that the particles of the ether repel each other and are attracted by the masses of macroscopic bodies.

Accordingly, the dynamical concept of ether involved the assumption that ether is originally elastic (because of the mutual repulsion of its particles) and that it is ponderous. Coming back to Kant’s theory of cohesion from the mid-1770s, we can now see how both the elasticity and the gravity of the ether are used to explain cohesion by the pressure of the ether: The ether is attracted and compressed by the macroscopic bodies because of its gravity; and because of its elasticity, this compression, reversely, causes the ether to compress the macroscopic bodies, resulting in the

384

Appendices

cohesion of the latter. That is, on the one hand, the ponderous ether is compressed by attracting bodies, on the other, these bodies are compressed by the pressure of the elastic ether as consequence of its being compressed. Here, we will not go into the question of whether this theory is convincing in terms of eighteenth-century mechanics. Rather, in our context, it is important to notice that even Kant’s mechanistic explanations are based on a dynamical theory of matter implying forces that act at a distance. As to our question whether the horizon of compromises between Newton and Euler, as we named it above, consists of an eclectic mishmash of mechanistic and dynamical theories or whether there are certain ruling principles, Kant’s explanation of cohesion by pressure of the ether shows that such seemingly mechanistic explanations are framed by a basic assumption about matter of a clearly dynamical character. If we had more space, we could show the same for Kant’s unshakeable adherence to Euler’s theory of the propagation of light. Instead we will go on to another, related, aspect of Kant’s concept of matter, namely his assumption of originally different kinds of matter. As cited above, among the essential features of his concept of matter listed in the glossary field of the term “Materie,” we found the following: c) The differences between different kinds of matter are not conceived of as resulting from being differently composed of a uniform basic matter. Rather, originally different basic matters are assumed – see the term “Materien.”

Summoning, accordingly, the term “Materien,” an interesting proposition occurs in the quotation field, again coming from a reflection in his private papers: [Different] kinds of matter can be taken to be as many different attracting points, however, of different degrees to which their mass is a compressed ether, and ether is, thus, not a particular kind of matter regarding impenetrability, but every matter consists of ether which is attracted to different degrees.5

For a minute understanding of this sentence, a lot of interpretation and reformulating would be required. Yet, the main idea seems to be clear after what we learned so far: Because of its gravity, the ether is attracted and, hence, compressed by macroscopic bodies. As a consequence, the ether is not everywhere of the same density but denser at some places than others according to the degree to which it is attracted by macroscopic bodies of different amounts of matter. Thus, ethers of different density come into being, and different kinds of matter are nothing other than these different ethers. Let us omit the question of how this conception would account for the initial origin of different densities, and sum up its main points: First, there is no categorical difference between ether and normal matter; second, the differences among kinds of matter can be reduced to differences of density; third, these latter differences result  “Die Materien können als so viel verschiedene anziehende Punkte angesehen werden, aber von verschiednen Graden, nach deren Maaße ihre Masse ein verdichteter aether ist, und so ist aether nicht eine besondere Art Materie, [sondern (so fern die] was die [expansibilitaet betrift] undurchdringlichkeit betrift, sondern alle Materien bestehen aus aether, der [auf] in verschiedenen Graden angezogen wird.” (AA XIV 334ff.) 5

Appendices

385

from different gravitational interactions according to the masses of the matters involved. By the third point, this conception contradicts that of Metaphysische Anfangsgründe where the different densities are thought to be derivable from different “combination[s] of the original forces of repulsion and attraction” (AA IV 532). As in the case of the determination of the definite extension of matter, we come across a considerable difference to the conception published in 1786, a difference which indicates deep problems and alternative solutions seriously pondered. Here, we cannot go into this question. Instead, we want to close this short demonstration of the database by casting a quick glance at some of the different kinds of matter addressed here. Looking at the list of specifications to the term “Materien,” we find kinds of matter that are now unknown but were of great importance for eighteenth-century physics, for instance, electric matter, magnetic matter, and the matter of fire. Let’s start with the last and summon the term “Feuer” with the specification “Elementarfeuer.” In the glossary field for this term, we get a lot of historical information on the two main theories of heat in the eighteenth century, one explaining the phenomena of heat by motions of the minute particles of bodies, the other by supposing a matter of heat. We learn that the understanding of the matter of heat underwent significant alterations when the famous discoveries of Black and de Luc became known in the 1770s. With respect to Kant, we can read: In De igne (1755) and in Negative Größen (1763), Kant appears as a follower of matter-of-­ heat theories considering the “elementary fire” to be nothing other than the ether which at the same time also served to explain the phenomena of light [...] magnetism, and electricity. [...] The reflection no. 54 [in AA XIV] dated to the late 1770s by Adickes shows that Kant then assumed a special matter of heat distinguished from the ether – compare the quotation (XIV 449) [...].

