The Quantification of Life and Health from the Sixteenth to the Nineteenth Century: Intersections of Medicine and Philosophy (Palgrave Studies in Medieval and Early Modern Medicine) 3031157249, 9783031157240

Table of contents :
Contents
List of Contributors
List of Figures
Introduction
1 The Meanings of Quantification
2 The Metaphysics of Quantity and Measurement
3 The More, the Less, the Whole, the Body
4 The Quanti-Mathe-Mechanization of Nature and the Human Body as a Laboratory
5 The Fall of Mechanization and the New Life of Quantity
6 Overlapping Paths
The More the Years the Less the Food: Alvise Cornaro on The Sober Life (1558)
1 Introduction
2 Cornaro and the Moral Question of Quantity
3 Quantity (of Food) Matters
4 Some Lies and ‘The Cumulative Advantages of Added Years’
5 Leonhard Lessius SJ, Exporting Cornaro and His Proportions
6 Dissolution as Conclusion
The Quantification of Talents: Education, Galenic Humoralism, and Classification of Wits in Early Modern Culture
1 Early Modern Educational Thought, Between Politics and Morals
2 The Qualitative Body in the Pseudo-Plutarchean De liberis educandis
3 “Queriendo reducir a arte esta nueva manera de filosofar”: Juan Huarte’s Work and the Beginnings of a Quantitative Approach to Educational Selection
4 Concluding Remarks: The Ingenium from Soul Faculty to Organic Function
Quali-quantitative Measurement in Francis Bacon’s Medicine. Toward a New Branch of Mixed Mathematics
1 Introduction
2 The Ontology of Measurement
3 Mixed Mathematics, Physics, and Medicine
4 The Quali-quantitative Approach to Measurement
5 Quali-Quantitative Measures in Medicine: Some Examples
5.1 General Quantitative Registers
5.2 Mensura Quanti
5.3 Mensura Temporis
5.4 Mensura Spatii
5.5 Mensura Fortitudinis, Mensura Peristaseos
6 Conclusion
Sanctorius’s Weighing Chair: Measurement, Metabolism, and Mind
1 Insensible Perspiration
2 Exercise of the Mind
3 Quantified Selfhood
4 Conclusion
The Rise of Quantitative Biology in the Cartesian Age: The Theories of Preformation
1 Introduction
2 Malebranche’s Theory of Preformation
3 Régis’ (Limited) Theory of Preformation
4 Conclusion
‘Nature is More Subtle Than Any Mathematician’: Giorgio Baglivi on Fluids in the Human Body
1 The Intricate Nature of Disease
2 An Overview of De praxi medica, bk. I, Chs. 10–11
3 Analogical Reasoning and Quantification in Physiology
4 Blood, Saliva and Bile Matters: ‘Anatomising’ Body Fluids
5 Conclusion
“The Human Body Should Be Investigated in All Its Details to the Most Precise Degree…”. Leibniz on the Quantification of Body in Medicine
1 Leibniz’s Directiones (1671). A Primer in Quantification?
2 Collecting Data
3 Anatomy
4 Medical Statistics
5 Instruments of Measure
6 The Interior of Nature and the Limits of Mechanization
Appendix: Leibniz “De re medica augenda”
Data vs. Mathesis. Contrasting Epistemologies in Some Mechanizations and Quantifications of Medicine
1 Introduction
2 Struggling for Certainty
2.1 Pitcairne and Keill
2.2 Axiomatic Reasoning and Medicine: Gaukes and Hoffmann
3 Quantifying Physiology: Contrasting Approaches
3.1 The Newtonians: From Ratios to Measurements
3.2 The Rationalists: Statics and Quantification
4 Conclusion
The Pulse Watch and the Physician’s Senses: John Floyer on the Quantification of the Body
1 Introduction
2 The Pulse Watch and the Mechanist View
3 Floyer on the Limits of the Mechanist View
4 The Necessity of the Pulse Watch
5 Conclusion
Against the Quantification of the Living: Hegel’s Critique of Romantic Naturphilosophie in the Phenomenology of Spirit
1 Hegel’s Conception of the Living Organism
2 Observing Reason and the Phenomenological Genesis of Romantic Naturphilosophie
3 The Controversy Concerning Romantic Naturphilosophie
3.1 The Inner-Outer Relationship in Romantic Naturphilosophie
3.2 Hegel’s Criticism of Phrenology
3.3 Hegel’s Criticism of the Schelling-Inspired Naturphilosophie
4 Conclusion
Measuring the Mind: The French Debate on Fechner’s Psychophysics in the Late Nineteenth Century
1 Introduction
2 Fechner’s Psychophysics and Its Introduction into France
3 Mathematical Issues of Fechner’s Law
4 Bergson and Fechner: Quality or Quantity?
5 Conclusion
Index

Citation preview

PALGRAVE STUDIES IN MEDIEVAL AND EARLY MODERN MEDICINE

The Quantification of Life and Health from the Sixteenth to the Nineteenth Century Intersections of Medicine and Philosophy

Edited by Simone Guidi · Joaquim Braga

Palgrave Studies in Medieval and Early Modern Medicine

Series Editors Jonathan Barry Department of History University of Exeter Exeter, UK Fabrizio Bigotti Institute for the History of Medicine Julius Maximilian University Würzburg, Germany

The series focuses on the intellectual tradition of western medicine as related to the philosophies, institutions, practices, and technologies that developed throughout the medieval and early modern period (500-1800). Partnered with the Centre for the Study of Medicine and the Body in the Renaissance (CSMBR), it seeks to explore the range of interactions between various conceptualisations of the body, including their import for the arts (e.g. literature, painting, music, dance, and architecture) and the way different medical traditions overlapped and borrowed from each other. The series particularly welcomes contributions from young authors. The editors will consider proposals for single monographs, as well as edited collections and translations/editions of texts, either at a standard length (70-120,000 words) or as Palgrave Pivots (up to 50,000 words). Associate Editors Alexandra Bamji, University of Leeds Carmen Caballero-Navas, University of Granada Ivano Dal Prete, Yale University David Gentilcore, University of Leicester Klaus-Dietrich Fischer, Johannes Gutenberg University Mainz Guido Maria Giglioni, University of Macerata Benjamin Goldberg, University of South Florida John Henderson, Birkbeck University Brooke Holmes, Princeton University Martin Kemp, University of Oxford Ian MacLean, University of Oxford Alexander Marr, University of Cambridge Cecilia Martini-Bonadeo, University of Padua Heikki Mikkeli, University of Helsinki William Royall Newman, Indiana University Bloomington Vivian Nutton, Centre for the Study of Medicine and the Body in the Renaissance Antoine Pietrobelli, Université de Reims Champagne-Ardenne Aurélien Robert, Centre d’Etudes Supérieures de la Renaissance Tours Hester Schadee, University of Exeter Giovanni Silvano, University of Padua Michael Stolberg, Julius Maximilian University Würzburg Alain Touwaide, Institute for the Preservation of Medical Traditions John Wilkins, University of Exeter Fabio Zampieri, University of Padua Fabiola Zurlini, Studio Firmano for the History of Medicine and Science Editorial Board Justin Begley, University of Helsinki Andreas Blank, Alpen-Adria Universität Klagenfurt Silvana D’Alessio, University of Salerno Hiro Hirai, Radboud University Nijmegen (Netherlands) Luca Tonetti, La Sapienza University of Rome Ruben Verwaal, University of Durham Alun Withey, University of Exeter Giulia Martina Weston, The Courtauld Institute of Art, London

Simone Guidi · Joaquim Braga Editors

The Quantification of Life and Health from the Sixteenth to the Nineteenth Century Intersections of Medicine and Philosophy

Editors Simone Guidi Institute for the European Intellectual Lexicon and History of Ideas National Research Council Rome, Italy

Joaquim Braga Department of Philosophy University of Coimbra Coimbra, Portugal

ISSN 2524-7387 ISSN 2524-7395 (electronic) Palgrave Studies in Medieval and Early Modern Medicine ISBN 978-3-031-15724-0 ISBN 978-3-031-15725-7 (eBook) https://doi.org/10.1007/978-3-031-15725-7 © 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. Cover illustration: Artokoloro/Alamy Stock Photo This Palgrave Macmillan imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

Introduction Simone Guidi and Joaquim Braga The More the Years the Less the Food: Alvise Cornaro on The Sober Life (1558) Laura Madella The Quantification of Talents: Education, Galenic Humoralism, and Classification of Wits in Early Modern Culture Luana Salvarani

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Quali-quantitative Measurement in Francis Bacon’s Medicine. Toward a New Branch of Mixed Mathematics Silvia Manzo

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Sanctorius’s Weighing Chair: Measurement, Metabolism, and Mind Jan Purnis

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The Rise of Quantitative Biology in the Cartesian Age: The Theories of Preformation Mariangela Priarolo

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CONTENTS

‘Nature is More Subtle Than Any Mathematician’: Giorgio Baglivi on Fluids in the Human Body Luca Tonetti “The Human Body Should Be Investigated in All Its Details to the Most Precise Degree…”. Leibniz on the Quantification of Body in Medicine Osvaldo Ottaviani

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Data vs. Mathesis. Contrasting Epistemologies in Some Mechanizations and Quantifications of Medicine Simone Guidi

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The Pulse Watch and the Physician’s Senses: John Floyer on the Quantification of the Body Marco Storni

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Against the Quantification of the Living: Hegel’s Critique of Romantic Naturphilosophie in the Phenomenology of Spirit Gaetano Basileo

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Measuring the Mind: The French Debate on Fechner’s Psychophysics in the Late Nineteenth Century Denise Vincenti

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Index

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List of Contributors

Gaetano Basileo University of L’Aquila, L’Aquila, Italy Joaquim Braga Department of Philosophy, Universidade de Coimbra, Coimbra, Portugal Simone Guidi Institute for the European Intellectual Lexicon and History of Ideas, National Research Council, Rome, Italy Laura Madella University of Parma, Parma, Italy Silvia Manzo Universidad Nacional de La Plata—IdHICS—CONICET, Buenos Aires, Argentina Osvaldo Ottaviani Technion, Israel Institute of Technology, Department of Humanities and Arts, Haifa, Israel Mariangela Priarolo Independent scholar, Pisa, Italy Jan Purnis Campion College at the University of Regina, Regina, Canada Luana Salvarani University of Parma, Parma, Italy Marco Storni University of Neuchâtel, Neuchâtel, Switzerland

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LIST OF CONTRIBUTORS

Luca Tonetti Department of Historical and Geographic Sciences and the Ancient World (DiSSGeA), University of Padua, Padua, Italy Denise Vincenti University of Milano-Bicocca, Milan, Italy

List of Figures

Introduction Fig. 1

The Latitudo sanitatis from Salvo Sclano’s Commentaria (1597)

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Sanctorius’s Weighing Chair: Measurement, Metabolism, and Mind Fig. 1

Sanctorian chair from J. Quincy’s edition of Medicina Statica (1718), courtesy of Wellcome Library, London

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The Pulse Watch and the Physician’s Senses: John Floyer on the Quantification of the Body Fig. 1

Fig. 2

Fig. 3

Jan Steen (and school), A medical practitioner examining the urine and taking the pulse of an elderly man (Source Wellcome Collection, London. Attribution 4.0 International [CC BY 4.0]) Matthijs Naiveu, A physician feeling the pulse of a seated woman patient (Source Wellcome Collection, London. Attribution 4.0 International [CC BY 4.0]) Lavoisier in his laboratory conducting an experiment on the respiration of a man at work (Source Wellcome Collection, London. Attribution 4.0 International [CC BY 4.0])

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LIST OF FIGURES

Fig. 4

Fig. 5

J. H. Barker, A physician taking the pulse of a young woman, her concerned mother is seated opposite him, with a servant in the background (Source Wellcome Collection, London. Attribution 4.0 International [CC BY 4.0]) Musée International d’Horlogerie, La Chaux-de-Fonds, INV I-1183. By kind permission of the head of the Museum

247 251

Measuring the Mind: The French Debate on Fechner’s Psychophysics in the Late Nineteenth Century Fig. 1

Illustration Weber-Fechner

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Introduction Simone Guidi and Joaquim Braga

measure […] is that by which quantity comes to be known. Aristotle

This volume sets out to charter a path at the intersection between the histories of medicine and philosophy concerning a topic that is prominent in contemporary debates, i.e. the translation of physiology, and accordingly pathology, into numerical terms. Indeed, “millions of people around the world are now routinely using […] technologies to track, document and analyse their physical activities, vital functions, and daily habits”1 in numerical terms. A contemporary phenomenon that, even if oriented toward the practical use of medical

1 Btihaj Ajana, Joaquim Braga, and Simone Guidi, ‘Introduction’, in The Quantification of Bodies in Health: Multidisciplinary Perspectives (Bingley: Emerald Publishing, 2022), 1–12: 1.

S. Guidi (B) Institute for the European Intellectual Lexicon and History of Ideas, National Research Council, Rome, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_1

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devices and techniques, has piqued leading scholars’ curiosity worldwide. Such a practice might appear mundane and unsurprising, due to the fact that quantification is widespread in our time and because the technological means to achieve this aim are so widely accessible. Yet, the quantitative trend in medicine is the outcome of a long, complex, and still only partially known history. In Western culture, its roots are traceable to the early modern era, and in a debate that in many ways puts medicine in dialogue with natural philosophy, epistemology, ethics, and—less obviously—metaphysics. With a specific focus on philosophical issues, and on the interplay between philosophy and medicine, the essays collected in this volume discuss some important moments in this exchange across the entire history of the quantification of the body and, accordingly, of medical practice, from the late Renaissance to the late nineteenth century. Hence, the aim of the book is not to outline a detailed and complete history of the quantification of life and health in medicine—a venture that would require more than a single collection of studies.2 Rather, it advances by a series of case histories, aiming to show how medicine and philosophy have

J. Braga Department of Philosophy, Universidade de Coimbra, Coimbra, Portugal 2 For some introductory references see Edward Tobias Renbourn, ‘The Natural History of Insensible Perspiration: A Forgotten Doctrine of Health and Disease’, Medical History, 4, 2 (1960), 135–152; Richard H. Shryock, ‘The History of Quantification in Medical Science’, Isis, 52 (1961), 215–237; Mirko D. Grmek, ‘L’introduction de l’expérience quantitative dans les sciences biologiques’ (Paris: Université de Paris, 1962); Hebbel E. Hoff, ‘Nicolaus of Cusa, van Helmont, and Boyle: The First Experiment of the Renaissance in Quantitative Biology and Medicine’, Journal of the History of Medicine and Allied Sciences, 19, 2 (1964), 99–117; Jerome J. Bylebyl, ‘Nutrition, Quantification and Circulation’, Bulletin of the History of Medicine, 51, 3 (1977), 369–385; Henry Oliver Lancaster, Quantitative Methods in Biological and Medical Sciences. A Historical Essay (New York: Springer, 1994), esp., 176–218; Frederic L. Holmes, ‘The Physical Sciences in the Life Sciences’, in The Cambridge History of Science. Volume 5—The Modern Physical and Mathematical Sciences, ed. by M. J. Nye (Cambridge: Cambridge University Press, 2002), 219–236; Body Counts: Medical Quantification in Historical & Sociological Perspectives, ed. by Gérard Jorland, Annick Opinel, and George Weisz (Montreal: McGillQueen’s University Press, 2005); Antonio Clericuzio and Maria Conforti, ‘Iatrochemistry and Iatromechanism in the Early Modern Era’, in Encyclopedia of Early Modern Philosophy and the Sciences, edited by Dana Jalobeanu and Charles Wolfe (Cham: Springer Nature, 2021); Santorio Santori and the Emergence of Quantified Medicine, 1614–1790: Corpuscularianism, Technology and Experimentation, ed. by F. Bigotti and J. Barry (Cham: Palgrave Macmillan, 2022).

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mutually influenced each other on the crucial problem of if, and how, it is possible to quantify that part of the world that is the human body. In particular, the volume discusses and contextualizes issues that are simultaneous of medical and philosophical import, such as the quantification of temperaments and complexions, the quantification of life processes and physiology, the quantification of embryology, the impact of quantified reasoning on the notions of virtue, vice, health, illness, personhood, certainty, as well as the various ways in which philosophers have rejected this reduction of life to a quantitative and numerical approach.

1

The Meanings of Quantification

In order to speak of the translation of the living body in quantitative terms—or, as Richard Shryock puts it, “the use of measurements and, in some cases, of related mathematics” in medicine3 —we appealed to a broad understanding of the term ‘quantification’. The exact semantic extension of this is actually one of the main problems at stake in this volume and an important element to clarify before accessing the more specific contents of the book. Effectively, the term ‘quantification’ can have many different meanings depending on how the term ‘quantity’ is understood, and this is reflected in the path proposed in this volume. One could say that it might have been easier to focus mainly on our contemporary notion of ‘quantification’, i.e. “capturing certain aspects of material things” by way of measurement and numerical magnitudes.4 However, adopting this exclusive focus would have betrayed the original polysemy of the notion of ‘quantity’ as found in the early modern and modern periods. Accordingly, it would have neglected important moments of this dialogue, and thereby misrepresented the whole debate. Our point of departure, instead, is that the contemporary understanding of quantification is a multi-layered concept and the result of a centuries-long process debate passing through the re-conceptualization of the body and its physiological functions. For a more precise and unambiguous definition of the notion, we might however refer to Rudolph Carnap (1891–1970), who dubbed

3 Shryock, ‘The History of Quantification in Medical Science’, 215. 4 Sophie Roux, ‘Forms of Mathematization (14th–17th Centuries)’, Early Science and

Medicine, 15, 4/5 (2010), 319–337.

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quantification as the process of assigning “a certain number to a certain body or process so we can say that this number represents the value of the magnitude of that body”.5 Measuring is thus the most refined and precise version of this process. In other words, quantification ultimately consists of translating comparative concepts (in a way, proto-quantitative, since they describe qualitative relationships of ‘more’ and ‘less’) based on qualitative, empirical observations, into numerical-quantitative values, which are thought to be more objective and precisely accurate. But, of course, some premises must be established for this process to be possible in the first place, a process that depends on objective methods, a solid mathematical understanding of physical phenomena, and above all, precise instrumentation.6 In effect, on their own, “scientific instrumentation – and especially measuring instruments – created the material conditions for the external world to be observed according to quantitative parameters”,7 and instruments alone allow us to bypass and simultaneously convert the qualitative and comparative nature of our sensory perceptions into numerical values. Only through precise instrumentation can we ‘read’ a natural process through a correspondence with what appears on an instrument, and it is only through the scale of values on the instruments that one can translate qualitative remarks about indirect observations into numerical values, finally translating phenomena into mathematical reconstructions. Yet still, setting up certain instruments to investigate natural phenomena relies in turn on philosophical and epistemological premises to justify the process of quantification, since the latter must be conceived as a moment of a qualitative cognitive process, within which it is designed to answer specific questions. As is well-known, such a theoretical effort could only be thought up within an experimentalist and scientific conceptual framework, something which existed only in an embryonic form before the scientific revolution in the early modern age. The Western world would have to await in particular the rise of that ésprit géometrique which d’Alembert (1717–1783) defined as “a spirit of calculation and

5 Rudolf Carnap, Philosophical Foundations of Physics. An Introduction to the Philosophy of Science, ed. by M. Gardner (New York: Basic Books, 1966), 62. 6 Carnap, Philosophical Foundations of Physics, 63–64. 7 Marco Beretta, Storia materiale della scienza. Dal libro ai laboratori (Milano:

Mondadori, 2002), 23 (our translation).

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combination”,8 or to use Koyré’s famous formula, the emergence of a “universe of precision”.9 But one of the points of this book is to show, by studying the specific case of the dialogue between philosophy and medicine, that the association between quantification (in Carnap’s sense) and scientific practice is far from being merely taken for granted. It depends on many different theoretical and lexical premises that were still overlapping in the early modern period, and which changed over time with respect to the constant introduction of pivotal novelties in technology, economy, and society, including those introduced in medicine. Moreover, even though they are barely indissociable, the mathematization and the mechanization of nature do not necessarily coincide with its quantification, understood as the systematic measurement of natural phenomena. Through the entirety of the seventeenth century and even up to the early eighteenth century, no common or uniform understanding of the terms ‘quantity’ and ‘measurement’ existed among scientists and philosophers, who continued to conceive ‘quantity’ and the emerging forms of quantitative-numerical reasoning as associated with a old comparative sense that is traceable all the way back to the ancient tradition, and in particular to the conception of geometry as the science of measure. The constant overlapping of these two senses of quantity, and the idea that their interplay is somehow possible only in some specific cases, is still emblematic of the early phase of the scientific world. Here it can be attributed, as Koyré argued, to a structural lack of precise instruments,10 but, as we shall argue, it appears to have its roots in the ancient philosophical belief that quantitative reasoning is possible only under the 8 Jean Le Rond d’Alembert, ‘Géometre’, in Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, ed. By D. Diderot and J. Le Rond d’Alembert (Neuchâtel: Samuel Faulche, 1751–1772), vol. 7 (1757), 628. 9 Alexandre Koyré, ‘Du monde de l’à peu près à l’univers de la précision’, Critique, 28 (1948), 806–823. 10 As Koyré has noted, “modern science finds itself at its beginnings in a rather strange and even paradoxical situation: it has precision for principle; it asserts that the real is, in its essence, geometrical and, consequently, subject of rigorous determination and measurement […]; it discovers and formulates (mathematically) laws that allow it to deduce and to calculate the position and speed of a body at each point of its trajectory and at each moment of its motion, and it is not able to use them because it has no ways to determine a moment, nor to measure a speed. Yet, without these measures the laws of the new dynamics remain abstract and void”, and often not well distinguished from purely rational speculation, or from the mere elevation of geometry as the model of a deductive more

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condition of a structural homogeneity between what is measured and what is employed as a unit of measure, enabling the overlapping between the comparative and the quantitative-numerical conception. This idea is so strong that it can be found still in one of the foundational texts of the Enlightenment, the Encylopédie. For instance, Formey and d’Alembert’s entry Quantité defines quantity as “everything that is susceptible to measurement” (a quantitative conception), but also— according to a centuries-long definition—that which “compared with something of the same kind, can be said to be bigger or smaller, or equal or unequal”11 (a comparative conception). Hence, for the encyclopédistes, measuring consists of using “a certain and known measure”, i.e. a unit of measure, “to determine and know precisely the extension, the size, or the quantity of some body, or the capacity of some vessel”. Yet, this understanding of ‘measure’ is operative only under the condition of homogeneity between the unit and the instrument of measure and what is measured12 —a premise that becomes problematic already when passing from solely spatial or solely temporal coordinates to spatiotemporal coordinates, as in the case of velocity.13

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The Metaphysics of Quantity and Measurement

To understand such a restriction to homogeneity, and hence the conceptual reasons behind this ban on passing simply and directly from comparative notions to quantitative-numerical values, one has to address the great influence exerted by the Aristotelian metaphysics of quantity on Western thought.14 Of course, Aristotle’s thought is not exhaustive of the geometrico epistemology (Alexandre Koyré, ‘An Experiment in Measurement’, Proceedings of the American Philosophical Society, 97, 2 (1953), 222–237, 225a). 11 Jean-Henri-Samuel Formey and Jean Le Rond d’Alembert, ‘Quantité’, in Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, vol. 12 (1765), 653 (our translation and italics). 12 See Section 2. 13 See Jean-Henri-Samuel Formey, ‘Vitesse’, in Encyclopédie ou Dictionnaire raisonné

des sciences, des arts et des métiers, vol. 17 (1765), 360–361. 14 On the philosophical reception of Aristotle concept of quantity in medieval and the early modern scholasticism (and then in early modern science), see especially Robert Pasnau, Metaphysical Themes: 1274–1671 (Oxford: Clarendon Press, 2011), 279–349; Tad M. Schmaltz, ‘The Metaphysics of Surfaces in Suárez and Descartes’, Philosophers’ Imprint, 19, 8 (2019), 1–20; id., ‘Quantity and Extension in Suárez and Descartes’, Vivarium,

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entire Greek stance on mathematics, quantity, and measurement. Yet, he is responsible for having established a centuries-long metaphysical treatment of quantity and magnitude which drew from the overall Greek conceptual approach to these notions15 and, from a philosophical perspective, would be incredibly influential up to the modern age. Hence, it is worth recalling that the very terms quantum and quantitas are Latin neologisms that were coined in late antiquity in order to translate the Greek notions of posot¯es and poson, which also indicate one of Aristotle’s categories and a crucial concept for his natural philosophy, logic, and rhetoric. In Aristotelian thought, quantity appears to be intrinsically connected with the metaphysical property of being a continuous magnitude or a discrete multiplicity,16 i.e. with the feature of a whole having continuous or discrete parts joined together, so that the whole is “divisible into two or more constituent parts of which each is

58, 3 (2020), 168–190; id. The Metaphysics of the Material World. Suárez, Descartes, Spinoza (Oxford: Oxford University Press, 2020); Simone Guidi, Baroque Metaphysics. Studies on Francisco Suárez (Coimbra: Palimage, 2020), 231–260. On the problem of measurement, see especially the two special issues of Miscellanea Mediaevalia edited by Albert Zimmermann (16, 1–2 [1983–1984], Mensura. Maß , Zahl , Zahlensymbolik im Mittelalter, and here in particular the papers by Israel Peri (‘Omnia Mensura et Numero et Pondere Disposuisti: Die Auslegung von Weish 11, 20 in der Lateinischen Patristik’, 1, 1–20) Horst Seidl (‘Bemerkungen zu Erkenntnis als Massverhältnis bei Aristoteles und Thomas von Aquin’, 1, 32–42); Edouard-Henri Weber, ‘Commensuratio de l’agir par l’objet d’activite et par le sujet agent chez Albert le Grand, Thomas d’Aquin et Maître Eckhart’, 1, 43–64), Michael Stadler, ‘Zum Begriff der Mensuratio bei Cusanus. Ein Beitrag zur Ortung der Cusanischen Erkenntnislehre’, 1, 118–131); George Molland, ‘Continuity and Measure in Medieval Natural Philosophy’, 1, 132–143). By Molland, see also Mathematics and the Medieval Ancestry of Physics (London: Routledge, 1995). See also the articles by John J. Contreni (‘Counting, Calendars, and Cosmology: Numeracy in the Early Middle Ages’, 43–83) and Wesley M. Stevens (‘Fields and Streams: Language and Practice of Arithmetic and Geometry in Early Medieval Schools’, 113–204), in Word, Image, Number. Communication in the Middle Ages, ed. by J. J. Contreni and S. Casciani (Firenze: Micrologus’ Library—Sismel—Edizioni del Galluzzo 2002) 15 On the other hand, it is true that Aristotle considered mathematics “as a datum, as an established portion of knowledge that is not to be contradicted” (Marco Panza, ‘Measure and continuity in Aristotle’s Physics V 3 (and neighbourhoods)’, in To Metron. Sur la notion de mesure dans la philosophie d’Aristote, ed. by G. Giardina (Paris, Bruxelles: Vrin, Ousia, 2020), 67–99), and embrace the general views of his time quite passively, trying to account metaphysically for them. 16 Cat. 4b 20–5a 35; Metaph. V, 13, 1020a 5–15.

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by nature a one and a ‘this’”.17 According to this model, both geometrical beings (the indivisible points, lines, and surfaces) and arithmetical elements (numbers) are included under the general category of ‘quantity’, along with others like space, time, speech, and material continua. Within this context, the notion of ‘magnitude’ proposed by Aristotle—and which continued to circulate up to the seventeenth century at least—is specifically dependent upon the concept of continuous quantity. In Metaphysics V, 13, he distinguished indeed between being numerable (arithmeton), which is a feature of discrete multiplicities, and being measurable (metritón), which is an exclusive property of magnitudes, i.e. “that which is divisible into continuous parts”.18 Reasoning with Aristotle, one enumerates or counts, and does not measure, how many starlings are in a flock (a discrete quantity); whereas one measures, and does not enumerate, how many square centimeters are in a book page (a continuous quantity). Such a distinction shows why there is no room in Aristotle for Carnap’s aforementioned understanding of measurement as precise ‘quantification’. Here measurement is nothing other than finding into how many homogeneous parts (units) a given continuous quantity can be broken down. Indeed, “the measure is always homogeneous with the thing measured”, for instance, “the measure of spatial magnitudes is a spatial magnitude”, so that the measure “of length is a length, that of breadth a breadth, that of articulate sounds an articulate sound, that of weight a weight, that of units (monadon) a unit”.19 Hence, it has been recently noted that for Aristotle a measure of a magnitude was another magnitude homogeneous to the former, entering this magnitude an exact number of times […] The measure of a quantity was, therefore, another quantity, homogeneous to the former: an aliquot part of it.20

Moreover, this conception of magnitude and measurement seems to be grounded on effectively two metaphysical pillars that, via the Aristotelian

17 Metaph. V, 13, 1020a 5–7. 18 Ibid. 19 Metaph. X, 1, 1053a 25–28. 20 Panza, ‘Measure and continuity’, 73.

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notion of ‘quantity’, would circulate implicitly in all of Western thought up to the early modern age. The first pillar is that Aristotle, reflecting an overall Greek notion, thinks that “magnitudes could be items, as distinct from intensive properties of them”,21 and likely magnitudes are items not really distinct from the quantities they belong to. The second pillar is that continuous quantities are holistic essential wholes, in which the parts are thought to be intrinsic components of a totality.22 Accordingly, Aristotle treats the magnitude of a quantity as the divisible, continuous whole itself, taken under the perspective of how many proportional subdivisions into which it can be broken. Apart from Boethius’ De Institutione Arithmetica 23 —a major reference for the medieval and Renaissance understanding of these problems— we can find a similar position already at the very core of Euclid’s Elements in Book V (through which it would also appear in Proclus and the whole Neoplatonic tradition): 1. A magnitude is a part of a magnitude, the less of the greater, when it measures the greater. / 2. The greater is a multiple of the less when it is measured by the less. / 3. A ratio is a sort of relation in respect of size between two magnitudes of the same kind, etc.24

In the case of the measurement of real magnitudes, this signifies grasping, according to the model of geometry, a proportional ratio between a continuous quantity and another homogeneous continuous quantity that plays the role of a specific unit of measure, then describing this ratio by an integer. Significantly, the great late Renaissance mathematician, 21 Ibid. 22 On Aristotle’s usage of the notions of part and whole in this context, see especially

Paul A. Bogaard, ‘Heaps or Wholes: Aristotle’s Explanation of Compound Bodies’, Isis, 70 (1979), 11–29; Sally Haslanger, ‘Parts, Compounds, and Substantial Unity’, in Unity, Identity, and Explanation in Aristotle’s Metaphysics, ed. by T. Scaltsas, D. Charles, M. L. Gill (Oxford, Clarendon Press, 1994), 129–170; Dougal J. Blyth, ‘Wholes, Parts, and Sequences in Aristotle’, International Philosophical Quarterly, 34, 4 (1994), 453– 463; Kathrin Koslicki, ‘Aristotle’s Mereology and the Status of Form’, The Journal of Philosophy, 103, 12 (2006) 715–736. Ignácio De Ribera-Martin, ‘Unity and Continuity in Aristotle’, Apeiron, l, 2 (2017) 225–246. 23 See Michael Masi, Boethian Number Theory. A Translation of the “De Institutione Arithmetica” (Amsterdam, New York: Rodopi, 2006). 24 Thirteen Books of Euclid’s Elements, vol. 2 (Books III–IX), trans. by Thomas L. Heath (Cambridge: Cambridge University Press, 1908), 113–114.

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Niccolò Tartaglia (ca1499–1577) still subscribed to this perspective in his influential General Treatise (1556): To measure a certain quantity means nothing more than to want to find how many times it can be found within a given known quantity, or what part, or how many parts it is of that famous quantity. [...] By known quantity is to be understood those sorts of measurements commonly used in the provinces, i.e. cities, in such measurements.25

The consequence of this perspective is that this understanding of ‘measuring’—even though suitable for instrumentally driven measurements conceived in terms of distance—is intrinsically comparative, qualitativeoriented, and ‘internal’ to a quantitative being. Above all, it is not conceived within a general conception of nature as provided with its own quantitative coordinates, and so as intrinsically homogeneous to the symbolic and analogical dimension introduced by measurement. Hence, in no way can it suggest the activity of translating such comparative properties into an external, numerical scale provided by a measurement device. Within this concept of magnitude and measurement, one can effectively measure a plot of land by a yardstick, time by a clepsydra, or the Earth’s circumference, but one cannot measure the physical temperature of a body by a thermometer, which involves an analogical relationship between two heterogeneous magnitudes (the heat of the body and the movement of the mercury in the thermometer), a quantitative understanding of temperature, and a precise theory that links these magnitudes.26 Moreover, there is another important correlate depending more specifically on Aristotle’s conceptual approach, and which would circulate through the Aristotelo-Scholastic notion of quantity until the early modern period.27 Famously (and despite some well-known views to the 25 Niccolò Tartaglia, La terza parte del general trattato, de numeri et misure (Venice: Curzio Troiano, 1560), c. 1, § 5, f. 1v (our translation). 26 See below, footnotes 83 and 94. 27 As of the mid-fifteenth century in particular (and starting in particular with Antonio

Piccolomini’s Commentarium de Certitudine Mathematicarum Disciplinarum [1547]), this whole debate is reassessed in the so-called Quaestio de certitudine mathematicarum, whose crucial question is whether mathematical demonstrations can be considered scientific demonstrations in the Aristotelian sense, and if mathematics is a true form of knowledge. This debate involves especially Giuseppe Biancani (1566–1624), Francesco Barozzi (1537–1604), Benedict Perera (1536–1610), Cristophorus Clavius (1538–1612),

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contrary which in effect would exert a great and progressive influence as of the fourteenth century),28 Aristotelian natural philosophy is far from being synonymous with mathematics. The latter is indeed understood by the Stagirite, against Plato, in physicalist-fictionalist terms,29 a position that Aristotle strongly upholds through his notion of the relationship between quantity, material substance, and the intelligibility of substance. If it is true that determinate spatial or temporal magnitudes are structural accidents of all continuous material quantities, it is nonetheless true that, for Aristotle’s conception of matter and mathematics, such magnitudes and their changes are accidental, qualitative, and cannot be thought of as intrinsically mathematical. Mathematics deals strictly with abstractions made by the intellect based on quantitative, perceivable, material, and individual substances, which are not instantiations of universal mathematical matter, or intelligible matter30 unto themselves. In the Middle Ages, Thomas Aquinas still stressed this concept in his Summa Theologiae, a work which was very influential for the early modern age:

the Coimbrans, Isaac Barrow (1630–1677), and John Wallis (1616–1703). See especially Paolo Mancosu, ‘Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments in the Quaestio de Certitudine Mathematicarum’, Studies in History and Philosophy of Science, 23, 2 (1992); id., Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (Oxoford: Oxford Univerrsity Press, 1996). 28 See Quantifying Aristotle. The Impact, Spread and Decline of the Calculatores Tradition ed. by D. A. Di Liscia and E. D. Sylla (Leiden, Bostn: Brill, 2022) and Sylvain Roudaut, La mesure de l’être. Le problème de la quantification des formes au Moyen Âge (ca. 1250–1370) (Leiden, Boston: Brill, 2022), here particularly 149–207. See also Edith Sylla, ‘Medieval Quantifications of Qualities: The “Merton School”’, Archive for History of Exact Sciences 8, 1/2 (1971), pp. 9–39; John Murdoch, ‘“Mathesis in philosophiam scholasticam introducta: The Rise and Development of the Application of Mathematics in Fourteenth Century Philosophy and Theology”’, in Arts libéraux et philosophie au Moyen Âge, Actes du Quatrième Congrès International de Philosophie Médiévale (Montreal: Institut d’études médiévales, 1969), 215–246; Michael R. Mcvaugh, ‘Quantified Medical Theory And Practice At Fourteenth-Century Montpellier’, Bulletin of the History of Medicine, 43, 5 (1969), 397–413; Joel Kaye, A History of Balance, 1250–1375 (Cambridge: Cambridge University Press, 2014). 29 See Henry Mendell, ‘Aristotle and Mathematics’, in The Stanford Encyclopedia of Philosophy (Fall 2019 Edition), ed. by E. N. Zalta. 30 As regards the rise of these notions and the debates concerning them in the early modern age see especially Claudio Buccolini, ‘Scetticismo e matematica nella Vérité des sciences di Mersenne’, Syzetesis, 6/1 (2019), 7–30.

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Mathematical species […] can be abstracted by the intellect from sensible matter, not only from individual, but also from common matter; not from common intelligible matter, but only from individual [intelligible] matter. For sensible matter is corporeal matter as subject to sensible qualities, such as being cold or hot, hard or soft, and the like: while intelligible matter is substance as subject to quantity. Now it is manifest that quantity is in substance before other sensible qualities are. Hence quantities, such as number, dimension, and figures, which are the terminations of quantity, can be considered apart from sensible qualities; and this is to abstract them from sensible matter; but they cannot be considered without understanding the substance which is subject to the quantity; for that would be to abstract them from common intelligible matter. Yet they can be considered apart from this or that substance; for that is to abstract them from individual intelligible matter.31

Quantity and its geometrico-mathematical features belong intrinsically to a given individual, i.e. to an individual material substance, and can be legitimately abstracted from it by mentally separating the quantitative aspects from the sensory/qualitative ones. Yet, this presence of quantitative features in each individual material being does not mean that a given substance and its qualitative properties can be determined quantitatively or mathematically. A substance is indeed a compound of quantitative, qualitative, and accidental elements simultaneously present in it, and the high degree of abstraction of mathematics is wholly unable to grasp its essence without lacking most of it. Therefore, capturing magnitudes or certain specific aspects in numerical terms is just an analogical process that occurs between beings, parts, and wholes falling under the same category of quantitas.

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The More, the Less, the Whole, the Body

The metaphysical conception of magnitude that went on to circulate in Western thought for centuries under this notion of quantity somehow explains the conceptual issues in conceiving quantification in Carnap’s terms and why, up to the late medieval age, medicine was affected by this conceptual stance, such that—even when attempting to quantify human physiology—it still conceived the medical body in non-numerical terms. 31 Thomas Aquinas, Summa Theologiae, I, 85, a. 1, ad 2; English translation by the Fathers of the English Dominican Province (Boston: Benziger Bros., 1947).

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Despite the fact that certain attempts to quantify some aspects of human physiology trace back to the Ancient period,32 neither Hippocrates nor Galen applied true quantitative instrumental and datadriven analysis to human anatomy and physiology, whose functions were understood qualitatively, in light of the notions of psyché and dynamis. Nonetheless, such non-use of numerical analysis of physiology has strong epistemological bases, according to a practice that would remain a part of Western medicine over the centuries. Indeed, Ancient physicians seem to have been convinced that they could determine the function of each organ or the nature of each ‘clinical picture’ by the use of their senses alone. Why, then, steal time from a busy practice to experiment or measure especially when such diversions were of no apparent aid to that practice?33

Starting with Hippocrates, medical reasoning was already strongly dependent upon empirical, qualitative observations.34 A fundamental trust in subjective sensory observation constituted the epistemological premise for qualitative knowledge of the qualitative functions of the body. Hence, the

32 They especially concern sphygmology (the study of the pulse—see Evan D. Bedford, ‘The Ancient Art of Feeling the Pulse’, British Heart Journal, 13, 4 (1951), 423–437; on Galen see Michel Boylan, ‘Galen: On Blood, the Pulse, and the Arteries’, Journal of the History of Biology, 40 (2007), 207–230) and uroscopy (the analysis of urine). In his The Revolutions of Wisdom (Berkeley, Los Angeles, London: University of California Press, 1987), 215–284, Geoffrey Ernest Richard Lloyd has seriously challenged Koyré’s idea (‘Du monde de l’à peu près à l’univers de la précision’) that the Greeks had no quantitative notions and technology and they were not even interested in develop a mathematical physics. As Lloyd argued “it is not the case that the epistemological and methodological assumptions at work in the [Greek] inquiry into nature were always and everywhere hostile to the pursuit of exactness in either of the two forms we are concerned with, that is, (1) the formulation of rigorous theories, and (2) the collection of precise data” and “the application of mathematics to the understanding of natural phenomena of various kinds was one of the most important and fruitful preoccupations of ancient science” (278–279). We are aware of the many examples provided by Lloyd against Koyré’s specific reconstructoion, and we acknowledge some of the most relevant cases in ancient medicine. We only point out that what differentiates early modern science is, however, an entirely quantitative and mathematical conception of natural phenomena, accompanied by technological devices able to ‘translate’ phenomena into the language of mathematics. 33 Shryock, ‘The History of Quantification in Medical Science’, 218. 34 A notion that would be continuously reassessed on the long path from simple

inductivism to scientific experimentalism.

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physician traditionally worked by observing, collecting, and comparing qualitative information about the ill body’s heath, smell, color, etc. This conceptual dominance of the qualitative dimension is clear even when considering a significant exception to this trend, and one of the most adamant attempts to ‘quantify’ (but not actually measure) living functions in the Ancient age, in the work of Herophilus (335–280 BC). As is well-known, Herophilus endeavored to analyze the human pulse by classifying the differences between various kinds of pulse, and grounded this attempt on quantitative bases: In general, then, pulse seems to differ from pulse in volume [mass], in size, in speed, in vehemence [strength], and in rhythm. From the fact that they differ in these respects, the pulse clearly at times becomes ‘fitting’ [oikeios, ‘conforming to its true nature’] at times not ‘fitting’. One pulse appears to differ from another, and in general to be recognized [as different], in rhythm, size, speed, and vehemence [strength], as was said. But if, in the same rhythm, one pulse appears to differ from another, then in speed, size, and vehemence.35

It would be hard to deny that the parameters invoked here are somehow quantitative: rhythm, size, speed, and strength. But, how could Herophilus satisfy such a quest for precision? Though he did not include the idea of ultimate, absolute quantitative dimensions of the whole physical world, he did draw from analogies and quanto-qualitative forms of measurement, grounded in the “analogy between harmonia in the body

35 See Heinrich Von Staden, Herophilus. The art of medicine in early Alexandria (Cambridge: Cambridge University Press, 1989), Fr. 6280–86 , 273–274.

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and musical harmony”.36 Indeed, by a formula that would be harshly criticized by Galenus,37 Herophilus defined rhythm as “motion which has a defined regulation in time”, a notion that is entirely shaped by way of analogy with metrics in music, and according to a geometric conception of magnitude: Up-beat and down-beat, arsis and thesis, were […] the general units Herophilus used to establish a basic analogy between musical rhythm and pulse rhythm, but he also developed the analogy in intricate detail. First, Herophilus established what he apparently called a ‘primary perceptible time unit’ […], defining it as the interval of time in which he usually found the artery of a new-born child dilating. This ‘primary perceptible time unit’ is characterized as analogous to the breve or short unit used in the feet of musical metres, and it becomes the basic unit (a) by which the length of each contraction and each dilation is measured (each can consist of one, two, etc. ‘primary perceptible time units’), and (b) by which the rhythm, i.e. the relation of the duration of contraction to the duration of dilation, is established.38

The two sides of this notion of rhythm—the idea of a primary perceptible unit of time, and that of an essential analogy and supposed homogeneity between musical and medical harmony—are quite telling about the idea that here observing and measuring ultimately consist in comparing 36 Von Staden, Herophilus, 278: “It has often been argued that Herophilus derived this conception of rhythm from the metrical theory of his contemporary, Aristoxenus of Tarentum, a Peripatetic philosopher and musical theorist who proposed a theory of metrical ‘feet’ (podes ) composed of long and short syllables. Aristoxenus’ famous concepts chronos prdtos […] and alogoi podes (‘irrational feet’ […]) might well have inspired Herophilus’ uses ofprdtos chronos and alogos sphygmos (‘irrational pulse’ […]), and Herophilus might also have found Aristoxenus’ analogy between harmonia in the body and musical harmony […] suggestive”. For more on the presence of this ‘musical’ understanding of the pulse in the Renaissance and early modern period, see in particular Werner F. Kümmel, ‘Der Puls und das Problem der Zeitmessung in der Geschichte der Medizin’, Medizinhistorisches Journal, 9, 1 (1974), 1–22. 37 Von Staden, Herophilus, 276: “is it the ratio of the time of dilatation to the time of contraction only, or does he also attribute to ‘rhythm’ the time of the pause [quiescence] which follows each of these two motions? […] Not even among those who are named ‘Herophileans’ after him is there agreement concerning just what Herophilus really thought about rhythms” (Galen, On Differentiating Between Pulses ). In On Prediction based on Pulses, Galen again complains that Herophilus “is confused and does not clearly articulate the distinction between contraction and rest”. 38 Von Staden, Herophilus, 277–278.

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different subjective impressions, establishing qualitatively conceived intervals and degrees between them. Of course, this does not prevent further endeavors toward instrumental precision, as witnessed by Herophilus’ setting up of a specific device, a water-clock, specifically designed for measuring the pulse and the temperature and calibrated for the patient’s different ages.39 Yet—according to a conceptual stance that one still finds in early modern medicine—, this instrumentation is not understood to pass from comparative to quantitative, numerical conceptions of the very examined phenomenon. Rather, it is set up to bring these observations, grounded on perceptible time units, to the highest possible degree of accuracy. By contrast, it should be noted that some embryonic elements of quantification, understood here as non-numerical and according to the logic of ‘more and less’ were present in Galenic medicine, and would continue to appear there in the Renaissance (also via Avicenna).40 Indeed, Galen formulated the pivotal notion of eucrasia, i.e. the right proportion and balance of humor in the organism, within the proportional terms recalled above; in particular, in terms of the proportional distance of intemperate mixtures from the ‘natural state’,41 according to the concept of latitudo sanitatis .42 Moreover, Galen himself classified the human 39 See Von Staden, Herophilus, 10: “The struggling but insistent Egyptian emphasis on

counting or measuring is particularly interesting in view of Herophilus’ use of a portable, adjustable water-clock – adjustable according to the age of the patient – to measure the pulse and […] to take the patient’s temperature. Egypt was a land rich in time-measuring devices including, in particular, clepsydrae. Although measurement, quantification, and the clepsydra were not unknown to pre-Alexandrian Greeks, it is not inconceivable that the sophisticated Egyptian water-clock technology, the Egyptian interest in quantification (more on this infra), and the keen interest of Greek Alexandrians in technology and gadgetry all combined to prompt or facilitate Herophilus’ introduction of his measuring device”. 40 See especially Kaye, A History of Balance, 187–189. 41 See in particular Kaye, A History of Balance, 135–182 and here especially 154–158. 42 See especially Kaye, A History of Balance, 151–154. As noted by Llyod, The Revolu-

tions of Wisdom, 256, “Galen, […] uses quantitative arguments on several occasions”, but they are limited to proportional relationships based on ‘more or less’ or easily measurable aspects. Indeed, as Lloyd himself stress, “in On the Use of Parts he remarks generally on the proportionalities between the fluids and solids taken into the body and those discharged or lost, and elsewhere he specifies actual amounts of, for example, pus expectorated. In On the Natural Faculties the difference in size between, on the one hand, the vena cava (together with the right auricle) and, on the other, the pulmonary artery is cited among the arguments to support the conclusion that some blood must pass directly

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organs by paying attention to their balanced position, shape, number, and magnitude (aequalitas membrorum).43 Finally, numerical measurement was constantly used in pharmacology, according to a practice that is as ancient as medicine and would evolve over the entire history of alchemy and chemistry, particularly as of the fourteenth century.44 Yet, especially when dealing with the quantification of drugs, Galen stressed a point which was characteristic of his entire medical thought. One insurmountable obstacle to the precise and universal quantification of medical activity was indeed the particular conditions of the individual patient,45 which forced the physician to think in terms of ‘more or less’ rather than by precise (numerical) quantitative prescriptions: I have often said that nothing in medical practice concerning drugs is incapable of expression at least as regards their general form; but the

from the right ventricle to the left through invisible pores in the septum, though – unlike Harvey – Galen does not attempt to measure the quantities or flow of blood exactly or even approximately”. 43 Galen, Ars medica, in Opera omnia (ed. Kühn, Lipsia 1821–1833), I, 314–315: “The sign of the healthiest bodies is that they are equally balanced in their members with respect to the four elemental qualities: heat, cold, dryness, and wetness; and that there is an equality in the organic members in terms of their quantity, construction, number, and the form of their component parts, both with respect to their instrumental functions and in their relationship to the whole” (English transl. from Kaye, A History of Balance, 151). 44 See Lloyd, The Revolutions of Wisdom, 250–252; Allen G. Debus, ‘Mathematics and Nature in the Chemical Texts of the Renaissance’, Ambix, 15, 1 (1968), 1–28; id., The Chemical Philosophy: Paracelsian Science and Medicine in the Sixteenth and Seventeenth Centuries (New York: Science History Publications, 1977); id., ‘Chemists, Physicians, and Changing Perspectives on the Scientific Revolution’, Isis, 89, 1 (1998), 66–81. See also Instruments and Experimentation in the History of Chemistry, ed. by F. L. Holmes and T. H. Levere (Cambridge, MA: MIT Press, 2000), 5–74 (the papers by Anderson, Newman, and Principe). See also Mcvaugh, ‘Quantified Medical Theory And Practice At Fourteenth-Century Montpellier’, and Ronald Edward Zupko, ‘Medieval Apothecary Weights and Measures: The Principal Units of England and France’, Pharmacy in History, 32, 2 (1990), 57–62. 45 On the relationship between universality and particularity of Galenic medicine, see especially Philip J. Van der Eijk, ‘Therapeutics’, in The Cambridge Companion to Galen, ed. by R. J. Hankinson (Cambridge: Cambridge University Press, 2007), 283–303, here 286– 288, and Riccardo Chiaradonna, ‘Universals in ancient medicine’, in Universals in Ancient Philosophy, eds. R. Chiaradonna and G. Galluzzo (Pisa: Edizioni della Normale, 2013), 381–423. On the problem of uncertainty in ancient science see Lloyd, The Revolutions of Wisdom, 109–171.

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precise quantity in each case cannot be expressed, or written down, or indeed taught in any way. But we do want somehow to come close to this in our exposition, saying ‘slightly’ or ‘very’ filthy, or thin or thick, or ‘extremely slightly’, ‘excessively greatly’, ‘moderately’, ‘very proportionately’, or whichever of the multiform ways of expression we use to come as close as possible to expressing quantity.46

In Renaissance Galenism especially, the quantification of temperaments, blood and drugs would be connected with some seminal aspects of a dietetics that is quantified according to these principles, and which would come to be at stake in the early quantification of life and health in early modern medicine up to the nineteenth century.47 Interestingly, in this context, through Aristotle’s overall ‘doctrine of the mean’, the classic understanding of quantity would confront yet another meaning of ‘measure’, i.e. the ethical one of “due measure” (pros to metrion) and hence the issue of moderation.48 This conceptual association was already stressed by Galen (aequalitas ad iustitiam) and Avicenna, and more openly argued by late medieval scholastics.49 However, these attempts at addressing nature and the human body in quantitative terms, continues to mirror metaphysical and epistemological conceptualities connected with the conceptual framework recalled above, especially the idea that nature is structured by natural proportions, or can be broken down into natural units. Hence, magnitudes would be naturally measurable in terms of ratios because every continuous being is a harmonic whole that is structured after ideal geometrical proportions between its parts. As is well-known, this view was deeply resonant over the 46 Galen, Opera omnia, X, 182. English translation from Galen, Method of Medicine, trans. by I. Johnston and Horsley (Cambridge, MA and London: Harvard University Press, 2011), 3.3. 47 See in particular Martin Gardner Gentilcore, Food and Health in Early Modern Europe—Diet, Medicine and Society, 1450–1800 (London: Bloomsbury, 2016), esp. 9– 48. See also Bylebyl, ‘Nutrition, Quantification and Circulation’; Anita Guerrini, ‘The Impossible Ideal of Moderation: Food, Drink, and Longevity’, in Lifestyle and Medicine in the Enlightenment: The Six Non-naturals in the Long Eighteenth Century, ed. by J. Kennaway and R. Knoeff (London: Routledge, 2020), 86–107 and, in the same volume, James Kennaway, ‘The Dietetics of the Soul in Britain in the Long Eighteenth Century’, in Lifestyle and Medicine in the Enlightenment: The Six Non-naturals in the Long Eighteenth Century, ed. by J. Kennaway and R. Knoeff (London: Routledge, 2020). 48 See, in this volume, Laura Madella’s paper on Cornaro. 49 Kaye, A History of Balance, 194–195; 207–210.

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course of the entire Renaissance and the early seventeenth century,50 and the idea of a metaphysical proportionality in nature has been taken very seriously by the cosmology, theology, and astronomy of prominent figures such as Nicholas of Cusa (1401–1464), Johannes Kepler (1571–1630),51 or Marin Mersenne (1588–1688),52 to mention just a few. Yet, regarding the human body, as of the late fifteenth century this theory was constantly associated with some ideas conveyed by the work of Vitruvius.53 A relevant feature of Vitruvius’s strong anthropocentric framework lies not only in subscribing to the Aristotelic-Euclidean notion of magnitude and measurement, but to contend that the human body is itself a (or better ‘the’) canonical and fundamental natural unit of measure. Vitruvius’ famous idea will recur in countless treatises on physiognomy in the early modern period and would inspire great figures like Leonardo (1452–1519) and Girolamo Cardano (1501–1576).54 It is that natural and artificial beings correspond intrinsically “to the likeness of a wellformed human being”.55 Like Aristotle and Euclid, Vitruvius’ reasoning proceeds in mereological terms,56 as he argues that the human body is

50 This fortune was due both to the rediscovery of Plato’s notion of matter as chora— matter that is intrinsically geometrical—and to a different assessment of the Biblical truth that God “ordered all things by measure, number, and weight” (Sap. 11:20). 51 See especially Albert van der Schoot, ‘Kepler’s Search for Form and Proportion’, Renaissance Studies, 15, 1 (2001), 59–78. 52 See Peter Dear, Mersenne and the Learnings of the Schools (Ithaca and London: Cornell University Press, 1988), 48–169, and Natasha Fabbri, De l’utilité de l’harmonie. Filosofia, scienza e musica in Mersenne, Descartes e Galileo (Pisa: Edizioni della Normale di Pisa, 2008). 53 See especially Frank Zöllner, Vitruvs Proportionsfigur: Quellenkritische Studien zur Kunstliteratur im 15. und 16. Jahrhundert (Worms: Wernersche Verlagsgesellschaft, 1987). As for Vitruvius’ inflence on Vesalius see Jackie Pigeaud, ‘Formes et normes dans le De Fabrica de Vésale’, in Le Corps à la Renaissance, ed. by J. Ceard et al. (Paris: Aux Amateurs de Livres, 1990), 399–421. 54 See Nancy Siraisi, The Clock and the Mirror. Girolamo Cardano and Renaissance Medicine (Princeton: Princeton University Press, 1997), 99–100. Cardano deals with Vitruvean proportions in chapter 11 of De subtilitate (1550). Parts of Cardano’s remarks are translated into English in Daniele Barbaro’s Vitruvius of 1567 , trans. and annotated by K. Williams (Cham: Springer, 2019), 200–202. 55 Vitruvius, De architectura, III, 1. English translation Ten Books on Architecture, trans. by I. D. Rowland (Cambridge: Cambridge University Press), 47. 56 Vitruvius’ reference to the notions of whole and parts could be perfectly understood by medieval and Renaissance thinkers, who had complex and articulated mereological

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composed as a perfect whole by nature, such that “in its proportions, the separate individual elements answer to the total form”. Hence, the human body is the canonical case of a complete analogy or symmetry between the parts, such that there is “a correspondence between the measure of individual elements and the appearance of the work as a whole”57 ; a correspondence that art must follow. In Vitruvius’ famous words: 1. Symmetry derives from proportion, which is called analogia in Greek. Proportion is the mutual calibration of each element of the work and of the whole, from which the proportional system is achieved. No temple can have any compositional system without symmetry and proportion, unless, as it were, it has an exact system of correspondence to the likeness of a well-formed human being. / 2. For Nature composed the human body in such a way that the face, from the chin to the top of the forehead and the lowermost roots of the hairline should be one-tenth [of the total height of the body]; the palm of the hand from the wrist to the tip of the middle finger should measure likewise; the head from the chin to the crown, oneeighth; from the top of the chest to the hairline including the base of the neck, one-sixth; from the center of the chest to the crown of the head, one-fourth. Of the height of the face itself, one-third goes from the base of the chin to the lowermost part of the nostrils, another third from the base of the nostrils to a point between the eyebrows, and from that point to the hairline, the forehead also measures one-third. The foot should be one-sixth the height, the cubit, one-fourth, the chest also one-fourth…58

As one can see, for Vitruvius, the human body is naturally structured in proportional parts that are internal subdivisions of a given whole, i.e. they are proportional, harmonic mutual relationships between the sections in which the holistic continuum of the body can be broken down, and not

thought. See especially Andrew Arlig, ‘Medieval Mereology’, in The Stanford Encyclopedia of Philosophy (Fall 2019 Edition), ed. by E. N. Zalta; id., ‘Is There a Medieval Mereology?’, in Methods and Methodologies: Aristotelian Logic East and West, 500–1500, ed. by M. Cameron and J. Marenbon (Leiden: Brill, 2011) 161–189; id., ‘Mereology’, in Springer Encyclopedia of Medieval Philosophy, ed. by H. Lagerlund, Dordrecht, Springer, 2011, 763–771; id. ‘Parts, Wholes and Identity’, in The Oxford Handbook of Medieval Philosophy, ed. by J. Marenbon (Oxford: Oxford University Press, 2012), 445–467; id., ‘Part-Whole Interdependence and the Presence of Form in Matter According to Some FifteenthCentury Platonists”, Bruniana & Campanelliana, 27, 1 (2022), 103–122. 57 Vitruvius, De architectura, III, 4, 47. 58 Vitruvius, De architectura, III, 1–4, 47.

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quantitative aspects that can be captured via ‘external’ measurements. This way, the whole macrocosmos of the natural world can be measured by way of an analogy to the microcosmos of the human body (anthropometric measures), which is intrinsically a quantifier without being really quantifiable—if not in terms of this general theory of the mutual correspondence of ratios. Hence, one can start from the human body by finding and measuring an internal ratio between the parts, and then finding these proportions in the whole natural world, which is structured according to the same logic and proportional ratios.59 Beginning in the late antiquity, this idea went to circulate also via Patristic sources and thereby went on to be embraced in the scholastic tradition up to the late Renaissance.60 Regarding the latter period, scholars have noted61 that these issues again take on a fundamentally philosophical appearance during the fourteenth and fifteenth centuries. It was indeed possible to associate such an anthropocentric metrology with a theological, metaphysical, or scientific skepticism, especially in light of the recovery of Protagoras’ much-criticized theory of man as the measure of everything. It is worth recalling here the case of Nicholas of Cusa, who stressed in his Idiot (De mente, 1450) the (false) etymological provenience of mensura from mens at stake also in his Learned Ignorance, and in the following terms: Mind is named from measure so that calculating measurements is the basis for the name […] Mind constructs the point as the limit of line and line as the limit of surface and surface as the limit of body. It constructs number 59 See Witold Kula, Measures and Men (Princeton: Princeton University Press, 1986), 24–28. 60 Take, for instance, the Commentaries on Aristotle (1593–1606) by the Coimbra Jesuits, a standard reference for all of early modern scholasticism: “As Augustine notes in Book 15 of De civitate Dei, chapter 26, the length of the human body, from the head to the feet, must be six times its width, which is [calculated as the interval of space] from side to side: and ten times its height, whose height the measure is in the interval of space between the back and the belly; as though you measured a supine man, or a prone man [and it was] six times as long, from the head to the feet, as it is with respect to the side from right to left, or from left to right, and ten times [as long] as he is high from the ground”. See Commentarii Colegii Conimbricensis S. J. In duos libros De Generatione et Corruptione Aristotelis Stagiritae (Coimbra: A. Mariz, 1597) I, c. 5, q. 14, 265 (our translation). 61 For instance Paula Blank, Shakespeare and the Mismeasure of Renaissance Man (Ithaca and London: Cornell University Press, 2006), 14–40.

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and thus multitude and magnitude stem from mind. Hence it measures everything. […] The mind is a kind of absolute measure which cannot be greater or smaller since it is not restricted to quantity. When you note the mind is a living measure that measures by itself (as if a living pair of compasses were to measure by themselves), then you grasp how it fashions a concept, measure, or exemplar.62

Measuring is a specific peculiarity of the human mind, which is itself an image of the mind of God from which ‘multitude’ and ‘magnitude’ stem. As is well-known, for Cusanus, the realm of more and less circumscribes that which the human mind can grasp, the starting point for a progressive, even though never complete, comprehension of God. And, in effect, in Cusanus’ work we find a significant example of just how metaphysical and mystical63 this notion of ‘measure’ could really be still in the fifteenth century, as well as how a Renaissance philosopher thinks it within the general project of decrypting the innermost secrets of nature. In his dialogue De Staticis Experimentis (Idiot, 1450),64 Cusanus comes up then with the idea of a general inventory of the weight of every kind of thing in the world, supposing that one can infer the qualitative differences in the natures of beings from the quantitative differences in their weight. This work effectively proposes some well-known experimental strategies, inclined toward a logic of precision, that yet are not so far off from those of Herophilus and some early modern natural philosophers. For instance: If you were to allow water to flow through the narrow aperture of a waterclock into a basin during the time that you counted the pulsebeat of a healthy adolescent one hundred times, and if you did a similar thing with respect to a sick adolescent, don’t you think that there would be a difference of weight between those [two collections of] water? […] Therefore,

62 Nicholas of Cusa, Idiota, de Mente, trans. by C. L. Miller (New York: Abaris Books, 1979), 43. See Michael Stadler, ‘Zum Begriff der Mensuratio bei Cusanus. Ein Beitrag zur Ortung der Cusanischen Erkenntnislehre’. The mens-mensura etymology was often invoked by Albert the Great (see Weber, ‘Commensuratio de l’agir par l’objet d’activite et par le sujet agent chez Albert le Grand, Thomas d’Aquin et Maître Eckhart’). 63 See Debus, The Chemical Philosophy, 37–45. 64 Nicholas of Cusa, On Wisdom And Knowledge, trans. Jasper Hopkins (Minneapolis:

The Arthur J. Banning Press, 1996), De staticis experimentis. This work would have been published in the sixteenth century as an appendix of Vitruvius’ De architectura).

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by reference to the weight of the [collections of] water we could ascertain a difference of pulses in the case of someone young, someone elderly, someone healthy, and someone sick. And, likewise, we could arrive at a truer knowledge of the illness; for, of necessity, there would be one weight with respect to one illness and another weight with respect to another illness. Hence, from a consideration of such different experimental results pertaining to the pulses, together with a consideration of the weight of urine, a more accurate judgment could be made than [could be made] merely from feeling the pulse and [assessing] the color of the urine.65

The case of this passage is particularly interesting since, apparently, here Cusanus circumvents the general rule of the homogeneity mentioned above, by directly relating the discrete quantity of the pulse (one hundred heartbeats) and the continuous quantity (the corporeal bulk) of the water by relating the continuous quantity of the water and that of the time passed during the one hundred heartbeats. According to him, one can relate the quantity of water that fell in the bucket and the hundred beats of the pulse, and from the quantity of water infer the different velocities of the pulsebeat. Yet two elements must be noted in this passage. The first one is that the pulse here is understood as a kind of natural clock, whose intrinsic rhythm is not the measured, but rather what measures.66 Cusanus thinks that the discrete quantity of the heartbeat ‘enumerates’ the continuous quantity of the water’s movement, as one can visualize the measured span of time passed by the quantity of water in the bucket.67

65 Nicholas of Cusa, De Staticis experimentis, 608. For some remarks about Cusanus’ thought experiments see Kümmel, ‘Der Puls und das Problem der Zeitmessung in der Geschichte der Medizin’; Stadler, ‘Zum Begriff der Mensuratio bei Cusanus’; Hoff, ‘Nicolaus of Cusa, van Helmont, and Boyle: The First Experiment of the Renaissance in Quantitative Biology and Medicine’. 66 This aspect is characteristic of the Renaissance and early modern understanding of pulse. See especially Kümmel, ‘Der Puls und das Problem der Zeitmessung in der Geschichte der Medizin’, and below, Cardano’s experiments. 67 Effectively, Cusanus’ experiment seems to implicitly follow Aristotle’s famous definition of time as the “number of movement in respect of the before and after” in Physics IV (220a 24–25). Here, indeed, Aristotle stresses that “Not only do we measure the movement by the time, but also the time by the movement, because they define each other. The time marks the movement, since it is its number, and the movement the time. We describe the time as much or little, measuring it by the movement, just as we know the number by what is numbered, e.g. the number of the horses by one horse as the unit” (220b 15–21).

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The second remark is that not yet having a definitive geometricomathematical understanding of space and time as absolute dimensions, Cusanus settles for simply relating two different quantities (according to the traditional model) nor even he attempts to measure the pulse beat in terms of numerically expressed distances, as Santorio Santorio (1561– 1936) would do thanks to the use of his pulsilogium device.68 Hence, this quantitative understanding of the natural phenomenon is still limited to comparative reasoning transposed to the level of (more precisely, since observable) quantities.69 Hence the problem of whether and how human physiology can be quantified calls into question a range of new premises, emerging in the late Renaissance. As of the sixteenth century, a mentality of precision became increasingly common, likely coming from the worlds of

68 Interstingly, Santorio’s colleague Ippolito Obizzi would contend that Santorio’s aphorisms are “direct plagiarism of Cusa’s statical trials in the dialogue Idiota”. See Fabiola Zurlini, ‘The Uncertainty of Medicine: Readings and Reactions to Santorio Between Tradition and Reformation (1615–1721)’, in Santorio Santori and the Emergence of Quantified Medicine, 1614–1790: Corpuscularianism, Technology and Experimentation, ed. by F. Bigotti and J. Barry (Cham: Palgrave Macmillan, 2022), 103–117, here 107–108. On the pulsilogium see Fabrizio Bigotti and David Taylor, ‘The Pulsilogium of Santorio: New Light on Technology and Measurement in Early Modern Medicine’, Societate si politica 11, 2 (2017), 53–113; Fabrizio Bigotti, David Taylor and Joann Welsman, ‘Recreating the Pulsilogium of Santorio: Outlines for a Historically-Engaged Endeavour’, Bulletin of the Scientific Instrument Society, 133 (2017), 30–35. 69 Nonetheless, Cusanus’ understanding of weight is far from being a merely physical

notion, and seems to be designed to identify more essential properties of species of beings than individual properties of individual beings: “it seems that the weight of each thing would have to be considered as the mean of its different weights at different latitudes. For example, if the weight of a man in comparison to [the weight of] some other animal were to be considered, then the man would have to be considered not as a northerner or as a southerner (where in both directions there is an extreme) but rather as an inhabitant of an in-between latitude”. As is well-known, Cusanus’ ideas and experiments would pique the interest of many, among which Jean Baptiste van Helmont (1579–1644) and Kepler in the seventeenth century, who endeavored (respectively) to continue his metaphysics of weights (see Walter Pagel, ‘The Position of Harvey and Van Helmont in the History of European Thought: To Commemorate H. E. Sigerist’s Essay on Harvey (1928)’, Journal of the History of Medicine and Allied Sciences 13, 2 (1958), 186–199; Hoff, ‘Nicolaus of Cusa, van Helmont, and Boyle: The First Experiment of the Renaissance in Quantitative Biology and Medicine’, 108–110, and Kümmel, ‘Der Puls und das Problem der Zeitmessung in der Geschichte der Medizin’), and to more precisely quantify pulse (see Kümmel, ‘Der Puls und das Problem der Zeitmessung in der Geschichte der Medizin’).

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mathematical sciences,70 craft, engineering,71 printing, trade,72 pharmacology and especially alchemy and chemistry, ultimately to affect the world of physiology and medicine. As is well-known, this conceptual revolution was led by a re-evaluation of the function of technological devices, including those used in measurement. Over the entire ancient and medieval period, instruments “had no other function than to operate as tools, capable of expanding the power of man’s power” and were used “especially in practical activities – in architecture, in navigation and to exert the art of war”, “as of the sixteenth century, a new phenomenon occurs, i.e. focusing the idea of the scientific instrument and its enhancement for the purposes of scientific research, in which it plays an essential role”.73 Renaissance Galenism is somehow sensitive to these attempts to develop forms of precision, even though it appears to be still marked by the idea that measuring consists in establishing mutual proportions, linear distances, and degrees between different magnitudes and intensities. In that, Renaissance natural philosophy could take advantage of the pioneering work put forward by Aristotelian eclecticism which, over the fourteenth century, circumvented Aristotle’s ban on understanding qualitative essences and changes in quantitative terms. Beginning with Buridan and Oresme,74 these authors already carried out seminal attempts to quantify intensities, still based on the logic of degrees and proportional ratios.75 In other words, “the establishment of a complete dialogue between quantified theory and quantified theoretical and experimental 70 See Morris Kline, Mathematical Thought from Ancient to Modern Times, vol. 1 (New York, Oxford: Oxford University Press, 1972), 216–249. 71 See especially Paolo Rossi, I filosofi e le macchine (1400–1700) (Milano: Feltrinelli, 2002), 25–78. 72 This aspect is particularly important. See Frank J. Swetz, Capitalism and Arithmetic: The New Math of the 15th Century, translated by D. E. Smith (Le Salle: Open Court Publishing, 1987). 73 Beretta, Storia materiale della scienza, 25 (our translation). 74 But already with Arnaldus de Villa Nova’s Aphorismi de gradibus (1303). 75 See again Roudaut, La mesure de l’être; Di Liscia and Sylla, Quantifying Aris-

totle; Sylla, ‘Medieval Quantifications of Qualities’; Murdoch, ‘Mathesis in philosophiam scholasticam introducta’, and Mcvaugh, ‘Quantified Medical Theory And Practice At Fourteenth-Century Montpellier’, Bulletin of the History of Medicine, 43, 5 (1969), 397– 413; Joel Kaye, A History of Balance, 1250–1375 (Cambridge: Cambridge University Press, 2014).

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procedure, between episteme and techne” is embryonic already in late Renaissance, even though it “is one of the principal changes that occurred in the seventeenth century”.76 The combination of these new attitudes fostered proto-allometric quantitative efforts in medicine, particularly with respect to matching quantitative information about weight, diet, and age, as well as attempts to measure the intensities of Galenic complexio as a balanced state of elements and humors, and as a key condition for health. Such measurements remain however conceived in terms of degrees and proportional distances. Salvo Sclano’s Commentaria on Galen (1597) is a good example of this latter tendency. It advances seminal forms of visual/spatial representation of health and illness with the idea of proportional degrees into which different humoral combinations can be mutually related.77 In his work, Sclano translates the Galenic notion of latitudo sanitatis in figurative terms (Fig. 1), as he represents health, illness, and the intermediate state as three consecutive triangles. Each diagram is further divided into degrees, representing as many states of departure from the ideal state of absolute health. Even though these notations are non-numerical, the spatial distribution of health and illness clearly leans toward some form of quantitative understanding of these fundamental medical concepts. And it establishes visual degrees and different proportions between qualitative states of the body via their statistical distribution. At the same time, other attempts at more precisely quantifying human physiology specifically concerned the pulse and the blood, even if these practices were thought up within the idea of the human body conceived as a natural unit of measure, and of measuring as based on linear distances and degrees. For instance, already in his De proportionibus (1570), Cardano reported having taken a quite accurate measurement of the human pulse in an hour (1000 beats), but he explains that he used this measure as a natural clock to calculate the speed of the movement of the air or the moon at great distances.78 Likewise, in the same work, he 76 Alistar Cameron Crombie, ‘Quantification in Medieval Physics’, Isis, 52, 2 (1961), 143–160. 77 Salvo Sclano, Commentaria in tres libros artis medicinalis Galeni (Venice: apud Ioannem Guerrilium, 1597), 243. We owe this reference to Fabrizio Bigotti. 78 Girolamo Cardano, De proportionibus (Basel, 1570), 50. See Kümmel, ‘Der Puls und das Problem der Zeitmessung in der Geschichte der Medizin’, 5.

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Fig. 1 The Latitudo sanitatis from Salvo Sclano’s Commentaria (1597)

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describes a kind of sophisticated chronometer (the Instrumentum Acolingen) he devised for calculating quantities of time, and which was based entirely on the unit of measure of the human pulse.79 In 1577, Leonardo Botallo (1530–1587) endeavored instead to determine the quantity of fresh blood produced daily by the liver.80 Interestingly, Botallo (like Galen) was aware of the impossibility of establishing universal and definitive values, depending on individual aspects such as one’s weight, activities, health, and the quantity of food consumed. Furthermore, he acknowledged the impossibility of exactly and directly measuring the amount of blood produced,81 but he nevertheless tried to quantify it by reasoning, i.e. by matching information about the quantity of food ingested and the quantity of blood expelled by haemorragics.82

4

The Quanti-Mathe-Mechanization of Nature and the Human Body as a Laboratory

In this volume, we primarily tell the story of the reassessment of many of the aforementioned philosophical premises recalled above, and the transformation of the body into a strategic laboratory for the development and the confirmation of a renewed quantitative conception of nature. In order to understand this specific passage, we should think of the mathematization and quantification of nature that took place between the seventeenth and eighteenth centuries not only as the rise of what

79 Cardano, De proportionibus, 80. 80 Leonardo Botallo, De curatione per sanguinis missione (Leiden: Huguetan, 1577),

159–164. See Bylebyl, ‘Nutrition, Quantification and Circulation’, 375–377. As noted by Bylebyl, here Botallo already refers to ‘insensible transpiration’, but without measuring it. On the other hand, this notion were circulated since the ancient period. As Lloyd, The Revolutions of Wisdom, 255, remarks, already Erasistratus “in a remarkable experiment recorded in Anonymus Londinensis, tried to prove that animals emit invisible effluvia, by keeping a bird in a closed vessel without food for a period and then weighing the bird and its visible excreta. Comparing this with the original weight, he found, we are told, that there had been a ‘great loss of weight’”. For other cases see Renbourn, ‘The Natural History of Insensible Perspiration: A Forgotten Doctrine of Health and Disease’. 81 Botallo, De curatione, 163–164. 82 Bylebyl, ‘Nutrition, Quantification and Circulation’, 375–377. Another case is that

of Fabrici d’Acquapendente. See Fabrizio Bigotti, ‘Logic, geometry and visualisation of the body in Acquapendente’s rediscovered Methodus anatomica (1579)’, Medical History, 65, 3 (2021), 227–246.

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we consider to be a proper scientific methodology. It is also—according to Bacon’s famous iconography in the frontispiece of his Great Instauration—a new exploration of the world which would not culminate until the late eighteenth century. Or, to speak in Kuhnian terms, a revolutionary phase. This venture is a process of re-evaluating nature in quantitative terms that constantly overlapped with the old paradigms, and passes at once through countless specific attempts. The constellations of novelties from the sixteenth and seventeenth centuries that shed the old image of the world by offering the chance to see it in quantitative terms were so numerous and so famous that it would be impossible to mention all of them here. Instead, it is important to stress here two particular aspects of what we call the ‘scientific revolution(s)’. The first aspect is that only in the middle of the scientific revolution did philosophers and scientists realize that they were contributing to shaping a new understanding of quantity; that is, of progressively leaving the traditional model behind and transforming the social, economic, industrial, and cultural world around them. This notion retains its roots in the traditional, metaphysical connotation of quantitas under the famous abstraction that wants mathematics to be the language into which our world has been written, and hence through which it can be read. Yet at the same time, it is somehow inseparable from the new methods of observing, classifying, reconstructing, and above all measuring the natural phenomena that have shaped it, at once discovering new understandings of matter, its inner structure, its conditions, and its properties. This emerging idea of quantity is indeed a notion that, even though remaining terminologically and conceptually linked to its Greek understanding, is elaborated outside the books. It proceeds via laboratories, experiments, new devices, and discoveries, as an open conception that only its operationalization can define.83 This turns this journey into 83 Operationalism’ is a current of contemporary epistemology of physics founded by Percy Williams Bridgman (1882–1961), especially in his work The Logic of Modern Physics (New York: Macmillan Company 1958 [1927]), 3ff. It “is based on the intuition that we do not know the meaning of a concept unless we have a method of measurement for it. It is commonly considered a theory of meaning which states that ‘we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations’” (Hasok Chang, ‘Operationalism’, The Stanford Encyclopedia of Philosophy (Fall 2021 Edition), ed. by E. N. Zalta. See also Hasok Chang, Inventing Temperature. Measurement and Scientific Progress (Oxford: Oxford University

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a constant compromise between old conceptions of quantity and new emerging ones, multiplying this notion in all the points of conjunction between its past and present forms. The second aspect is that all of the natural and philosophical breaks of early modernity—the Copernican revolution, Vesalius’s explorations in anatomy, the rebirth of ancient Pyrrhonism, the discovery of analytic geometry, the idea of an ultimate mathematical foundation of the physical world and of human knowledge along with the rise of a technological culture as a successful extension of experimentalism—converge as in a crucial and common meeting point on the problem of the body and its physiology. Due to a specific cosmological configuration mentioned above, none of these novelties could have changed the image of the natural macrocosmos without simultaneously delving into the microcosmos of the body, especially the human one. And the venture of understanding natural phenomena by attributing to them a precise measurement, needed to pass through the precise measurement of human physiology, as well as through a quantitative conception of the very notions of ‘life’ and ‘health’. From a widespread and rather cliché narrative, one could thus say that this adventure of the early modern quantification of the body followed that of the general quantification of the physis as a part, or a consequence, of it. But on second and more attentive thought, it is quite evident that the experimental approach to the macrocosmos goes handin-hand with an attempt to quantify the body and its living functions, itself the outcome of a common previously standing debate over method

Press, 2004), esp. 159–219. On the other hand, as Kuhn (Thomas S. Kuhn, ‘The Function of Measurement in Modern Physical Science’, Isis, 52, 2 (1961), 161–193, here 188–189) argues through the significant example of the thermometer: “many of the early experiments involving thermometers read like investigations of that new instrument rather than like investigations with it. How could anything else have been the case during a period when it was totally unclear what the thermometer measured? Its readings obviously upon the ‘degree of heat’ but apparently in immensely complex ways. ‘Degree of heat’ had for a long time been defined by the senses, and the senses responded quite differently to bodies which produced the same thermometric readings. Before the thermometer could become unequivocally a laboratory instrument rather than an experimental subject, thermometric reading had to be seen as the direct measure of ‘degree of heat’, and sensation had simoultaneously to be viewed as a complex and equivocal phenomenon dependent upon a number of different parameters”.

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as advanced by sixteenth-century philosophers.84 If Galileo Galilei (1564– 1642) published his Sidereus Nuncius in 1610, his colleague Santorio— who had already given his Methodi vitandorum errorum omnium to the printer in 1602—would have published his Ars de statica medicina soon after in 1614.85 And despite the fact that Sanctorious’ work has been read erroneously for decades as an embodiment of Galileo’s ideas in medicine,86 it rather constitutes an autonomous and as important research path to that of other great scientists of his time. In the story we tell here, Santorio’ oeuvre can be seen as a watershed, as he associated medical experimentalism guided by quantitative reasoning, appropriate instrumentation, and the utmost accuracy in carrying out scientific observations. As has recently been argued, his endeavor to quantify the human metabolism via the measurement of the perspiratio insensibilis, he “turns out to be part of a wider and fully fletched programme of quantification”, which includes, not by accident, a radically corpuscular understanding of matter.87 Santorio’s program “grapples with the homeostatic balance of the body in its complexity: from weight change to pulse frequency, from body temperature to the

84 It is especially the case of Jacopo Zabarella, as noted by Fabrizio Bigotti and Jonathan Barry, ‘Introduction’, in Santorio Santori and the Emergence of Quantified Medicine, 1614– 1790, 1–63, here 9 and in the same volume (65–102) Fabrizio Bigotti, ‘“Gears of an Inner Clock’: Santorio’s Theory of Matter and its Applications”, here 67. See William F. Edwards, ‘Paduan Aristotelianism and the Origins of Modern Theories of Method’, in Aristotelismo veneto e scienza moderna, ed. by L. Olivieri (Padua, 1983), 205–220, and here also Wilhelm Risse, ‘Zabarellas Methodenlehre’ (155–172), Paolo Rossi, ‘Aristotelici e moderni: le ipotesi e la natura’ (125–154) and Giovanni Papuli, ‘La teoria del regressus come metodo scientifico negli autori della Scuola di Padova’ (221–277). See also Heikki Mikkeli ‘The Foundation of an Autonomous Natural Philosophy: Zabarella on the Classification of Arts and Sciences’, in Method and Order in Renaissance Philosophy of Nature. The Aristotle Commentary Tradition, ed. by D. Di Liscia, E. Kessler and C. Methuen (Aldershot: Routledge, 1997), 211–228; id., ‘Jacopo Zabarella (1533–1589): The Structure and Method of Scientific Knowledge’, in Philosophers of the Renaissance ed. by P. R. Blum (Washington, DC: The Catholic University of America Press, 1997), 181–191. 85 As for the relationship between Santorio and Galileo see Bigotti and Barry,

‘Introduction’. 86 Such subalternity has been questioned recently, especially by Bigotti and Barry, ‘Introduction’. 87 See Bigotti and Barry, ‘Introduction’, 38. For more see Fabrizio Bigotti, ‘Gears of an Inner Clock’: Santorio’s Theory of Matter and its Applications’, in Santorio Santori and the Emergence of Quantified Medicine, 65–102.

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humidity of the air, to the ultimate structure of matter”.88 He can be credited for three major innovations in particular: [1] Equilibrium is defined as a standard problem of ‘statics’ consisting in the capacity of the body to re-balance daily losses and gains. [2] The focus of medicine is shifted from the study of multiple Galenic faculties to the evaluation of a single, fundamental, and quantifiable process (metabolism). [3] Instruments of precision are invented and then applied in everyday practice to correct and replace the subjective appreciation of natural phenomena.89

Yet, besides its novelty, Santorio’s stance is emblematic of the ideas circulating at the beginning of the seventeenth century, not only because it consisted of a substantial rejection of the traditional methods, but also because of some of the notions at stake in this renewal, which were only partially new. Keeping the Galenic idea of latitudo sanitatis , “Santorio’s instruments are meant to provide a measure of such a distance”,90 as “operationalisation[s] of the Galenic concept of intensity”.91 Indeed, “he considers them as devices that extend the perception of the physician beyond his usual limits by allowing him to spatially visualize the difference between normal and pathological conditions as well as necessary aids in order to avoid errors in diagnosis”.92 Despite Santorio’s mechanical framework and conception of matter, his use of quantifying instruments and mathematization was not yet aimed at newly understanding human metabolism as an entirely physicomathematical phenomenon. It was rather addressed at enhancing conjectural reasoning by “expand[ing] the limits of human perception and correct[ing] the fallacies implicit in an unwarranted generalization of empirical data”,93 so as to confirm, by its operationalization, the Galenic idea that illness can be represented as degrees of separation from the 88 Bigotti and Barry, ‘Introduction’, 38. 89 Ibid. 90 Ibid., 35. 91 Fabrizio Bigotti, ‘The Weight of the Air: Santorio’s Thermometers and the Early

History of Medical Quantification Reconsidered’, Journal of Early Modern Studies, 7, 1 (2018), 73–103. 92 Bigotti and Barry, ‘Introduction’, 35. 93 Bigotti, ‘“Gears of a Inner Clock”’, 90.