The passage from reflection no. 54 referred to, found in the quotation field of this record, reads as follows: The fire element is that which more than anything else drives away the ether. Hence, it is not absorbed by the same but compressed and driven into other bodies which [...] are set trembling and, thus, expanded by it.6

Naturally, we cannot go here into the details of Kant’s theory of heat. In our context, the important point is that he introduced a peculiar kind of matter which apparently is not considered to be simply matter (or ether) of a special density. Is this a singularity occurring only in connection with heat? What about electric and magnetic matter? At the term “Materien” with the specification “electrische,” we read in the glossary field of the record: Kant, whose views on electricity were strongly influenced by the works of Äpinus [...], apparently considered in the 1750s and 1760s the ether to be that subtle matter on which

 “Das Feuerelement ist das, was am meisten den aether vertreibt. Daher es von demselben nicht verschlungen, sondern zusammengedrükt und in andere Korper, welche durch [...] dasselbe auch in Zitterungen und also ausdehnung versetzt werden, getrieben wird.” (AA XIV 449) 6

386

Appendices

explanations for electro-static and magnetic phenomena can be based [...]. As indicated by the quoted reflection no. 27 [in AA XIV] dated to 1764–68 by Adickes, he seems, in particular, to have thought that the ether would only be able to produce electro-static phenomena if compressed to a certain degree [...].

Looking up the cited passage from reflection no. 27, we read in the quotation field of this record: Maybe it [sc.: electric matter] is nothing other than the compressed air of heaven from Centro gravitatis coeli to the centre of the Earth.7

The expression “air of heaven (Himmelsluft)” that Kant sometimes used means ether. Except for the phrase “from Centro gravitatis coeli to the centre of the Earth” which we can ignore for the present, the reflection is quite comprehensible. It states that the electric matter consists of compressed ether. After what we have learned so far, this idea is not at all striking but can be considered an accommodation to the increasing realm of imponderabilia then prevailing in natural philosophy, an accommodation completely compatible with Kant’s dynamical concept of matter. However, going back to the glossary field and reading the subsequent text, we find: The later reflections no. 46 (XIV 427) and no. 50 (XIV 443), however, dated to the second half of the 1770s by Adickes, can be read as if Kant then assumed a specific electric matter [...].

We won’t quote these reflections here since it would require too much effort to make this reading convincing. If granted for the present that this reading is correct, we encounter here a case parallel to that of heat. Precisely at the same time (in the second half of the 1770s) and again in the domain of so-called imponderabilia, Kant dismissed his initial conception that an ether of a certain density could account for the physical phenomena in question in favour of the assumption of a peculiar kind of matter. With this, we break off our tour. Perhaps we could convey through it a first impression of how our database helps us to become aware of some conceptual embeddedness of Kant’s dynamical conception of matter which may be unexpected judging from the explicit conceptual relations in Kant’s writings. Hopefully, through this example, we have been able to display the principles we have used to render Kant’s concepts, the interrelationships among them, and their connections to contemporary theories in the database – not in the way of a continuous text but through a flexible net of different kinds of information which allows one to walk around the networks of these concepts in a unlimited variety of ways depending of what one is looking for.

 “Vielleicht daß sie [sc. die elektrische Materie] die Zusammengedrükte Himmelsluft [d.i. der Äther] selber ist von Centro gravitatis Coeli an bis zum Centro der Erde.” (AA XIV 097) 7

Appendices

387

The Databases The work presented here consists of four linked databases: –– –– –– ––

“Begriffe” – the core piece of the work, “Kant-Texte” – allowing access to and searching in the selected texts of Kant, “Personen” – containing information on persons mentioned by Kant, “Literatur” – documenting chiefly contemporary literary sources.

–– In the following we point out the main functions of these databases. “Begriffe” This database contains ca 2200 concepts, each with a record (“concept record”), and there are ca 750 additional records for purposes of reference (“reference records”). Besides natural scientific concepts, the database also contains metrological and some mathematical terms of now uncommon usage. Furthermore, since the eighteenth-­century distinction between science and philosophy was different from the present, we included ca. 350 philosophical terms in the database which are closely linked with scientific concepts, especially methodological and ontological terms. Rendering Networks of Concepts Kant’s terms are taken up exactly as found in his writings.8 This is crucial in order to secure that the networks rendered by the database are of genuinely Kantian terms rather than of concepts ascribed to him. We place special emphasis on this distinction. Whatever the assets of database employment in the humanities, information retrieval always remains crucially geared to the original input. (Hence, the database is designed from the German original, and a passive command of German poses a minimal requirement for its use.) Indeed, it may be sometimes difficult to distinguish between “original” and interpretation when searching the entries in the different fields of a record. Except for quotations from Kant’s writings, which are displayed in a special field (Zitate – see below), only the selected Kantian terms are guaranteed “original Kant”; all else is interpretative. But a mere selection is also interpretative. And what is more, the list of Kantian terms chosen has not been created mechanically by a computer, but is an arrangement by our hand. This arrangement has been conducted in ways to facilitate the retrieval of terms through different lists. To enable retrieval of composite as well as simple concepts, every record contains three fields where a Kantian term may have been entered (the fields Begriff, Spezifikation 1, and Spezifikation 2). As a result, lists of related

 Following, however, the spelling of the Akademie edition rather than the originals.