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healthy and natural condition, and quantified by breaking these degrees down: I make use of four instruments by means of which I ascertain the quantity of this distance [from the natural condition]. The first one is an instrument that I invented and is called a pulsilogium, through which we grasp how much in each day each individual departs from their best condition. The same result is provided by the second instrument, by means of which, by putting in movement a leaden ball attached to a suspended thread and, from its movement on the thread, and from the greater or smaller lengthening, anyone will be able to observe the natural motion of the pulse and its distance from the natural condition.94

At the same time, the exploration of these new paths raised questions that were not only physiological, but even philosophical, specifically in the psychological and moral senses.95 Santorio’s investigation ended up 94 Santorio Santorio, Commentaria in Artem Medicinalem Galeni libri tres (Leiden: ex Officina Johannis Pillehotte 1631 [1612]), Tertia pars, 842a–b. Translation from Bigotti and Barry, ‘Introduction’, 35. See also Santorio Santorio, Commentaria in primam fen primi libri canonis Auicennae (Venice: apud Iacobum Sarcinam, 1625), 215: “…sunt aliae tres causae, quae medicinam efficiunt coniecturalem: quarum prima est morborum quantitatis, de qua loquens Galenus 9 Methodi cap. 15 habet hanc sententiam: ut verum exhibeatur remedium non solum oportet cognoscere morbi speciem, sed etiameius quantitatem, quae est certa mensura recessus a statu naturali, quam sola coniectura assequi possumus. Nos vero instrumentis variis adinvenimus quantitates sive certas affectuum mensuras ante nos non animadversas; sicuti pulsilogio certam mensuram frequentiae, et raritatis pulsus reperimus”. Likewise, it is also interesting to note that also Santorio’s notion of ‘temperature’, which he measured by his thermometers, “was not the modern one. For Santorio, the reference point for measuring the temperature of a body was the ‘temperate state’ of that same body, i.e. the state in which hot and cold balanced each other exactly. Thus, in Aristotelian-Galenic terms, a healthy human body, a healthy animal and a temperate climate would all have had the same Aristotelian-Galenic ‘temperature’: a temperate one. It is not by chance that the ‘temperature’ of human blood remained a fixed point” (Arianna Borrelli, ‘The Weatherglass and its Observers’, in Philosophies of Technology. Francis Bacon and His Contemporaries, ed. by C. Zittel et al. (Leiden, Boston: Brill, 2008), vol. 1, 67–130, here 111). See then Bigotti, ‘The Weight of the Air’, agreeing with Borrelli’s reading. As noted by Fabrizio Bigotti ‘Mathematica Medica: Santorio and the Quest for Certainty in Medicine’, Journal of Healthcare Communications, 1, 4 (2016), and by Bigotti and Taylor, ‘The Pulsilogium of Santorio’, Santorio even speaks of ‘mathematical certainty’: “The first instrument is our pulsilogium, by means of which we can measure with mathematical certainty and not by conjecture the utmost degree of how much the pulse…” (Bigotti and Taylor, ‘The Pulsilogium of Santorio’, 89–90). 95 See Jan Purnis’ paper in this volume and Fabrizio Baldassarri, ‘Santorio, Regius, and Descartes: The Quantification and Mechanization of the Passions in Seventeenth-Century

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addressing some very relevant questions. For instance, that of the nonconscious aspects of our metabolism (dependent or independent of the activity of the soul), or the relationship between invisible perspiration and the passions of the soul. And, even more interestingly for today’s readers, Santorio explored and for the first time accurately reported the subjective experience of an embodied mind objectifying its own body through the practice of understanding its body in terms of machineries and instrumental quantification.96 Admittedly, while this endeavor could be seen as more literary than scientific, it should not be altogether neglected. As we constantly argue in this book, physicians and philosophers have continuously swapped their perspectives over the whole history of the quantification of bodies up until even today. The complexity of the human body, its philosophical, moral, cultural, and psychological imports, raise questions for the physician that go beyond the limits of medicine. At the same time, the new methodologies, instruments, and discoveries developed by physicians confront philosophers from several angles and press them to refine their models. However, besides these aspects, Santorio is not alone in embodying new experimental devices and doctrinal elements into traditional theories, as this can be seen in all the great reformers of early modern science. Herein, though, one sees a still ambivalent notion of quantification, that overcomes the qualitative and subjective ‘more or less’ and sets to work the precision of quantitative relationships without really mathematizing the natural phenomena within a geometrico-mechanical model of the whole physical world. And it is no coincidence that a similar stance can be found in another great contemporary of Santorio, Francis Bacon, who

Medicine’, in Santorio Santori and the Emergence of Quantified Medicine, 1614–1790, 165–190. 96 On this aspect see especially Fenneke Sysling, ‘Introduction’ to Measurement, SelfTracking and the History of Science, ed. by Fenneke Sysling, special issue of History of Science 58, 2 (2020), 108–115.

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systematically used measurement to quantify his experiences,97 without grafting them onto a geometrico-mathematical model of nature. In order to make instrumentally driven quantification a phase of the mathematization of natural phenomena, it is of course crucial to have a mathematico-mechanical model of nature, and a notion of matter that entirely fits with this model. As is well-known, these elements were already present in Galileo, but reached their apex with the introduction of entirely geometrical notions of matter and space, as well as of analytic geometry and eventually the calculus; so, under the mutual auspices of Cartesianism and, above all, Newtonianism. Yet this implies that over the various phases of this passage in the seventeenth century, several understandings of quantity overlapped through different mechanist views of the relationship between mathematics and nature, and for several decades the notion of quantity wavered between new and old understandings of the mathematics applied then to physics: Galileo used the Euclidean-Eudoxian language of proportions to express the law of free fall, formulating it in terms of ratios between distances and the squares of elapsed times, rather than as a second-degree equation linking distance covered to elapsed time. Because the 1637 publication of Descartes’ Géométrie marked the first appearance of analytic geometry, it is no surprise that Galileo did not employ its techniques to state his results. Nevertheless, the Galilean preference for the traditional language of ratios and proportions reminds us that the mathematics employed by seventeenth-century natural philosophers is, in many cases at least, firmly rooted in classical Greek doctrines. Even Newton, who developed his

97 See Silvia Manzo’s paper in this volume and Graham Rees, ‘Quantitative Reasoning in Francis Bacon’s Natural Philosophy’, News from the Republic of Letters, 2 (1985), 32– 33; id., ‘Mathematics and Francis Bacon’s Natural Philosophy’, Revue Internationale de philosophie, 40, 159 (1986), 399–426; Cesare Pastorino, ‘Weighing Experience: Experimental Histories and Francis Bacon’s Quantitative Program’, Early Science and Medicine, 16, 6 (2011), 524–570; Dana Jalobeanu, ‘“The Marriage of Physics with Mathematics”’: Francis Bacon on Measurement, Mathematics, and the Construction of a Mathematical Physics’, in The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the 17th Century, ed. by G. Gorham, B. Hill, E. Slowik, C. K. Waters (Minneapolis, London: University of Minnesota Press, 2016), 51–80.

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calculus of fluxions some two decades before the publication of the Principia, chose to develop his celestial mechanics in the classical language of ratios and proportions drawn from book 5 of the Euclidean Elements.98

However, despite this conceptual confusion, the quantification of the body, life, and health continued in the form of a pragmatic, often goal-oriented, exploration of new scientific opportunities offered by the mechanical model. In the aftermath of William Harvey (1578– 1657)’s De motu cordis (1628) (which introduced not only the pivotal notion of blood circulation, but also some quantitative arguments for it)99 this mathematically more mature mechanism would arouse—under the general understanding of ‘life’ as the “circulation of the blood produced by the hearth and the arteries”100 —the endeavors of the most industrious and gifted minds of the seventeenth and eighteenth centuries. Within the matter of a few decades, this effort resulted indeed in the mechanization, mathematization, and quantification of most of ‘animal economy’; especially bodily fluids—notably the quantity of blood (Giovanni Alfonso Borelli [1608–1679], James Keill [1673–1719])—, 98 On Barrow See also Douglas Jesseph, Ratios, Quotients, and the Language of Nature, in The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the 17th Century, 160–177, here 160. Jesseph especially stresses the contrast between Barrow’s and Wallis’ understandings of mathematics. See also Derek Thomas Whiteside, ‘Patterns of mathematical thought in the later seventeenth century’ Archive for History of Exact Sciences, 1 (1961), 179–388. 99 See especially F. R. Jevons, ‘Harvey’s Quantitative Method’, Bulletin of the History of Medicine, 36, 5 (1962), 462–467; Walter Pagel, William Harvey’s Biological Ideas: Selected Aspects and Historical Background (Basel-New York: S. Karger), 71–88; Roger French, ‘Harvey in Holland: Circulation and the Calvinists ’, in The Medical Revolution, ed. by R. French and A. Wear (Cambridge: Cambridge University Press, 1989), 46–86; Roger French, William Harvey’s Natural Philosophy (Cambridge: Cambridge University Press, 1994), 90–91. See here 90: “Harvey was seeking to defend his thesis of the forceful systole by showing that blood emerged from the heart with some force and in some quantity. If only as little as one-eighth of the contents of the ventricle - perhaps a drachm in weight - was ejected at each systole, then in the course of half an hour, 1,000 heartbeats later, 1,000 drachms of blood will have been ejected from the heart, argued Harvey”. Another great figure to associate to Harvey is certainly Jean Pecquet (1622–1674), who in his New Anatomical Experiments (London, 1653) for the first time treats circulation systematically. Pecquet discovered the lacteal vesselss and drew on his experiments with the barometer to explain systole and diastole in terms of weight and air pressure. See Holmes, ‘The Physical Sciences in the Life Science’, 221–222. 100 Archibald Pitcairne, The Whole Works of Dr. Archibald Pitcairn (London: E. Curll 1727 [second edition]), 99.

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muscular activity, including pulse and the force of the ventricular contraction and blood pressure (Borelli, Richard Lower [1631–1691], Nicolas Steno [1638–1686], Lorenzo Bellini [1643–1704], Johann Bernoulli [1667–1748], Giorgio Baglivi [1668–1707], Keill, Stephen Hales [1677– 1761], Bryan Robinson [1680–1754]), digestion (Borelli, Archibald Pitcairne [1652–1713]), respiration (Borelli) and the endocrine and the nervous system, including the brain (Thomas Wharton [1614–1673], Steno). Not to mention those—as John Floyer (1649–1734)—who worked on precise techniques for the calculation of the pulse even when at odds with the overall framework of iatromechanism.101 Yet, it should be stressed again that iatromechanics was not only a frontier of early modern science, but also an attempt to explore the physiology of the body in parallel with nature. This is why this process elicited several philosophical puzzles and reactions—not only in more conservative philosophies—and turned the mechanization of life sciences into a strategic conceptual laboratory for the dialogue between medicine and philosophy. Indeed, if mechanistic philosophy was used to establish specific uses for mathematics in medicine, medicine was expected in turn to improve the precision of the observations and reasoning of mechanistic philosophy, to a level that was compatible with mathematics.102 This venture inspired many crucial reflections within the overall body of the ‘new science’, and undoubtedly contributed to the enrichment of its theoretical capacity. Here, we can mention at least six major questions that together outline a single conceptual perimeter in the early modern age: first, an insightful epistemological reflection on the role of experimental devices in natural research, as well as on the epistemological nature of an instrumentally driven science; second, a proper interrogation of the human sensory experience and experimental reasoning in the construction of complete knowledge of nature, especially with respect to the traditional empirical nature of medicine and to the possible reassessment of the notion of ‘natural history’; third, how—and from what premises—to approach what is invisible to the human eye, and even what is not observable by instrumentation, but lies at the ground of physiological process, and whether hypothetical reasoning should or should not be invoked in these cases; four, a reflection on the notion of ‘data’, its distinction from

101 See Storni’s chapter in this volume. 102 See the papers by Ottaviani and Guidi in this volume.

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experience and its treatment as a specific cognitive item, even in mathematical terms; five, the relationships between mechanical physics and chemistry, as well as those between iatromechanism and iatrochemistry, their mutual compatibility and their possible dialogue; six, the epistemological status of mathematization itself, and especially the question of whether ‘life’ and ‘health’ can be entirely reduced to a geometricomathematical model, or rather result from the combination of multiple dimensions of nature.

5 The Fall of Mechanization and the New Life of Quantity Over the late seventeenth and the early eighteenth centuries, physicians and natural philosophers enthusiastically welcomed the mechanization of physiology, which fit perfectly within the ‘quantifying spirit’103 of the era. The early and the mid-eighteenth century especially witnessed a strong rooting of the new tree of science within society, economy, science, politics, and philosophy, and in these decades, scientific practice underwent a radical change, fostered by the rise of systematics and of statistical methods. An idea that was already embryonic among the great minds of the seventeenth century, like Jacob Bernoulli (1655–1705) and Christiaan Huygens (1629–1695), but is applied in health especially by John Graunt (1620–1674), William Petty (1623–1687), Jan de Witt (1625–1672), and Jan Hudde (1628–1704).104 Furthermore, the ideal of a universal mathematical language accompanied the development of more accurate measurement devices, matching the introduction of more precise units of measurement.105 103 See especially The Quantifying Spirit in the 18th Century, ed. by T. Frängsmyr, J. L. Heilbron, and R. E. Rider (Berkely, Los Angeles, Oxford: University of California Press, 1990). See also Kula, Measures and Men. 104 See Ander Hald, A History of Probability and Statistics and Their Applications before 1750 (New Jersey: Wiley, 2003) and Lorraine Daston, Classical Probability in the Enlightenment (Princeton: Princeton University Press, 1988); Lancaster, Quantitative Methods in Biological and Medical Sciences, 58–72. Seminal elements of medical statistics are already in Santorio himself; see Bigotti, ‘The Weight of the Air: Santorio’s Thermometers and the Early History of Medical Quantification Reconsidered’. 105 See John L. Heilbron, ‘The Measure of Enlightenment’, in The Quantifying Spirit in the 18th Century, 207–242; Theodor M. Porter, ‘Perspective Economics and the History of Measurement’, History of Political Economy, 33 (2001), 4–22.

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This process involved medicine too, which had already been affected by the establishment of a more accurate conceptual domain for ‘biology’.106 However, as for the challenges opened by the quantification of life sciences and medicine, their solution would end up being more complicated than expected, thus being a harbinger of new epistemological problems to come. Many of the questions enumerated above were, in fact, destined to remain unanswered and to meet further obstacles in the ability of the mechanical model to explain life, health, and illness. How are we to explain, in purely mechanical terms, puzzling phenomena like animal (and vegetal) reproduction?107 Are health and illness entirely geometrico-mechanical notions? And, somehow more importantly for medicine: even if the entire ‘animal economy’ could be translated into physico-mathematical terms, would diagnostics and pathology really be able to take any advantage of this translation? In the mid-eighteenth century, these and several other issues brought the dialogue between medicine and philosophy to the stage as described in the entry for Pouls in the Encylopèdie, authored by Jean-Joseph Menuret de Chambaud (1739–1815)108 —a French physician who championed many of the ideas of the Montpellier vitalist school109 : The etiology of the pulse developed in the system of the Mechanists appeared at first glance to be quite satisfactory; it received a new and

106 See especially Jacques Roger, The Life Sciences in Eighteenth-Century French Thought (Standford: Stanford University Press, 1998), parts II and III. 107 See Roger, The Life Sciences, 205–366 and Priarolo’s chapter in this volume. 108 See Storni’s paper in this volume. 109 See Elizabeth A. Williams, A Cultural History of Medical Vitalism in Enlightenment

Montpellier (London: Routledge, 2017) and already ead., The Physical and the Moral: Anthropology, Physiology, and Philosophical Medicine in France (1750–1850) (Cambridge: Cambridge University Press, 1994), 20–175; Roselyne Rey, Naissance et développement du vitalisme en France de la deuxième moitié du 18 e siècle à la fin du Premier Empire (Oxford: Voltaire Foundation, 2000). Raffaele Carbone, Medicina e scienza dell’uomo. Paul-Joseph Barthez e la Scuola di Montpellier (Naples: Federico II Univeristy Press / FedOA Press, 2017). See also Charles T. Wolfe and Motoichi Terada, ‘The Animal Economy as Object and Program in Montpellier Vitalism’, Science in Context, 21, 4 (2008), 537–579; by Wolfe see also ‘Vitalism and the Resistance to Experimentation on Life in the Eighteenth Century’, Journal of the History of Biology, 46 (2013), 255–282 and ‘On the Role of Newtonian Analogies in Eighteenth-Century Life Science. Vitalism and Provisionally Inexplicable Explicative Devices, in Newton and Empiricism, ed. by Z. Biener and E. Schliesser (Oxford: Oxford University Press, 2014).

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greater articulation, more impressive than its alleged agreement with the laws of mechanics, by the calculations with which it has been entangled, and under which it has actually been wrapped; it seemed that it should participate in the truth and the demonstration which is thought to be inseparable from the mathematical sciences, and which is indeed so when they are well applied. But it is easy to see, by the few successes of illustrious scholars, by the gross errors into which they have fallen, by their prodigious variety on the same point – see the works of Keill and Borelli – […], that geometry is in no way applicable to the physics of the human body.110

Likewise, d’Alembert himself famously criticized the application of mechanical science to the human organism, and thereby banned “any calculation allowing the establishment of constant relations between the quantities entering into the movement of that machine that the body is”.111 It is worth reading his words inscribed in one of the most influential works of the early modern age: geometers sometimes abuse this application of algebra to physics. Lacking appropriate experiments as a basis for their calculations, they permit themselves to use hypotheses which are most convenient, to be sure, but often very far removed from what really exists in Nature. Some have tried to reduce even the art of curing to calculations, and the human body, that most complicated machine, has been treated by our algebraic doctors as if it were the simplest or the easiest one to reduce to its component parts. […] As for us who are wiser or more timid, let us be content to view most of these calculations and vague suppositions as intellectual games to which Nature is not obliged to conform, and let us conclude that the single true method of philosophizing as physical scientists consists either in the application of mathematical analysis to experiments, or in observation alone, enlightened by the spirit of method, aided sometimes by conjectures when

110 Jean-Joseph Menuret de Chambaud, ‘Pouls, in Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, vol. 13 (1765), 219 (our translation). 111 Jean-Luc Martine, ‘De la machine à la mecanique, l’article “mechanique” de l’Encyclopédie’, in Les Lumières en mouvement: La circulation des idées au XVIIIe siècle, ed. by I. Moreau (Lyon: ENS Éditions, 2009), 268.

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they can furnish some insights, but rigidly dissociated from any arbitrary hypotheses.112

As is well-known, one can find several similar affirmations over the entire eighteenth century, when vitalism reappeared in all its philosophical strength. Here, it accompanies new interpretations of the notion of ‘force’, sometimes metaphorical ones,113 that would trigger the development of an active notion of matter that was irreducible to the passive substratum of geometrico-mathematical properties.114 At the same time, Albrecht von Haller’s (1708–1777) notions of ‘irritability’ and ‘sensibility’,115 —which called into question the law of the equality of action and reaction, as well as the idea of purely quantitative interactions at the foundation of all natural phenomena—famously emerged as pivotal elements against the full mechanization of the organism.116 As for medicine, much has been said and written on this passage which today’s scholars have seen either as an abrupt abandonment of the paths taken by Descartes and Newton117 or as its legitimate evolution.118 112 Jean Le Ronde d’Alembert, ‘Discours préliminaire des editeurs’, in Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, vol. 1 (1751), VII (our translation). 113 See Wolfe, ‘On the Role of Newtonian Analogies in Eighteenth-Century Life Science’. 114 See especially Stephen Gaukroger, The Collapse of Mechanism and the Rise of Sensibility. Science and the Shaping of Modernity, 1680–1760 (Oxford: Oxford University Press, 2011), 328–383. See also Sara Landreth, ‘Science in the Long Eighteenth Century’, in The Cambridge Companion to Eighteenth-Century Thought, ed. by F. De Bruyn (Cambridge: Cambridge University Press, 2021), 58–97 and Jean-Claude Guédon, ‘Chimie et matérialisme: la stratégie anti-newtonienne de Diderot’, Dix-Huitième Siècle, 11 (1979), 185–200. 115 See Hubert Steinke, ‘Haller’s Concepts of Irritability and Sensibility and Their Reception in France’, in Mécanisme et vitalisme, ed. by M. Saad (La lettre de la Maison française d’Oxford, 2001), 37–69, id. ‘Irritating Concepts: Haller’s Concept and the European Controversy on Irritability and Sensibility, 1750–1790’ (Amsterdam: Rodopi, 2005) and Dominique Boury, ‘Irritability and Sensibility: Key Concepts in Assessing the Medical Doctrines of Haller and Bordeu’, Science in Context, 21, 4 (2008), 521–535. 116 See especially Gaukroger, The Collapse of Mechanism and the Rise of Sensibility, 387–420. 117 Theodore M. Brown, ‘From Mechanism to Vitalism in Eighteenth-Century English Physiology’, Journal of the History of Biology, 7, 2 (1974), 179–216. 118 See Wolfe, ‘On the Role of Newtonian Analogies in Eighteenth-Century Life Science’.

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However, it also shows that the mechanization, mathematization, and experimental quantification of life and health have contributed to rising new questions, and to reverse the very perspective from which it started. Above all, it suggests that the age of the experimental quantification of nature is concluded with respect to its role as an overall explanation of the world, but it is already there in disguise. On one hand, indeed, quantification persists in the core of modern medicine—like in modern physical science, broadly speaking119 —as a fundamental medical practice, especially in pathology and diagnostics. It is the case, for instance, of the continual attempts at further quantification which took place in physiology in the late eighteenth and nineteenth centuries, with the work of Daniel Bernoulli (1700–1782), Daniel Passavant (1722–1799), Antoine Lavoisier (1743–1794), Jean-Léonard Marie Poisseuille (1797–1869), Gustav Theodor Fechner (1801–1887), the great Hermann von Helmholtz (1821–1894), Adolf Eugen Fick (1829– 1901), and Carl von Voit (1831–1908), just to mention the most famous cases.120 An era in which the very notion of medical quantification was gradually reshaped by the application of statistics to medicine, thanks in particular to Philippe Pinel (1745–1826), Pierre Charles Alexandre Louis (1787–1872), and Luis-Denis-Jules Gavarret (1809–1890).121 On the other hand, the mathematization of life has become a major philosophical problem, and continues to serve as a battleground of 119 In the eighteenth century this quantitative approach concerns especially chemistry. See Henry Guerlac, ‘Quantification in Chemistry’ Isis, 52, 2 (1961), 194–214 and Instruments and Experimentation in the History of Chemistry, part II (the papers from Crosland, Levere, Holmes, Bensaude-Vincent, Golinski, Smeaton). 120 As is well-known, in these cases the development of quantitative conceptions is especially fostered by the quantification of chemistry (in general), and more specifically of digestion and respiration, that took place as of the mid-eighteenth century, thanks especially to Lavoisier. See Friedrich L. Holmes, Lavoisier and the Chemistry of Life (Madison: The University of Wisconsin Press, 1985) and id., Antoine Lavoisier: The Next Crucial Year (Princeton: Princeton University Press, 1997), 7–11. 121 See Oscar B. Sheynin, ‘On The History Of Medical Statistics’, Archive for History of Exact Sciences, 26 (1982), 241–286 and Stephen M. Stigler, Statistics on the Table. The History of Statistical Concepts and Methods (Harvard: Harvard University Press, 1999), 203–273. And again Hald, A History of Probability and Statistics and Their Applications before 1750; Daston, Classical Probability in the Enlightenment; and Lancaster, Quantitative Methods in Biological and Medical Sciences. As for the economico-political background of this form of quantification see Karin Johannisson, ‘Society in Numbers: The Debate over Quantification in 18th-Century Political Economy’, in The Quantifying Spirit of the Eighteenth Century, 343–380.

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clashing, though ever-changing, factions, and alliances. Biology—and, thereby, physiology—is indeed the pivotal point around which, still in the nineteenth century, different images of the relationship between the world and human knowledge meet. We see this in nineteenth-century Idealism, with its dialectical understanding of the inside and outside of the organism, and its harsh critique of scientific observation,122 but even in Positivism. Despite the supreme epistemological role which Comte attributed to mathematical knowledge in whatever scientific process, he nevertheless had to acknowledge that calculation cannot in any way capture the complexities of life. Whereas, indeed, the mechanical model applies to the living universal laws that effectively shape and explain every organic function, our computational power is too weak to mathematically explain the constantly changing nature of living beings: The phenomena of the inorganic world are, for the most part, simple enough to be calculable: those of the organic world are too complex for our management: but this has nothing to do with any difference in their nature. And this is the view which both geometers and biologists should bear in mind. / If in astronomy our calculations are baffled when we pass beyond two or three essential conditions, it is evident how impracticable they must be amidst the inextricable complications of physiology. And again, this complexity prevents our ever effecting a mathematical disclosure of the elementary laws of the science. This excludes all idea of this method of philosophizing in biology; for these laws are no otherwise accessible than by the immediate analysis of their numerical effects. Now, whichever way vital phenomena are looked at, they present such endless and incessant variations in their numbers, that geometers are baffled as completely as if those degrees were entirely arbitrary. […] However hurtful may have been the incursions of the geometers, direct and indirect, into a domain which it is not for them to cultivate, the physiologists are not the less wrong in turning away from mathematics altogether. It is not only that without mathematics they could not receive their due preliminary training in the intervening sciences: it is further necessary for them to have geometrical an mechanical knowledge, to understand the structure and the play of the complex apparatus of the living, and especially the animal organism. Animal mechanics, statical and dynamical, must be unintelligible to those who are 122 See Basileo’s chapter in this volume. On these debates see also Stefano Poggi, ‘Neurology and Biology in the Romantic Age in Germany: Carus, Burdach, Gall, von Baer’, in Romanticism in Science. Science in Europe, 1790–1840, ed. by S. Poggi and M. Bossi (Cham: Springer, 1994), 143–160.

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ignorant of the general laws of rational mechanics. The laws of equilibrium and motion are […] absolutely universal in their action, depending wholly on the energy, and not at all on the nature of the forces considered: and the only difficulty is in their numerical application in cases of complexity.123

At once, we see that the philosophical and physiological disputes over which living functions can or cannot be reduced to the quantitative model gradually widened to include the relationship between physiology and psychology. The mind, consciousness, and its relationship with the brain remained for some time all too rarely addressed by quantitative methods, despite a centuries-long tradition of studying the anatomy of the nervous system, and attempts to quantify individual psychology dating back all the way to the sixteenth century.124 Too complex to observe and quantify directly until the twentieth century, the mind and its perceptions would be one of the strongholds of the qualitative understanding of the world. By contrast, late eighteenth-century neuroscience and experimental psychology (in particular with Fechner and Helmholtz) would endeavor to quantify this domain by mathematically determining the relationship between outer excitements and inner sensations, so as to develop a true physics of the mind.125

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Overlapping Paths

Through a collection of case histories, this volume collects eleven essays that address the dialogue between medicine, philosophy, and quantification from the late sixteenth century to the late nineteenth century. Laura Madella’s chapter (The More the Years the Less the Food: Alvise Cornaro on The Sober Life [1558]) addresses the writings of the Venetian Alvise Cornaro on The Sober Life and their Latin translation in the 123 Auguste Comte, Positive Philosophy, vol. 1, trans. by H. Martineau (Kitchener: Batoche Books, 2000), 386–387. 124 See Salvarani’s chapter in this volume. 125 See Vincenti’s chapter in this volume and Donald Laming, The Measurement of

Sensation (Oxford: Oxford University Press, 1997). See also Edwin G. Boring, ‘The Beginning and Growth of Measurement in Psychology’, Isis, 52/2 (1961), 238–257 and Michael Heidelberger, ‘The Unity of Nature and Mind: Gustav Theodor Fechner’s NonReductive Materialism’, Romanticism in Science. Science in Europe, 1790–1840, ed. by S. Poggi and M. Bossi (Cham: Springer, 1994), 175–189.

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seventeenth century by Leonard Lessius. Cornaro’s work, published in the second half of the sixteenth century, is considered to be one of the founding texts of contemporary theories on geriatrics as a holistic approach to aging. It is one of the best examples of how the autobiographical record intertwines with theoretical proposals. In her chapter, Madella also offers a valuable insight into this. She focuses on Cornaro’s use of quantitative reasoning for the articulation of nutrition through human longevity, stressing how an early form of quantification serves, in this sense, to stress the harmful effects of excessive eating on health, and control them and guarantee a temperate life. In turn, Cornaro is aware that bad humors could influence physical but also psychological health. More importantly, as Madella stresses, Cornaro’s quantification of diet involves an ethical imperative, above all because it aims to promote the elimination of vice and the restoration of virtue. If temperance is a quantifiable virtue, this is because the body itself is brought to the center of moral life, insofar as it the ethical foundations for general well-being are established through the preservation of its physiological harmony. This moral perspective, fostered by the conjunction of Aristotelian philosophy and the Galenic theory of humors, greatly influenced other famous early modern attempts at setting up a direct connection between physiology and psychology, in order to improve individuals’ education levels. As Luana Salvarani argues in her chapter (The Quantification of Talents: Education, Galenic Humoralism, and Classification of Wits in Early Modern Culture), the theoretical interest in the quantification of the body appears at the beginning of the modern age as the most viable scientific way to guarantee an integral education. As a supposed semiotic reference, this practice had certain biological features that were thought to reveal the degree of intelligence (ingenio) of individuals and their possible improvement. Such was the scope of the great Spanish physician and psychologist, Juan Huarte de San Juan. In his famous book, Examen de ingenios para las sciencias, Huarte contends that the education of intellectual faculties must always be anchored in a rigorous observation and classification imposed on the body. What is significant in this approach lies in the power attributed to the quantification of temperaments as a basis for reading indirectly the soul–body relationship. Which, in turn, can be translated into the following pedagogical precept: medicine, due to the quantitative observation methods at its disposal, can precede and enhance the work of educators.

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Starting in Silvia Manzo’s paper (Quali-Quantitative Measurement in Francis Bacon’s Medicine. Toward a New Branch of Mixed Mathematics ), the volume then proceeds to address the spirit of the early seventeenth century, though it does not entirely depart from the temperamental conceptions mentioned above. Against a widespread narrative, recent scholarship stresses how Francis Bacon’s natural philosophy subscribed to any use of mathematics, especially under the premise that natural phenomena must be expressed in a quantitative manner to be known and manipulated. Therefore, only the alliance of physics with mathematics would be the guarantor of the highest precision possible in operative knowledge. Manzo defends the idea that Baconian medicine is scientifically supported by “a quali-quantitative methodology of measurement”. She partly justifies this position by pointing out the fact that famously, Bacon conceived nature by way of a notion of matter in which qualitative elements are articulated in quantitative terms. As Manzo notes, Bacon undertook many different approaches to measuring chemical and physical phenomena, including doses of medicine, of time, of space, and even the relationship between quantitative and qualitative elements in purgatives—aspects that Bacon recorded by the use of general quantitative registers. The work of Jan Purnis (Sanctorius’s Weighing Chair: Measurement, Metabolism, and Mind) deals with the pivotal work of Santorio, and the quantification processes that he developed in his experimental approach. The results of Santorio weighing experiments concern not only the first complete early modern attempt to establish new quantitative criteria for the perfect metabolic balance. Indeed, according to Purnis’s reading, the measurement and control of the physical states of the organism also intertwine with the emotional lives of individuals. Analogical reasoning comes into play here since, as Santorio used mechanical principles to conceive the operations of the organism, his considerations about the identification and the distinction of basic emotions—such as fear and joy—, are likewise pursued in terms of lightness or heaviness. According to his formulations in Medicina Statica, since the quantification of weight arouses qualitative effects on the human mind, self-quantification, as he practiced daily, is highly recommended for all who wish to maintain healthy and invariable body weight. This last insight, as stated by Purnis, makes Santorio’s work an unavoidable reference for the current studies on the use and effects of new self-tracking technologies.

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The Cartesian theory of the res extensa marks the starting point for Mariangela Priarolo’s reading of the rise of quantitative embryology (The Rise of Quantitative Biology in the Cartesian Age: The Theories of Preformation). For René Descartes, quantification and extension are synonymous terms, thus supporting his famous view that bodies, either animate or inanimate, are ruled by the same mechanical principles and laws of motion attributed to machines. Famously, exactly how animal generation can occur within this model remains highly enigmatic. Influenced by Descartes, Nicolas Malebranche, and Pierre Sylvain Régis solved this conundrum by stressing the connection between mechanistic natural philosophy and a theological explanation of the universe, opening the door to forms of finalism. Both subscribe to “preformation theory”, according to which all individuals are pre-determined by God. In this model, as Priarolo argues, the general laws of motion are not directly responsible for the formation of the fetus, but rather by a particular motion triggered by God at the beginning of humankind. Other issues, however, stem from the early modern application of mechanisms to medicine. As Tonetti stresses in his chapter devoted to Giorgio Baglivi (“Nature is more subtle than any mathematician”: Giorgio Baglivi on Fluids in the Human Body), a very common view describes iatromechanism—which seeks to explain any bodily process, even pathology, on a purely mechanical basis—as opposed to iatrochemistry, focusing instead on medicine through the lens of chemistry. A supporter of a mechanistic and solidistic view, Baglivi shows how misleading this strict distinction can be. While disapproving of the chemical medicine of his time, particularly Helmontianism, Baglivi dealt with numerous issues in chemistry, strictly pertaining to the role of bodily fluids, through rigorous and vetted testing and experiments. Such an “anatomy of fluids” would play an indispensable role in explaining diseases, finding new remedies, and understanding the body itself. Baglivi realized that due to the corruption of fluids, diseases are not as easily examined as those involving solids and that, ultimately, pathology is not merely as simply described as malfunctioning machines. In Baglivi’s view, this knowledge should rely only on direct experience with nature. As is well-known, the quantitative efforts of early modern iatromechanism directly corresponded to the clash between different understandings of geometrization and the mechanization of nature, i.e. those of Cartesianism and Newtonianism. The general category of ‘iatromechanics’, then, conceals different views about how mathematics and mathematical

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physics should be applied in medicine, and thereby how the body can be quantified and mathematized. Mechanism, quantification, and mathematization are indeed different, albeit interrelated, notions, which overlap without ever becoming identical, and all of which depend upon the overall epistemological debate over the method for finding truth in science. Looking at this picture, Simone Guidi’s chapter (Data vs Mathesis: Contrasting Epistemologies in some Mechanizations and Quantifications of Medicine) compares the epistemological thought of Pitcairne, Keill, Guakes, and Hoffman, and contends that contrasting understandings and uses of quantification in medicine related to different conceptions of the epistemological status of mathematics and its connection with experience especially. Guidi then focuses on how the experimental quantitative approach represented by Santorio is understood in these different scenarios. Another great early modern mind, Gottfried Wilhelm Leibniz, stands as the main figure of Osvaldo Ottaviani’s reconstruction (“The Human Body Should Be Investigated in All Its Details to The Most Precise Degree…”. Leibniz on Quantification in Medicine). Ottaviani argues that Leibniz is among those thinkers who enthusiastically embraced both mathematization and quantitative criteria in medicine, as a solution to the scientific articulation of empirical observations and research. Leibniz’s attention toward anatomy, data collection, and statistical reasoning applied to medicine are all particularly relevant. At the same time, in Leibniz’s day, the mechanistic view of the human body implied the increase of technological mediation, mainly to overcome the boundaries imposed by observation and to expand scientific knowledge about organs and physiological functions. In this respect, the microscope and the thermometer were the paradigmatic instruments, whose use Leibniz welcomed. At the same time, as Ottaviani remarks, Leibniz thematized the famous issue of the infinite complexity of natural bodies, and the internal and external parts of nature. He promoted a developmental, always-provisional approach to the medical body, going from effects to the mechanical causes given our structural impossibility of getting direct access to the interior of nature. As a precious appendix of this chapter, Ottaviani posts the first edition of Leibniz’s brief text, De re medica augenda. In turn, Marco Storni’s chapter (The Pulse-Watch and the Physician’s Senses: John Floyer on the Quantification of the Body) offers a detailed view of the quantitative methods employed by English physician, John Floyer,

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who was one of the most important figures in the development of the measurement of pulse in the eighteenth century. In Storni’s reconstruction, Floyer’s work marks a point of convergence between two factions in his contemporary debate on pulse, i.e. the defenders of pure mechanism and the supporters of a holistic approach. The use of a pocket watch to measure patients’ pulse, made famous by Floyer in his treatise, The Physician’s Pulse-Watch, integrates tradition with new techniques and devices. As Storni warns, Floyer goes beyond mechanism and continues to think of the physician as an “artisan of healthcare”, provided with a modest theoretical background but capable of using their senses as well as simple measuring instruments. Likewise, for Floyer, irregular changes in pulse measurement can suggest several medical diagnoses, so that they all need to be compared with the body’s physiological state, as Galen’s humoral theory had suggested centuries before. Yet, Floyer also considers the active role of the “intelligent patient” who can adopt the pulse-watch method, even though such a patient would still need the mediation of a physician, not having sufficient knowledge to establish correspondences between altered pulse rates and their causes. Gaetano Basileo’s piece provides a study of Hegel’s criticism of the natural philosophy of his time by analyzing the classic passage from the Phenomenology of Spirit on ‘Observing Reason’ (Against the Quantification of the Living: Hegel’s Critique of Romantic Naturphilosophie in the Phenomenology of Spirit). Hegel’s critiques are largely directed toward the various attempts to quantify the relationships between the internal and external structures of the organism (going back to Leibniz), as exemplified in physiognomy and phrenology. The alleged natural psychological laws follow an expressivist principle according to which exteriority necessarily reflects interiority. Rejecting this expressivist approach, Hegel, in the Phänomenologie des Geistes, even designates the object of physiognomy as a totes Ding (“dead thing”). If, for Hegel, laws, and numbers represent inert contents—that is, abstract meanings devoid of vitality— this is because the relations they intend to determine also imply the separation and reification of the relata themselves, by which they lose their organic unity and individuality. That the Hegelian critique of Naturphilosophie presupposes the irreducibility of philosophical knowledge to mathematical knowledge is clearly present in the pages of the Phänomenologie des Geistes. But, as Basileo rightly asserts, the opposition between philosophy and mathematics is, in Hegel’s work, only valid to support his criticisms of eighteenth-century Naturphilosophie.

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Finally, Denise Vincenti’s chapter (Measuring the Mind: The French Debate on Fechner’s Psychophysics in the Late Nineteenth Century) addresses the reception of Gustav Theodor Fechner’s Psychophysics, and especially Henri Bergson’s reaction. In the Late nineteenth century, several French authors—psychologists, physicists, and philosophers—took very critical positions against the quantification theory of the mind proposed by German physicist and philosopher, Fechner. His scientific goal was to measure and quantify sensations, but as these transcended the limits of measurability, the only feasible solution was to use a comparative method and determine the differences between them, especially those concerning intensity. Vincenti’s chapter describes and analyzes the responses to Fechner’s intentions given by French thinkers of the time. Among these is Bergson , who calls into question the whole idea of applying quantification methods to the field of psychology. Famously, in Time and Free Will, Bergson contends that measurement processes belong to the sphere of the extensive, of what is barely given according to spatial criteria and, therefore, it becomes spurious to subject the intensive sphere of sensations to those criteria. On the contrary, according to Bergson, the qualitative elements of psychic phenomena, as well as their intrinsic temporal nature, dictate their irreducibility in relation to every attempt at quantification procedures.

The More the Years the Less the Food: Alvise Cornaro on The Sober Life (1558) Laura Madella

1

Introduction

The relationship between food and health has always received great attention from scientists, scholars and the laymen. The almost universal accessibility of the experience of eating, even in times when observing the practice was not the recognized basis of the knowledge system in force, has made it a natural object of continuous and constant investigation, in all ages and in every culture, and has produced general rules of behaviour that have become part of the shared popular wisdom. Among these, many revolve around the principle of moderation in nourishment, variously declined in the direction of a generic moderation (vaguely similar to Horace mediocritas ) and a personalized measure between two extremes (reminiscent of Aristotle’s doctrine of the mean). In the medical field, Galen also fixed the temperance in eating and drinking among the basic principles of a prudent diet, whereas diet stood as the most available instrument to preserve humoural balance and manage the imbalance. Nor was Galen the only physician in the early history of Western medicine to

L. Madella (B) University of Parma, Parma, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_2

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systematically apply this theory, and he was certainly not the first, but the celebrity he achieved in his lifetime and the posthumous dissemination and influence of his works (i.e. books) give him unparalleled primacy in this regard. As in 1558 the Venetian Luigi Cornaro (1484–1566)1 wrote the first Discorso sulla Vita Sobria (‘Discourse on a Sober Life’), the Galenic paradigm was still undisputed in the professional and popular medical culture and it is well recognizable in the notions that Cornaro expounds and in the advice he dispenses, including the advice around which the message of the work revolves: as man grows older, he must reduce the amount of food and beverages consumed, so as not to fatigue the digestive system, avoid humoural imbalance and preserve, ultimately, a better state of health. The content of Cornaro’s Discourse has no disruptive or even new features; just as it does not present any remarkably singular aspects in its form—a neat, fluid and brilliant Italian prose, but without poetic or rhetorical flights, all in all traditional, with no trace of the stylistic restlessness of the late Renaissance. Yet since its publication, the work has enjoyed unprecedented success. The princeps editio became a real bestseller, so much so that Cornaro decided to publish two more booklets on the same subject in the following years, albeit with some changes.2 Moreover, half a century later the first Discourse of 1558 was translated in Latin and included by the Swiss Jesuit Leonhard Lessius (1554–1623) in his work Hygiasticon seu vera ratio valetudinis bonae et vitae ad extremam senectute conservandam (Antwerp, 1614) and thus reached a wider audience outside of Italy.3 Together with the Hygiasticon, in 1634 the first

1 The author’s real name was Alvise Corner, but in his books he had it printed in the Italian form of Luigi Cornaro, so as so it sounded less Venetian. 2 After the first Discourse (1558), while still alive, Cornaro wrote and published Compendio breue de la vita sobria (‘Short compendium on the sober life’, 1561) and Ammoreuole essortatione […] alla vita sobria (‘Caring admonition […] on the sober life’, 1565). In 1591, a nephew of Cornaro collected those three treatises adding a letter on the same subject written from Cornaro to the Patriarch of Aquileia and published in Venice Discorsi della vita sobria del sig. Luigi Cornaro (‘Discourses on the Sober Life by Mr. Luigi Cornaro’). 3 On Leonhard Lessius’ work see C. Casalini and L. Madella, ‘The Jesuit Cultivation of Vegetative Souls: Leonard Lessius (1554–1623) on a Sober Diet’, in Vegetative Powers. The Roots of Life in Ancient, Medieval and Early Modern Natural Philosophy (Cham: Springer, 2021), 177–198.

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Discourse was translated into English, entering the Protestant world and undergoing several reprints until the eighteenth century.4 In Anglo-Saxon culture, then, the Discourse on Sober Living eventually emancipated itself from Lessius’s work, and began to be studied and, again, republished, as a seminal work in the history of ideas about ageing and prolongevity, and so it is still considered today in this field of research.5 What has made this book so renowned, according to scholars, is the mix of autobiographical narrative, human sympathy and moral rigour, which while treating the subject of senility seriously does so with cordial and optimistic accents, lightening the generally snooty tones of moral and medical treatises; and on this one could not agree more. But I believe that there is also a more specific aspect in the work that catalyses the reader’s attention and distinguishes Cornaro’s Discourse. Such is the issue of the amount of food in relation to the age of man and its moral and symbolic implications, direct and indirect, which the author reiterated and declined in different ways throughout the work.

2

Cornaro and the Moral Question of Quantity

Both in the author’s intentions and in the form it takes, this work is a kind of regimen. Regimina were handbooks of practical advice on hygiene and behaviour with a prestigious medieval tradition. The advice usually involved the so-called six “non-natural” Galenic elements, that is to say those factors of human life that could influence a man’s health and complexion, and upon which the man could act: air; food and drink; sleep and wakefulness; rest and motion; repletion and evacuation; passions of the mind. But differently from the traditional regimen, Cornaro made his handbook distinctively autobiographic, perhaps beyond the real truth but with a very realistic literary performance, rather uncommon for the topic, which was usually based on ancient literary authorities. Furthermore, he mostly dealt with the category of nutrition and confined the other five 4 Hygiasticon’s 1634 English translation was reprinted in 1636 (Cambridge), 1678 (London), 1742 (London) and 1743 (London). Actually, the first German translation had been earlier (1614) but its success decreased in the following decades and centuries. 5 The first and most reprinted English translation of Cornaro’s works was Sure and certain methods of attaining a long and healthful life, with means of correcting a bad constitution (London, 1702). We quote passages from a 1903 translation by W. F. Butler reprinted in Luigi Cornaro, The Art of Living Long (New York, 2005), from now onwards Living Long

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factors to a very narrow role. Finally, while he opened the treatise basically declaring to write in order to persuade young and adult men to follow and appreciate the temperate life (= diet), he gradually addressed his argument towards elders. To properly frame Luigi Cornaro’s treatise, it is necessary to recall the moral framework in which the author places his speech. In fact, it is evident from the very first lines of the text that the author does not confine the terms of its treatise to the medical field. After all, Cornaro had neither the training nor the experience of a doctor. Instead, he was a businessman who had become rich by reclaiming the marshy lands of the Republic of Venice, and who combined great socio-economic ambition with a sincere interest in architecture, theatre, music and literature,6 and his writing seems moved by an ethical urgency: Three evil customs have gradually gained a foothold in our own Italy. The first of these customs is adulation and ceremony, the second is heresy, and the third is intemperance. These three vices, cruel monsters of the human life as they truly are, prevailed so universally as to have impaired the sincerity of social life, the religion of the soul, and the health of the body.7

It seems useful to note that ‘heresy’ is the English rendition to generalize and neutralize the original Italian ‘Luteranesimo’ (‘Lutheranism’), an attack against Protestants that was frequent as well as rhetorical and even ritual in the literature of the Counter-Reformation. More notably, the English word ‘intemperance’ applies either to general excess, both physical and moral, or to excess in eating and drinking; while the original Italian text has ‘crapula’, closer to ‘crapulence’, which refers purely to gluttony, to excess in eating and drinking and to its debauched 6 As for Cornaro’s biography see: Giuseppe Fiocco, Alvise Cornaro: Il suo tempo e le sue opere (Padova, 1965); Emilio Menegazzo, ‘Alvise Corner: Un veneziano del Cinquecento nella terraferma Padovana’, in Storia della cultura veneta: Dal primo Quattrocento al Concilio di Trento, vol. 2 (Vicenza, 1980) and Colonna, Folengo, Ruzante e Cornaro: ricerche, testi e documenti (Roma, 2001); Lionello Puppi, Alvise Cornaro e il suo tempo Catalogo della mostra (Padova, 1980); Klaus Bergdolt, Alvise Cornaro: Vom massvollen Leben (Heidelberg, 1991); Paolo Sambin, Per le biografie di Angelo Beolco, il Ruzante, e di Alvise Cornaro (Padova, 2002); Marisa Milani, ‘Introduction to Cornaro’. In Writings on the Sober Life: The Art and Grace of Living Long (Toronto, 2014), 3–71. 7 Cornaro, Living Long, 40. Here and in the following quotations from Cornaro, emphases are mine.

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consequences. The location of the statement, in the opening, makes the concept more pervasive: just like deceit and falsehood in public and social life (‘adulation’) and just like deceit and falsehood in faith, crapulence, i.e. eating and drinking in unbridled quantity, is morally evil. And, as a result, letting one own’s body be shuttered by excess is evil too. Cornaro blames a mundane life for such malpractice, as its rituals reverse the actual moral value of excess and moderation: For though it is well known by all that intemperance proceeds from the vice of gluttony, and temperance from the virtue of restraint, nevertheless the former is exalted as a virtuous thing and even as a mark of distinction, while temperance is stigmatized and scorned as dishonorable, and as befitting the miserly alone. These false notions are due entirely to the force of habit.8

In the Renaissance, the culture of receiving and hosting had become fundamental not only at the courts of princes and noblemen, but it was a habit gradually acquired from any group of people who needed to entertain formal relationships. Scarce food, scarce beverage, a thrifty banquet would be held as unrespectful; abundance and lavishness were required, so that it was not easy to distinguish generosity from excess. Thus, crapulence proceeds firstly from social habits: And these truly immoral banquets of thine [O Italy!] now so commonly the custom – feasts so great and intolerable that the tables are never found large enough to accommodate the innumerable dishes set upon them, so that they must be heaped, one upon another, almost mountain high – must we not brand them as so many destructive battles! Who could ever live amid such a multitude of disorders and excesses!9

Cornaro evokes the banquet reversing its traditional symbolic meaning (celebration, collective joy, triumph over the limitations of nature) into a negative light with a sort of simulated moral undertone. The meaning of this passage can be better understood keeping in mind the role of the banquet as a staple of Renaissance culture. According to Bakhtin, food

8 Cornaro, Living Long, 40. 9 Ibid., 41.

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images and imagery were intimately connected with body and procreation, and banquets were a practical way to learn and experience the world through social events: The original system of images symbolized the working people, continuing to conquer life and food through struggle and labour and to absorb only that part of the world that has been conquered and mastered […] The banquet images preserve their initial meaning: their universalism, their essential relation to life, death, struggle, triumph, and regeneration. This is why banquet imagery went on living in the creative life of the people […] At the time of Rabelais [which was also Cornaro’s time] the banquet images still had a meaningful and artistically creative life. In the act of eating, as we said, the confines between the body and the world are overstepped by the body; it triumphs over the world, over its enemy, celebrates its victory, grows at the world’s expense. This element of victory and triumph is inherent in all banquet images.10

Cornaro’s description of the banquet as a ‘destructive battle’ does only apparently refer to the moral aspects of the social ritual (‘adulation and ceremony’); while the latter envelops moral life in a web of falsehoods, the banquet as a physical action is much more dangerous, destroying life itself because of the excess of food. Therefore, Cornaro makes clear that his main aim is not to propose the usual act of moral reform but to act directly on the body. In the footsteps of Galenic tradition, moral improvement can only follow health improvement, and individual happiness is a direct consequence of correct dietary choices.

3

Quantity (of Food) Matters

Luigi Cornaro’s ‘sober life’ began around his forties when, after a series of health problems that were getting more and more debilitating, the Venetian gentleman decided to follow the advice of doctors and moderate his lifestyle, which until that moment included an immoderate consumption of wine and food of any kind chosen only from among the ones that satisfied his taste. The first decisive input to moderate the quantity of food and beverages comes, so to say, from the established medical authority and it does not have anything to do with ageing:

10 Mikahil Bakhtin, Rabelais and His World (Bloomington, 1984), 282–283.

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I was, between my thirty-fifth and fortieth years, reduced to so infirm a condition that my physicians11 declared there was but one remedy left […] That remedy was the temperate and orderly life, they assured me.12

The inverse proportional relationship between food and age is an aspect that Cornaro reaches after several phases, and we could assimilate this process to the behaviour of a patient suffering from addiction: Cornaro’s first reaction to the doctors who had prescribed him diet and fasting was to lie, affirming he had limited the intake of wine and food in order to continue in secret exactly as before. Then, cornered by the drastic worsening of his health conditions, he chose clearly, but also in a somewhat drastic fashion, to abandon forever his old habits and dedicate himself to the new ones more intensely than he was asked to: I entered upon my new course so heartily that I never afterward swerved from it, nor ever committed the slightest excess in any direction.13

According to his account, Cornaro undertook the new lifestyle by adapting to his needs the two variables of Galen (ca129–ca216) on the intake of food: quality and quantity. As for the quality, Cornaro was not able to establish a proper rule other than an empirical application that differed from case to case: the proverb which states ‘Whatever tastes good will nourish and strengthen’ sounds untrue—every individual tolerates or suffers different products regardless of his or her taste and must avoid the harmful ones. As for the quantity, Cornaro’s diet became so strict that, at a certain point, doctors and relatives got worried about how little he ate and drank and insisted on increasing the daily doses of food and beverages. This was Cornaro’s answer: I, on the other hand, brought forward my reasons to the contrary: namely, that nature is satisfied with little; that my spare diet had been found sufficient to preserve me in health all these many years; and that, with me, this abstemious habit had long since become second nature. I maintained, 11 Cornaro always refers to more than one doctor, perhaps to suggest his connection with the scientific Paduan world and his social status (common people had no ‘referring doctor’). But in so doing, he intentionally confines the image of physician in a rather elusive and virtual dimension, highlighting his marginal role in such a question. 12 Cornaro, Living Long, 44. 13 Ibid., 46.

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furthermore, that it was in harmony with reason that, as my age increased and my strength lessened, I should diminish, rather than increase, the quantity of my food. This was true; since the digestive powers of the stomach were also growing weaker in the same proportion as my vigour became impaired. Wherefore I could see no reason why I should increase my diet.14

This is a very rich passage, where Cornaro concentrates the main arguments of his theories that elsewhere he takes up and repeats individually. First: in this exact formulation, the concept cannot but remind us of the words of Michel de Montaigne (1533–1592) in his Apologie for Raymond Sebond (‘It is wonderfull to see with how little nature will be satisfied, and how little she hath left for us to be desired’).15 And, as Montaigne himself recalls, it has very ancient origins, which root it deeply in Western thought. The Apologie of Sebond cites the Stoics, but it is important to mention at least the Book of Sirach, which in the early Christian communities was widely read and commented on precisely because of its practical and moral wisdom and which contains an appeal to temperance with a temperamental overtone: ‘Be not unsatiable in any dainty thing, nor too greedy upon meats:/ For excess of meats bringeth sickness, and surfeiting will turn into choler’ (XXXVII, 29–30).16 Such a deep suggestion is followed by consideration of the value of individual experience and judgement, and from a further statement of confidence in the will of the human being that rests on the Aristotelian axiom of habit becoming second nature. The passage closes with a complete and concise enunciation of the focus of the essay: the exhortation to reduce the consumption of food at the same pace with the advancement of age, so to avoid straining the stomach and causing imbalances in the amount of humours contained in the body. Which I eat and drink – always being such as agrees with my constitution and, in quantity, such as it should be – after it has imparted its invigorating

14 Ibid., 54. 15 Michel de Montaigne, The Essays done into English by John Florio (London, 1893),

168. 16 The Book of Sirach is thought to have been written at the beginning of the second century BC. The Hippocratic theory of the conception and digestion of foods had already been widespread for several centuries.

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elements to my body, leaves it without any difficulty and without ever generating within it any bad humors.17

According to the precepts of Galenic medicine accepted by Cornaro, ‘bad humours’ could influence not only physical health but also emotional and, we would say today, psychological health. He compares his own sober lifestyle to the one he kept as a young man, and eventually concludes that he feels much quieter and clearer since following the temperate life; but he also compares himself to his brother, inferring that the latter’s anxious and melancholic temper depends on the immoderate lifestyle he leads. And eventually he concludes that: It is thus clear that neither melancholy nor any other disorder can seriously injure bodies governed by the orderly and temperate life […] The regular life I had led for many years had united, equalized, and disposed all my humours so well that they could not possibly be subject to so great alteration.18

The insistence of doctors and relatives to increase the amount of food and drink ingested in a day is bound to be counterproductive, since it inserts a disturbing element in Cornaro’s established routine. At this point, finally, Cornaro attributes a numerical quantity to the sobriety of his daily diet: This increase, however, was by only two ounces in weight; so that, while, with bread, the yolk of an egg, a little meat, and some soup, I had formerly eaten as much as would weigh in all exactly twelve ounces, I now went so far as to raise the amount to fourteen ounces; and, while I had formerly drunk but fourteen ounces of wine, I now began to take sixteen ounces.19

Trying to understand what the measures expressed in ‘ounces’ by Cornaro are equivalent to, let us just remember that in early modern Italy units of measurement varied enormously not only from state to state, but often from city to city. As for the Venetian ounces, I retrieve a corresponding weight of 22–39 gram each one. That means that Cornaro ate around

17 Cornaro, Living Long, 48. 18 Ibid., 53. 19 Ibid., 55.

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270–470 grams in a day and drank around 320–550 grams20 —a very small amount even for a weak subject. Of course, such an equivalence would make sense if Cornaro was telling the truth. But this cannot be ascertained, nor can we fully trust the author, since there is evidence that he tended to ‘retouch’ some information of particular interest.

4

Some Lies and ‘The Cumulative Advantages of Added Years’

In the many pieces of biographical information released by Cornaro voluntarily and involuntarily in the course of his long existence, scholars found many inconsistencies that follow a single constant: having reached his full maturity, Alvise Cornaro began to lengthen his life not only by adjusting his diet but also by anticipating the year of his birth. Over time, information about his age has been inferred from what he stated in his writings21 ; for a long time he was supposed to have been born in 1464 and died at the venerable age of 102. Such extraordinary longevity served as evidence of his theories, lending the Sober Life great authority. Archival research recounts a different story though, establishing 1484 as the most reliable year of Cornaro’s birth.22 Another small clue that leads us to suspect Cornaro to have included in the treatise On the Sober Life, if not lies, a more sweetened version of reality, comes from a letter from Sperone Speroni (1500–1588), a man of letters very active on the cultural scene of the time, in particular in theatrical controversies, and a regular visitor of villa Cornaro. In 1562, Speroni wrote to Cornaro that he judged his diet too extreme and questioned the opportunity to extend its practice indiscriminately; and he adds:

20 As for the equivalence among Venetian ounces and Metric System, see Antonio Clementini, Delle misure dei pesi e delle monete che hanno corso nel Regno Lombardo-Veneto (Venezia: Rodondi, 1845). 21 Although in different writings, he declared different years of birth. 22 Emilio Menegazzo stated 1484 to be the most likely, because it appears on a paper

signed by Cornaro before the Venetian Court, which made it an official document in which he was supposed to tell the truth (Menegazzo. ‘Alvise Corner: Un veneziano del Cinquecento nella terraferma Padovana’, 32).

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However, I remember seeing you very bent over, with your back bent towards the ground; and this is because your bones are too dry, because they lack the humour and strength to stand upright, since too much sobriety fails to find superfluous wet substance to dry and so consumes the radical one.23

To Speroni, who was fifteen years younger than Cornaro and reached almost ninety, his friend did not appear so fresh and energetic. Nor is it a banality how Speroni explains the reason why a too strict diet cannot sustain a man: Since we do not live on food alone, who is sober in food must be sober in many other things [...] and if we weigh wine and bread, we should also weigh thoughts, writing, reading and similar things which impede digestion.24

Alvise Cornaro’s essays, and the first Discourse most of all, found their autobiographical appeal in the confidence and precision with which the author links the stages of his experience to his age, to the number of years he lived. We have already seen, just above, that in Cornaro the most serious health problems manifested themselves from the age of 35, and that the conversion to the Sober Life was completed between 35 and 40. And several other times we find exact numerical indication of the author’s ages. First of all, he cares that the reader knows how old he is while composing the work: To prevent so great an evil for the future, I have decided to point out, in this brief treatise, what a fatal abuse is the vice of intemperance […] I undertake all the more willingly, since I have been pressed thereunto by a number of young men of the brightest intellect, who are well aware that intemperance is a fatal vice; for they have seen their fathers die from its effects in the flower of manhood, while, on the other hand, thet behold me hale and flourishing at my great age of eighty-three years.25

23 Speroni’s letter is transcribed in a nineteenth-century edition of Cornaro’s 1591 collected work: Discorsi di Luigi Cornaro intorno alla vita sobria (Venezia), 94. 24 Cornaro, Discorsi, 94. 25 Cornaro, Living Long, 42–43.

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Among the most important formative moments of his journey into sober living is surely the one in which he finds confirmation that a temperate diet helps to manage emotions and keeps bouts of melancholy under control: The truth of this statement I learned by my own experience at the age of seventy.26

A tasty anecdote, and equally circumstantial about his age, tells us indirectly that Cornaro had a self-esteem that bordered on self-worship. As he enumerates all the pleasurable intellectual activities that his excellent health allowed him to pursue, he says that he had recently composed a play, at 83, and compares himself to none other than Sophocles, who is said to have composed his last work, a tragedy, at 73. But from Cornaro’s singular extra-literary perspective, Sophocles’ work is less valuable: Now, if that good old man, a Greek and a poet, was so highly commended for having written a tragedy at the age of seventy-three, and was, by reason of this deed, regarded as vigorous and sound minded – although tragedy, as I have just said, is a sad and melancholic form of poetry – why should I be deemed less fortunate or less hale than he, when I have, at an age greater than his by ten years, written a comedy, which, as everybody knows, is a cheerful and witty kind of composition? Assuredly, if I am not an unfair judge of myself, I must believe that I am now more vigorous and more cheerful than was that poet when burdened with ten years less of life.27

The frequency and regularity with which Cornaro gives numerical indications of his age adds to the precepts of his treatise an almost mechanical character, which adds to the motif of inverse proportion and fixes in the reader the connection between the years of old age, diet and its benefits in a rather vivid way. And this association, in turn, turns out to be something remarkable even from the quantitative point of view, because countless are the advantages that come to the elderly man from leading a temperate life. Educator and scholar Gerald Gruman used the happy expression ‘the cumulative advantages of added years’:

26 Ibid., 50. 27 Ibid., 71.

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Extra years give one a decided advantage in gaining knowledge, wisdom and honors. It is not surprising that this new European class engaged in the persevering collection of wealth and status.28

Actually, Cornaro lists all his virtues and advantages; he is ‘strong’ and ‘able to mount my horse without assistance’, and to ‘climb a whole hill on foot’; but also ‘cheerful, happy, and contented’ and then free from ‘all perturbations of the soul and from every vexatious thought’; other activities include: conversing; reading good books; writing; enjoying his beautiful estates and their gardens, both in the city and the country; going hunting; meeting friends; listening to music; hosting artists and scholars.29 It seems to me that in this list there is an inverse proportion too: the more we grow old and reduce the food and the process of our bodily organs, the more we increase psychological, intellective and spiritual faculties. The proportional relationship proposed for the food/age elements is maintained inversely in the food/benefit pair. On the other hand, if we observe the relationship between benefits and quantitative aspects of the body, the proportion is direct when for quantitative aspects we consider the number of years, and inverse when for quantitative aspects we consider instead the matter of the body (elemental, humoural) which, thanks to the joint action of the natural process of ageing and a temperate diet, is reduced and thinned.

5

Leonhard Lessius SJ, Exporting Cornaro and His Proportions

Take so much Rubarb, learned Galen sayes; Take so much Cassia, so much Aloes, So much of th’other, And of such and such

28 Ibid., xxiii. 29 Ibid., 68–70.

What e’re the Doctour gives, he does put to it Fasting: Take this, and fast; and it will do it See! Without Fasting Physick can cure none:

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Give me this Recipe, Take not too much

But Fasting will cure almost all, alone30

How Leonhard Lessius SJ translated Cornaro into Latin and created the conditions for its European circulation has already been mentioned. But it is equally important to note that the Swiss theologian, in his essay, takes from Cornaro himself several passages on the subject of proportion and quantity, and readjusts them to suit his aims and his audience. The terms become more assertive, convey a greater need and possibility for precision and lean on philosophical and theological references, albeit in a non-dogmatic way: Now the Measure of the food ought to be exactly proportionable, as much as possible may be, to the qualitie and condition of the stomack.31 What is but reasonable to a young and strong bodie, is more then twice or thrice too much for an old or infirm person: as Thomas, following Aristotle, doth well prove, 2.2.q. 141 art. 6, and is indeed of itself without proof manifest.32

And when it comes to indicating to the reader the numbers of the ideal diet, Lessius does not hesitate to expose Cornaro’s diet as a generally valid line, when in fact the Venetian had reiterated several times that it was calibrated on his own experience and needs: Yet notwithstanding generally for them who are stept in years, and for those who are of weak complexions, it seems twelve, thirteen, or fourteen ounces of food a day should be enough; accounting into this proportion bread, flesh, eggs, and all other kinde of victuals; And as many, or but a few more ounces of drink would suffice.33

30 The little anonymous poem is written just before the beginning of Lessius’ preface, in Hygiasticon; or, The Right Course of Preserving Life and Health unto Extream Old Age: Together with Soundnesse and Integritie of the Senses, Judgement, and Memorie (Cambridge, 1634). 31 Lessius, Hygiasticon, 17. 32 Ibid., 24. 33 Ibid., 24.

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In order to better place Cornaro in the religious framework of his cultural horizon, Lessius compares the Discourse on the Sober Life with some testimonies of the Holy Fathers and establishes that, all things considered, Cornaro is more trustworthy because he was no holy man, thus closer to him and his audience. Then he even compares some Fathers’ clues on food quantities and qualities to Cornaro’s similar information, dwelling at length on a curious matter. One of the recurrent dishes in Cornaro’s diet and, according to the Venetian, particularly suitable for elderly people because it is nutritious and easy to digest is panatella, or panada, a soup made with meat broth and a mixture of eggs and breadcrumbs. Lessius seems to take this subject very seriously and wonders how much this soup should weigh, how much the respective ingredients should weigh and whether the broth should be considered a food or a beverage, etc.: Now whereas some may here object, that Panada although it weigh seven, or eight, or nine ounces the messe, yet the water or broth being deducted, there remains not in truth above three or foure ounces of bread, or other solid ingredients. The Solution is easie. For when meats and drinks are mingled (as in Panada, and other such like suppings) they are to be severally weighed and reduced to the making up of the just measure of that kinde, to which they properly belong.34

The reason for Lessius’s particular interest in the rustic Italian dish can perhaps be traced back to the symbolic value of its main ingredients. Relying once again on the popular wisdom of the Book of Sirach: ‘The chief thing for life is water, and bread’ (XXVII, 21). Surely, the wise, energetic yet self-centred Alvise Cornaro would have appreciated the seriousness and respect with which Lessius quoted his work.

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Dissolution as Conclusion

There is one last aspect that Cornaro associates with the inverse proportionality between age and food and that Lessius retains and reworks in his essay as an incentive to pursue a temperate diet. Gradually reducing foods supports the natural process of material dissolution of the body through time, which alone in the world can guarantee a sweet death, without suffering: 34 Ibid., 55–56.

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The universal rule is that they who wish not only constantly to enjoy perfect health and to attain their full limit of life, but finally to pass away without pain or difficulty and of mere exhaustion of the radical moisture, must lead the temperate life […] the end is caused merely by the failure of the radical moisture; which, consumed by degrees, finally becomes completely exhausted, after the manner of a lamp which gradually fails. Hence they pass away peacefully, and without any kind of sickness, from this earthly and mortal life to the heavenly and eternal one.35

Thus, dying well becomes a matter of quantity, while spirit and soul come as a consequence. The theme is fascinating, it gives Cornaro the opportunity to practise repeated praise of nature (‘the daughter of the same God’, 19) and its dynamics (‘she does not deny us the power of living many years’, 8), with light but undeniable alchemical and Neoplatonic references: Yet beautiful and desirable, indeed, is that death which Nature provides for us byway of the dissolution of the elements […] I feel certain that not only will my end, by the blessing of God, be very different, but also that my soul, which has so agreeable a habitation in my body – where it finds nothing but peace, love, and harmony, not only between the humours, but also between the senses and reason.36

Cornaro’s Discourses on the Sober Life are still considered among the founding texts of contemporary theories on geriatrics as a holistic approach to ageing. The English edition from which we have taken the quotations of this short essay dates back to 1903, and has been republished in the twenty-first century in Springer’s ‘Classics in Longevity and Aging Series’ together with a selection of passages from Francis Bacon (1561–1626)’s History of Life and Death, and from William Temple’s Health and Long Life, highlighting how Renaissance humanistic culture, both Catholic and Protestant, elaborated a similar reasoning about growing old, paving the way to the contemporary theories on geriatrics and ‘the belief that it is possible and desirable to increase significantly the length of life by natural means’.37

35 Cornaro, Living Long, 65. 36 Ibid., 74. 37 Ibid., XXIII and ff.

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Notwithstanding the weakness of Cornaro’s theory on the medical side and its narrative exaggerations, the success of the book is understandable. On the Sober Life proposes a new perspective on the ancient role of the senex, whose duty was to rule the community and act exemplarily thanks to his superior wisdom and detachment from earthly passions. On the contrary, Cornaro’s old man chooses to avoid banquets in order to have a better health and free-flowing energies to pursue the enjoyments of life. His old age is neither ascetic nor educational. He does not pursue sobriety to teach morals and manners to young people or to reach some form of metaphysical perfection: he reduces food to enhance his private happiness, thus making his work progressively more interesting for seventeenth- and eighteenth-century readers, when the role of aristocratic society with its rituals was slowly but inexorably drifting towards irrelevance.

The Quantification of Talents: Education, Galenic Humoralism, and Classification of Wits in Early Modern Culture Luana Salvarani

1 Early Modern Educational Thought, Between Politics and Morals Renaissance and Reformation have been crucial eras for the development of educational thought. The central role of humanae litterae and the responsibilities of the magister in the education of the leaders created a complex and precarious equilibrium of values which goes under the name of “civic humanism”,1 bringing the noble pupils’ daily toil of learning Latin and Greek and studying classical texts to the forefront of the political and social construction of modernity.

1 For reference see Hans Baron, The Crisis of the Early Italian Renaissance. Civic Humanism and Republican Liberty in an Age of Classicism and Tyranny (Princeton: Princeton University Press, 1955); James Hankins (ed.), Renaissance Civic Humanism. Reappraisals and Reflections (Cambridge: Cambridge University Press, 2000); Nicholas Scott Baker and Brian Jeffrey Maxson (eds.), After Civic Humanism: Learning and Politics in Renaissance Italy (Toronto: Centre for Reformation and Renaissance Studies, 2015).

L. Salvarani (B) University of Parma, Parma, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_3

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More in detail, as far as roles are concerned, the humanist longing for the construction of an ideal society based on classical philosophy and morals put on teachers and educators the responsibility of such re-enactment: first of all, on scholars-philologists able to restore and transcribe original classical works, and transmit this knowledge to pupils; and then on leaders, who were expected to act as an example for their subjects through the practice of moral philosophy and wisdom in civic life. Of course, things were not so simple, and Renaissance society turned to be as violent and unfair as much as it was cultivated and forwardlooking. The age of the Reformation (and, consequently, the CounterReformation) focused even more on education to propagate religious values hoping for the regeneration of man through the Scriptures, philologically reviewed, and read through the lens of humanism. Reformation brought the Humanist connection between education and social life on a larger scale indeed, and also in this case, historians of ideas have designed a concept to describe the complexities of such action, i.e., Sozialdisziplinierung.2 The interest of contemporary critics in the political side of Renaissance and Reformation educational thought has kept the body in the background in the discourse on education, focused on the soul in its learning action and its shaping under the rule of moral discipline. Both the relationship between mentor and pupil in the building of civic humanism and the powerful machine of popular Protestant schooling looked like emphasizing the intellectual aspects of learning and dismissing the emotional and bodily side. The main perspective was the one stated by Aristotle in the Politics: “Therefore in the first place it is necessary for the training of the body to precede that of the mind, and secondly for the training of the appetite to precede that of the intelligence; but the training of the appetite must be for the sake of the intellect, and that of the body

2 The concept was defined by Oestreich in a landmark 1969 essay: Gerhard Oestreich, ‚Strukturprobleme des europäischen Absolutismus‘, included in his book Geist und Gestalt des Frühmodernen Staates: Ausgewählte Aufsätze (Berlin: Duncker & Humblot, 1969). For other developments connected with the field of education, see Gerald Strauss, Luther’s House of Learning: Indoctrination of the Young in the German Reformation (Baltimore– London: The Johns Hopkins University Press, 1978); id., ‘The Social Function of Schools in the Lutheran Reformation in Germany’, History of Education Quarterly, 28, 2 (1988), 191–206; Paolo Prodi, ed., Glaube und Eid. Treueformeln, Glaubensbekenntnisse und Sozialdisziplinierung zwischen Mittelalter und Neuzeit (München: Oldenburg, 1993).

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for the sake of the soul”,3 in which the education of the body is merely instrumental to the development of the soul and intellect. Nevertheless, the direct reading of sources gives a different image of the educational discourse, in which the body is indirectly but pervasively considered in humanist treatises and later gains center stage with a revival of Galenic humoralism in its connection with talents and educability, especially in the well-known work of Juan Huarte de San Juan (ca1530–ca1591). While in the Reformation, the role of the body was mainly linked to the continuity of some German traditions such as the Fastnachtspiel for civic ritual and community-building purposes,4 in treatises and scholarship, the body is subjected to a more scientific approach and especially to a progressively more quantifying perspective. This article will try to offer an overview of this process of quantification of the body in the educational realm.

2 The Qualitative Body in the Pseudo-Plutarchean De liberis educandis Because of its crucial role in building the Humanist educational tradition, we should begin with the opening text of the Plutarchean Moralia. The short treatise, known in the Latin version as De liberis educandis, is by far the most influential educational source of the Renaissance era. The Latin translation provided by the celebrated Italian preceptor Guarino Veronese (1374–1460) was read all over Europe and was the primary source of almost all Renaissance and early modern educational treatises, which borrow substantial points of their arguments and sometimes entire paragraphs from this text. The treatise was then re-translated from the original Greek in several modern languages throughout the sixteenth century, together with other texts from the Moralia (here we will quote from a fifteenth-century incunabulum of the translation by Guarino Veronese).

3 Aristotle, Politics, translated by H. Rackam, Loeb Classical Library vol. 264 (Cambridge, MA: Harvard University Press, 1932), b 7, 1338b. 4 See Jacob M. Baum, Reformation of the Senses. The Paradox of Religious Belief and Practice in Germany (Urbana: University of Illinois Press, 2018); Glenn Ehrstine, Theater, Culture, and Community in Reformation Bern, 1523–1555 (Leiden: Brill, 2002); Luana Salvarani, ‘In Flesh and Bone: Bodily Image and Educational Patterns in Early Reformation Theatre’, Paedagogica Historica, 54, 1–2 (2018), 83–95.

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It is interesting to see how Plutarch begins the treatise with a topos which encompassed the classics and popular medicine, recalling the necessity of fathers to choose their partner carefully and avoid reproduction when under the influence of alcohol. The point is scarcely developed and abandoned after a few paragraphs, but it puts this classic on education under the sign of the body and how it affects morals and behaviors. Without a properly composed body, education cannot deploy its full potential; the perspective, both for the author of De liberis educandis and Humanist educators, still was the Aristotelian one: “measures must be taken to ensure that the children produced may have bodily frames suited to the wish of the lawgiver”.5 This point will be recalled very explicitly by Juan Huarte in the proemial section of his Examen de ingenios. Plutarch elaborates on the allegory of agriculture for education, explaining how hard work and care can overcome even the most inept nature. This will be the point on which, later, the medical—Galenic reflection on education exemplified by Juan Huarte will discuss proposing a totally different perspective about the limits and potentialities of education, in which the nature of the body, carefully measured, will define individual attitudes for learning and the limits that even the most talented educator is unable to overcome. Nevertheless, in Plutarch, the bodily composition is not irrelevant, and its awareness constitutes a fundamental precondition in dealing with children and young people. Giving the tone to the whole educational tradition that will draw on this text in the Renaissance, the action of education is represented by Plutarch as limiting the natural intemperance arising from the young body. For example: I shall next pass to the period of adolescence, and say a very few words about it. […] But the iniquities of early manhood are often monstrous and wicked — unlimited gluttony, theft of parents’ money, gambling, revels, drinking-bouts, love affairs with young girls, and corruption of married women. The impulses of young men should therefore be kept fettered and restrained by careful supervision. For life’s prime is prodigal in its pleasures, restive, and in need of a curb.6

5 Aristotle, Politics, 7, 1335a. 6 Plutarch [attr.]/Guarino Veronese [transl.], De liberis educandis

(Venice: [no publisher], 14…), incunabulum, no page numbers. Bayerische Staatsbibliothek, Inc. s.a. 179 t.: “Ego vero postquam de puerili iam institutione ac ornamento disserui:

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The harsh depiction of adolescence, the age of intemperance for which education coincides with repression (impetus … cohercendi reprimendique) is directly connected with its vigor (petulans vigor aetatis ), that is, with the energy of growth and therefore the prevalence of the body on rational control. Galenic medicine connected this phenomenon with the unleashing of innate heat while the body started drying from the extreme wetness of childhood, even if, according to Galen, the absolute quantity of heat was the same in childhood and adolescence. With Galen’s own words in De temperamentis: Thus, after consideration on very many occasions of children, a large number of young men and youths, and of the same child both as infant and when grown to youth, I have not found any difference in heat between childhood and the prime of life. It is only, as already stated, that in children the heat appears to the touch more vaporous, and also appears full and pleasant, while in those in their prime it appears slight, dry and not equally pleasant. For much of a child’s substance, which is wet, flows away to the outside, but little in the prime of life, when it is dry.7

With its filiations and influxes, this medical theory lays at the basis of the whole humanist approach to education. We find the same argument in Vergerius’ De ingenuis moribus et liberalibus studiis adulescentiae (written around 1400), and in all treatises more or less inspired by this seminal book: Again, they are excessively credulous, for lacking worldly experience, they believe that whatever they hear is true. Also, their opinions change easily, since their humors are in motion due to growth and they have in abundance the heat which is the principle cause of motion. The soul, in fact,

ad adolescentium aetatem transeundum paucis esse censeo. […] At iuvenum peccata immensa plerunque sunt & miseriarum plena: ventris immodestia: paternorum bonorum expilatio, alea: saltandi protervia: aebrietates: amores virginum: mulierum corruptiones: adulteria. Horum igitur impetus omni cura & diligentia cohercendi reprimendique fuerant. Petulantem enim vigorem aetatis non facile a voluptatum observabis incursu”. English translation: Plutarch, Moralia I , “The Education of Children”, translated by Frank Cole Babbitt, Loeb Classical Library 197 (Cambridge, MA: Harvard University Press, 1927), 57–58. 7 Galen, Works on Human Nature, vol. I ‘Mixtures (De Temperamentis )’, ed. P. N. Singer and Philip J. van der Eik (Cambridge: Cambridge University Press, 2018), 121.

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follows the complexion of the body, and thus, just as those who lack something are quick to desire it, so they are swiftly satisfied once they have obtained what they want. The young follow their passions above all and do everything with great vigor because they have great desires which their bodily heat spurs on, while the rational powers and prudence that could moderate their desires are weak.8

Needless to say, this approach is essentially qualitative and, in its humanist rendition, does not give an account of individual differences (while Galen was adamant in saying that general phenomena had to be always measured in individual situations). There is no attempt in classifying attitudes or wits according to natural tendencies. The responsibility of understanding the pupil’s individual talents was entirely given to the educator, whose ability and charisma were deemed able to change pupils’ nature, bringing it to a global evolution impossible to assess in quantitative terms. In the realm of humanist pedagogy, the testimonies of Vittorino da Feltre’s former pupils,9 even if clearly biased by the admiration for their mentor, give an account of the “holistic”, global approach of humanist pedagogy and its disinterest in quantifying knowledge or abilities. The body was always present, but more to be curbed and disciplined than to claim its own rights. Vittorino took good care of the physical education of his pupils, but the torments and fasting he inflicted on his own body were considered proof of his exemplarity. Education accompanied the passage from adolescent to man, and therefore the fading away of bodily exigencies and the progressive dominance of moral philosophy. According to the author of De liberis educandis, For as regards the care of the body men have discovered two sciences, the medical and the gymnastic, of which the one implants health, the other 8 Petrus Paulus Vergerius, De ingenuis moribus (Venice: Chistophorus Valderfer), incunabulum, no page numbers: “Sunt item creduli nimis: ex defectu namque experientiae rerum vera credunt esse quaecumque audiunt: atque etiam de facili mutant opiniones: quoniam sunt eorum humores in motu propter augumentum corporis & abundant calor: qui maxime ad motiones facit. Anima vero complexione sequit corporis. Ideoque ut facile carentes concupiscunt: Ita potiti faciant cito. Passiones vero suas maxime prosequuntur: & omnia faciunt valde: quoniam concupiscentias habent acutas: quas calor incitat: neque vigent ratione & prudentia: qua illas moderari possint”. Translation by Craig Kallendorf, Humanist educational treatises (Cambridge, MA: Harvard University Press, 2002), 9. 9 See William Harrison Woodward, Vittorino da Feltre and other Humanist Educators (Cambridge: Cambridge University Press, 1905).

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sturdiness, in the body; but for the illnesses and affections of the mind philosophy alone is the remedy. For through philosophy and in company with philosophy it is possible to attain knowledge of what is honourable and what is shameful, what is just and what is unjust, what, in brief, is to be chosen and what to be avoided […] and, most important of all, not to be overjoyful at success or overmuch distressed at misfortune, nor to be dissolute in pleasures, nor impulsive and brutish in temper. These things I regard as pre-eminent among all the advantages which accrue from philosophy.10

As medicine and gymnastics take care of the body, philosophy takes care of the soul, avoiding that our animal part takes over (beluarum animos induamos ) and elevating man according to his spiritual potential. The influence of the education of the body on the soul takes the form of a general containment and regulation so that the body, with its fluids and heat, does not hinder spiritual and intellectual development. On these points, sixteenth-century medical humanism will trigger a radical change of perspective.

3 “Queriendo reducir a arte esta nueva manera de filosofar”: Juan Huarte’s Work and the Beginnings of a Quantitative Approach to Educational Selection The most important work representing the late sixteenth century shift in this regard, Juan Huarte’s Examen de ingenios, was born at the crossroads between the full maturity of medical humanism (which, according to Vivian Nutton, started to develop in the mid-fifteenth century, even

10 Plutarch/Guarino Veronese, De liberis educandis, no page number: “Ad corporis quidem curam duplicem scientiam humana excogitavit industria: medicinam dico: atque gymnasticam; quarum alter sanitatem, altera bonam importat habitudinem. Animorum autem aegritudines atque langores: sola est quae curet medeaturque philosophia. Per hanc enim & cum hac scire licet quid honestum: quid turpe: quid iustum: quid iniustum: & summatim quid diligendum: quid fugiendum, […] &, quod maximum est in prosperis fortunae successibus laetitia non effundi: nec in adversis casibus tristitia deprimi: nec omnino voluptatibus esse deditos: nec ita per iracundiam affici: ut beluarum animos induamos: quae omnibus philosophiae bonis antiquissima iudico”. Plutarch, Moralia I , 35.

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before the 1525 Aldine edition of Galen11 ) and a Spanish Renaissance season of treatises on princely education, in parallel with the national unification process. J. Quintana Fernández speaks of a “tradición española del ingenio”,12 borrowing the expression from a 1917 by Rodriguez Carracido. According to Carracido, this tradition was born with Juan Huarte and continued until the end of the eighteenth century. Quintana argues that this tradition lasted much longer, ending at the end of the nineteenth century and beginning in the fifteenth century, in the same age of medical humanism. Quintana highlights the role of works such as Rodrigo Sanchez de Arévalo, Brevis tractatus de arte, disciplina et modo aliendo et erudiendo filios pueros et iuvenes (1440s–50s.); Alonso Ortiz, Liber de educatione (1490 ca.); Elio Antonio de Nebrija, De liberis educandis libellus (1509) in building the framework in which Huarte’s work would act as a novelty in the realm of pedagogy. The aforementioned texts defined the concept of ingenio, elaborating on the (pseudo)-Plutarchean perspective and substantially confirming the primacy of moral philosophy in the education of the ruling class. Sánchez de Arévalo often paraphrases directly the De liberis educandis, and Nebrija, in turn, drew largely on Sánchez de Arévalo. Here ingenium established itself as a conceptual tool to confirm and consolidate the topoi of humanist pedagogy. In the context of an educational thought that did not find a way to develop itself beyond the classics, Renaissance Galenism was the new component and the trigger for change. This outcome was possible only because of the “innate flexibility” of Galenism, as explained by Vivian Nutton: Galenism had an innate flexibility. The sheer size of Galen’s own achievement and the writings of his followers allowed for dissent on certain topics, and even, at times, the abandonment of large areas of Galenic thought without necessarily destroying everything. Even Galen, for all his professions of consistency, changed his mind over details, and the Aldine edition of 1525 made clear, almost for the first time , the tension between his

11 Vivian Nutton, ‘The Rise of Medical Humanism: Ferrara, 1464–1555’, Renaissance Studies, 11, 1 (1997), 2–19. 12 J. Quintana Fernández, ‘Los Orígenes de la “Tradición Espanola del Ingenio”’, Revista de Historia de la Psicología, 22, 3–4 (2001), 505–515.

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empirical tendencies and his desire for a cogent theoretical substructure. Galenism also had an advantage over all its competitors. The language of humoral medicine was familiar to everyone, expressed in works of literature, plays and sermons as well as in manuals of self-help […] Galenism’s ubiquity permitted a variety of interpretations that would all qualify under that title.13

Thus, during the late sixteenth-century Galenic medicine came again to the forefront, with the new attention to the body which followed the expansion of anatomic discipline (which at the time was still able to coexist with Galenism), informing Juan Huarte’s Examen de ingenios (1574); the book was soon translated in several European languages, despite the condemnation by the Inquisition. The work, as we will see, tried to classify human abilities according to the different combinations allowed by the theory of temperaments, to draw a table of correspondence between such abilities, disciplines and professions, and to quantify the degrees of temperaments in order to optimize human reproduction for the best needs of the development of science and the prosperity of the State. Through the re-evaluation of his theory operated by the early Jesuit Antonio Possevino (1533–1611), Huarte’s theory would have inspired the classificatory dispositifs of Jesuit educational institutions. On the Reformation side, Melanchthon (1497–1560) wrote his De Anima commentarius (Wittenberg 1540), drawing heavily on medical sources and putting his extensive knowledge of classical tradition at the service of the convergence between anatomy, medicine, Aristotelian psychology and religion. In this paper, of course, there is no space to develop full-blown hypotheses about this phenomenon. Indeed the transformation of political structures from the individual/familiar manifestation of power to the increasingly centralized and bureaucratic administration of large monarchies urged a reflection on the education of the members of the political élite and posited the necessity of an appropriate selection of talents. Moreover, the religious schism had emphasized the idea of a radical renewal in culture and the necessity of new protocols for educating the man and the subject.

13 Vivian Nutton, ‘Renaissance Galenism, 1540–1640: Flexibility or an Increasing Irrelevance?’, in Brill’s Companion to the Reception of Galen (Leiden: Brill, 2019), 482.