8

388

Appendices

concepts are already generated from alphabetic sorting of records with the same term in the field Begriff. As a matter of principle, each of Kant’s terms may, however, be registered in each of the three fields, i.e., as a concept with or without further specifications and/or as specification of a composite concept. The list of all records in which a certain term occurs in one of the three fields exhibits a further series of mutual relations and thus additional networks among concepts. This variety of lists results, however, from our arrangement of terms and depends therefore, as should be born in mind, on our interpretation. Through these lists, the database gives an implicit rendering of relations among concepts. It is also possible, however, to establish explicit relations by means of fields with references to synonymous, antonymous, and/or related concepts. Such explicit references are of particular importance, for instance, with respect to the overly frequent occurrence of synonyms in Kant’s scientific writings. In part this is due to the fact that Kant wrote in German and Latin, so that there are many German and Latin equivalents. A second and probably more important reason is that no standard scientific terminology had yet developed in eighteenth-century Germany. Context I – The Location of Concepts in Kant For locating a concept in Kant’s body of thought, the database provides two facilities. First, on each record a field (Zitate) is reserved for a characteristic quotation from Kant. Such a quotation may cover a sentence or sometimes entire paragraphs. It may illuminate the meaning, be a characteristic application, or consist of a more or less formal definition of the concept in question. Often, however, this field remains empty because no characteristic citation was found. Second, there is a field (Schriften) on each record that contains information indicating in which of Kant’s respective writings the concept occurs. Often the use of a concept is limited to a particular period in Kant’s development. Context II – The Location of Concepts in Contemporary Science Each record includes a field for glossary entries (Glossar). The explanations, commentaries, and historical sketches given in the glossary indicate the position occupied by Kant’s concepts within eighteenth-century science. These entries, usually brief and in lexicon-style, comprise the core piece of our interpretative work. They outline the contemporary meaning of Kantian concepts against the background of the knowledge of his time and prevailing theories and traditions, as well as beliefs and controversies surrounding these concepts. Where possible, Kant’s relation to these traditions and schools of thought is indicated. To avoid repetition or unnecessary fragmentation, often one concept was selected for such an entry, while a reference to this entry was added in the records of other concepts of concern. This, of course, gives rise to a new network. We checked contemporary lexicons and textbooks to decide whether Kant’s use of terms was standard or non-standard. When standard, usually a reference is made to these sources with no further comment.

Appendices

389

When non-standard or ambiguous, the variety of meanings is indicated. The glossary field sometimes also contains explanations of uncommon terms. An empty glossary field indicates one of four possibilities: –– the term in question was of no contemporary conceptual import and has not been subject to any notable change in meaning from past to present; –– the term is composite, and the glossary entry occurs under the more inclusive concept; –– the term is a very general one (like “Kraft”), and entries are to be found only among its specified composites; –– the term is well-known and has been abundantly investigated in the easily accessible philosophical literature. Grouping According to Fields of Knowledge Each concept record includes a field (Wissensgebiete) in which this concept is attributed to one or more particular areas of knowledge. These areas of knowledge are a product of our classification and are in accordance with neither the structure of eighteenth-century science nor its modern division. This is a pragmatic listing of subject matters to facilitate the tracing of concepts when it is unknown how they were formulated by Kant, e.g., of chemical names employed in the eighteenth century. However, as some concepts were assignable to one area of knowledge only, but others to two or more, this classification also provides at least some provisionary clue as to the range of applicability of these concepts and hence their role in integrating knowledge. The Additional Databases Three additional databases are associated with the main database “Begriffe”: “Kant-­ Texte,” “Personen,” and “Literatur.” The database “Kant-Texte” provides access to the pertinent writings of Kant, i.e., to the volumes 1, 2, and 14 of the Akademie edition and furthermore to selected texts from the volumes 10, 23, and 29. It is known that the Akademie edition of Kant’s works does not meet modern standards of critical editing. But there is no other edition available which is nearly as complete and internationally renowned. The database offers the complete texts, thus allowing exhaustive searches for terms. Therefore no independent index of locations was needed. The database “Personen” scrutinises the historical context of Kant’s scientific work from a different angle. The 280 records of the database cover all persons mentioned by Kant in the writings involved. When a person also occurs in a glossary entry of the database “Begriffe,” or his works are listed in the database “Literatur,” a reference is given. For less well-known persons, brief biographical information is added.

390

Appendices

The database “Literatur” comprises ca. 4000 titles and is divided as follows. The first division is a documentation of the writings of Kant mentioned above  – the original editions, classic editions and, moreover, all editions of these writings in German, English, French, and Italian that merit special attention because of their introductions, commentaries, etc. The second division documents contemporary scientific works definitely or most probably used by Kant and, moreover, works summarised in journals which were owned by Kant. To the best of our knowledge, these summarised works never before have been identified or bibliographically recorded. The third division documents scientific works which were located in the Königsberger Schloßbibliothek where Kant served as librarian from 1766 to 1772. The fourth, and most extensive, division documents further contemporary (and also older) scientific works which are of potential interest in the context of Kant’s natural philosophy. Finally, two further divisions contain a selection of secondary literature.