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An attempt to employ medicine to quantify and classify human talents was a possible response to such needs. Again, the base materials of this theory of education were not new: the novelty was the use of medicine to analyze not only the character and morals of the pupil but also his prospective abilities. From this novelty came the (albeit initially) quantitative approach to temperaments. The consequence of this assumption was the subordination of the educator to medical knowledge: any educational action not following the physical complexion of the pupil was doomed to failure, and the appropriate examen de ingenios became the most crucial act of all the path toward adulthood. Moreover, the harmonious development of all faculties (the analogous of Galen’s “ideal mixture” of temperaments) must be abandoned in favor of the development of the one and only talent of the pupil, for his personal achievement and the improvement of the State. A well-known passage in Juan Huarte’s preface to his work states clearly the point: To the end that the Works of all Artists may attain the utmost Pitch of Perfection, and be of the greatest use to the Common-Wealth, it seems very Reasonable that by a Law it should be provided, that the Carpenter should not interfere with the Husbandman, nor the Weaver with the Architect, nor yet the Lawyer play the Physician, nor the Doctor the Advocate, but that each should stick close to the Profession most agreeable to his Talent, and let the rest alone. For considering how short and limited the Wit of Man is to one thing and no more; I have been always of Opinion, that no Man could understand two Arts perfectly well, without proving defective in one of them: And that accordingly none might err in the Choice of that which was most agreeable to the Bent of his Natural Inclination, there should be Triers appointed by the State, Men of approved Sagacity and Knowledge, to search and found the Abilities of Youth, and after due Search, to oblige them to the Study of that Science their Heads leaned most to, instead of abandoning them to their own Choice.14

14 Juan Huarte de San Juan, Examen de ingenios para las sciencias (Baeza: en casa de Juan Baptista de Montoya, 1574), fol. 1r–1v: “Para que las obras de los Artifices tuviessen la perfection que convenia al uso de la republica, me parescio (Catholica real Magestad) que se avia de establecer una ley. Que el Carpintero no hiziesse obra tocante al oficio del labrador, ni el Texedor del Archtecto, ni el Iurisperito curasse, ni el Medico abogasse; sino que cada uno ejercitase sola aquel arte para la cual tenia talento natural: y dexasse las demas. Por que considerando quan corto y limitado es el ingenio de el hombre, para una cosa y no mas: tuve siempre entendido que ninguno podia saber dos

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Huarte’s aim is totally different from the ones of most Renaissance educators interested in proper princely education and, therefore, in preparing to exercise power. Here the perspective includes the whole of the State and, while Huarte explicitly states the importance of making studies accessible to talented children from the lower classes, he also recognizes that this is impossible in his time. Therefore education must focus on the middle and higher classes to prepare for the various professions and provide the State with high-quality and performing functionaries, from law to medicine to philosophy and the military. The Design of this Work is to know and distinguish the Natural Differences of Human Understanding, and how with Skill to apply to each the Science he may most Excel in.15

To reach this aim, “universal” education or the Humanist conception of “integral humanhood” becomes useless when not discouraged. In order to provide a proper examination of wits, the medical and temperamental bases of such wits must be evaluated and, as much as possible, quantified. Huarte claims for an educational science able to classify human nature “with distinction and clarity”, to identify the various aptitudes and to develop a semeiotic of talents: All the Antient Philosophers have found by Experience, that where Nature disposes not a Man for Knowledge, ‘tis in vain for him to labour in the Rules of the Art. But not one of them has clearly and distinctly declar’d what that Nature is, which renders a Man fit for one, and unfit for another Science, nor what difference of Wit is observed among Men, nor what

artes con perfection, sin que enla una faltasse: y por que no errasse en elegir la que a su natural estava mejor, avia de aver diputados en la Republica, hombres de gran prudencia y saber, que en la tierna edad descubriessen a cada uno su ingenio, haziendole estudiar por fuerça la ciencia que le convenia: y no dexarlo a su election”. Juan Huarte/Edward Bellamy [transl.], Examen de ingenios, or, The tryal of wits discovering the great difference of wits among men […] published originally in Spanish by Doctor Juan Huartes; and made English from the most correct edition by Mr. Bellamy (London: Richard Sare, 1698), no page number. 15 Huarte, Examen, fol. 8r: “Saber pues distinguir y conoscer estas differencias naturales del ingenio humano, y aplicar con arte a cada una, la sciencia en que mas ha de aprovechar, es el intento desta mi obra”. English translation Huarte/Bellamy, Examen, no page number.

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Arts and Sciences are most suitable to each Man in particular, nor by what Marks they may be discern’d, which is of the greatest Importance.16

Huarte’s theory elaborates with passion and, often, with a harsh satirical tone on the traces left by Galen in his Quod animi mores temperamenta sequantur, taking inspiration especially from its emphasis on the role of the body in building individual character and, therefore, the primacy of medicine on education in the realm of morals. As summarized by Fabrizio Bigotti in his book on Renaissance Galenism, The Quod animi mores closes with a frontal attack on Stoic ethics for its precepts cannot be squared with the origin of evil; in other words, it is not possible for human beings to be born good and then be corrupted by society. The origin of evil must be sought inside the human soul and it lies in the anthropological continuity between man and animal and to the prevalence of irrational instincts in both, accounting for errors of judgment as well as for false opinion. The human inclination toward evil is thus an imprint that everyone carries from birth, impossible to be rooted out but amenable to control by keeping company with one’s betters and seeking the help of a good physician.17

Even if Huarte could not know the last chapter of Quod animi mores in the original Greek text (which was recovered later), current editions at his time drew from the Medieval translation by Niccolò da Reggio, which thus enjoyed a long life in the Humanist editions and was able to bring in the Renaissance debate the last and most polemic section of the Galenic treatise. More specifically, a comparison of the direct quotations included in the Examen with the existing Latin editions of Galen shows that Huarte read from the translation by Bartholomeus Sylvanius, as printed in the Giunti edition by Agostino Gadaldini, printed in

16 Huarte, Examen, fol. 2r–2v: “Todos los pilosophos antiguos, hallaron por experiencia: que donde no hay naturaleza que disponga al hombre a saber, por demas es trabajar en las reglas del arte. Pero ninguno ha dicho con distinction ni claridad, que naturaleza es laque haze al hombre habil, para una ciencia: y para otra incapaz: Ni quantas differencias de ingenio se hallan enla especie humana: ni que artes y sciencias responden a cada uno en particular: ni con que señales se avia de conoscer, que era lo que mas importava”. English translation Huarte/Bellamy, Examen, no page number. 17 Fabrizio Bigotti, Physiology of the Soul. Mind, Body, and Matter in the Galenic Tradition of the Late Renaissance (1550–1630) (Turnhout: Brepols, 2019), 110.

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Florence in 1541–1542, or in the almost identical Froben edition, printed in Basel in 1542.18 In his elaboration of Galen’s theory, Huarte associates with each predominant individual temperament (hot–humid, hot–dry, cold–humid, leaving aside cold–dry associated with the decline and death) a mental faculty (imagination, intellect and memory) and therefore predicts from temperament the right educational path and future profession for each individual. Of course, the child is always more humid than the adult and the young hotter than the old man, but the humanist ideal of a common path toward perfection was opposed in the name of the plurality of possible individual and unbalanced “perfections”. Even if there are all sorts of subtle ramifications in the system (together with some theological implications which fall out of the scope of this article), the general structure of Huarte’s theory is very easy to understand. The author is glad to expound it in a narrative form in order to make it suitable as a practical instrument: for the father to choose the relevant studies for the children, for the preceptor to find the pupil’s talent (or lack thereof), for the couple to manage the techniques which will allow them to have a male child good for the profession he will likely embrace according to his origins. Measure and quantities intervene at all stages of the argument, but especially in the book’s second part, the most clearly aimed at regulating reproduction. The classical assumptions of the temperamental theory are reconsidered to provide suitable combinations of the male and female temperaments. Both sexes can have one of the four combinations (hot– humid, hot–dry, cold–humid, cold–dry), but the base temperament of the female being cold and humid, and the base temperament of the male being hot and dry, these “background tones” are subdivided in three degrees each, to facilitate the best combination. MAN hath not his Temperament so limited as Woman: For he may be hot and dry (which Temperament Aristotle and Galen are of Opinion is that which best agrees with his Sex) as also hot and moist, and temperate; but cold and moist, and cold and dry, will not be admitted, so long as the

18 The comparison in its entirety was presented as a paper at the 2021 RSA Annual Meeting. See Luana Salvarani, Retracing Galen: The Origin and Meaning of Galenic Quotes in Huarte’s Examen de Ingenios. Handout available at https://rsa.confex.com/ rsa/21virtual/meetingapp.cgi/Session/4833 (accessed November 20, 2021).

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Man is in Health, and not some way amiss, so that for the same reason, as there is no Woman hot and dry, nor hot and moist, nor temperate; even so, there is no Man cold and moist, nor cold and dry, in comparison of Women, unless in a Case as I shall presently shew. A Man hot and dry, or hot and moist, or temperate, has as many Degrees in his Temperament, as a Woman has of Cold and Moist; insomuch that we have need of Tokens to discern what Man is, in what Degree, to assign him a Wife answerable to him in Proportion. You are to know then, that from the Principles from which we have collected the Woman’s Temperament, and her Degrees of Cold and Moist, the same we shall make use of to know which Man is Hot and Dry, and in what Degree.19

The quantification of temperaments, of course, implies a correlative quantification of attitudes and personalities of the men and women pertaining to the different degrees and, in perspective, the behavior to be observed before and during conception. Nevertheless, the quantification has not only a taxonomical aim: it also acts as a diagnostic, and measuring the material body (or parts of it) is often indicated as the only possible way to measure immaterial qualities such as memory, rationality or artistry, without recurring to time-consuming and fallible observations. The bulk of Body which a Temperate Man ought to have, as Galen says, is not a thing precisely determined by Nature, because he may be tall, short or of a middle Stature (in proportion to the quantity of temperate Seed, he had in time of his formation). But for what regards the Wit, the Middle-size is better among Temperate Men than over-tall or short: And if it should incline to either Extreme, it is better too Short, than Tall, for Bones and Flesh as we have proved before, from the Opinion of 19 Huarte, Examen, fol. 297v–298r: “El hombre no tiene tan limitado su temperamento como la mujer; porque puede ser caliente y seco (y esta temperatura piensa Aristóteles, y Galeno, que es la que más conviene a este sexo), y caliente y húmido, y templado. Pero frío y húmido, y frío y seco, no se puede admitir (estando el hombre sano y sin ninguna lesión); porque por la mesma razón que no hay mujer caliente y seca, ni caliente y húmida, ni templada, así no hay hombres fríos y húmidos, ni fríos y secos en comparación de las mujeres, si no es de la manera que luego diré. El hombre caliente y seco, y caliente y húmido, y templado, tiene los mesmos tres grados en su temperamento que la mujer en la frialdad y humidad; y, así, es menester tener indicios para conocer qué hombre en qué grado está, para darle la mujer que le responde en proporción. Y, por tanto, es de saber que de los mesmos principios que coligimos el temperamento de la mujer y el grado que tenía de frialdad y humidad, de esos propios nos habemos de aprovechar para entender qué hombre es caliente y seco, y en qué grado”. English translation Huarte/Bellamy, Examen, 416–417.

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Aristotle and Plato much incommode the Wit. Agreeable here unto the natural Philosophers are wont to ask. Why those of little Stature are Wiser for the most part than those of a tall Stature? […] But this is not the Reason thereof, it is rather because Big-men have much Moisture in their Composition, which dilates the Flesh, and makes it more pliant to receive the Augmentation, which the natural Heat procures. It fares quite contrary in little Bodies, for through their over-dryness, the Flesh cannot take its Course, nor the natural Heat enlarge or stretch it out, and therefore they remain of a low Stature. But among the first qualities, we have prov’d before, there is none so prejudicial to the Operations of the Rational Soul, as much Moisture, nor that so quickens the Understanding as Dryness.20

Huarte tries to design a system in which medicine (but he calls it, with Aristotelian term, natural philosophy, in order to distinguish it from practical medicine) can give to humanity clear-cut information on how to procreate responsibly for the public good; how to qualify and quantify exactly individual talents; to give scientific advice on how to maintain and develop talents through food, exercise—and only marginally through discipline and teaching. This plan intersects with many aspects which make the text quite entertaining, such as Huarte’s declared antipathy for language scholars and professors of other disciplines which require strong memory (and therefore the humid and cold temperament which is opposite to the hot and dry of the philosopher, and which is connected with negative qualities such as being childish or womanly), and his 20 Huarte, Examen, fol. 262r–263r: “La cantidad de cuerpo que ha de tener el hombre templado (dixe Gal.) que no esta determinada por naturaleza: por que puede ser grande, pequeño, y de mediana estatura (conforme a la cantidad de simiente templada, que ubo al tiempo que se formo). Pero para lo que toca al ingenio, mejor es la moderada estatura, en los hombres templados, que la grande, ni pequeña. Y si al uno de los dos extremos ha de inclinar, mejor es a pequeño, que a grande; porque los muchos huessos, y carne (provamos atras de opinion de Pla. y Aris.) que haze mucho daño al ingenio. Conforme a esto: suelen los philosophos naturales preguntar Cur homines, qui brevi sunt corpore, prudentiores magna ex parte sunt quam qui longo? Como si dixera: que es la causa, que por la mayor parte, los hombres pequeños son mas prudentes, que los largos? […] Pero no es esta la razon: sino que los hombres largos tienen mucha humidad en su composicion, la cual haze las carnes muy dilatables, y obedientes a la aumentacion, que procura hazer siempre el calor natural. Al reves acontesce en los pequeños de cuerpo: que por la mucha sequedad, no pueden hazer correa sus carnes, ni el calor natural las puede dilatar, ni ensanchar: por donde quedan de breve estatura. Y entre las calidades primeras (tenemos probado atras) que ninguna echa tanto a perder las obras del anima racional como la mucha humidad, ni quien abive tanto al entendimiento, como la sequedad”. English translation Huarte/Bellamy, Examen, 374–375.

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polemic against the structure of Universities and their programs based on Latin and grammar. The whole of these passions and tensions make the arguments sometimes less clear, but the base concept remains the same: temperaments can and must be measured, and the preference for a temperament instead of another cannot make an exact quantification less desirable and necessary. For though cold and dry are two Qualities requisite to the Understanding, yet they ought to keep a certain Measure and Quantity: which once exceeded, they do rather harm than good. As appears in very old Men, who through the abundance of Coldness and Dryness dot and fall into many Follies.21

The emphasis on “Measure and Quantity” is the most characterizing novelty of the book, even if Huarte does not provide instruments of measure which go beyond the tradition of Galenic observation and semeiotic repertoire. As we will see later, for the beginning of proper quantification in medicine, we must wait for Sanctorius’s (1561–1636) work and his instruments, built to transform Galenic and Huartian degrees into actual measures.22 Nevertheless, refusing the idea of a perfect temperament which constitutes the point of reference for all other temperaments and the coincidence of health and intelligence with equilibrium, Huarte constitutes the starting point of research in which the (later measurable) differences among temperaments and the respective talents could act to classify and practically assign a “score” to each type of ingenium. The shift from theory to the practical side is described by Huarte as being a passage from a manera de philosophar to an arte: Therefore being resolved to reduce this sort of Philosophy to Practice, and to evidence it in In|stances of some Wits, Your Majesty’s presents as one of

21 Huarte, Examen, fol. 338v–339r: “[…] por que puesto caso que la frialdad y sequedad, son dos calidades, que ha menester el entendimiento: pero han de tener cierta medida y cantidad; de la qual passando, antes haze daño que provecho. Como parece en los hombres muy viejos: que por la mucha frialdad y sequedad, los vemos caducar y dezir mil disparates”. English translation Huarte/Bellamy, Examen, 482. 22 See Bigotti, Physiology of the Soul, Chapter 6.

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the most Eminent, which Surprizes the whole World, in observing a Prince of so vast Knowlege, and such Consummate Wisdom and Prudence.23

A paradigm of education was changing, while the humanist ideal of the cultivated prince had lost its fascination and capable functionaries were required instead. The body needed to be programmed before birth through appropriate reproductive techniques, then carefully quantified and classified along with individual talent in order to be developed at best. Even if this phase in the history of education did not last long, it opened the path to political and anthropological modernity, contributing to the contemporary perception of the human self, its struggle for power and its unavoidable fragmentation.

4 Concluding Remarks: The Ingenium from Soul Faculty to Organic Function The change in educational thought that took place during the sixteenth century, described above, basically ended the history of the Humanist paradigm of the perfectus magister—with his all-encompassing maieutic power—and opened the door to a more functional and measurable idea of cultivating the ingenium. Galen, as we have previously seen, introduced the strict derivation of talents (and moral inclinations) from temperaments in the last section of the Quod animi mores. Huarte quotes several times the example with which the Galenic work abruptly ends: because of the bad influence of climate on the body, Scythia could boast only a philosopher, while at Athens there were many of them. It can be said that Huarte envisaged a sort of continuation or completion of Quod animi mores, just as he wanted to develop the last paragraphs written by Galen: But those who hold that the soul is not benefited and harmed by the mixture of the body have no account to give of the difference among children, and have no cause to provide of any of the benefits which we derive

23 Huarte, Examen, fol. 3v: “Queriendo pues reduzir a arte esta philosophar: y probarla en algunos Ingenios, luego me ocurrio el de por ser mas notorio: de quien todo el Mundo se admira, viendo un saber y prudencia […]”. English translation Huarte/Bellamy, Examen,

nueva manera de Vuestra Magestad Principe de tanto no page number.

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from daily regime, not, indeed, of the distinctions in character traits – which obviously vary between spirited and lacking in spirit, intelligent and unintelligent.24

In Galen’s footsteps, Huarte’s theory put forward very clearly the necessity to measure temperaments, assessing through observation the quantity of bodily fluids, as the only way to establish the features of ingenium and therefore trace the most fruitful educational path for each individual. Even if Huarte conceived the three faculties (intellect, memory and imagination) as faculties of the rational soul, according to the Aristotelian tradition, he insisted on the fact that their prevalence and operation was strictly dependent on the temperament and on physical substances: “por que pensar que el anima racional (estando en el cuerpo) puede obrar sin tener organo corporal que le ayude, es contra toda la philosophia natural”.25 Huarte tries to preserve the incorporeality and uniformity of the rational soul in general and abstract terms, but the fact that individuals have different talents is explained by the nature of intellect as “corporeal faculty”: that if one man Reasons better than another, it comes from the Understanding’s being an Organic Power, and better dispos’d in one than another, and not for any other Reason.26

The statement establishes that intellect—i.e., in Huarte’s system, the more refined human ability—is neither a spiritual faculty nor a faculty of the soul, but a corporeal one, thus radically changing the perspective of possible knowledge and assessment of the intellect itself. Moreover, a corporeal faculty cannot be taught but only improved through the body, thus establishing the primacy of the physician in respect to the educator, which is the main feature of the Examen.

24 Galen, Psychological Writings, ‘The Capacities of the Soul depend on the Mixtures of the Body’, ed. by P. N. Singer, Daniel Davies and Vivian Nutton (Cambridge: Cambridge University Press, 2013), 409. 25 Huarte, Examen, fol. 66r. 26 Huarte, Examen, fol. 85v: “[…] Y veemos por experiencia que un hombre entiende

mejor que otro y discurre major: luego ser el entendimiento potencia organica, y estar en uno mas bien dispuesta que en otro, lo causa; y no por otra razon ninguna”. English translation Huarte/Bellamy, Examen, 163–164.

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According to Fabrizio Bigotti, Huarte’s ingenium merges this concept of intellect and a more intuitive side of the soul, and therefore can be both described in quantitative and qualitative terms: The criticism here directed at the Aristotelian notion of separation is made with an obvious purpose in mind. Indeed, by claiming that the intellect or, better yet, judgment, is a corporeal faculty (entendimiento potencia organica), Huarte frames the concept of genius in such a way as to bring into it two kinds of faculties that Aristotle had kept separate: on the one hand are those faculties which are given by nature and are ‘gradable’ (and which can be designated by the Greek term δʋναμις); ´ on the other, are those faculties which are governed by intuition (νoε‹ν, θιγε‹ν), representing ‘possession in actuality’ and not admitting of any gradation, in that they preside over functions whose value can only be either true or false.27

With the seventeenth century and the evolution of instruments and medical theory, particularly with Santorio Santori, actual quantification will progressively take the place of the Galenic approach based on degrees. The needs for such change were not only about shifting paradigms in the history of medicine and science but involved the whole realm of educational thought and, with it, the system of institutions that performed the task to bring pedagogical theory into practice.

27 Bigotti, Physiology of the Soul, 126.

Quali-quantitative Measurement in Francis Bacon’s Medicine. Toward a New Branch of Mixed Mathematics Silvia Manzo

1

Introduction

Different studies dedicated to re-examining the value and historiographical accuracy of the thesis of the mathematization of nature during the Scientific Revolution have held that mathematization acquired different forms throughout the history of science.1 One of them is quantification, which, based on the work of Sophie Roux, we define as the capture in numerical form of certain aspects of material things, through measurements that are made with certain techniques, devices, and precise

1 Sophie Roux, ‘Forms of Mathematization (14th–17th Centuries)’, Early Science and

Medicine, 15, 4/5 (2010): 319–337; Geoffrey Gorham, Benjamin Hill, Edward Slowik, and C. Kenneth Waters, eds. ‘Introduction’, in The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century (Minneapolis-London: University of Minnesota Press, 2016), 1–28.

S. Manzo (B) Universidad Nacional de La Plata—IdHICS—CONICET, Buenos Aires, Argentina e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_4

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records.2 As we shall see, Francis Bacon’s (1561–1626) philosophy represents an early modern example that lies halfway between a purely qualitative and a tout court quantitative scientific outlook. Indeed, in his philosophy there is an experimental program that considers measurement as a key element to produce works useful to humans, that is, to transform nature through human intervention. This includes works aimed at the care of one’s own body, the prevention and cure of diseases, and the prolongation of life.3 However, not all variables that Bacon indicates should be measured are expressed through a metric and precise numbers. In this chapter we will argue, firstly, that Bacon’s engages in a peculiar form of mathematization of nature that develops a quali-quantitative methodology of measurement. Secondly, we will show that medicine is one of the disciplines where that dual way of measurement is practiced. In the first section of the chapter, we will expose the ontology involved in the Baconian proposal of measurement of nature. The second section will address the place that mixed mathematics occupies in Bacon’s scheme of scientific branches and will suggest that a proper advancement of medicine can generate a new branch of mixed mathematics. The next section will reconstruct Bacon’s approach to measurement and expose its quali-quantitative import. In the last section, we will show some examples of medicine in which this quali-quantitative measurement is applied. 2 Roux, ‘Forms of Mathematization (14th–17th Centuries)’, 325. I agree with her approach that conceives mathematization in a wider sense embracing different forms and practices. Yves Gingras, ‘What Did Mathematics Do to Physics?’ History of Science, 39, 4 (2001): 383–416, 408 n10, distinguishes quantification (understood in terms similar as Roux) from mathematization (i.e., the writing of abstract geometric or algebraic formulations of physical phenomena). 3 For studies on medicine in Bacon, see Helmut Minkowski, ‘Einordnung, Wesen und Aufgaben der Heilkunst in dem Philosophisch-Naturwissenschaftlichen System des Francis Bacon: Zur Kenntnis der Beziehungen zwischen Medizin und Philosophie im 16. Und 17. Jahrhundert’, Sudhoffs Archiv für Geschichte der Medizin und der Naturwissenschaften 27, 3/4 (1934): 299–327; Ian Box, ‘Medicine and Medical Imagery in Bacon’s “Great Instauration”’, Historical Réflections/Reflexions Historiques, 16, 2/3 (1989): 351–365; Jeffrey Boss, ‘The Medical Philosophy of Francis Bacon (1561–1626)’, Medical Hypotheses, 4, 3 (1978): 208–220; Benedino Gemelli, ‘Formation and Preservation of Life Between Speculation and Experiment in the Writings of F. Bacon’, Medicina nei secoli, 15 (2003): 155–176; id, ‘Francis Bacon: un riformatore del sapere tra filosofia e medicina’, Cronos. Cuadernos valencianos de Historia de la Medicina y de la Ciencia, 7, 2 (2005): 227–275; Stephen Pender, ‘Examples and Experience: On the Uncertainty of Medicine’, The British Journal for the History of Science, 39, 1 (2006): 1–28. See also other studies cited in this chapter.

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The Ontology of Measurement

Recent studies have insisted on the appetitive character of Baconian matter. This characterization is undoubtedly accurate and essential to understand both Baconian science in general and medicine as one of its branches.4 However, there is another characteristic of Baconian matter that is fundamental and especially relevant to the analysis we will do in this chapter: its quantitative character.5 What did Bacon think about quantity in nature in general? From an ontological point of view, quantitas is a form, the most abstract and separate from matter among all forms.6 The conjunction of the conception of quantity plus the conception of matter entails that nature has variables that are measurable. Throughout his various works, Bacon assumed and stated emphatically that the total amount of the material mass of the universe always remains the same. Once created by God, the total amount of matter did not increase or decrease. There is an appetite for self-preservation that accounts for this quantitative principle: the strongest appetite of every single particle of matter resists being annihilated. Since the 1590s, Bacon expressed certain intuitions regarding the distribution of matter in the cosmos and celestial movements according to the system of Alpetragius († ca1204). From there on, he was integrating throughout his different works ideas from different philosophical traditions that could complete all aspects and material levels of this world system. In this process, Bacon changed his mind regarding several questions, such as, for example, the nature of the causes to be investigated by natural philosophy, the atomic 4 This interpretation of Baconian matter is found especially in Guido Giglioni, ‘Mastering the Appetites of Matter. Francis Bacon’s Sylva Sylvarum’, in The Body as Object and Instrument of Knowledge, ed. by Charles T. Wolfe and Ofer Gal (Dordrecht: Springer, 2010). 5 A monograph arguing for the quantitative aspect of Baconian matter is found in Silvia Manzo, Entre el atomismo y la alquimia. La teoría de la materia de Francis Bacon (Buenos Aires: Biblos, 2006). For specific points maintained in this section see Silvia Manzo, ‘Holy Writ, Mythology, and the Foundations of Francis Bacon’s Principle of the Constancy of Matter’, Early Science and Medicine, 4, 2 (1999): 114–126; ‘The Ethics of Motion: Self-Preservation, Preservation of the Whole, and the “Double Nature of the Good” in Francis Bacon on Motion and Power, ed. by Guido Giglioni, James Lancaster, Sorana Corneanu, and Dana Jalobeanu (Cham: Springer, 2016). 6 Francis Bacon, ‘De augmentis scientiarum’, in The Works of Francis Bacon, ed. by James Spedding, Robert Leslie Ellis, and Douglas Denon Heath (London: Longman, 1867–1876), vol. I, 576–578.

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constitution of matter, and the existence of the vacuum. However, despite these changes, the principle of the conservation of mass remained as an axis of unshakeable continuity both in the background and in the foreground of his conception of matter and nature. Thus, again and again we find the categorical affirmation of the principle of constancy of the quantity of matter in different contexts: in the early Cogitationes de natura rerum (1604), in addition to his endorsement of the atomic hypothesis, he sketches his main ideas about matter and motion; in the allegorical works (De sapientia veterum (1609) and De principiis atque originibus (c. 1612?) where he presents the stages of the formation of the world through the myths of Coelum, Pan, and Cupid, and when he refers to the limits of the vexation of matter in experimentation through the figure of Proteus; in Novum organum (1620), regarding the classification of motion; in Historia densi et rari (1623), a work dedicated exclusively to the theme of the quantity of matter; in Phaenomena universi (1612), Historia vitae et mortis (1623), Sylva Sylvarum (1626), etc., when interpreting numerous experimental instances or establishing the provisional rules (canones moviles ) obtained from natural history.

3

Mixed Mathematics, Physics, and Medicine

In the Baconian architecture of the sciences quantity is the object of mathematics, an appendix of natural philosophy that is divided into two kinds: pure mathematics and mixed mathematics. The first (composed of arithmetic and geometry) has as its object the abstract quantity, without any relation to matter. In turn, mixed mathematics considers quantity as it serves as an auxiliary to elucidate and prove the axioms of physics, and also to operate according to them. Mathematics is an inescapable tool for the success of science. Without its assistance, many parts of nature “can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated to use with sufficient dexterity”.7 Besides, the investigation of the extensions and motions of matter cannot be successfully applied to practice, without a prior quantitative inquiry of its different components. Consequently, the absence of a

7 ‘De augmentis scientiarum’, in The Works of Francis Bacon, vol. I, 578; vol. IV, 431.

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correct measurement generates sciences that perhaps will be “pretty as speculation, but fall flat in practice”.8 Perspective, music, astronomy, cosmography, architecture, and machinery [enginery; machinaria] and “some other” belong to mixed mathematics.9 Thus, Bacon integrates into the field of mixed mathematics the arts of the medieval quadrivium along with some of the mechanical arts of the Renaissance. However, he also believes that if research is conducted properly, scientific progress will make it possible for other branches of natural philosophy to take the form of mixed mathematics: “I predict that there will be more kinds of them [mixed mathematics], if men be not idle. For as physics advances farther and farther every day and develops new axioms, it will require new works [opera nova] from Mathematics in many things, and so the kinds of mixed mathematics will be more numerous”.10 We can assume that he believes that medicine will generate a new kind of mixed mathematics. This makes perfect sense because in the Baconian perspective medicine stands out for its great benefits in the material life of human beings, so that it is a discipline in which the instrumental aspect of mixed mathematics is very necessary. As Rees points out, the goal of prolonging life is the end of Baconian science as a whole. Medicine is the discipline in charge of fulfilling this objective, along with the objective of preserving health and curing diseases.11 It is noteworthy that this practical function seems to be the main reason why Bacon introduces mathematics into his scientific architecture. 8 Francis Bacon, ‘Novum organum’, in The Instauratio magna. Part 2: Novum organum and Associated Texts, ed. by Graham Rees, and Maria Wakely, in The Oxford Francis Bacon (hereafter OFB) vol. XI, book 2, aphorism XLIV (Oxford: Clarendon Press, 2004), 366–367. 9 ‘De augmentis scientiarum’, in The Works of Francis Bacon, vol. I, 578; vol. IV, 371. 10 Ibid. (translation slightly modified). See Dana Jalobeanu, ‘“The Marriage of Physics

with Mathematics”’: Francis Bacon on ‘Measurement, Mathematics, and the Construction of a Mathematical Physics’ in The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the Seventeenth Century, ed. by Geoffrey Gorham, Benjamin Hill, Edward Slowik, and C. Kenneth Waters (Minneapolis—London: University of Minnesota Press, 2016). Jalobeanu argues that the prospect of an increasing number of branches of mixed mathematics was held by other authors at Bacon’s time. She points out the case of Thomas Digges, author of A Geometrical Practical Treatise Named Pantometria (1571). For another interpretation of Bacon’s mathematics see Giuliano Mori, ‘Mathematical Subtleties and Scientific Knowledge: Francis Bacon and Mathematics, at the Crossing of Two Traditions’, The British Journal for the History of Science, 50, 1 (2017): 1–21. 11 Graham Rees, ‘Introduction’, in OFB, vol. VI, lxi–lxix.

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He acknowledges the existence of precedents in this regard, expressly attributing to Aristotle the very idea that the union between “Physics and Mathematics produces Practice or Mechanics”.12 This attitude is in line with the tradition of mixed sciences and was a widespread position in the late sixteenth and early seventeenth centuries, in which a relationship is established between mathematics, mechanics, and practical utility.13 The correct measurement of bodies and virtues becomes, therefore, a fundamental precept: “every thing to do with natural phenomena, be they bodies or virtues, should (as far as possible) be set down, counted, weighed, measured and defined. For we are after works not speculations, and, indeed, a good marriage of Physics and Mathematics begets Practice”.14 This product of the union of physics and mathematics is called “mechanics”, which in Bacon’s scheme is nothing but a form of “operational physics”.15 Physics is a part of natural philosophy, which investigates the efficient and material causes through the schematisms and latent processes of bodies (imperceptible configurations and motions of the microscopic particles of macroscopic bodies). By introducing measurements and calculations, mathematics has an instrumental value in permitting the low-level axioms discovered by physics to be translated into practical effects manipulating nature for human benefit. In this way, the measurement of nature’s variables is not a secondary byproduct

12 ‘De augmentis scientiarum’, in The Works of Francis Bacon, vol. I, 576; vol. IV, 369. It has already been noted since Ellis’ edition, that here Bacon alludes to the PseudoAristotelian. Quaestiones mechanicae, a work that circulated widely in Europe during the sixteenth and seventeenth centuries. On the early modern reception of this work see Paul Lawrence Rose and Stillman Drake, ‘The Pseudo-Aristotelian Questions of Mechanics in Renaissance Culture’, Studies in the Renaissance 18 (1971): 65–104; Joyce Van Leuween, The Aristotelian Mechanics: Text and Diagrams, chapter 6 (Cham: Springer, 2016). 13 Gingras, ‘What Did Mathematics Do to Physics?’, 384; Jalobeanu, ‘The Marriage of Physics with Mathematics’, 55–60. 14 Francis Bacon, ‘Parasceve ad historiam naturalem’, in OFB, vol. XI, 464–465; cf. ‘Novum organum’, in OFB, vol. XI, book 2, aphorism viii, 212–213. 15 Sophie Weeks, ‘The Role of Mechanics in Francis Bacon’s Great Instauration’, in Philosophies of Technology: Francis Bacon and his Contemporaries, 2 vols., ed. by Claus Zittel, Romano Nanni, Gisela Engel, and Nicole Karafyllis (Leiden: Brill, 2008), 176. She offers a very valuable interpretation of Bacon’s mechanics in terms of “operative physics”. However, she undervalues the importance of the role that mathematics plays in it. On the contrary, Cesare Pastorino, ‘Weighing Experience: Experimental Histories and Francis Bacon’s Quantitative Program’, Early Science and Medicine, 16, 6 (2011): 542–570, notes the connection to mixed mathematics and underlines the operative role of measurement.

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of the project of the restoration of learning, but a fundamental requirement to realize one of its most distinctive goals: the transformation of nature through human power for the well-being of human beings.

4 The Quali-quantitative Approach to Measurement In different works, Bacon postulates a classification of “measures” (mensurae). They intend to measure different variables of what we would call “properties” of bodies and that Bacon calls motions (motus ), forces (vires ), and actions (actiones ) of bodies. Already in the early Valerius terminus (1603), he regretted that “the calculating and ordination of the true degrees, moments, limits, and laws of motions and alterations (by means whereof all works and effects are produced)” had never been properly put into practice.16 Later, in Novum organum the mensurae of motions are presented as “Mathematical Instances” and “Instances of Measure” (Instantiae Mathematicae, Instantiae Mensurae), which belong to a group of instances specifically useful for operation, namely “Practical Instances” (Instantiae Practicae).17 In Abbecedarium novum naturae (1622) they are simply called “mathematics, or measures and scales of motions”18 and in De augmentis scientiarum (1623) they are presented, like mathematics, as “appendix to [abstract] physics or measures of motions [mensurae motus ]”.19 Bacon argues that the motions of the universe at its various levels of complexity are nothing more than manifestations of the appetites of bodies, that is, desires or rejections of the inner parts of bodies with respect to other internal or external material units. Sometimes, the different types of tangible or pneumatic matter that reside within the same body have appetites opposed to each other; at other times, they oppose the appetites of the surrounding bodies. In this field of struggle between

16 Francis Bacon, ‘Valerius terminus’, in The Works of Francis Bacon, vol. III, 243–244. 17 ‘Novum Organum’, in OFB, vol., XI, book 2, aphorism xliv, 366–699. 18 Francis Bacon, ‘Abecedarium novum naturae’, in The Instauratio magna. Last

Writing, ed. by Graham Rees, in The Oxford Francis Bacon, vol. XIII (Oxford: Clarendon Press, 2000), 210–211. 19 ‘De augmentis scientiarum’, in The Works of Francis Bacon, vol. I, 516; vol. IV, 357.

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the appetites, different variables intervene in which motions are “circumscribed and measured”: space (Mensura Spatij or Instantiae Virgae); time (Instantiae Curriculli or Mensura Temporis ); quantity (Instantiae Quanti sive Doses Naturae, or Mensura Quanti); the degree of bonding of the inner parts of bodies (Mensura Vinculi); and the ascendancy of virtues over each other or their submission to each other (Instantiae Luctae). This last variable unfolds as follows in some classifications: on the one hand, the determination of the strength (Mensura Fortitudinis/Vis aut Hebetudinis Rei) of one motion with respect to others; on the other hand, the circumstances that cause the diminution or augmentation of the strength of the same motion by virtue of the friendly or enemy bodies that surround it (Mensura Peristaeos/Stimulus Peristaeos ).20 Precision is considered fundamental for measurement to fulfill its instrumental purposes. Certainly, in most cases operations fail due to the “inaccurate determination and measurement of the forces [vires ] and actions [actiones ] of bodies”.21 Bacon regrets that in previous natural histories “we find nothing (…) duly examined, verified, counted, weighed and measured”.22 If motions are not “well counted and weighed and defined, the doctrine of motions, may falter and not be reliably translated into practice”.23 Measures “should be sought from the things themselves and not from likelihoods or conjectures”.24 This entails that the measurements of time, space, and quantity should be expressed numerically, with precision, and through a metric. No doubt, Bacon is engaged

20 There are three systematic presentations of the different kinds of measures which

appear in ‘Novum organum’, in OFB, vol. XI, book 2, aphorism xlv–xlviii, 368–417; ‘Abecedarium novum naturae’, in OFB, vol. XIII, 210–215; ‘De augmentis scientiarum’, in The Works of Francis Bacon, vol. I, 561. Besides slight linguistic variations, some conceptual differences between them are to be found. While the measures of time, space, and quantity appear in all three works, the measure of ascendancy presented in Novum organum, becomes unfolded into a measure of strength and a measure of surrounding circumstances (peristaseos ) in Abecedarium novum naturae and De augmentis scientiarum. In addition, in Abecedarium a measure is added that is not in the other two, namely the measure of bonding. 21 ‘Novum organum’, in OFB, vol. XI, book 2, aphorism xliv, 366–699: “male determinatas and mensuratas Corporum vires and actiones.” 22 ‘Novum organum’, in OFB, vol. XI, book 1, aphorism xcviii, 156–157. 23 ‘Abecedarium novum naturae’, in OFB, vol., XIII, 110–111. 24 ‘Novum organum’, in OFB, vol. XI, 382–383; cf. ‘De augmentis scientiarum’, in The Works of Francis Bacon, vol. I, 625.

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in obtaining measurements of increasing precision. Accurate and definite calculations—whenever possible—must be produced. However, when the highest accuracy is not possible, rough estimates must be admitted, provided that they are precise enough to the goals of the investigation:25 “where precise proportions are not available to us we must for sure fall back on rough estimates and comparisons”.26 A case in point is the calculation of “the abundance or paucity of the matter contained and spread out within the same space” (in other words, density and rarity). Bacon notices that the density and the rarity of different bodies can be “reduced to calculation”: in some bodies, they can be reduced to “precise and certain” proportions; in others, to “indefinite proportions”.27 In contrast, Bacon does not engage in the numerical and precise recordings of the other measurements. Regarding the ascendancy or submission of motions, their strength, and peristasis, he only proposes qualitative estimates.28 In so doing, the general background is the goal to which each appetite and motion tends. Accordingly, he places them in a hierarchy according to certain rules that govern not only the natural order, but also the ethical and political order. The most general rule states that in nature those appetites and motions whose goal is the greatest good for the greatest amount will predominate.29 Something that is striking to contemporary eyes is that Bacon places these numerical measurements of time, space, and quantity of matter on the same level and hand in hand with the qualitative measurement of strength, ascendancy, or peristasis. Everything indicates that, while maintaining that these variables must be calculated and measured, he is not thinking of providing numerical values, but of roughly determining whether a motion is more or less “strong” than others, has more or less “vigor” than others. Since his theory of motion ultimately reduces all kinds of motion, even local motion, to the appetites of matter, it would 25 In this interpretation, I follow Jalobeanu, ‘The Marriage of Physics with Mathematics’, 65–68. For a study noticing the value of precision in Baconian measurement, see Pastorino, ‘Weighing Experience’. 26 ‘Parasceve’, in OFB, vol. XI, 467. 27 Francis Bacon, ‘Phænomena universi’, in OFB, vol. VI, 11. 28 We can say little about the measure of bonding, since, as noted above, his

presentation is too brief. 29 On this this rule and its implications in nature and ethics, see Manzo, ‘The Ethics of Motion’.

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not come as a surprise that this peculiar way of measuring motions has a qualitative meaning. If by a quantitative model of science, we conceive that the magnitudes contained in a scientific proposition must be able to be expressed exactly or approximately only under numerical expressions according to a given metric unit, it is obvious that Bacon did not apply this model universally for all the variables involved in his account of body properties. Regarding the measure of the quantity of matter, space, and time, Bacon’s proposal tends to a quantitative model. In fact, he himself developed a method to measure specific gravities and constructed tables with defined values of different substances, after having compared the results obtained empirically.30 Also in cases where he proposes to measure time and space, he does so with the intention of assigning precise numerical expressions to variables, although in practice—as we will see—he does not always apply the maximum degree of precision.We know that his method for the determination of specific gravities was objected by his lack of mathematical and experimental skills. However, this does not override the quantitative approach recognizable in his classification of the mensurae and in his own scientific practice, manifested not only in his much-studied research about specific gravities, but also in his investigations on a medical matter, that we will consider in the next section. Thus, the Baconian mixed mathematics develops a methodology of quali-quantitative measurement, which is perfectly compatible with the double character of matter mentioned above. Precisely because matter has appetites, and a constant amount that determines certain limits to transmutations, two forms of measuring nature coexist: a qualitative form— which notes the dynamics and tension between material appetites—and a quantitative form—which registers the quantity of matter, time, and space. This dual characteristic of both ontology and methodology is an important element to bear in mind when reconstructing the peculiar form of mathematization of nature proposed in Bacon’s project of the reform

30 See Pastorino, ‘Weighing Experience’, 55–62; Jalobeanu, ‘The Marriage of Physics with Mathematics’, 66–68.

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of learning.31 In the next section, we will see that medicine was a field in which Bacon applied this dual methodology for measurement.

5

Quali-Quantitative Measures in Medicine: Some Examples 5.1

General Quantitative Registers

In Bacon’s medicine there are references to certain quantitative registers, such as pulse and body temperature, that are taken as symptoms for the detection of diseases and were part of the usual practices of his time. The pulse belongs to the “Summonsing Instances” (Instantiae Citantes ) that “reduce the imperceptible to the perceptible”. On the one hand, pulse is said to tell us about the condition of the human body, for it makes perceptible what lies “hidden by bodies in between, and which cannot be conveniently opened up”.32 The pulse speed, in fact, varies with age: young people have a strong and rapid pulse, while the elder have a fainter

31 As Pastorino, ‘Weighing Experience’, 562–569, noticed, the importance given by Bacon to quantification and mathematics has been underestimated for a long time by scholarly studies. This reading was greatly influenced by the Kuhnian distinction into classical mathematical sciences and Baconian experimental sciences (Thomas S. Kuhn, ‘Mathematical vs. Experimental Traditions in the Development of Physical Science’, Journal of Interdisciplinary History, 7 (1976): 1–31). However, already in the 60’s Mary Hesse, ‘The Philosophy of Francis Bacon’, in A Critical History of Western Philosophy, ed. by Daniel O’Connor (New York: The Free Press, 1964), argued that Bacon did not oppose radically to the use of mathematics in his project of reform of learning. Graham Rees’ works, ‘Quantitative Reasoning in Francis Bacon’s Natural Philosophy’, News from the Republic of Letters, 2 (1985): 32–33; ‘Mathematics and Francis Bacon’s Natural Philosophy’, Revue Internationale de philosophie, 40, 159/4 (1986): 399–426 were pioneer in noticing that Bacon proposes an extensive quantitative research program and advocates the expansion of mixed mathematics (nevertheless, Rees argued that Bacon’s cosmological model is qualitative, in ‘Mathematics and Francis Bacon’s Natural Philosophy’, 418–421). Pastorino, ‘Weighing Experience’, showed that Bacon proposes a program of data quantification that could serve as a preliminary to the development of mixed mathematics. Jalobeanu, ‘The Marriage of Physics with Mathematics’, offered new arguments in favor of the existence of a mathematical research program in Bacon. 32 ‘Novum organum’, in OFB, vol. XI, book 2 aphorism xl, 346–347.

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and slower one.33 In addition, it indicates not only the physical condition but also the emotions of the individual.34 As for the body temperature, we find only a few mentions of fever as a symptom. Bacon interprets the “burning fevers” as a sign that the heat of putrefied humor had overcome the native heat of the body to the point of extinguishing or dissipating it.35 That notwithstanding, Bacon pays special attention to the relationship between life, age, and heat. He holds that “Heat is requisite to Growth: But after a Man is come to his Middle Age, Heat consumeth the Spirits”.36 Hence, he concludes that, to prolong life, it is necessary to contain that consumption by means of cold.37 Since cold is hardly found in nature, opiates and niter serve as its succedanea: they prevent consumption by condensing the vital spirits.38 Bacon proposes to investigate the different heats in different parts and members of the same animal and complains that no one has investigated “what degree of heat exists in the brain, the stomach, heart and other

33 Francis Bacon, ‘Historia Vitae & Mortis’, in The Instauratio magna Part III. Historia Naturalis and Historia Vitae, ed. by Graham Rees, and Maria Wakely, in The Oxford Francis Bacon vol. XII (Oxford: Clarendon Press, 200), 342–343. 34 Francis Bacon, ‘Sylva sylvarum’, in The Works of Francis Bacon, vol. II, Ex. 97, 380: “we see the affects and passions of the heart and spirits are notably disclosed by the pulse”. 35 ‘Historia Vitae & Mortis’, in OFB, vol. XII, 332–333. For more references to fever see pages 249, 55. 36 ‘Sylva sylvarum’, in The Works of Francis Bacon, vol. II, Ex. 354, 458–459. 37 Bacon’s theory of the prolongation of life—that discusses Renaissance theories,

among others Cornaro’s—engages in a quantitative approach. Notably, he states: “age is nothing in itself (it is after all only a measure of time)” (‘Historia Vitae & Mortis’, in OFB, vol. XII, 164–165). Since the topic of longevity and prolongation of life has been already addressed by some scholars, I have preferred to focus my analysis on other aspects of Baconian medicine. See Giglioni, ‘The Hidden Life of Matter: Techniques for Prolonging Life in the Writings of Francis Bacon’; Roger Marcus Jackson, ‘The Prolongation of Life in Early Modern English Literature and Culture, with Emphasis on Francis Bacon’, PhD Dissertation, University of North Carolina at Chapel Hill, 2010; Luciana Zaterka, ‘Francis Bacon e a questão da longevidade humana’, Scientiae Studia, 13, 3 (2015): 495–517; Marta Fattori, ‘Prolongatio Vitae and Euthanasia in Francis Bacon’, in Francis Bacon on Motion and Power, ed. by Guido Giglioni, James Lancaster; Sorana Corneanu, and Dana Jalobeanu (Cham: Springer, 2016). 38 Bacon recommends the procedure of apothecaries, “who, when they do not have the appropriate simple, take its succedaneum”. See ‘Novum organum’, OFB XI, book 2, aphorism i, 428–429. About niter and opiates, see ‘Historia Vitae & Mortis’, in OFB, vol. XII, 246–262.

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organs”.39 Besides, he measures the activity of the body members by their heat, assuming that it diminishes with age.40 An important background against which Bacon discusses the variations of body’s temperature across age is the theory of radical moisture, whose origins date back to Galenic medicine. Interestingly, Bacon’s strictures on this theory include a quantitative concern. As Jackson has remarked: “He finds it ‘very difficult to believe’ that the same puny amount of primigenial moisture “which can only spread out but not increase in quantity” can come to occupy “a body in as great a diversity of mass as may between a tiny child and an adult”. That a tiny bit of radical moisture can suffuse an animal’s entire body is hard to swallow”.41

The introduction of quantitative variables is most noticeable in Bacon’s therapeutics.42 We will focus on the case of purgatives.43 Contrary to readings that held that their effects are derived from “a hidden propriety, a specifical virtue, and a fourth quality”,44 Bacon states that their true 39 ‘Novum organum’, in OFB, vol. XI, book 2, aphorism xiii, 241. 40 ‘Historia Vitae & Mortis’, in OFB, vol. XII, 316–317. 41 Jackson, ‘The Prolongation of Life’, 163. He quotes Francis Bacon, ‘De vijs mortis’, in Philosophical Studies, ed. by Graham Rees, in OFB VI (Oxford: Clarendon Press, 1996), 270–273; cf. ‘Historia Vitae & Mortis’, in OFB, vol. XII, 144–146; 342. The quantitative aspect of Bacon’s criticism of radical moisture is conjoined with qualitative aspects. See, for instance, the following passage: “For in animals all things are completely repaired while they are growing up and still youthful; indeed for a time they increase in size and improve in quality [Quantitate augentur, Qualitate meliorantur], so that the matter of repair could be practically everlasting, if the means of repair did not break down” (‘Historia Vitae & Mortis’, in OFB, vol. XII, 146–147). A detailed analysis of Bacon’s confutation of the radical moisture is beyond the scope of this article. For an excellent historical study of the evolution of the theory of radical moisture and Bacon’s stance, see Jackson, ‘The Prolongation of Life’, 158–168. 42 According to Richard Shryock, ‘The History of Quantification in Medical Science’, Isis, 52, 2 (1961): 215–237, the quantitative approach of therapeutics was a common practice from ancient medicine on. 43 For an exposition on purgatives of one source with which Bacon was probably familiar, see Jean Fernel, ‘Therapeutices Universalis [Methodi Medendi]’, in Universa Medicina, book III, De purgandi ratione (Paris: Andreas Welchem, 1567). Bacon mentions critically Fernel in ‘Temporis partus masculus’, in The Works of Francis Bacon, vol. III, 531. 44 In describing this property as “fourth quality” Bacon alludes to the medical tradition that distinguished a kind of scale of qualities, namely, qualitates primas, secundas, tertias

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causes can be easily known through experience. He lists a number of processes that can happen in the internal parts of the human body by ingestion or topical application of purgatives: “expulsion” of substances by vomits, diarrhea, etc., when the stomach is overloaded; “mordication” (that is, corrosion) of orifices of body parts, especially the mesentery veins; “attraction” of humors; “flatulency” caused by the spirits of the purgative; “compression or crushing” out of purulent matter, etc.; “lubrifaction and relaxation” of the stomach and “abstersion” or scouring the more viscous humors.45 In explaining these processes carried out by the purgatives, Bacon appeals to the different kinds of measurements mentioned in the previous section. We will have a look at each of them. 5.2

Mensura Quanti

Bacon points out that a “great” quantity of purgative is needed to bring about the expulsion by vomits, diarrhea, etc.: “As we see in a great quantity of new milk from the cow; yea and a great quantity of meat; for surfeits many times turn to purges, both upwards, and downwards”.46 Again, several medicines “in greater quantity move stool, and in smaller quantity urine”.47 These cases are examples of the mensura quanti or doses naturae, which measures “virtues according to the Quantum of

et quartas. According to the Leuven professor of medicine Fortunatus Plempius, some physicians called the “occult” qualities “qualitates quartas”. A case in point is the purgative property: “Quartas denique ajunt esse, quae effectus edunt abdita & imperceptibili quadam ratione: ut purgatrices facultates.” Vopiscus Fortunatus Plempius, Fundamenta medicinae, book II, chapter 3 (Leuven: H. Nempaeus, 1654), 39 (italics in the original). Keith Hutchison, ‘What Happened to Occult Qualities in the Scientific Revolution?’, Isis, 73, 2 (1982): 233–253, pointed out that in “Renaissance science ‘occult’ qualities were commonly characterized as insensible, as opposed to ‘manifest’ qualities, which were directly perceived”, 233. Bacon criticizes the distinction into manifest and occult qualities. See, for instance, in ‘Novum Organum’, in OFB, vol. XI, book 1, aphorism lxvi, 104–105. 45 The most detailed exposition on purgatives is to be found in ‘Sylva sylvarum’, Ex. 36–44, in the Works of Francis Bacon, vol. II, 355–358. When possible, I had modernized Bacon’s medical terminology in this passage. 46 ‘Sylva sylvarum’, ex. 36, in The Works of Francis Bacon, vol. II, 355. 47 Ibid., ex. 44, 358. We see a similar idea in Fernel, Therapeutices, liber III, cap. X,

397: “Sua autem est & definita cuiusque quantitas, qua id conuenientem atque moderatum purgationis modum praestare solet (…). Quantitatem vel augere vel minuere pro purgandi facilitate difficultateve cogimur.”

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bodies, and show what the Quantum of a Body does to influence the Mode of the Virtue”. Every inquiry must note the “dose” of the body needed to produce a given effect, and “add a guidance concerning Too Much and Too Little”.48 Certainly, this example does not show a precise numerical quantification. In contrast, in his personal pharmacopoeia, collected in the text known as Medical remains, are found in precise amounts.49 There Bacon collects a series of recipes indicating precise doses of different medicines, the exact amount of the ingredients required for their preparation, intervals and hour to take the medicine, etc. We also find further indications for corporeal self-care, including diets, exercises, baths, etc. Regarding purgatives, for example, there is a recipe “to open the liver”: Take rhubarb two drams, agaric trochiscat one dram and a half, steep them in claret wine burnt with mace; take of wormwood one dram, steep it with the rest, and make a mass of pills with syrup acetos simplex. But drink an opening broth before it, with succory, fennel, and smallage roots, and a little of an onion.50

It is not by chance that the first two “provisory rules” (canones moviles ) of Historia vitae & mortis refer to the quantity of matter and the weight variations resulting from internal bodily processes, imperceptible to the naked eye. The first provisory rule expresses the principle of the constancy of the quantity of matter in the specific case of the human body: “Consumption does not happen unless what is lost from one body takes up 48 ‘Novum organum’, in OFB, vol. XI, book II, aphorism, xcvii, 380–383; ‘De augmentis scientiarum’, in The Works of Francis Bacon, vol. I, 576; ‘Abecedarium novum naturae’, in OFB, vol. XIII, 210–211. Bacon says that he takes from medicine the label “doses naturae”. This label was common in the pharmacological literature of his time, such as the Antidotarium by Johannes Wecker (Basle, 1588), which is conjectured to be one of the sources consulted by Bacon. See Spedding (‘Historia Vitae & Mortis’, in The Works of Francis Bacon, vol. II, 155) and Rees (‘Historia Vitae & Mortis’, in OFB, vol. XII, 440). “Much and little” are introduced as “common adiuncts of things” in Francis Bacon, ‘The Advancement of Learning’, in OFB, ed. by Michael Kiernan, vol. IV (Oxford: Clarendon Press, 2000), 76–77; ‘De augmentis scientiarum’, in The Works of Francis Bacon, vol. I, 543–544; ‘Abecedarium novum naturae’, in OFB, vol. XIII, 216–219. 49 It is conjectured that this text was composed around 1623, or after that date. 50 Francis Bacon, ‘Medical remains’, in The Works of Francis Bacon, vol. III, 827. Cf.

‘Historia Vitae & Mortis’, in OFB, vol. XII, 298.

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residence in another”.51 This rule is later explained by stating that things are never destroyed and that whatever is consumed either escapes into the air or is absorbed by some other body nearby. Let’s see how this quantitative statement intervenes in the explanation of the physical process involved in the medical use of cupping glasses. Bacon rejects the explanation that, due to the heat of the cupping glass applied on the skin, the air inside rarifies and escapes through the pores of the glass, thereby reducing its amount. From this assumption, the suction of flesh was said to be brought about by the reduction of the air’s quantity. And this would happen on account of matter’s appetite of connection (“motion of connection”) by which bodies do not put up with being separated from another body, rejoice in mutual connection, and avoid a vacuum. While Bacon fully endorses the existence of the appetite of connection, he points out that the suction does not occur by the escape of rarefied air, but by the air’s contraction once it has been cooled down. As the air occupies less space, the flesh is suctioned by the appetite of connection.52 Notably, this case clearly shows the quali-quantitative approach, by conjoining quantitative (changes in space, matter’s quantity, temperature) with qualitative variables (material appetite of connection). The second provisory rule of Historia vitae & mortis resorts to a quantitative measurement, the weight, as an outstanding way to interpret the internal changes of the pneumatic matter inside tangible bodies. By an operation called “attenuation”, spirits enclosed in tangible bodies destroy the tangible parts, and “preyed on the moisture of the body and whatever else it could digest into new spirit; after which the pre-existing and newmade spirit gradually escape together”. These internal changes in bodies are not directly perceived, but they can be “reduced to the senses”, and can be proved or demonstrated (“Hoc ex probatione ea, instar omnium, euincitur”) by registering weight changes: “We see this very well in the weight loss of bodies dried out by perspiration. For whatsoever is given out it was not spirit when it had weight, nor was it other than spirit when

51 ‘Historia Vitae & Mortis’, in OFB, vol. XII, 346–347. 52 ‘Novum organum’, in OFB XI, book 2, aphorism i, 422–423; cf. ‘De vijs mortis’, in

OFB, vol. VI, 348–350. For Bacon definition of the motion of connection see ‘Novum organum’, in OFB, vol. XI, book 2, aphorism xlviii, 382–383.

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it escaped”.53 Furthermore, Bacon points out that it is necessary to evaluate whether and to what extent variations of quantity entail variations of degree in the body’s properties (variations of quality): “Now we must not dwell on indefinite quantities but we must also look into the Relationship of the Quantity of a body to the mode of its virtue”.54 5.3

Mensura Temporis

The case of rhubarb leads us to another relevant variable of medical measurement: time. Rhubarb has several internal particles with opposed medicinal properties: some of them are purgatives, while others are astringents. Which of these properties will predominate in medical treatment? It depends on the duration of the infusion of the rhubarb in water. If the infusion lasts only one hour, then its purgative power will be more powerful and the astringent effect will be mild. In contrast, if the infusion lasts twenty-four hours its purgative effect will be less intense.55 In addition, Bacon draws attention to the lapse of time required in order to obtain the intended effects in the human body: “generally (…) the working of purging medicines cometh two or three hours after the medicines taken”.56 These cases are obvious examples of what Bacon calls mensura temporis, that measures nature by moments of time. For “every natural motion or action takes place in time –some more quickly, others more slowly– but, at all events, in definite [certis ] intervals which are known to nature”. In addition, the measure of time involves an estimation of the “intervals in which the beginnings, ends, returns, or periods and so on of motions happen”.57

53 ‘Historia Vitae & Mortis’, in OFB, vol. XII, 346–349; cf. ib. 172–174. 54 ‘Novum organum’, in OFB, vol. XI, 382–383; cf. ‘De augmentis scientiarum’, in

The Works of Francis Bacon, vol. I, 625. See for instance, Francis Bacon, ‘Historia ventorum’, in OFB, vol. XII, 72–75: “In vapours quantity [copia] and quality [qualitas ] are significant. A small quantity produces gentle breezes; a moderate quantity stronger ones, and a large quantity burdens the air and produces rains either with or without winds.” 55 ‘Novum organum’, in OFB, vol. XI, book 2, aphorism xlvi, 380–381; Francis Bacon, ‘Sylva sylvarum’, ex.19, in The Works of Francis Bacon, vol. II, 345; cf. ib. ex. 98, 381. 56 ‘Sylva sylvarum’, ex. 36, in The Works of Francis Bacon, vol. II, 355–356. 57 ‘Novum organum’, in OFB, vol. XI, book 2, aphorism xlvi, 374–375. Cf.

‘Abecedarium novum naturae‘, in OFB, vol. XIII, 212–213.

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5.4

Mensura Spatii

Like time, space also plays a role in medicine. The measure of space is related to the “orb of virtue” (orbis virtutis), namely, the “distance which the forces [vires ] of bodies may travel to, stop at, build up to and die down from. Whether the operation occurs by contact alone, or at a [greater or] lesser distance, whether it be not excited well over the shortest distances, or slacken off over the longest, and the like”.58 These distances have “degrees” (gradus spatiii) which are “neither indefinite nor random, but definite and certain”. It should be added that the limits of the extent of virtue may be a consequence of the quantity of matter, the intensity of the virtue, or the conditions imposed by the medium. All these factors must also be subjected to calculations when determining the specific limits of each property in several circumstances.59 Again, the use of purgatives provides examples of the measurement of this variable. Some purgatives act at a distance, as they draw humors down from above when they are at a certain distance from them. In contrast, other medicines, like ointments and plasters, produce therapeutic effects through direct contact with the epidermis.60 Another interesting example of the measurement of space in a medical context is observed in the functioning of the sense organs. In perception the need for distance varies depending on the sense organ and the perceived object. Generally, Bacon claims, in hearing the closer the source of sound, the better the reception in the ear, while in vision a certain distance between the eye and the object to be seen is necessary.61 However, the ear also requires some distance, as “the Caue of the Eare doth hold off the Sound a little from the Organ”.62 In turn, the eye needs light and a medium to perceive, so that it cannot see an object that is in direct contact with it. Larger bodies can be seen accurately “at the point of a cone, when the rays of an object converge at

58 ‘Abecedarium novum naturae’, in OFB, vol. XIII, 210–213 (translation slightly modified). 59 ‘Novum organum’, in OFB, vol. XI, book 2, aphorism xlv, 368–369; aphorism xlvi, 374–375. 60 Ibid.; cf. ‘Sylva sylvarum’, ex. 38 in The Works of Francis Bacon, vol. II, 356. 61 ‘Novum organum’, in OFB, vol. XI, aphorism xlv, 370–373; Sylva Sylvarum, in The

Works of Francis Bacon, vol. II, ex. 272, 431. 62 ‘Sylva sylvarum’, ex. 272, in The Works of Francis Bacon, vol. II, 431.

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some distance”.63 However, in certain very exceptional circumstances, a tiny object can be seen by contact and Bacon’s explanation appeals to the difference between the pupil size and object size. Bacon also notes the distance needed to see tiny objects increases, especially at advanced age. 5.5

Mensura Fortitudinis, Mensura Peristaseos

Finally, in purgatives we also find qualitative measurements, which, of course, articulate with quantitative ones. Let’s look at examples of the measurement of the strength of a motion (or appetite) as compared to others. Vomits or diarrhea (i.e., different sorts of “expulsion”) are brought about either “by the quality” or “by the quantity” of the purgative used in the medical treatment. The qualities might be (a) extreme bitterness, (b) loathsome and horrible taste, and (c) “secret malignity and disagreement towards man’s body not appearing much in the taste”. Moreover, Bacon adds that, if a substance has only the quality (c) and neither of the other two qualities (a and b), it acts by corrosion or “by a secret malignity and enmity to nature”. Hence, that substance “is to be held suspected as a kind of poison”.64 Notably, terms like “disagreement”, “enmity”, etc., suggest a conflict between the material appetites of the purgative and those of the human body. The “strongest” appetites involved in such conflict will prevail over the weaker ones. A case of mensura peristaseos is found in Bacon’s considerations about purgatives working by attraction. He claims that purgatives have a “direct force of attraction” by which they draw several humors of the human body. But different purgatives attract differently; some purgatives draw one humor more, some another. The difference lies in the “sympathy” existing between the purgative and the respective humor: while rhubarb draws choler, agaric draws phlegm.65 The sympathy between the members of each pair enforces the attraction exerted by the purgative. This is precisely what peristasis consists of according to Bacon’s typology. Many medical examples are found, where therapeutic effects are explained in terms of sympathy and antipathy exerted in herbal medicines, diets,

63 ‘Novum organum’, in OFB, vol. XI, book 2, aphorism xlv, 370–373; Sylva Sylvarum, in The Works of Francis Bacon, vol. II, ex. 272, 431. 64 ‘Sylva sylvarum’, ex. 36, in The Works of Francis Bacon, vol. II, 355. 65 Ibid., ex. 38, vol. II, 356.

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ointments, stones, bracelets, etc.66 As he says in the introduction to the natural history of sympathy or antipathy: “Fight and amity in nature are stimuli of motions and keys of works”.67 To conclude this section, it is worth citing the following passage from De viis mortis which exhibits the quali-quantitative approach informing Bacon’s medicine: The vigour and quality [qualitas ] of a Spirit is no less important than its quantity [ipsum quantum], for whenever we find a sharp and impetuous spirit in any thing and if it is nevertheless mingled with the thing sparingly in a scanty and meagre quantity [quantitate], the action it performs is weak.68

6

Conclusion

In this chapter we have shown that the form of mathematization promoted by Francis Bacon’s project of the reform of learning is committed to the creation of new branches of mixed mathematics, whose main task is to build a bridge between the axioms reached by the theoretical part of science and the practical application of that knowledge. We maintain that medicine, noted for its great usefulness in promoting the physical well-being of the human being, is one of the scientific branches with special potential to generate its own branch of mixed mathematics. We have further argued that while the key to mixed mathematics is measurement, it is not limited to exclusively quantitative terms. Bacon promotes the measurement of different variables, some that he expresses—or tries to express—with the greatest numerical precision (quantity of matter, space, time), and others that he presents through qualitative estimates (strength, peristasis). Both types of variables are not mutually exclusive and often appear conjoined. In this way, Bacon develops a quali-quantitative measurement methodology. In medicine we find this dual methodology put into practice. Thus, for example, certain 66 Ibid., ex. 95–97, vol. II, 379–380, ex. 960–998, vol. II, 660–671. 67 ‘Historia sympathiae & antipathiae rerum’, in The Works of Francis Bacon, vol. II,

81: “Lis et amicitia in nature stimuli are motuum, et claves operum.” 68 ‘De vijs mortis’, in OFB, vol. VI, 346–345. To make the reading easier, this quotation does not transcribe the typographical additions to the MS introduced by the OFB edition.

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purgatives attract certain bodily humors more than others because they have “greater sympathy” with them (qualitative measurement); in turn, a higher dose—e.g. one more grain of the purgative—will have a more potent effect, and that also depends on the time that passes after it has been ingested, on how long the purgative was prepared in an infusion, etc. (quantitative measurement). The coexistence of qualitative and quantitative measurements is directly related to the ontology of matter that shapes Baconian nature. Matter has an ample variety of both harmonic and conflicting appetites and has a total amount that remains constant and sets limits for transmutations between bodies. The appetitive (qualitative) and quantitative character of matter informs the quali-quantitative methodology that constitutes Baconian mixed mathematics. That is why medicine studies and intervenes in the human body and its relationship with the environment and with the different therapeutic means in two ways. On the one hand, it measures and puts exact numbers or rough estimates to the doses and ingredients of medicines, times and intervals, distances, temperature, pulse, changes in weight of the individual, etc. On the other hand, it measures in comparative and approximate terms the field of dispute in which life takes place, the conflicts and harmony between the internal appetites of the different members of the human body—without ignoring the affections and emotions of the individual—and the appetites of the surrounding environment, medicines, diets, and other therapeutic resources.

Sanctorius’s Weighing Chair: Measurement, Metabolism, and Mind Jan Purnis

Sanctorius ’s Physique is the Body and Scales: Weigh Right, and mend: Thanke thy selfe, if Health failes.1

In his 1661 A Survey of the World in Ten Books, from which my epigraph is taken, Barten Holyday (1693–1661) includes “Of Physicians” as Book VI. He begins the book with Hippocrates and Galen but goes on to devote three of its one hundred couplets (or 3%) to Sanctorius (1561– 1636). Born in the Venetian Republic, Sanctorius (or Santorio) became professor of theoretical medicine at the University of Padua in 1611. Sanctorius worked within the humoral tradition of Hippocrates (ca.460– ca.370 BC) and Galen (129–ca.AD 216), but in order to measure more accurately the phenomena central to it, he invented or improved upon 1 Barten Holyday, A Survey of the World in Ten Books (Oxford: William Hall, 1661), bk. VI, couplet 555, 66, Early English Books Online. When quoting from early modern texts, I have preserved the original spelling and capitalization but have silently altered the long s.

J. Purnis (B) Campion College at the University of Regina, Regina, Canada e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_5

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precision instruments, such as the pulsilogium and thermometer.2 He is believed the first to have employed such instruments in medical practice and is credited with introducing quantitative experimentation into biological science, and he is considered a forefather of modern metabolic balance studies and self-quantification.3 Sanctorius used the analogy between an organism and a clock, later also used by Descartes (1596–1650), and “expressed ideas that prefigured the mechanistic explanations of the iatrophysical school.”4 As Holyday’s poetic summary illustrates, Sanctorius was especially well-known for his experiments with “the Body and Scales.” Over the course of several decades, he regularly weighed himself, his consumption, and his excretion through urine and faeces, applying mathematics to determine the quantity of bodily evacuation that occurred through “insensible perspiration” under a wide range of circumstances. He also 2 For an overview and contextualization of Sanctorius’s life, works, and inventions, see Fabrizio Bigotti, and Jonathan Barry, ‘Introduction’, in Santorio Santori and the Emergence of Quantified Medicine, 1614–1790: Corpuscularianism, Technology and Experimentation, ed. by Jonathan Barry and Fabrizio Bigotti (Cham: Palgrave Macmillan, 2022), 1–63, https://doi.org/10.1007/978-3-030-79587-0_1. For an examination of Sanctorius in the context of processes of knowledge transformation in early modern medicine through a material culture lens, see Teresa Hollerbach, Sanctorius Sanctorius and the Origins of Health Measurement (Springer Cham, 2023), https://doi.org/10.1007/978-3-031-301 18-6, published as this volume was going into production. 3 Encyclopaedia Britannica, s.v. ‘Santorio Santorio’, https://www.britannica.com/bio graphy/Santorio-Santorio (accessed February 11, 2022); Fabrizio Bigotti, and David Taylor, ‘The Pulsilogium of Santorio: New Light on Technology and Measurement in Early Modern Medicine’, Soc Politica 11, 2 (2017): 53–113; Mirko D. Grmek, ‘Santorio, Santorio’, in Complete Dictionary of Scientific Biography (Detroit, MI: Charles Scribner’s Sons, 2008), 12, 101, Gale In Context: U.S. History (GALE/CX2830903839); Garabed Eknoyan, ‘Santorio Sanctorius (1561–1636)—Founding Father of Metabolic Balance Studies’, American Journal of Nephrology, 19, 2 (1999): 226–233, https://doi. org/10.1159/000013455; Fenneke Sysling, ‘Introduction’, in Measurement, Self-Tracking and the History of Science, ed. by Fenneke Sysling, special issue, History of Science, 58, 2 (2020): 108–109, 115, https://doi.org/10.1177/0073275319865830. 4 Grmek, ‘Santorio, Santorio’, 101. As Stephen F. Keevil notes, “scholarly opinions differ” as to whether “changes in the philosophy and practice of science” resulting from the “scientific revolution” were “truly revolutionary, or merely the logical outworking of ideas originating in the medieval period and earlier.” ‘Physics and Medicine: A Historical Perspective’, Lancet, 379 (2011): 1518, https://doi.org/10.1016/S0140-6736(11)602 82-1. See also Fabrizio Bigotti’s argument for a need for philosophers of science “to re-think categories, such as ‘revolution’ and ‘paradigm.’” ‘Mathematica Medica: Santorio and the Quest for Certainty in Medicine’, Journal of Healthcare Communications, 1, 4 (2016): 7, https://doi.org/10.4172/2472-1654.100039.

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experimented on others.5 To undertake these experiments, he used a specially designed weighing chair adapted from the balance [see Fig. 1].6 Sanctorius published his findings as a series of aphorisms in Ars de statica medicina (1614), responding to the criticisms of Ippolito Obizzi (ca.1550–after 1634) in a later edition.7 The first English translation of 1676 was followed in 1712 by that of John Quincy († 1722), which included explanations, digressions, and an introduction entitled “Of Mechanical Knowledge, and the Grounds of Certainty in Physick.” Sanctorius’s statical medicine and his efforts to quantify digestive processes offer a useful lens through which to consider the impact of quantification on conceptions of the nature of the self, including the mind-body and self-world relationships, as well as insight into the ways in which medical discourse influences embodied self-experience. My chapter complements recent renewed interest in Sanctorius, much of which either focuses on his place in medical history or on his influence on the eighteenth, rather than seventeenth, century. To my knowledge, there has been little in the way of extended attention to the intersections of the physiological and psychological in discussions of Sanctorius’s weighing experiments.8 After introducing the digestive theory inherited by the early moderns, I highlight key findings presented by Sanctorius (and Quincy’s explanations of them), focusing particularly on those addressing the mind–body relationship. I then consider the impact of quantification in medical discourse on self-experience, and the interaction of mind and body in quantifying methodologies themselves, touching briefly on the use of weighing metaphors to describe thought processes.

5 Teresa Hollerbach writes, “According to his own claim, Sanctorius observed more than ten thousand subjects over the course of around thirty years.” ‘The Weighing Chair of Sanctorius Sanctorius: A Replica’, N.T.M , 26 (2018): 127, https://doi.org/10.1007/ s00048-018-0193-z. 6 Lucia Dacome explores “how the image came to symbolize the attempt to transform dietetics into an experimental practice, and accordingly preserve its pivotal significance in the medical world.” ‘Balancing Acts: Picturing Perspiration in the Long Eighteenth Century’, Studies in History and Philosophy of Biological and Biomedical Sciences, 43 (2012): 379, https://doi.org/10.1016/j.shpsc.2011.10.030. 7 See Bigotti and Barry, ‘Introduction’, 18. 8 Fabrizio Baldassarri includes a brief discussion of Sanctorius in ‘Santorio, Regius,

and Descartes: The Quantification and Mechanization of the Passions in SeventeenthCentury Medicine’, in Santorio Santori and the Emergence of Quantified Medicine, 176– 179, https://doi.org/10.1007/978-3-030-79587-0_6.

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Fig. 1 Sanctorian chair from J. Quincy’s edition of Medicina Statica (1718), courtesy of Wellcome Library, London

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Insensible Perspiration

In humoral medicine, digestion was understood as a primarily heat-based process in which food was transformed into blood in the liver daily. The digestive process also played a role in the production of spirits and humours: black bile (melancholy), yellow bile (choler), phlegm, and blood, which were classified according to temperature and moisture. The proportion of humours within an individual influenced health and psychological experience. Emphasizing the “psychophysiology” or “psychological materialism” of humoralism, Gail Paster outlines how there were understood to be six “non-naturals” affecting bodies and health: air, food and drink, repletion and evacuation, sleeping and waking, exercise, and the passions of the mind.9 Other factors also played a role in humoral complexion: for example, women were considered to be colder than men and thus to have weaker digestion. Moderation and balance were cornerstones of medical advice, and purgations were central to medical therapy. Because the line between food and medicine was blurred, and because food and mood were related, diet also played a crucial role in efforts to achieve humoral balance and well-being. Sanctorius’s experiments with his weighing chair concentrated on digestive processes, particularly the evacuation of waste material—sensibly, through urine, faeces, and sweat, and insensibly, through the pores or through expiration by way of the mouth. Although he has sometimes been described as the discoverer of insensible perspiration, also called transpiration, Edward Tobias Renbourn notes that by Sanctorius’s time, “the concept was already some twenty centuries old,” as was the “doctrine” of the negative repercussions of “suppressed or obstructed insensible perspiration.”10 Sanctorius himself writes that “it is known to all, of how great concern in the medical faculty, the knowledge of insensible perspiration is,” though he goes on to write that “men are more apt

9 Gail Kern Paster, Humoring the Body: Emotions and the Shakespearean Stage (Chicago: University of Chicago Press, 2004), 4. 10 Edward Tobias Renbourn, ‘The Natural History of Insensible Perspiration: A Forgotten Doctrine of Health and Disease’, Medical History, 4, 2 (1960): 138, 136, https://doi.org/10.1017/s0025727300025229.

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enviously to oppose, than studiously to promote the advancement of new designs,” assigning a role to emotions like envy in the history of science.11 Sanctorius’s innovation was in his attempt to quantify the physiological phenomenon, which by its very nature was not easily accessible to the senses (it was also translated as “secret” or “occult”).12 “Sanctorius to the Reader” opens with Sanctorius’s claim for the originality of his method and findings, as well as his emphasis on reason and experience: It is a thing new, and not before heard of, in Medicine, that any one should be able to find out the exact weight of insensible perspiration, nor has any one of the Philosophers or Physicians attempted the doing of any thing in that part of the Medical Faculty. I am the first that has essay’d it, and (if I am not mistaken) brought the Art to perfection, by reason, and the experience of thirty years.13

But even this claim requires some contextualization. Richard Shyrock relates how Erasistratus (ca.304–ca.250 BC) “weighed the intake and outgo of birds and found a loss of weight ‘perceptible only to the reason,’ thereby anticipating seventeenth-century work on the ‘insensible perspiration.’” He adds, “Here an actual discovery could be credited to measurements. The phenomenon revealed by measures was not apparent to the senses — a very early instance of this sort.”14 As Fabrizio Bigotti remarks, “the concept of weight becomes central” in Sanctorius’s thought.15 Sanctorius aptly used a modified balance in his investigation of how to achieve balance. In his first aphorism he states,

11 Santorio Santorio, Medicina Statica: Or, Rules of Health, in Eight Sections of Aphorisms, trans. J[ohn] D[avies]. (London: John Starkey, 1676), A3v, Early English Books Online. 12 See also Renbourn on Greek and Latin terminology that emphasized the process’s invisibility. ‘Insensible Perspiration’, 135. 13 Santorio, Rules of Health, A3r. 14 Richard H. Shyrock, ‘The History of Quantification in Medicine’, History of Science

Society, 52, 2 (1961): 217, https://www.jstor.org/stable/228680. For additional contextualization of Sanctorius’s weighing experiments in relation to earlier references, which may be to projected or theoretical, rather than actual, experiments, see also Hebbel E. Hoff, ‘Nicolaus of Cusa, van Helmont, and Boyle: The First Experiment of the Renaissance in Quantitative Biology and Medicine’, Journal of the History of Medicine and Allied Sciences (1964): 99–117, http://jhmas.oxfordjournals.org/. 15 Bigotti, ‘Mathematica Medica’, 5, n14.

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“If there daily be an Addition of what is wanting, and a Subtraction of what abounds, in due Quantity and Quality, lost Health may be restor’d, and the present preserv’d,” noting in the next aphorism that a physician who attends only to sensible evacuations will “deceive his Patient, and never cure him” because “he only who knows how much, and when the Body does more or less insensibly perspire, will be able to discern, when, and what is to be added or taken away, either for the Recovery or Preservation of Health.”16 His static experiments revealed that the quantity of insensible perspiration outweighed that of the sensible.17 He claimed, in two of his most frequently repeated aphorisms, that “if eight Pounds of Meat and Drink are taken in one Day, the Quantity that usually goes off by Insensible Perspiration in that Time, is five Pounds,” and that in the space of one night, sixteen ounces of urine, four ounces of stool, and forty or more ounces of perspiration are “generally” evacuated.18 Of respiration through the mouth, he writes that in the space of a day, this “amounts to about the quantity of half a Pound,” and he calculates that “insensible Steam or Vapour,” as opposed to sweat, “in Winter time exhales to about the Quantity of Fifty Ounces in the space of one natural Day.”19 As Shigehisa Kuriyama observes of Sanctorius’s findings, physicians since Hippocrates had attended to sensible evacuations in diagnosing disease and attempting cures, but it now appeared that they had missed a “staggering” quantity of evacuated material, and thus had overlooked the primary cause of illness.20 Importantly, Sanctorius emphasizes that “the Quantities insensibly perspir’d, vary according to the Differences of Constitutions, Ages, Countries, Seasons, Distempers, Diet, and the rest of the Non-naturals,” and, relatedly, the quantity varies over time: “The Body does not perspire at 16 Santorio Santorio, Medicina Statica: Being the Aphorisms of Sanctorius, Translated into English with large Explanations. Wherein is given A Mechanical Account of the Animal Oeconomy, and of the Efficacy of the Non-Naturals, either in bringing about or removing its Disorders, trans. John Quincy (London: William Newton, 1712), sec. 1, aph. 1, 1 (hereafter quotations from Sanctorius are cited as 1.1.1), 1.2.2, and 1.3.2, Eighteenth Century Collections Online. 17 Ibid., 1.4.2. 18 Ibid., 1.6.4, 1.59.31. 19 Ibid., 1.5.3, 1.21.10. 20 Shigehisa Kuriyama, ‘The Forgotten Fear of Excrement’, Journal of Medieval and Early Modern Studies, 38, 3 (2008): 416, https://doi.org/10.1215/10829636-200 8-002.

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all times alike, for in the first five Hours after Eating, there wasts about a Pound; the next seven Hours, about three Pound; and from the twelfth to the sixteenth (at which Time there will be need of a fresh Supply) hardly half a Pound.”21 Sanctorius includes his observations on the effects of these variables in sections generally corresponding to the six non-naturals, although as Lucia Dacome notes, he has given sexual activity its own section.22 Perhaps reflecting changing sensibilities, Quincy explains that he had considered omitting this section, but adds that for the sake of completeness, “I have inserted it in its place, and I hope in such Terms as are as chast and inoffensive, as our Language will bear.”23 Sanctorius instructs readers on how to determine the appropriate quantity of insensible perspiration for themselves, highlighting the tension between individualization and standardization arising with quantification. He writes: Take notice in a Morning, following a plentiful Supper, of the greatest Quantity that perspires in the space of twelve Hours: Suppose it to be fifty Ounces: Some other Morning observe the same, after eating no Supper, (and provided there was no Excess in the former Days Dinner) which suppose to be twenty Ounces: Then chuse such a settled Quantity of Food, and keep to such a use of the Non naturals, as will bring the Quantity perspired to a Mean between fifty and twenty Ounces, which is thirty five Ounces; and by this means may a Person be brought to such a perfect Standard of Health as may last to a Hundred Years.24

Again, balance is emphasized, and the “Standard of Health,” as I interpret it, is a personalized standard, with the stated quantities presented as examples.25 Of this aphorism, Quincy remarks that he believes it will be “thought too troublesome ever to be put in Practice,” and “for a Person to go thorough the Experiment, with all the Kinds of his Food, to find the several Quantities necessary to keep this Standard, would be

21 Santorio, Medicina Statica (1712), 1.7.4, 1.56.30. 22 Dacome, ‘Balancing Acts’, 381. 23 John Quincy, preface to Medicina Statica, by Santorio Santorio, v. 24 Santorio, Medicina Statica (1712), 1.64.34. 25 As Quincy notes, however, a different “Computation of the Quantity perspired” appears in sec. 3, aph. 41, in which a more standardized 22 ounces (the mean between 40 and 14 ounces) is recommended for “an healthful old Age.” Ibid., 133.

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a Task, that very few would care for, as hardly to be rewarded by the largest Enjoyments of this Life.”26 This attitude might partially explain the development of more generalized guidelines. In the section “Of Meats and Drink,” Sanctorius categorizes specific foods as either promoting or hindering perspiration and makes recommendations about number, time, and size of meals.27 Sanctorius gives considerable attention to the health consequences of body weight, noting that it is generally best to strive for consistency. He observes, “If a Body returns to the same Standard every Day, without any change in the Quantity of Perspiration, there will be constantly preserved a perfect Health, and no need of Critical Evacuations,” but “bad Qualities arise when the Body is not one Day the same in Weight as another.”28 He acknowledges, however, that there is a healthy weight range for each individual, writing that the body is “most free from a Distemper” when it is in the “Mean of a Healthful Standard” not by medical or “Spontaneous” evacuations or by abstinence, but “by the Means only of such insensible Perspiration, as goes off in Sleep, after a perfect Digestion.”29 As Quincy explains of this aphorism, It is not to be supposed, that a Body cannot gain or lose a little of its Weight without falling into a Distemper; therefore all that Latitude of Alteration a Body is capable of undergoing with respect to its Weight, without being distemper’d, is call’d by Sanctorius here, and in several Places of his Aphorisms, a Healthful Standard; the greatest Weight it is capable of, is its greatest Healthful Standard, and its least, the lowest Standard, and between both, its mean or middle Healthful Standard; and all these are different, at different Ages and Seasons, as will hereafter further appear.30

26 Ibid., 34–35. 27 Anita Guerrini refers to Sanctorius in a study of efforts to quantify moderation. ‘The

Impossible Ideal of Moderation: Food, Drink, and Longevity’, in Lifestyle and Medicine in the Enlightenment: The Six Non-Naturals in the Long Eighteenth Century, ed. by James Kennaway and Rina Knoeff (London: Routledge, 2020), 99–100, https://doi.org/10. 4324/9780429465642. 28 Santorio, Medicina Statica (1712), 1.15.7, 1.16.7. 29 Ibid., 1.63.33. 30 Ibid., 34; italics in the original. This concept of “healthful standard” is translated as the “latitude of healthy ponderation” in the 1676 English translation, 1.63.22.

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Sanctorius claims that even those men who live moderately will experience temporary weight gain every month, as women do, and he outlines seasonal fluctuations: “Temperate Persons weigh in Summer time about three Pounds less than in the Winter,” but “they escape the Autumnal Distempers, who can preserve their Bodies of the same Weight, as in Summer-Time.”31 He also elsewhere cautions that the extra weight at the upper limit of the healthful standard “hastens old Age.”32 It is no wonder, then, that Holyday’s takeaway message from Sanctorius is to “Weigh Right, and mend” or suffer failing health. But the “right” weight and “standard of health” is personal. I read Sanctorius’s inclusion of specific body weights as hypothetical examples for the purpose of illustration, although they have also been interpreted as specific guidelines.33 Some later seventeenth-century writers who refer to Sanctorius’s experiments when undertaking their own quantification offer insight into the shift toward generalization and standardization. For example, in calculating the insensible perspiration of an elephant, Allan Mullen (d. 1690) draws upon Sanctorius’s statement that a man will insensibly transpire fifty ounces or more over the course of a winter’s day. Mullen translates this into a proportion of body weight, writing that it amounts to about a 54th part of an “ordinary” man’s weight, which he takes to be “about 170 l., “suggesting that Sanctorius seems to have undertaken his experiments on this same “meaning.” Mullen then applies this proportional measurement to the elephant, which was reported to weigh 2.5 “Tuns” or “5000 l.,” although he acknowledges that elephants may transpire differently because of the outer “scab” on their skin and that he has to rely on reports of others about this weight.34 31 Santorio, Medicina Statica (1712), 1.65.35, 2.23.89, 2.43.100. 32 Ibid., 1.79.44. While the 1676 translation suggests a comparison of an individual at

200 vs 205 pounds, Quincy’s 1712 translation suggests two people of different weights are being compared. 33 Hollerbach claims that Sanctorius “defines a healthy weight range between 200 libbre and 205 libbre (Sanctorius 1614: 18v),” adding in note 10 that the unit of measurement used by Sanctorius “was variable between the different Italian states.” ‘Weighing Chair’, 128, 146. Hollerbach is referring to aphorism 1.79, discussed above and in my note 32; however, both the 1676 and 1712 translations employ the verb suppose in presenting these body weights, suggesting they are more illustrative of the point about excess weight and ageing than they are suggestions of an ideal weight. 34 Allan Mullen, An Anatomical Account of the Elephant Accidentally Burnt in Dublin on Fryday, June 17 in the year 1681 sent in a letter to Sir. Will. Petty, fellow of the Royal

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In his 1694 Dissertation Of the Cure of Fevers by Evacuations, Archibald Pitcairn (1652–1713) includes an explanation and demonstration of the theorem of Laurentius Bellinus (1643–1704) that “the whole quantity of Perspiration coming every Minute from a Shred, whose weight is a Scruple, is 1200 part of a Scrup.”35 Where Sanctorius had emphasized that the rate of perspiration varied over the course of a day and according to myriad factors, Bellinus has presented a standard rate of perspiration, not just over the course of a twenty-four hour period, but per minute. In his demonstration, Pitcairn goes into complicated detail, but what is most relevant here is that he bases his calculations on the aphorism “that in the space of 24 Hours the Perspiration is 50 Ounces,” without Sanctorius’s seasonal specification, and on an assumption that “the midle quantity of the weight of the Body of Man is 160 lib. which are equall to 60,000 Scr.”36 After basing his calculations on this assumed average weight, which differs from Mullen’s, he goes on to explain that “because the weight of Perspiration, all things being considered, is according to the weight of the Body perspiring,” it is possible to make a similar proportional calculation for “a Body of 120 lib. or 45,000 Scrup.” and arrive at the same evacuation rate of 1/1200 of a scruple per minute.37 In both of these examples, body weight is presented as the primary determinant of perspiration rate, and decreased emphasis on the effect of non-naturals is foregrounded in Pitcairn’s vague “all things being considered” and Mullen’s attention to the effect of elephant skin texture (not a nonnatural variable) on perspiration.38 In a study of the medicalization of obesity, Garabed Eknoyan points to a further shift: from the average to the ideal. “Once platform scales became accessible in the second half of the nineteenth century,” he writes, “accrued information on body weight Society… (London: Sam. Smith, 1682), 10–11; italics in the original, Early English Books Online. 35 Archibald Pitcairn, Apollo Staticus. Or, The Art of Curing Fevers by the Staticks Invented by Dr. Pitcairn, and Publish’d by Him in Latine: Now Made English by a WellWisher to the Mathematicks (Edinburgh: J.W., 1695), 22; italics in the original, Early English Books Online. 36 Ibid. 37 Ibid., 23–24. 38 The translator of Pitcairn’s dissertation challenges his methodology and mathematical

calculations in the preface. See also Stephen M. Stigler’s, ‘Apollo Mathematicus: A Story of Resistance to Quantification in the Seventeenth Century’, Proceedings of the American Philosophical Society, 136, 1 (1992): 93–126.

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became gradually available for analysis,” and insurance companies started reporting ideal weights for age and height, instead of averages.39 Interestingly, Sanctorius’s weighing experiments are not just quantitative but also qualitative. He takes into account the relationship between the objective weight of the body, determined by weighing device, and the subjective experience of it. He states: “Weight, with relation to the Perception of it in a living Body, is Equivocal; because it is consistent, that at the same time a Body may actually be heavier, and yet seem lighter; and on the contrary it may be render’d lighter than usual, and yet at the same time feel heavier.”40 In his commentary, Quincy differentiates between the “greater or lesser Sense a Person has at that time of a Weight upon him,” which “may be called Relative, and that by which a Person is said to weigh so many Pounds exactly, without any regard to the Perception the Person has himself, [which] may be termed Absolute Weight.”41 This distinction foregrounds how the balance and other quantifying instruments work to measure phenomena more precisely by not relying on “the Perception the Person has himself,” or the perception of others. As Bigotti and Barry articulate it, “another essential principle that Medicina statica introduced into European medicine” was “the distinction between ‘perceived’ (ad sensum) and ‘measured’ (ad stateram) reality.”42 Importantly, Sanctorius does not dismiss subjective, embodied experience. Instead, he offers a medical interpretation of differences between perceived and actual weight, claiming that “that State of Body, which has a sense of a greater Weight when there is none, is much worse than when it perceives a greater Weight, and there really is so,” while, on the other hand, if “a Person perceives himself lighter than usual, and that at the same time there is no increase in his Absolute Weight, ‘tis a certain Indication of Health.”43 Quincy notes of the former case that “the Reason is, because if a Person feels a Heaviness” without being heavier “‘tis a certain Indication that he is under some wast of Spirits, 39 Garabed Eknoyan, ‘A History of Obesity, or How What Was Good Became Ugly and Then Bad’, Advances in Chronic Kidney Disease, 13, 4 (2006): 426. Eknoyan also notes that the BMI or Quetelet index, named for a Belgian who lived from 1795 to 1844, attempted to define the “average man.” Ibid. 40 Santorio, Medicina Statica (1712), 1.29.14; italics in the original. 41 Ibid., 14–15, italics in the original. 42 Bigotti and Barry, ‘Introduction’, 19. 43 Santorio, Medicina Statica (1712), 1.28.13, 1.30.15; italics in the original.

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for a Diminution of Strength or Vigour will produce the same Sense as an actual increase of Weight.”44 He also remarks that “People frequently express themselves upon several Indispositions, that they have a Heaviness upon them, although at the same time perhaps they are actually lighter, but only through a decay of Spirits and Strength are not so able as before to support their usual Bulk.”45 In cases where there is a perception of being lighter than the scale indicates, Quincy suggests that “such a Perception can arise from nothing else than a plentiful Invigoration of the Solids by a good stock of Spirits, which likewise depends upon a perfect Digestion, and a regular Discharge of all the Animal Functions, and therefore nothing can be a more certain sign of Health, unless it be in Manaicks and Delirious Persons.”46 Quincy here qualifies the assertion that feeling lighter is always a sign of good health by referring to unhealthy conditions that might contribute to such feelings, conditions relating to mental states with physiological underpinnings.47 The experience of one’s body weight is influenced not just by feeling (and not just by actual weight) but also by medical interpretations of body weight and by cultural norms, all of which attribute morality and degrees of positivity or negativity to body weight. Knowing one’s absolute weight, as is readily available these days, will in turn affect one’s perception and experience of the body, particularly (as also with Sanctorius) in relation to its medicalization, something I return to below. I want to emphasize, here, though, the interplay of measured body weight and unmeasured feelings, feelings that, as becomes clear in later aphorisms, can be related to emotional experience, the effects of which Sanctorius attempts to weigh.

44 Ibid., 14. 45 Ibid., 14–15. 46 Ibid., 15; italics in the original. 47 Sanctorius mentions maniacs in 2.13.83, and in his commentary Quincy refers to

the dissections of “Manaical Persons” by Giorgio Baglivi (1668–1707), which revealed “the Dura Mater to have been harden’d to a very great degree, and to be almost dry,” which he interprets as the reason they are not affected by changes in the air. Santorio, Medicina Statica (1712), 84; italics in the original.

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2

Exercise of the Mind

For Sanctorius, insensible perspiration is a psychophysiological process. In the section “Of Exercise and Rest,” he writes: “There are two kinds of Exercise, one is of the Mind, and the other of the Body; that of the Body discharges the sensible Excrements; but that of the Mind, rather the insensible, and more especially, those of the Heart and Brain where its seat is.”48 Quincy confesses that By Exercise of the Mind, in this, I cannot guess what is meant, unless that Power by which the vital Functions, especially those of the Heart and Brain are carried on, which is meerly Mechanical, and depends upon the particular Make and Constructure of those Parts. But in the following Aphorisms, it is plain he intends those Faculties and Powers which the Soul hath, and can make use of in changing the usual Procedure of the vital Offices. By the Exercise of the Mind therefore here, is to be understood nothing else than that State of Inactivity, wherein no Change is brought about in the Body, but such as is the necessary Result of the vital Functions[.]49

He goes on to assert that the heart and brain can be said to be the organs most concerned with various processes but disagrees with Sanctorius in stating that they are not “any more the Seat of the Mind than other Parts of the Body.”50 Of the relative effect of each form of exercise on perspiration, Sanctorius claims, “Too much Inactivity of the Mind, checks Perspiration, more than that of the Body,” and those who “are subject to vehement Passions, shall waste more by Perspiration lying in Bed, than such, who enjoy a Serene Mind, by the most violent Exercises of the Body; as it appears by those who play at Tennis.”51 Quincy puzzles over this aphorism, agreeing “Nothing is more observable than that violent Motions of the Mind, wast the Spirits, and bring great Disorders upon the Constitution,” which he explains “they seem to do as Stimuli, universally irritating and twitching the Nerves, in such a Manner as disturbs their regular Contractions,”

48 Santorio, Medicina Statica (1712), 5.14.228. 49 Ibid., 228; italics in the original. 50 Ibid., 229. 51 Ibid., 5.15.229, 5.17.230; italics in the original.

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adding, however, “but how they should occasion such large Discharges of the perspirable Matter, as violent Exercise, I cannot conceive.”52 Sanctorius again emphasizes the benefits of moderation when he asserts, “Violent Exercise both of the Mind and Body, renders Persons lighter but it hastens on old Age, and threatens untimely Death; for according to the Philosopher, those who are exercised, dye sooner than those who are not.”53 Although Sanctorius includes passions as exercises of the mind in several of his aphorisms in section five, section seven is devoted entirely to them.54 Sanctorius focuses on the reciprocal relationship between the passions and perspiration, paying scant attention to the humours specifically, although interested in material substances nonetheless. The first aphorism states: “Amongst the Affections of the Mind, those of Anger and Joy, make Persons lighter; those of Fear and Sorrow, more heavy; and the other Affections operate in Proportion to their Participation of these.”55 He thus identifies only four basic emotions, grouping them in pairs, relating all other emotions to them. His articulation of their effects on bodies uses the comparative language of “lighter” and “more heavy,” giving the impression of measurement but without providing specific quantities.56 The next aphorism provides some explanation of the first, claiming that “in Fear and Sorrow the lightest perspires, but the heaviest Matter remains behind; in Anger and Joy there is a good Perspiration of both.”57 Thus “those who are subject to Fear and Sorrow, are apt to be 52 Ibid., 230; italics in the original. For the influence of the “nerve model of the mind–body connection” on theories of the emotions, see James Kennaway, ‘The Dietetics of the Soul in Britain in the Long Eighteenth Century’, in Lifestyle and Medicine in the Enlightenment: The Six Non-Naturals in the Long Eighteenth Century, ed. by James Kennaway and Rina Knoeff (London: Routledge, 2020), 265, 274–277. 53 Santorio, Medicina Statica (1712), 5.19.231. 54 See also ‘Those Exercises of the Mind, which are most conducive to exhale the

Spirits, are Anger, sudden Joy, Fear and Sorrow’ (5.16.230), which Quincy notes seems to contradict some of the aphorisms in section seven. 55 Ibid., 7.1.263. 56 Hollerbach briefly discusses the section on the passions in her description of the

recent effort to replicate Sanctorius’s weighing chair and experiments, observing that Sanctorius only specifies precise quantities in the first four sections of the treatise, “whereas he confines himself to more general and rather qualitative statements in sections V to VII.” ‘Weighing Chair’, 141. 57 Santorio, Medicina Statica (1712), 7.2.266.

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troubled with Obstructions, a Hardness in some Parts, and to hypocondriacal Affections”; they are also more likely to “feel Weariness” when travelling than those who are angry or cheerful, whose “bodies easily perspire the gross Matter.”58 While these aphorisms emphasize the effects of the passions on perspiration, perspiration also contributes to emotional experience. Sanctorius claims that if the “heavy part of perspirable Matter” is “more than usually retained in the Body, it will dispose a Person to Fear and Sorrow,” whereas if “the lighter Part” is “obstructed” it will dispose a person “to Anger or Joy.”59 Quincy explains this aphorism as a reverse of the first in the section, writing that “universally it holds good with the Alterations that are brought about in the Body by the Mind, and the Changes which are made in the Affections of the Mind by the different Temperature of the Body, that what is the Cause at one time, may be the Consequence another, and vice versâ.”60 As Quincy explains it, joy promotes “a more plentiful Secretion of Spirits in the Brain” and gives to the body “both Strength and Facility of Motion” by promoting “a good brisk Circulation” and keeping the blood “duly fluxile,” which will “also raise the Mind with more agreeable Impressions, and dispose it either to Joy or Anger, as the Person happens to be entertained by external Objects.”61 On the other hand, fear and sorrow, “by checking the Motion of the Spirits, and hindring Circulation and Digestion, give a Heaviness and Sluggishness to the Juices, and occasions Obstructions” and so whatever “obstructs the perspirable Matter, and induces a Lentor in the Blood” will “also dispose the Mind to those Uneasinesses which arise from Sorrow, or Fear.”62 Sanctorius continues the tradition of linking food and mood by identifying specific foods that promote perspiration and bring joy (parsley, for example), or obstruct it and bring sorrow (pulse, fat meats).63 Following the tradition of therapy by contraries, he states that “Anger and Hope

58 Ibid., 7.3.266, 7.4.267. He also writes, “Nothing more contributes to a free Respiration, than Comfort and Satisfaction of Mind.” Ibid., 7.6.268. 59 Ibid., 7.5.267. 60 Ibid., 267; italics in the original. 61 Ibid., 267–268. 62 Ibid., 268; italics in the original. 63 Ibid., 7.30–31.288.

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remove Fear, and Joy takes away Sorrow: for a Passion of the Mind is not to be conquered by Medicine, but by some contrary Passion; for Contraries are under the same Genus.”64 Relatedly, he states that if joy immediately follows anger, or vice versa, “allowing the same proportion of Food, Bodies will the next day be lighter, than if Anger or Joy alone had continued,” and that a variety of passions is more beneficial than the continuation of one, even a positive one.65 Sanctorius also claims that the effects of melancholy and of foul air are similar in the diseases they give rise to because they both obstruct perspirable matter, grief “intrinsically” and foul air “extrinsically.”66 Sanctorius explicitly links his observations on the passions to his weighing experiments in his statement that “Fear and Sorrow, as it appears from Staticks, are removed by a substraction of the grosser perspirable Matter: but Anger and Joy, by that of the thinner.”67 But for Quincy, The manner how the Mind or Thought works upon the Body, is a Mystery, and no Way at least to be brought under a mechanical Way of Reasoning; because it is not possible to represent and delineate, as we do corporeal Sustances, that which never comes under the Notices of our Senses, but in its Effects[.]68

He acknowledges, however, that it is “certain that the Actions of the Mind, that is, the Thoughts that pass thorough it, especially when sudden and intense, do influence very much and alter the Constitution,” adding that “the wisest must herein be contented, to establish his Rules upon Observation only, and therefore it is no great Wonder to find even Sanctorius hereupon very obscure, and often contradictory to himself as in this Aphorism[.]”69

64 Ibid., 7.12.281; italics in the original. 65 Ibid., 7.20.285, 7.47.292. 66 Ibid., 7.14.282. 67 Santorio, Medicina Statica (1712), 7.22.286; italics in the original. 68 Ibid., 229. 69 Ibid.; italics in the original. These comments appear in Quincy’s explanation of aphorism 15 in section 5, ‘Of Exercise and Rest’.

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3

Quantified Selfhood

Not only did Sanctorius apply his statics to consideration of the interrelationship of psychological and physiological processes, but his weighing experiments likely influenced emotional experience. In the approach known as historical phenomenology, “the very language of physiology […] helps determine phenomenology. The way we describe the workings of our bodies and minds, and how we characterize our habitation in the world, may shape and color our emotional experiences.”70 The reach of Sanctorius’s quantifying experiments and their implications not just for individuals’ relationships with food but nearly every aspect of daily life are all understood to have an impact on insensible perspiration and therefore on well-being. Although he is less specific in his measurements of the effect of many of these activities and phenomena, they are presented as quantifiable nonetheless at least in terms of determining degree of perspiration. In his preface, Quincy draws attention to the potential impact of Sanctorius’s weighing experiments on individuals, writing: “I am not at all unaware how severe some will be hereupon, in requiring how often they must weigh themselves, and whether they ought to eat and drink by the Ounce,” adding that because Sanctorius “by the Ballance has already done enough to convince any serious Person” of the body’s “natural Discharges,” “their Proportions to one another,” and “all the Consequences of those Discharges from the least to their greatest Quantities possible, any Person may soon be a Judge of the present State of his Constitution, without going into a Pair of Scales.”71 For this reason, he has not “been nice in searching into the Exactness of the Sanctorian Calculations ” since the main thing is “knowing that there are such Discharges, how they are to be influenced, and what will be the Consequences of their Disorders.”72 Yet, he also acknowledges that the English climate and lifestyle would skew the results.73 As Dacome has outlined, however, there were people in the eighteenth

70 Gail Kern Paster, Katherine Rowe, and Mary Floyd-Wilson, ‘Introduction’, in Reading the Early Modern Passions: Essays in the Cultural History of Emotion, ed. by Gail Kern Paster, Katherine Rowe, and Mary Floyd-Wilson (Philadelphia: University of Pennsylvania Press, 2004), 16. 71 Quincy, preface, vi–vii; italics in the original. 72 Ibid., vii; italics in the original. 73 Ibid.

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century who took weighing themselves and their intake very seriously, often to unfortunate consequences, making them the subject of criticism by Joseph Addison (1672–1719), editor of The Spectator.74 And certainly, the notion of eating and drinking “by the ounce” has become pervasive in an era of recommended daily intake of calories, water, vitamins, minerals, etc., alongside recommended quantities of daily exercise and sleep. While fear is one of the four passions about which Sanctorius has most to say, relating to causes and effects, as Kuriyma argues, humoralism’s emphasis on the dangers of obstructed evacuation may well have triggered a “fear of excrement” that has been “forgotten.”75 Although it is not possible to gauge fully the impact of medical theory on lived experience, the pervasiveness of purgatives is suggestive.76 Relatedly, but inversely, in a 1689 text, William Cole (1635–1716) uses quantification, directly referencing Sanctorius, in his attempt to counter anxiety about one of these purgative therapies: blood-letting. Cole notes that “very able Physitians” have “concluded” that the quantity of blood that is “naturally” in the body is 16–25 pounds, depending on “the bulk and constitutions of persons,” adding that this amount is increased by “full feeding” and lack of exercise.77 A key part of his argument is that there are people who live for some time without eating despite continuing to evacuate, at least by way of transpiration, and since “according to the observations of the accurate Sanctorius ” this is the greatest of the evacuations and so must diminish the quantity of blood below “the proportion” any physician “dares” through bleeding, he concludes that people ought to put aside “panick fears” about “comparatively plentiful evacuation this way,” which is “dreaded by many,” not just “the unconsidering vulgar” but “even persons of all degrees, and education, and even many Physitians of great name.”78 Of the thermometer, Volker Hess has argued that “surprisingly and contrary to the fears of opponents of quantification or emulators of 74 Dacome, ‘Balancing Acts’, 383–384. 75 Kuriyama, ‘The Forgotten Fear of Excrement’. 76 For instance, Louis XIII of France “endured no less than 212 enemas, 215 purgations, and 47 venesections—all in the course of a single year.” Ibid., 429. 77 William Cole, A Physico-medical Essay Concerning the Late Frequency of Apoplexies. Together with a General Method of their Prevention and Cure. In a Letter to a Physican (Oxford: The Theater, 1689), 184, Early English Books Online. 78 Ibid., 184–186; italics in the original.

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Foucault, the thermometer served as a vector of democratization in medicine” by removing some of “the subjectivity of the physician’s judgement” and by making “the sick person … the fully responsible subject of his or her malady, an active agent rather than a passive patient.”79 Sanctorius’s weighing device and aphorisms similarly seem to give individuals agency over their own health, instructing them in how to live to be a hundred years old. However, with this agency and personal responsibility comes the potential for assigning blame to individuals for their illnesses or for not weighing “right,” a blame that can be internalized: as Holyday moralizes, “Thanke thy selfe, if Health failes,” a moral less applicable to body temperature. Not only does Sanctorius attempt to measure the body–mind relationship through his weighing device, but he also offers some insight into the mind–body interaction in acts of quantification. In his address to the reader, he writes: But, if they are desirous to be followers of the truth, I shall so far satisfy them all, as that they shall not only apprehend the pure refined truth in their minds and understandings, but they shall see it with their Eies, and feel it with their Hands, if they shall but strictly examine, by the Ballance, all those things which I have delivered in this Book, concerning the ponderation of insensible Perspiration ….80

It is worth noting the linguistic connection between the mental activity of reflection—pondering—and acts of weighing and measuring, a connection emphasized in the 1676 translation and in other, more familiar, English expressions relating to mental weighing or measuring.81 In his introductory defence of “Mechanical Reasoning,” which is “much talked of now in Physick” but “the greatest number of Professors in Medicine are declared Enemies to it,” Quincy emphasizes the need for 79 Gérard Jorland, and George Weisz, ‘Introduction: Who Counts?’ in Body Counts: Medical Quantification in Historical & Sociological Perspectives: La Quantification médicale, perspectives historiques et sociologiques, ed. by Gérard Jorland, Annick Opinel, and George Weisz (Montreal: McGill-Queen’s University Press, 2005), 8. 80 Santorio, Rules of Health, A4r. 81 Similarly, Quincy also makes use of a weighing metaphor, writing that “one farther

Reason for taking Sanctorius ’s Account herein, which with some Persons may have considerable weight, altho’ with my self I confess it has but little, and that is Authority […].” Preface, vii; italics in the original.

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an individual setting out upon “any Enquiry” to “be first well acquainted with the Powers and Capacities of his own Mind[.]”82 He goes on to describe the different mental processes involved in ascertaining certainty depending on category: historical certainty, moral certainty, and demonstration, the last of which depends “upon the Testimony of our Senses.”83 Like Sanctorius, Quincy draws attention to the role of emotions, with their physiological underpinnings, in shaping the history of science, writing that mechanical diagrams included in “Physical Books” are “apt to move either the Contempt or Laughter of those conceited People, who meerly for want of Acquaintance with themselves, and the Powers and Capacities of their own Mind, are, just as their Blood happens to circulate, either Enthusiasts or Scepticks.”84 Quincy argues that achieving “any manner of Certainty” about the human body requires “taking it to Pieces like any other Machine,” but he also states that in addition to “Physical Agents,” there is in a human body “the Mind, or Soul, or Power of Thought, whatsoever it is called,” adding that “by not being able to determine the Force and Efficacy of such Agents as cannot be brought under the Notices of our Senses, we are obliged to proceed by other Measures, and trust altogether to Observation and Experience.”85 Observation and experience become the “other Measures” by which the operations of the mind are measured.

4

Conclusion

Sanctorius’s static medicine deserves further consideration for several reasons. One of these is that there has been a tendency in early modern scholarship to stress a conceptual shift in understandings of the body as increasingly bounded and separated from its environment.86 Sanctorius’s

82 Quincy, preface, ix; Quincy, ‘Introduction’, xiii. 83 Quincy, ‘Introduction’, xvii. 84 Ibid., xxxv; italics in the original. 85 Ibid., xlii; l–li. 86 See, for example, Paster, Rowe, and Floyd-Wilson’s description of the influence of Descartes and Locke (1632–1704) in this regard. ‘Introduction’, 15. See also David Hillman’s reference to Norbert Elias’s articulation of the homo clausus . Shakespeare’s Entrails: Belief, Scepticism and the Interior of the Body (Houndmills, Basingstoke, Hampshire: Palgrave Macmillan, 2007), 7.

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calculation of the quantity of insensible perspiration, and continued references to his experiments well into the eighteenth century, undermine this notion by emphasizing the highly porous boundary between bodies and their environments. Sanctorius focused attention not on the workings of invisible supernatural forces but on those of natural metabolic processes. As Kuriyama observes, Sanctorius “was probably the first person in history to weigh himself daily; he was certainly the first whose self-weighing became renowned, and it was his example that first inspired emulation. He was also the first—and this surely is the most crucial point—to advance the key justification for this practice: to urge some vital connection between the numbers read off a scale and a person’s state of being.”87 He was certainly not the last, and the legacy of his attempt to quantify the metabolic effects of nearly every aspect of daily life and of the impact of such quantification on self-experience continues in the ubiquity of personal devices measuring everything from heart rate to calories burned to sleep patterns.88

87 Kuriyama, ‘Forgotten Fear’, 416. 88 For his influence on eighteenth-century weight watchers, see Lucia Dacome, ‘Living

with the Chair: Private Excreta, Collective Health and Medical Authority in the Eighteenth Century’, History of Science, 39, 4 (2001): 468–500, https://doi.org/10.1177/007327 530103900404. For his relationship to modern measuring devices and implications of more recent self-tracking on selfhood, see Sysling, ‘Introduction’.

The Rise of Quantitative Biology in the Cartesian Age: The Theories of Preformation Mariangela Priarolo

1

Introduction

Early modern mechanism is undoubtedly one of the landmarks within the history of the quantification of bodies. This is because, as is well known, mechanism is founded precisely on the thesis that bodies are beings that can and, above all, must be conceived only through their quantitative properties. For instance, one could consider René Descartes (1596–1650)’ Principles of Philosophy published in 1644, in which the philosopher wrote,

Descartes’ and Malebranche’s writings will be will be quoted by using the following abbreviations followed by the volume number and the page number: AT = Oeuvres de Descartes, edited by Charles Adam and Paul Tannery, 11 vols (Paris: Vrin); CSM = The Philosophical Writings of Descartes, edited by John M. Priarolo (B) Independent scholar, Pisa, Italy e-mail: [email protected]

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_6

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the nature of matter, or body considered in general, consists not in its being something which is hard or heavy or coloured, or which affects the senses in any way, but simply in its being something which is extended in length, breadth and depth’.1

As Descartes explains in the following articles, the notion of quantity is equivalent to the notion of extension.2 Therefore, since extension is the essence of a corporeal substance, which is the matter that constitutes all bodies,3 the bodies are nothing more than a definite amount of quantity of matter or, more precisely a definite amount of space.4 What distinguishes the bodies and their several features (including shape,

Cottingham. Robert Stootholf and Rupert Murdoch, 3 vols (Cambridge: Cambridge University Press); OC = Oeuvres complètes de Malebranche, directed by André Robinet (Paris: Vrin-CNRS, 1958–1967) 22 vols. SAT = The Search after Truth, edited by Thomas M. Lennon and Paul J. Olscamp) Cambridge: Cambridge University Press, 1997); DM = Dialogues on Metaphysics and on Religion, edited by Nicholas Jolley and David Scott (Cambridge: Cambridge University Press, 1997). If not specified, the translations are mine. 1 René Descartes, Principles, II part, art. 4, AT VIII, 42, CSM 1 224. 2 See Descartes, Principles, II part, art. 8: ‘There is no real difference between quantity

and the extended substance; the difference is merely a conceptual one, like that between number and the thing which is numbered’, AT VIII 44, CSM 1 226. 3 See Descartes, Principles, II part, art. 22: ‘It can also easily be gathered […] that celestial matter is no different from terrestrial matter. And even if there where an infinite number of worlds, the matter of which they where composed would have to be identical’, AT VIII 52, CSM 1 232. 4 See Principles, II part, art. 11: ‘Suppose we attend to the idea we have of some body, for example a stone, and leave our everything we know to be non-essential to the nature of body: we will first of all exclude hardness, since if the stone is melted or pulverized it will lose its hardness without thereby ceasing to be a body; next we will exclude colour, since we have often seen stones so transparent as to lack colour; next we will exclude heaviness, since although fire is extremely light it is still thought of as being corporeal; and finally we will exclude cold and heat and all other such qualities, either because they are not thought of as being in the stone, or because if they change, the stone is not on that account reckoned to have lost its bodily nature. After all this, we will see that nothing remains in the idea of the stone except that it is something extended in length, breadth and depth. Yet this is just what is comprised in the idea of a space’, AT VIII, 46, CSM 1 227.

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width, colour, density, temperature and appearance)—that is, their principle of individuation—is motion.5 This motion is ruled by a few laws that God established while creating the world. Consequently, according to Descartes, there is no difference in the nature of a stone, a planet, a table, a tree, a cat or a human being. Inasmuch as they are all bodies, they are nothing but definite portions of extension organised by the laws of motion. Accordingly, all bodies, including the human body, can be seen as mere machines.6 Hence, even the functions traditionally ascribed to the soul can be explained in mechanical terms. As Descartes puts it at the end of the Treatise on Man (1630–1633), all the functions I have ascribed to this machine … [i.e. digestion, respiration, nourishment, movement of the limbs, beating of the heart, etc.] follow from the mere arrangement of the machine’s organs every bit as naturally as the movements of a clock or other automaton follow from the arrangement of its counter-weight and wheels.7

Against Aristotelian thought and the analysis proper of Galenism, widespread in his time,8 Descartes insists that there is no need to suppose

5 See Principles, II part, art. 23: ‘any variations in matter or diversity in its many forms

depends on motion’, AT VIII 52, CSM 1 232. 6 The parallel between a man and a machine has been deeply and frequently discussed starting with Canguilhem 1965, who stated that the comparison with a machine implies a teleological reading of the formation of bodies. See on this Geneviève Rodis-Lewis, ‘Limitations of the Mechanical Model in the Cartesian Conception of the Organism’, in Descartes. Critical and Interpretive Essays, ed. by M. Hooker (Baltimore and London: John Hopkins University Press, 1978), 152–170; François Duchesneau, Les modèles du vivant de Descartes a Leibniz (Paris: Vrin, 1998); Dennis Des Chene, Spirits and Clocks. Machines and Organism in Descartes (New York-London: Cornell University Press, 2001); Emanuela Scribano, Macchine con la mente. Fisiologia e metafisica tra Cartesio e Spinoza (Roma: Carocci, 2005). I will discuss this point infra in the main text. 7 AT, XI 202, CSM 1 108. 8 As stated, the early modern refusal of spiritual entities was strictly connected with the

refusal of Galenism. A useful overall presentation of Galenism in early modern philosophy is Matteo Favaretti Camposampiero. ‘Galenism in Early Modern Philosophy and Medicine’, in Encyclopedia of Early Modern Philosophy and Science, ed. by D. Jalobeau and C. Wolfe (Cham: Springer, 2018). On the reception of Galenism between the seventeenth and the nineteenth century, see Maria Pia Donato, ‘Galen in an Age of Change (1650–1820)’, in Brill’s Companion to the Reception of Galen, ed. by Bouras-Vallianatos and B. Zipser (Leiden-Boston: Brill, 2019), 487–507.

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the existence of a soul or in general of any internal ‘principle of movement and life’ to explain such functions. All we need is ‘blood’ and ‘spirits’, which are agitated by the heart of the fire burning continuously in its heart—a fire which has the same nature as all the fires that occur in inanimate bodies.9

This thesis is also present in one of the last writings of Descartes, Description of the Human Body (1648), which testifies to his everlasting interest in explaining all bodily functions in mechanical terms. Here Descartes claims that. we […] have no more reason to think that it is our soul which produces in it the movement which we know by experience are not controlled by our will than we have reason to think that there is a soul in a clock which makes it tell the time.10

In the same writing, Descartes states that not only the functioning of living beings but also their generation can be explained mechanically, for the formation of an animal derives from ‘a disorganised mixture of two fluids.’11 The two fluids respectively belong to the two sexes and ‘act on each other as a kind of yeast, generating mutual heat.’12 Such heat agitates the particles of matter, giving rise to the movement of other material particles that ‘little by little’ produces ‘the state required for the formation of the parts’.13

9 AT, XI 202, CSM 1 108. On the medical doctrine of ‘animal spirits’, see Christopher Upham Murray Smith et al. (eds), The Animal Spirit Doctrine and the Origins of Neurophysiology (Cambridge: Cambridge University Press, 2012). 10 AT XI 226, CSM 1 315. 11 According to Descartes there is no difference between fluids and solids except the

motion of their particles: ‘all living bodies which required nutrition to sustain them (i.e., animals and plants) are continually undergoing change, So there is no difference between those parts we call fluid, such as the blood, the humours and the spirits, and those we call solid, such as bones, flesh, nerves and skin, beyond the fact that each particle of these latter parts moves much more slowly than the particles of the former’ (AT IX 247, CSM 1 319). 12 AT XI 253. 13 Ibid.

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The idea that animal generation results from an epigenetic process that begins with matter and ends with life is also present in Descartes’ most important work on this subject, First Thoughts on Animal Generation, firstly published in 1701 and—despite its title—probably written after 1648. Here a famous statement in favour of spontaneous generation can be found, which is justified by evoking the simplicity of animals: Since therefore so few things are necessary to make an animal, it is assuredly not surprising to see so many animals, so many worms, so may insects form spontaneously in all putrefying matter.14

The premature death of Descartes stopped his attempts to find the ultimate answer to such problems and made it difficult to state what would have been his final words on the subject,15 Nonetheless, Descartes’ contemporaries considered him a champion of an all-encompassing mechanism—a concept that led many thinkers to discuss his (alleged) confidence in a mechanical explanation of every phenomenon. One of them was Pierre Gassendi (1592–1655). Even without knowing Descartes’ Treatise on Man and his other physiological works, published after Gassendi’s death, he cast a great deal of doubt on the fact that mechanism could explain the constitutions of living beings. According to Gassendi, the reason is that, to understand the organisation of plants, animals and human beings, one must suppose a principle that represents their end or the end of their parts or limbs. Without knowing that the end of an eye, for instance, is seeing, we cannot truly understand its constitution. Analogously, without knowing that a certain tree’s aim is to make apples, we cannot explain why it needs specific kinds of roots. If this is true and living beings require an end to be explained, the research of final causes cannot be eliminated from the study of the nature: You will say that it is the physical causes of this organization and arrangement which we should investigate, and that it is foolish to have recourse to purposes rather than to active causes or materials. But no mortal can possibly understand or explain the active principle that produces the

14 AT XI 505. 15 The complexity of Descartes’ position on generation is well described by Denis Des

Chene in the above mentioned Spirits and Clocks.

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observed form and arrangement of the valves which serve as the openings to the vessels in the chambers of the heart.16

Descartes’s reply to Gassendi is well known. Since we cannot know ‘God’s purposes’, final causes must be banned by natural explanations that should look only for efficient causes17 : The points you make to defend the notion of a final cause should be applied to efficient causation. The function of the various parts of plants and animals etc. makes it appropriate to admire God as their efficient cause – to recognize and glorify the craftsman through examining his works; but we cannot guess from this what purpose God had in creating any given thing.18

The lack of any reference to internal finality has pushed some scholars to question Descartes’ denial of it. For instance, in her article Limitations of the Mechanical Model in the Cartesian Conception of the Organism, Geneviève Rodis-Lewis, recovers an idea already present in Ferdinand Alquié.19 Thus, she observed that one cannot exclude that Descartes here was only rejecting the hazardous speculation popularised by examples attributed to the Stoics.20 Other scholars, such as Georges Canguilhem, 16 Gassendi, Fifth set of Objections, AT VII 309, CSM 2 215. The most extensive rejection of Descartes’ denial of final causes can be found in Gassendi’s Disquisitio metaphysica seu dubitationes, et istantiae adversus Renati Cartesii metaphysicam, et responsa, in Gassendi 1964 [1658] 3, 269–410. An analysis of Gassendi’s doctrine of final causes in Margaret J. Olser, ‘Whose Ends? Teleology in Early Modern Natural Philosophy’, Osiris, 16 (2001): 151–168. On Gassendi’s thought, see Antonia Lolordo, Pierre Gassendi and the Birth of Early Modern Philosophy (Cambridge: Cambridge University Press, 2006). 17 AT VII 375, CSM 2 258. 18 AT VII 374–5, CSM 2 258. 19 See the Alquié’s comment quoted by Rodis-Lewis: ‘One wonders whether Descartes’s

disagreement with Gassendi is as great as it seems. Though he rejects the search for final causes, does he not recognizes the existence of what is generally called ‘finality’ by admitting the use of each part of a living body?’ (René Descartes, Oeuvres philosophiques, 2 vols, ed. by Ferdinand Alquié, vol. 2, n. 2 (Garnier: Paris, 1967), 821. 20 ‘Does the literal repetition of Gassendi’s words imply that he does recognize at least

an internal finality which subordinates the part to the whole and that he only rejects the hazardous speculation popularised by examples attributed to the Stoics? One cannot be sure on the basis of this text, in which only the efficient cause is to account for the construction of the parts and their situation in the body as a whole’, Rodis-Lewis, ‘Limitations of the Mechanical Model in the Cartesian Conception of the Organism’, 160.

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have claimed that Descartes’ notion of machine did not exclude in principle the notion of finalism21 but only because we ignore God’s aims. A consequence of similar readings is that Descartes’ use of mechanism as a general model of explanation seems to depend more on an epistemological limitation of human beings than on the real ways things are.22 It is beyond the scope of these pages to deeply discuss the meaning and extent of Descartes’ mechanism or his commitment to different forms of finalism. Rather, what I would like to stress is that long after Descartes the attempt to give a mechanical description of those natural phenomena that seem to escape this kind of explanation, like generation, became increasingly rare.23 In my opinion, one reason for explaining such disappearance can abscribe to two Cartesian philosophers, such as Nicholas Malebranche (1638–1715) or Pierre-Sylvain Régis (1632–1707). Contrary to Descartes, they think that we can say something on the ways in which God had created the world and try to overcome Gassendi’s objection to Descartes’ denial of final causes by proposing a peculiar theory of generation. This theory, although providing a kind of external finalism has been considered compatible with mechanism, and would have great success for its explanatory power precisely in the Cartesian milieu. I am referring to preformationism, also known as the theory of pre-existing germs.24

21 Georges Canguilhem, La connaissance de la vie (Paris: Vrin, 1965), 114. 22 On the different ways of conceiving mechanism in Descartes see Des Chene, Spirits

and Clocks, 72. 23 The persistence of this lack of a quantitative and mechanical explanation of the phenomena concerning life is well drawn by Kant’s famous sentence about the ‘Newton of the blade of grass’ (‘we may confidently assert that it is absurd for human beings even to entertain any thought of so doing or to hope that maybe another Newton may some day arise, to make intelligible to us even the genesis of but a blade of grass from natural laws that no design has ordered. Such insight we must absolutely deny to mankind’, Kant, Dialectic of Teleological Judgment, § 75, Critique of Judgement, Immanuel Kant, Critique of Judgment, ed. by N. Walker (Oxford: Oxford University Press 2007), 228. See also §77: ‘It is utterly impossible for human reason, or for any finite reason qualitatively resembling ours, however much it may surpass it in degree, to hope to understand the generation even of a blade of grass from mere mechanical causes’, 238. 24 Following Peter Bowler’s suggestion (Peter J. Bowler, ‘Preformation and Preexistence in the Seventeenth Century: A Brief Analysis’, Journal of the History of Biology 4, 2 [1971]: 221–244), many scholars thought that we must distinguish between preformation and pre-existence theory, because the first would state that the individual is formed in the seed or in the egg of his parents before birth, the second more strongly that

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Preformationism, especially in its Malebranchean version, which I will present in the first part of this chapter, has been repeatedly accused of abandoning the Cartesian aim of a naturalistic explanation of all phenomena. For instance, in Jacques Roger’s classic book Les Sciences de la vie (1963), one reads: By adopting the pre-existence of germs, Malebranche renounced more than just the most debatable portion of his master’s work. The moment he took away from nature and gave to God alone the power to form living beings, he destroyed all of Cartesian science. As soon as it escaped from the laws of motion, the formation of beings escaped the human mind, and with respect to this question, science was no longer possible: men found themselves confronted immediately with the mystery of God.25

Roger acknowledged that Malebranche wanted to limit this mystery by claiming that God always acts through general laws and obeys the Order, the basic law that according to Malebranche, leads all other laws of and in nature,26 by considering God’s behaviour ‘scientific’. However, according to Roger, ‘by crediting pre-existent germs, Malebranche was renouncing the simple and general laws’,27 and therefore mechanism. Forty years later, Andrew Pyle proposed a similar view, and accused Malebranche’s preformationism of being ‘pure supernaturalism’,28 and of betraying Descartes’s project of building a mechanical model of nature. Nonetheless, as I intend to demonstrate, such judgements appear excessive. Although it cannot be denied that Malebranche or Régis distanced

the individual was formed at the beginning of the time. However, seventeenth-century thinkers did not rigidly follow this distinction and had no problems in using preformation to indicate pre-existence theories. Leibniz, for instance, is one of them. On Leibniz’s use of the term, see Alessandro Becchi, ‘Leibniz, the Microscope and the Concept of Preformation’, History and Philosophy of Life Sciences, 39, 5 (2017): 1–23, 5. 25 Jacques Roger, The Life Sciences in Eighteenth-Century French Thought [1963] (Stanford: Stanford University Press, 1997), 355–356. 26 See Malebranche, Méditations chrétiennes: ‘God has two kinds of laws which rule him in his conduct. The one is eternal and necessary, and this is Order; the others are arbitrary, and these are the general laws of nature and of grace. But God established the latter only because order required that he acts in that way’. OC X 73. 27 Jacques Roger, The Life Sciences, 356. 28 Andrew Pyle, Malebranche (London-New York: Routledge 2003), 166.

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themselves from their master and justified preformationism with arguments that, in some sense, could be considered as belonging to the supernatural domain, the preformation theory must be seen as a theory completely committed to natural explanation as far as it is a way to enlarge a mechanical explanation of generation29 In fact, as we will see, far from being opposed to mechanism, Malebranche’s and Regis’ recourse to finalism to explain the complexity of the organisation of the living could be seen precisely as a way of defending mechanism from critics. Such critics like the above mentioned Pierre Gassendi, used finalistic arguments against Descartes to menace the ‘pureness’ of a quantitative description of nature. In this regard, preformationism should be considered an important attempt to preserve mechanism from the objections posed by ‘biological’ phenomena.30

2

Malebranche’s Theory of Preformation

Descartes’ analysis of living beings is not marginal in Malebranche’s philosophy. On the contrary, Malebranche became a philosopher precisely after he encountered Descartes’ physiological writings—or more specifically, after legendarily encountering Clerselier’s just published edition of the Treatise on Man (1664)—which contained also the Description of the Human Body (under the title Description of the Formation of the Foetus ).31 Malebranche’s literature has lengthily discussed the reason for Malebranche’s interest in the Treatise. After all, Malebranche was a Catholic priest, who studied Theology, the Bible and all the religious matters that a Catholic priest was supposed to cultivate if he was living in a religious institution focused on the instruction of the priests, like Oratory. Some of these scholars, for instance Henri Gouhier, claimed 29 I partly agree, therefore, with Karen Detlefsen. In an important essay on Malebranche’s preformationism (Detlefsen, 2003), she makes claim for the scientific status of it, but states that Malebranche’s preformationism ascribes a sort of activity to nature. However, I believe it is very difficult to make this activity coherent with Malebranche’s occasionalism. 30 Of course, the use of the term biology before the second half of the eighteenth century is anachronistic. On the birth of biology see Giulio Barsanti, ‘Lamarck and the Birth of Biology’, in Romanticism in Science. Science in Europe, 1790–1840, ed. by S. Poggi, and M. Bossi (Dordrecht-Boston: Kluwer, 1994), 47–74. 31 See on this Delphine Antoine-Mahut, and Stephen Gaukroger (eds), Descartes’ Treatise on Man and its Reception (Cham: Springer, 2016).

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that Malebranche could find in Descartes’s dualism, which is underlined in the Preface to the 1664 edition of the Treatise, the great proof for the immortality of the soul. Accordingly, the scientific ideas present in the Treatise would have been useful, to Malebranche’s eyes, only for apologetic reasons.32 However, another important commentator, André Robinet,33 has proposed a different interpretation and stated that Malebranche had not only a religious vocation but also a strong scientific one. A hint of this is the number of scientific works that Malebranche read in the ten years between his encounter with Descartes’ Treatise and the publication of his masterpiece, Recherche de la veritè (1674). Two books that Malebranche mentioned since the first editions of the Recherche are particularly notable: Marcello Malpighi’s On the Formation of the Chicken in the Egg (1672) and Jan Swammerdam’s, The Miracle of the Nature or the Structure of the Female Uterus (1672).34 Thanks to a new instrument, the microscope, the two anatomists, through different experiments and with different aims, demonstrated the centrality of the egg in explaining animal generation.35 More importantly, they suggested that future animals were already contained in their germs, which eventually would develop in their definitive form. As has been remarked,36 the thesis of the pre-existence of the germs could be seen as resulting from more of a shift in the criteria used for understanding the nature, than of the effectiveness of the observations. The Aristotelian idea according to which one states the existence of something only if one observes it—a criterion Bernardi calls ‘strong

32 Henri Gouhier, La philosophie de Malebranche et son expérience religieuse (Paris: Vrin, 1926). 33 See André Robinet, Système et existence dans l’oeuvre de Malebranche (Paris: Vrin, 1965). 34 On Malpighi, see Domenico Bertoloni Meli, Mechanism, Experiment, Disease: Marcello Malpighi and Seventeenth-Century Anatomy (Baltimore: Johns Hopkins University Press, 2011). A useful presentation of Swammerdam’s work and his context is Saskia Klerk, ‘Natural History in the Physician’s Study: Jan Swammerdam (1637–1680), Steven Blankaart (1650–1705) and the “Paperwork” of Observing Insects’, British Journal for The History of Science, 53 (2020), 497–525. 35 See on this Clara Pinto Correia, The Ovary of Eve: Egg and Sperm and Preformation (Chicago: University of Chicago Press, 1997). 36 Walter Bernardi, Le metafisiche dell’embrione. Scienze della vita e filosofia da Malpighi a Spallanzani (1672–1793) (Firenze: Olschki, 1986).

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visibility’37 —gave way to the thesis already present in Democritus that something can exist even if it cannot yet be seen—that is, the criterion of ‘weak visibility’.38 Hence, it is not surprising that Malebranche introduced preformation theory in a book dedicated to errors of sight, according to Malebranche (and to the most part of the Western philosophical tradition), ‘the first, the most noble, most extensive’ of all the senses39 : With magnifying glasses, we can easily see animals much smaller than an almost invisible grain of sand; we have seen some even a thousand times smaller. These living atoms walk as well as other animals. Thus, they have legs and feet, and bones in their legs to support them (or rather on their legs, for the skin of an insect is its skeleton). They have muscles to move them, as well as tendons and an infinity of fibers in each muscle; finally, they have blood or very subtle and delicate animal spirits to fill or move these muscles in succession. Without this, it is impossible to conceive how they should live, nourish themselves, and move their tiny bodies from place to place according to the various impressions of objects.40

Our imagination, Malebranche continues, gets lost in this small universe, as does our sight, which has a very limited perception of the matter. However, our intellect can help us by showing its true idea, i.e. an infinite, Cartesian, extension, which can then be infinitely divided: We have clear mathematical demonstrations of the infinite divisibility of matter, and although our imagination is shocked at the thought, this leads us to believe that there might be smaller and smaller animals to infinity.41

The rational idea of the matter perfectly fits the experiences proposed by Malpighi and Swammerdam and allows us to state that we can apply to

37 Bernardi, Le metafisiche dell’embrione, 34. 38 Ibid., 35. 39 Malebranche, Recherche de la verité, OC I 79, SAT 25. 40 OC I 80, SAT 25–26. 41 OC I 81, SAT 26.

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every living being what we see regarding the tulip, namely, the fact that a tulip seed contains all the parts of the grown plant42 : An entire tulip is seen in the seed of a tulip bulb. Likewise, a chicken that is perhaps entirely formed is seen in the seed of a fresh egg that has not been hatched. Frogs are to be seen in frogs, eggs, and still other animals will be seen in their seed when we have sufficient skill and experience to discover them. But the mind need not stop with the eyes, for the mind’s vision is much more extensive that the body’s. We ought to accept, in addition, that the body of every man and beast born till the end of time was perhaps produced at the creation of the world. My thought is that the females of the original animals may have been created along with all those of the same species that they have begotten and that are to be begotten in the future.43

It is easy to see why Malebranche’s preformationism is also called the theory of ‘emboîtement des germes’ (‘encapsulation theory’)—an expression, by the way, Malebranche never used and that first appeared in the works of Charles Bonnet in the eighteenth century.44 According to preformationism, at the beginning of time God created all the individuals that would appear on the Earth and put them ‘in miniature’45 in their first parents. All future living beings result from the development of these tiny beings, which already exist, pre-exist, preformed in their ancestors. This is the reason why we can also define this theory as a preformation theory.46 42 ‘When one examines the seed of a tulip bulb in the dead of winter with a simple magnifying lens or convex glass, or even merely with the naked eye, one easily discovers in this seed the leaves that are to become green, those that are to make up the flower or tulip, that tiny triangular part which contains the seed and the six little columns that surround it at the base of the flower. Thus it cannot be doubted that the seed of a tulip bulb contains an entire tulip’ (OC I 81, SAT 26). 43 OC I 82–83, SAT 27. 44 See on this Rieppel 1985. 45 OC I 81, SAT 26. 46 On the distinction between preformation and pre-existence, see above note 24.

There is a lot of discussions amongst scholars about the grounds of Malebranche’s theory of preformation: a revival of saint Augustine’s thought (Roger, The Life Sciences in Eighteenth-Century French Thought, 236, see also 332 and 343, Gouhier, La philosophie de Malebranche et son expérience religieuse), and more specifically of the doctrine of the seminal reasons (Jules M. Brady, ‘Augustine’s Theory of Seminal Reasons’, The New

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In the first presentation of the preformation theory two reasons support it: one rational—the infinite divisibility of matter—and one empirical—the discoveries of the microscopic world. Almost ten years later, in the Méditations Chrétiennes (1683), Malebranche would add another pivotal argument: the internal organisation of living beings or the functional holism of living beings, as Karen Detlefsen named it.47 Since each part of a living being has a function, it has an end. Therefore, it cannot be explained only through the laws of motion, though it supposes a specific intelligent project: Everything is formed here [the organized bodies] for a determined aim and through particular volitions: for it is evident from the situation and the construction of the eyes that they are made for seeing, and that every part that composes the body of animals is aimed to certain uses. And everything it is formed here through particular volitions, for the organized bodies cannot be produced by the sole laws of the communication of motion. The laws of the Nature cannot but give them little by little their ordinary growth.48

The same argument becomes pivotal in Malebranche’s Entretiens sur la métaphysique published in 1688, more precisely in the eleventh Entretien, in which Malebranche definitely states the preformation theory starting by considering the simplicity of the laws of motion. As Malebranche explains,

Scholasticism, 38 [1964]: 141–158; Hiro Hirai, Le concept de semence dans les théories de la matière à la Renaissance. De Marsile Ficin à Pierre Gassendi [Turnhout: Brepols, 2005]), the new discoveries obtained through the microscope (Andrew Pyle, ‘Malebranche on Animal Generation. Preexistence and the Microscope’, in The Problem of Animal Generation in Early Modern Philosophy, ed. by J. Smith (Cambridge: Cambridge University Press, 2006), 194–214; Becchi, ‘Leibniz, the Microscope and the Concept of Preformation’, or the rise of ovism (Bowler, ‘Preformation and Pre-existence in the Seventeenth Century: A Brief Analysis’ [1971]; Pinto Correia, The Ovary of Eve: Egg and Sperm and Preformation). 47 Karen Detlefsen, ‘Supernaturalism, Occasionalism, and Preformation in Malebranche’, Perspectives on Science, 11, 4 (2003): 443–483. 48 OC X 71.

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since the laws of motion cannot construct bodies composed of an infinity of organs, it is a necessity, therefore, that flies be contained in the larvae from which they hatch.49

Here, although refusing Descartes’ attempt to explain animal generation ‘from the mixture of the seed of the two sexes’,50 Malebranche gives Descartes the benefit of the doubt. Since it is impossible that the union of the sexes, as Descartes wrote, is ‘the cause of the organisation of the parts of the animal, and of a particular animal’,51 Descartes probably only wanted to make us understand ‘how the laws of motion suffice to cause the parts of animals to grow little by little. But that these laws are able to form them and connect them all together, is something no one will ever prove. Apparently Mr. Descartes recognized this himself, for he did not press his ingenious conjectures very far.’52 Malebranche explains that Descartes’s hypothesis was ‘very foolhardy (témeraire)’ not because he attributed the formation of the animal to the laws of motion but because he tried ‘to explain the construction of animals as God has made them’ without knowing the ‘infinity of parts that 49 OC XII 253, DM 195. The same idea is developed in the last edition of Recherche de la vérité (1712): ‘Furthermore, there is a great difference between the formation of living and organized bodies, and that of the vortexes of which the universe is composed. An organized body contains an infinity of parts that mutually depend upon one another in relation to particular ends, all of which must be actually formed in order to work as a whole. For it need not be imagined with Aristotle that the heart is the first part to live and the last to die. The heart cannot beat without the influence of the animal spirits, nor these be spread throughout the heart without the nerves, and the nerves originate in the brain, from which they receive the spirits. Moreover, the heart cannot beat and pump the blood through the arteries unless they as well as the veins that return the blood to it are already complete. In short, it is clear that a machine can only work when it is finished, and that hence the heart cannot live alone. Thus, from the time this projecting point that is the heart of the chicken appears in a setting egg. the chicken is alive; and for the same reason, it is well to note, a woman’s child is alive from the moment it is conceived, because life begins when spirits cause the organs to work. Which cannot occur unless they are actually formed and connected. It would be wrong then to pretend to explain the formation of animals and plants and their parts, one after the other. on the basis of the simple and general laws governing the communication of motion; for they are differently connected to one another by virtue of different ends and different uses in the different species. But sure is not the case with the formation of vortexes; they are naturally born from general laws, as I have just in part explained’ (OC I 343–344, SAT 4565). 50 OC XII 264, DM 205. 51 Ibid. 52 Ibid., DM 205.

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need to be before we look for the causes of their formation’.53 However, Malebranche observes, apparently he did not think of this. For we would not be wise were we to wish to explain exactly how a watchmaker makes a watch, without knowing in advance of what parts comprise this work.54

Here lies Malebranche’s point: the fact that God should intervene intentionally and in detail in the first formation of the animals does not deny the truth of mechanism, because even by preforming animals at the beginning of time God acted mechanistically, using only matter and movement to create the first living beings: God surely made the most perfect work though the most general and simplest ways. He foresaw that the laws of motion would suffice to conserve in the world whatever species of insect you please. He willed to draw all possible applications for His laws, in order to render His work more complete. Thus, first He formed the entire species of that insect, by means of a wonderful division of a certain portion of matter. For we must indeed always keep in mind that it is by motion that everything happens in bodies, and that in the first determination of motion it was an issue indifference to God whether He moved the parts of matter one way or another, as there were no general laws of the communication of motion before bodies collided with one another’.55

Hence, the difference between living and not living beings lies only in their formation—which is caused by matter and motion, though by a particular, intentional motion—but not in their nature, which can always be mechanistically explained: ‘Give me extension and there is nothing I cannot make from it by means of motion’, the God of Malebranche says.56 As one reads in the XV Elucidation to the Recherche de la vérité dedicated to occasionalism, written by Malebranche against those philosophers, like Pedro da Fonseca (1528–1599) and Francisco Suárez (1548–1617), who, in his opinion, state that only by ascribing a real

53 Ibid. 54 Ibid. 55 OC XII 271, DM 211. 56 OC XII 236, DM 181.

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causal power to finite beings can we understand the difference between living and not living things, If it were necessary, I would prove here that the principle of a dog’s life is not very different from that of the motion of a watch. For the life of bodies, whatever they might be, can only consist in the motion of their parts; and it is not difficult to judge that the same subtle matter that produces the fermentation of blood and animal spirits in a dog, and which is the principle of its life, is no more perfect than that which gives motion to the mechanism of watches or which causes heaviness in the weights of clocks, which is the principle of their life, or to speak as do others, of their motion.57

In Malebranche’s eyes, then, the real enemy of mechanism is not the external finalism implied in preformationism. On the contrary, preformationism means reinforcing a mechanical vision of nature by avoiding the real risk that a finalistic objection, like the objection of Gassendi, could raise: the attribution of a power of self -organisation to nature. According to Malebranche, such a kind of power would ‘divinise’ nature,58 since a similar power could be explained only with spiritual principles. In this regard, God’s intervention, at the beginning of time and afterward as occasionalism stated,59 by eliminating every entity that cannot be reduced to quantitative properties, would guarantee a world avoid of nothing but matter and motion.

57 OC III 211–212, SAT 661. Compare this passage with Descartes’ Treatise on Man: ‘In order to explain these functions, then, it is not necessary to conceive of this machine has having any vegetative or sensitive soul or other principle of movement and life, apart from its blood and its spirits, which are agitated by the heart of the fire burning continuously in its heart—a fire which has the same nature as all the fires that occur in inanimate bodies’ (AT XI 202, CSM 1 108). 58 See Recherche de la verité, VI, II, III: ‘We […] admit something divine in all the bodies around us when we posit forms, faculties, qualities, virtues, or real beings capable of producing certain effects through the force of their nature; and thus we insensibly adopt the opinion of the pagans because of our respect for their philosophy (OC II 319–320, SAT 446). 59 It must be remarked that Malebranche’s occasionalism does not imply the continuous intervention of God. See on this Mariangela Priarolo, ‘Force de loi. The Debate on the Laws of Nature and Malebranche’s Occasionalism’, in Occasionalism From Metaphysics to Science, ed. by M. Favaretti Camposampiero, M. Priarolo, and E. Scribano (Turnhout: Brepols, 2018), 107–126 also for further references on this topic.

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Régis’ (Limited) Theory of Preformation

The desire to assure that nature can be explained only through the quantitative principles of matter and motion is also pivotal to the work of ‘the Prince of Cartesian philosophers’,60 Pierre-Sylvain Régis, a harsh critic of Malebranche.61 Régis pleaded his case for Cartesianism throughout France, defending Descartes’ philosophy against the criticism of his adversaries and personally suffering bishop Harlay’s condemnation of Cartesianism in 1671.62 Nonetheless, Régis does not merely repeat the philosophy of his mentor, but approaches it in an original way.63 It is possible to find a trace of this attitude in Régis’ conception of natural philosophy, in which, just like Malebranche, he abandons Descartes only to follow the discoveries of Marcello Malpighi, Francesco Redi or Thomas Willis.64 If one opened his monumental work, Cours entier de philosophie ou Systême general de la philosophie de Descartes,65 one would find eight books entirely devoted to physics, which includes two parts: one that concerns the knowledge of the effects, the other that consists of the knowledge of the causes; the first can be called Practical Physics, the other Speculative Physics. Therefore, the practical part of Physics consists of the exact observation of the effects that every physical body can produce;

60 See Pierre-Daniel Huet, Nouveaux mémoires pour servir à l’histoire du cartésianisme (Amsterdam: Desbordes, 1693), 3–4. 61 See Tad M. Schmaltz, Radical Cartesianism. The French Reception of Descartes

(Cambridge: Cambridge University Press, 2004), part III. 62 On Harlay’s condemnation and his consequences in the Cartesian milieu, see Roger Ariew, Descartes and the First Cartesians (Oxford: Oxford University Press, 2015). 63 See on this, Antonella Del Prete, ‘Né con Descartes né con Malebranche: l’antropologia di Pierre-Sylvain Régis’, in Alle origini dell’umanesimo scientifico: dal Rinascimento all’Illuminismo, ed. by G. Paganini, and L. Bianchi (Napoli: Liguori, 2010), 119–133; ead, ‘Un cartésianisme “hérétique”: Pierre-Sylvain Régis’, Corpus. Revue de philosophie, 61 (2011), 189–203. 64 On Régis’ scientific references, see Dennis Des Chene, ‘Life after Descartes: Régis on Generation’, Perspectives on Science, 11, 4 (2003): 410–420, 412. 65 Régis’s Cours has been published for the first time in 1691 and would have several further editions. It was divided in three tomes and contained sections on metaphysics, logic and morals. All quotations are from the first edition published in Amsterdam, chez Huguetan (Régis 1691 followed by the number of the tome and of page). All translations are mine.

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the speculative part consist of the reasoning that we can perform in order to discover the causes of these effects.66

In the part in which he discusses ‘practical physics’, Régis first recalls of all the Cartesian definition of body. Like Descartes, he states the body to be an extended substance: There is no one that does not know that there is a substance which is extended in length, width and depth, which is called body.67

Under the category of ‘bodies’, therefore, Régis recollects several different beings, which have in common not only their being natural phenomena, but also, above all, their being quantitative entities. Amongst these, Régis mentions the following: stars and planets, which he described in the third book; the features of earth, minerals and stones analysed in the fourth book; the meteorological events presented in the fifth book; plants in the sixth book; animals in the seventh book; and, in the eighth book, human beings, which he considers like any other mentioned body, i.e. definite portions of matter. The fifth and sixth books are the most interesting for our topic, since it is here that Régis’ preformation theory surfaces. In the preface to the fifth book, Régis begins by distinguishing plants from other kinds of bodies, like minerals and ‘meteors’, which, in Descartes’ work, included many phenomena (parhelia, rainbows, atmospheric phenomena, etc.).68 The reason is that, while plants are inanimate, minerals and meteors are not. Here Régis affirms something that would have surprised a Cartesian reader at first glance. According to him, indeed, there is no problem in considering the word animate as synonymous to ‘endowed with a soul’. As Régis puts it, we will not have problems in attributing to plants a soul and a life, since we see that they contribute a lot by themselves to nourish and to preserve themselves, contrary to minerals and meteors as we discussed, which are

66 Régis 1691, 1 274. 67 Régis 1691, 1 279. 68 On Descartes’ analysis of meteors and its relationship with the Scholastic thought,

see Lucian Petrescu, ‘Cartesian Meteors and Scholastic Meteors: Descartes against the School in 1637’, Journal of the History of Ideas, 76, 1 (2015), 25–45.

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bodies that we call inanimate, because they do not contribute at all by themselves to their nourishment and their growth.69

However, Régis is not recovering Aristotle’s hylomorphism or Renaissance vitalism, as one might think at first impression. As Régis explains, the life of plants must not be considered a spiritual principle, something differing from the matter that constitutes the plant. Conversely, what Régis calls ‘life’, only consists in the arrangement of their essential or organic parts and in a particular disposition of the pores, which causes the juices to circulate there in a manner that is appropriate for nourishing the plants of each species.70 The use of the words soul or life should not be misunderstood, for by these terms Régis means only the particular disposition of the parts, that is, their functional organisation, which shall be explained as a combination of matter and motion, although a particular one. In other words, to Régis’ and Malebranche’s eyes, even life should be considered a material, quantitative process. This process, however, cannot be directed by chance. In fact, as Régis stresses after a few lines, one cannot conceive that the casual encounter of several atoms could form such a large number of similar and organic parts, which enter into the composition of each plant.71 Consequently, it is necessary to conclude that all plants, which are complex beings possessing an internal organisation, ‘have been formed at the same time, and they are comprised one within the other, so that the last are but a development of what is contained in the first’.72 Like Malebranche, then, Régis introduces the preformation theory to justify the internal organisation of living beings. In his account, which differs from Malebranche’s, living beings can be said to possess an internal principle of activity. As we have seen, this principle can be described in a mechanical way regarding its nature, but not its function, which requires a finalistic explanation excluded by Cartesian mechanism. It is because of finalism that Régis recovers the words life and soul . Although, as we have seen, he paradoxically does not think that these words indicate spiritual principles.

69 Régis 1691, 2 464. 70 Régis 1691, 2 465. 71 Régis 1691, 2 466. 72 Ibid.

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Such denial of spirituality to living beings is also evident in the sixth book, in which he proposes an analogous reading for animals. The term animals implies they are ‘animated’. Therefore, like plants, they could be said to have ‘life’ or ‘soul’ within them. However, even in this case, it is not possible to ascribe to them a spiritual principle different from their matter, since by the term life we do not mean nothing else than the heat of their blood and the particular movements of the sense organs which depend on it.73 Like plants, the complexity of animals cannot be explained only ‘by the fortuitous of the parts of the soil’.74 Hence, it must be assumed that it is God who endowed them with their first organisation, which can and must be described mechanically: We will assume that God formed at the beginning of time the first two animals of each species, not in fact immediately, because God produces only the substances in this way and the animal bodies are modal beings, but mediately, since he wanted to spread movement through matter in such a way that it was divided into parts of which some had just the size and shape that were necessary to make them take on the order and arrangement in which the form of the two first animals of each species consisted.75

Unlike Malebranche’s God, who perfectly shapes every living being which will appear on earth in saecula seculorum, Régis’ God only set up the first exemplars of every species. Such a ‘creation’, however, occurs with a particular quantity of motion, which explains either the generation of the first beings and the ‘power’ they have to give rise to their offspring. In fact, according to Régis, generation is nothing but ‘a certain movement, which depends on the male seed’.76 It is this movement that ‘makes the germs capable of receiving the nourishment they require with the opening and development of their parts in close arrangement with one another’.77

73 Régis 1691, 3 506. 74 Régis 1691, 2 508. 75 Ibid. 76 Régis 1691, 2 643. 77 Ibid.

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As Règis points out, generation is nothing but a certain movement in order to mark what it has in common with the other natural movements.78 With Malebranche, then, Règis insists on denying that living beings, which clearly differ from inert objects, diverge in nature from rocks or tables. Living or not, all beings are definite quantities of matter. Nonetheless, living beings have something that rocks and tables do not: they are internally organised totalities, meaning that their parts have specific functions. Contrary to Malebranche, however, Régis does not think that ‘soul’ is synonymous with ‘activity’, or in other words that to be active is a property that belongs only to souls. Consequently, even if the first organisation resulted from God’s decision, as in Malebranche, for, as we mentioned, organisation cannot derive from chance, such a decision does not imply the denial of an inner activity, as Malebranche maintain. After all, such activity can be explained as a ‘virtual power’ present since time began, and transmitted via ancestors to their offspring.79 In brief: both Malebranche and Régis agree that the functionality of living beings cannot be explained only by recurring to mechanism, and that their structure’s organisation requires a kind of finalism to be explained. Moreover, both refuse to identify the source of such finalism in a spiritual principle present in nature, and ascribed to God’s first action of creating its ultimate source. Therefore, the only difference between the two appears to be the way they interpret the source of powers in nature—completely external, in Malebranche and partly internal in Régis. In both cases, what they want to preserve is a mechanical reading of nature, which must exclude all principles that cannot be quantitatively interpreted.

4

Conclusion

In the already mentioned Les sciences de la vie, Jacques Roger claimed that, despite its intentions, preformationism is a true and real betrayal of Descartes’ project.80 According to Roger, the main reason for such a statement is that preformationism abandoned Descartes’ attempt to

78 Ibid. 79 Regarding this, Detlefsen’s interpretation of Malebranche’s preformationism, which

I recalled above, seems to fit Régis’ account of preformationism perfectly. 80 Roger 1997, 128.

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explain nature only through natural principles and resorted to using God to ‘save (biological) phenomena’. Hence, unlike Descartes’ mechanism, preformationism ‘is a supernaturalist theory par excellence’.81 In my opinion, this interpretation underestimates two remarkable points. The first one is the role that God possesses even in Descartes’ natural philosophy. Indeed, Descartes poses an abyss between the human mind and the domain of God, as the famous doctrine of the creation of eternal truths clearly attests.82 Nonetheless, God still plays a pivotal role in his explanation of the physical world. In this regard, one could mention the first (and main) physical work of Descartes, The World, in which he describes in detail all natural phenomena starting from the description of what God does in creating them.83 Descartes’ conviction that all motions ultimately depend on God—a conviction long considered the root of early modern occasionalism84 —has led some scholars to see his mechanical philosophy as ‘a significant interruption to the development

81 Andrew Pyle, ‘Animal Generation and the Mechanical Philosophy: Some Light on the Role of Biology in the Scientific Revolution’, History and Philosophy of the Life Sciences, 9, 2: 225–254, 246. 82 As is well known, in a series of letters written in Spring 1630 Descartes stated that the so called eternal truths are created as well as ‘the rest of his creatures’ (Descartes to Mersenne, April, 15, 1630, AT I 145, CSM 3 23). For this reason, ‘it is certain that these truths are no more necessarily attached to his essence than are other created things’ (Descartes to Mersenne, May, 27, 1630, AT I 152, CDM 3 25), and therefore we cannot infer anything about the mind of God by starting from our (true) knowledge of the world. On Descartes’ eternal truth the literature is endless. See Gregory Walski, ‘The Cartesian God and the Eternal Truths’, Oxford Studies in Early Modern Philosophy, 1 (2004): 23–44, for an overview of the discussion on the subject. 83 ‘Let us suppose […] that God really divides [matter] into many such parts, some larger and some smaller, some of one shape and some of another, however we care to imagine them […]. From the first instant of their creation, he causes some to start moving in one direction and others in another, some faster and others slower […] and he causes them to continue moving thereafter in accordance with the ordinary laws of nature. For God gas established these laws in such a marvellous way that even if we suppose he creates nothing beyond what I have mentioned, and sets up no order or proportion within it but composes from it a chaos as confused and muddled as any the poets could describe, the laws of nature are sufficient to cause the parts of this chaos to disentangle themselves and arrange themselves in such good order that they will have the form of a quite perfect world’ (AT XI 34, CSM 1 91). 84 See for instance the essays collected in Steven Nadler (ed), Occasionalism: Causation among the Cartesians (Oxford: Oxford University Press, 2010).

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of naturalism’.85 Accordingly, either one claims that references to God in describing the world make physics a supernatural theory of nature, and then Descartes would fit this picture as well as Malebranche or Régis, or alternatively, one limits the accusation of supernaturalism to those theories—which Lorraine Daston proved became very rare in the seventeenth century—that use God or divine entities to explain phenomena that mechanism or other natural explanation cannot explain.86 The second point is that Malebranche and Régis, and all those who adopted Descartes’ mechanism, harbour a precise notion of nature in mind, according to which nature is a geometrical, quantitative extension with no intrinsic power(s). According to this picture, bodies are mere configurations of space, pure quantities, whose unity depends on something other than them, but that can be described in the same quantitative terms, that is motion. Preformationism only states that in the case of a particular kind of body, living beings and their particular and specific configuration do not result from general laws of motion but rather from a particular motion impressed by God at the beginning of time. As we have seen, for Régis this particular motion produced in the offspring of the first ancestors the capacity for movement. In Malebranche, it only developed a predetermined figure. For both philosophers, however, living bodies are nothing but extension and motion. In this regard they evoke God’s intervention precisely for the opposite reason that Roger has stated, i.e. to ‘naturalise’ the world. In fact, it is thank to God’s ‘original motion’ that to explain the organisation of living beings, one needs not to recur anymore to substantial forms, souls and forces that all represent, in Malebranche’s words, ‘something divine in all the bodies’.87

85 Keith Hutchison, ‘Supernaturalism and Mechanical Philosophy’, History of Science, 21, 3 (1983): 297–333. 86 See Lorraine Daston, ‘Marvelous Facts and Miraculous Evidence in Early Modern Europe’, Critical Inquiry, 18, 1 (1991): 93–124. On the seventeenth century use of mechanism to explain strange phenomena like divining rods, see Mariangela Priarolo, ‘Demoni o corpuscoli? La bacchetta divinatoria e la nuova scienza alla fine del XVII secolo’, Intersezioni, 3 (2020): 333–358. 87 OC 2 310, SAT 446.

‘Nature is More Subtle Than Any Mathematician’: Giorgio Baglivi on Fluids in the Human Body Luca Tonetti

1

The Intricate Nature of Disease

A still widespread narrative distinguishes two main approaches in early modern medicine: the first one, namely iatromechanics or iatrophysics, interprets the human body in terms of matter and movement, while explaining physiological and pathological processes within a quantitative physics. In contrast, the second one, iatrochemistry, describes the human body as a chemical laboratory, whose functions are the result of a variety of chemical reactions. Giorgio Baglivi (1668–1707) is broadly considered to be one of the most radical exponents of the first tradition. A passage

A preliminary version of this paper was discussed in Scientiae Conference 2021. See also: Luca Tonetti, ‘Machines and Diseases: Giorgio Baglivi and his Mechanistic Physiopathology’, in Wired Bodies. New Perspectives on the Machine-Organism Analogy, edited by Nicole Dalia Cilia and Luca Tonetti (Roma: CNR Edizioni, 2017), 37–44. L. Tonetti (B) Department of Historical and Geographic Sciences and the Ancient World © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_7

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from his main work, De praxi medica (1696), is usually quoted in support of this interpretation1 : For whoever takes an attentive view of its fabric [i.e., the body], he’ll really meet with shears in the jaw-bones and teeth, a phiol in the ventricle, hydraulick tubes in the veins, arteries, and other vessels, a wedge in the heart, a sieve or straining-holes in the viscera, a pair of bellows in the lungs, the power of a leaver in the muscles, pulleys in the corners of the eyes, and so on.2

While emphasising a form of mechanistic reductionism, Baglivi also developed an innovative physiology and pathology that both focus on the role of solids and discard ancient humourism. As a solidist, he is a fortiori interested in the way solids act on fluids in the body, and thus in the notions of elasticity, resistance, force and balance—that could be quantified and translated into mathematical language (broadly intended). Not

(DiSSGeA), University of Padua, Padua, Italy e-mail: [email protected] 1 See: Mirko D. Grmek, ‘Osservazioni sulla vita, opera ed importanza storica di Giorgio Baglivi’, in Atti del 14. Congresso internazionale di storia della medicina, Roma-Salerno, 13–20 settembre 1954 (Roma: Guerra e Belli, 1960), 423–437; id., ‘La vita e l’opera di Giorgio Baglivi medico raguseo e leccese (1668–1707)’, in Il nucleo filosofico della scienza, ed. by Guido Cimino, Ubaldo Sanzo and Gabriella Sava (Galatina: Congedo, 1991), 93– 111. On Baglivi’s iatromechanics: Maria Vidal, ‘Giorgio Baglivi tra osservazione clinica e speculazioni iatromeccaniche,’ Atti del centro ricerche storiche di Rovigno 20 (1990), 133–214; Tonetti, ‘Machines and Disease’. All quotations from Baglivi’s works, unless otherwise indicated, are from the 7th edition of Baglivi’s complete works: Giorgio Baglivi, Opera omnia medico-practica, et anatomica, 7th ed. (Leiden: Anisson and Joannis Posuel, 1710); hereafter, Opera, followed by the page number. All English translations are mine with the exception of Baglivi’s De praxi medica (abbreviated in PM ) for which I have used the following English translation: The Practice of Physick… 2nd ed. (London: D. Midwinter et al., 1723). 2 PM , bk. I, ch. 10, §7 (in Opera, 126): “Nam si compagem illius attente quis lustraverit, inveniet profecto in mandibulis, ac dentibus forficem, in ventriculo phialam, in venis, arteriis, caeterisque canalibus tubulos hydraulicos, in corde embolum, in visceribus cribrum, seu secernicula, follem in thorace, vectis potentiam in musculis, trochleas in angulis oculorum, & sic de reliquis.”.

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surprisingly, Baglivi confessed that all those interested in the relationship between solids and fluids should turn to Giovanni Alfonso Borelli’s works.3 However, the true nature of disease seems to elude any ‘mathematical’ axiomatisation and any overly rigid explanatory scheme. Even the difference between iatromechanics and iatrochemistry does not work because there is no such clear-cut distinction and both mechanical and chemical explanations help to describe the functioning of the human body in early modern medicine.4 Baglivi’s work testifies to the problematic nature of this type of approach in medicine and shows how challenging it is to explain pathology from a mechanistic perspective. Body fluids play a crucial role in this scenario. In this paper I will first comment on Chapters 10 and 11 from Baglivi’s De praxi medica, which are devoted to the development of medicine (De variis medicinae aetatibus, ejusdemque progressibus ) and the main sources for theory and practice (De fontibus theoriae & praxeos ), respectively. While questioning the application of theories/systems in medicine (even those derived from a mechanistic perspective), because they can affect the normal perception of reality, Baglivi does not deny the heuristic value of analogical reasoning, which allows him to explain essential physiological processes such as muscle contraction or human respiration. Baglivi argues that one theory alone cannot successfully explain bodily processes under both normal and morbid conditions. Any explanation of a disease, and therefore also its treatment, cannot be deduced from the theory with which we are supposed to explain the functioning of our body. This does not mean that pathology is not part of the mechanistic explanation, but that such knowledge cannot be acquired independently of experience. Baglivi thus places himself at the very heart of the debate on rationalism and empiricism in medicine, as he seeks a third point of view 3 See Opera, 366: “Oportet vero, ut qui recte velit percipere materiam de solidis, & liquidis corporis animati tractantem; apponat sibi prae oculis opera, quae edidit doctissimus Borellus, Romanae Academiae nobile sydus, is enim de proprietatibus liquidorum in genere plura scripsit in aureo libro de motionibus naturalibus a gravitate pendentibus. De vi autem solidorum, in libro de vi percussionis in solidis, & in fluidis projectis a solidis: ubi modus expenditur considerandi solidum seorsim a fluido, fluidum seorsim a solido, & utraque simul.” 4 See Antonio Clericuzio and Maria Conforti, ‘Iatrochemistry and Iatromechanism in the Early Modern Era’, in Encyclopedia of Early Modern Philosophy and the Sciences, ed. by Dana Jalobeanu and Charles Wolfe (Cham: Springer, 2021).

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that can be an alternative to the two sides.5 In the De praxi medica he shows that it is possible to establish a new medicine that is totally focused on experience. Experience, however, should be underpinned by a new methodology, whose purpose is to guide the physician in observing nature and to show how to derive from experience all the information needed to explain diseases, identify the most suitable therapeutic indications and find new remedies. After briefly describing Baglivi’s theory of muscle contraction, I will discuss the main disorders involving our fibres and the concept of ‘balance’ on which Baglivi’s pathophysiology is based. Baglivi’s concept of equilibrium is actually a kind of ‘proportion’ between the parts of the body—between solids and fluids—that cannot be easily translated into a given quantity. It is not a numerical proportion, but a balance between solids and fluids in the body that cannot be deduced a priori and is assumed to vary from individual to individual. It can be inferred from first-hand experience and perception at the patient’s bedside. Finally, I will show that even though solids exert greater force and resistance than fluids, fluids are still a challenging issue that can be of fundamental importance in pathology.

2

An Overview of De praxi medica, bk. I, Chs. 10–11

In De praxi medica, Baglivi describes medicine as facing a significant crisis: indeed, medicine has abandoned the wisdom of the ancients (prisca sapientia) and has turned out to be an uncertain and sometimes

5 The dichotomy between rational method and empirical practice in early modern medicine in Italy is well represented by Malpighi-Sbaraglia dispute at the end of the seventeenth century. The implications for medicine have been thoroughly examined in Domenico Bertoloni Meli, ‘Mechanistic Pathology and Therapy in the Medical Assayer of Marcello Malpighi’, Medical History, 51 (2007), 165–180. See also: Marta Cavazza, ‘The Uselessness of Anatomy: Mini and Sbaraglia versus Malpighi’, in Marcello Malpighi: Anatomist and Physician, ed. by Domenico Bertoloni Meli (Florence: L.S. Olschki, 1997), 129–145; Domenico Bertoloni Meli, Mechanism, Experiment, Disease: Marcello Malpighi and Seventeenth-Century Anatomy (Baltimore, MD: Johns Hopkins University Press, 2011), ch. 11. On Baglivi’s view, see: Raphaële Andrault, ‘What Does it Mean to Be an Empiricist in Medicine? Baglivi’s Praxis Medica (1696)’, in What Does it Mean to Be an Empiricist? Empiricisms in Eighteenth Century Sciences, ed. by Siegfried Bodenmann and Anne-Lise Rey (Cham: Springer, 2018), 169–188.

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misleading form of knowledge (incertam & praestigiatricem),6 which is able to only provide a ‘probabilem rationem’7 for every disease. And, as a result, therapeutics also has no solid foundation. At the heart of this crisis lies a crucial issue about the role of observation: by abandoning the focus on observation, medicine would have succumbed to the ‘lure’ of theoretical systems and lost its own mission. Any attempt to reform medicine, however, should first examine the major obstacles and challenges that have hindered its progress. Compared to the golden age, which is represented by Hippocratic medicine, Baglivi identifies three events in history which favoured the separation between ratio and observatio: (1) the influence of the Arabic medicine; (2) the spread of the Paracelsian-Helmontian tradition; (3) the development of ‘new philosophies’ against the medical practice (novi motus contra praxim excitati sunt a tot novis Philosophiis ).8 According to Baglivi, the dissemination of Arabic medicine in the West, at the beginning of the tenth century, led to the transformation of the Greek medical tradition ‘in quandam ingenii agitationem, disputationumque exercitationem.’9 Baglivi believed that the distinction between theory and practice had been introduced at this time by Arabic physicians. However, late Renaissance medicine tried to reverse this trend by recovering the Greek ‘prisca sapientia.’10 6 PM , Praefatio (in Opera, [xi]). 7 Ibid. (in Opera, [xiii]). 8 In his letter to William Sherard, May 20, 1702 (in RS, Sherard Collection, MS/252/ 574), Baglivi wrote: “Io qui ho molto da fare: attendo alla stampa di molte altre cose, e non perdo tempo, accio prima di morire veda ristabilita la prattica di medicina, come era a tempi felici del grande Ipocrate” (I have much to do here: I attend to the printing of many other things, and waste no time, so that before I die I may see the praxis of medicine re-established, as it was in the fortunate days of the great Hippocrates). The contrast between “prisca sapientia” and “nova medicina” is reiterated, for example, in PM , bk. I, ch. 1, §3 (in Opera, 2): “Naturae, non hominis voce loquitur Hippocrates Medicorum Romulus; cui nec aetas prisca vidit parem in re medica, nec videbit futura, nisi demum resipiscant Medici, & velut ab alto somno excitati, videant quantum differat historica, & mascula Graecorum Medicina, à speculativa, & pensili novorum Hominum.” 9 PM , bk. I, ch. 10, §1 (in Opera, 119). 10 PM , bk. I, ch. 10, §2 (in Opera, 120): “Primi Itali, inter quos M. Fabius Calvus,

Mercurialis, Martianus, Septalius &c. eosque secuti Galli, & prae caeteris ex nobili Parisiensium Academia Duretus, Ballonius, Hollerius, & Jacotius &c. post excussum Arabicae servitutis jugum, ad restituendam priscam Graecorum de re medica sapientiam omni studio contenderunt.” All the authors mentioned here are involved in the early modern

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One further event was the transmission of Paracelsian-Helmontian views. Assumptions (such as that of the ‘tria prima’—the three principles, namely salt, sulphur and mercury, that compose all bodies), which Paracelsianism uses to explain the causes of diseases or find new treatments, are not confirmed by nature. Making hypotheses without first finding evidence in experience and observation is one of Baglivi’s main concerns, because the process of hypothesis-building has immediate implications in clinical practice—for instance, in the application of remedies, such as phlebotomy or vesicants. In the short essay De usu et abusu vesicantium, Baglivi shows that any blistering agent—whose application in medicine was denied by Helmontian medicine due to its toxicity—could instead be administered under specific conditions. Those conditions can be determined through observations and experiments on live animals. Finally, Baglivi discusses the new trends in natural philosophy of his time—Cartesian, Democritean, mechanical and physical–mechanical philosophy.11 The influence of mechanistic and corpuscular theories in medicine is considered highly inappropriate, as those ‘systems’ bring methods, conceptual tools and issues into areas (like medicine) that should instead be constitutively beyond any theoretical speculation. This overlap between theory and practice has turned physicians into philosophers and medicine into pure dialectics (philosophia contentiosa).12 As already emphasised, Baglivi does not abandon geometricmechanical laws or chemical principles, because physiopathological phenomena do indeed appear to be characterised by a complex

rediscovery of Hippocratism in medicine, although they are still closely concerned with traditional approaches, namely translation and textual criticism of the Hippocratic corpus. See: Iain M. Lonie, ‘The “Paris Hippocratics”: Teaching and Research in Paris in the Second Half of the Sixteenth Century’, in The Medical Renaissance of the Sixteenth Century, ed. by Andrew Wear, Roger K. French, and Iain M. Lonie (Cambridge: Cambridge University Press, 1985), 155–174. On Baglivi’s Hippocraticism, see Ian M. Lonie, ‘Hippocrates the Iatromechanist’, Medical History, 25 (1981), 113–150; Ingo W. Müller, ‘Der Hippokratismus des Giorgio Baglivi’, Medizinhistorisches Journal, 26, 3–4 (1991), 300–314. 11 PM , bk. I, ch. 10, §4 (in Opera, 121): “Cartesiana, inquam, Democritaea, Mechanica, Physico-Mechanica […].” 12 Ibid.: “Horum exemplo Medici, facti omnino Philosophi, (ab abstractae sapientiae tranquillitate allecti) praxim medicam, quae lectulos aegrorum vix, ac ne vix quidem deserere potest in philosophiam contentiosam converterunt.”

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of chemical and mechanical motions (complexum motuum chymicomechanicorum).13 Physics and chemistry—although chemical processes are reducible to physical–mechanical laws—should therefore necessarily be part of medical education. However, at this early stage in his elaboration of a solidistic pathophysiology, which still does not include a clear definition of ‘fibre,’ Baglivi distinguishes between solids and fluids. If, in fact, all morbid states were exclusively related to a disorder in the solids, then the physician could easily determine their causes and identify the necessary remedies by applying physical–mechanical laws. However, most diseases are supposed to involve fluids that cannot be understood through any physical-mechanical hypothesis due to their minimal components and configuration: For the ablest philosopher and the greatest master of the best hypothesis that is, will be forc’d to acknowledge, after all his meditations and labour in tracing the true constituent parts of any humours, that the minima, or least particles of any humour of the body whether natural or sickly, lie beyond the reach of all Art and Speculation.14

Therefore, ‘all the advances of physicians upon this head are nothing but wild-fire, that do not so much as touch upon the substance of the thing.’15 Still something inexplicable remains. However, this does not represent an obstacle to medical practice: But after all, tho’ the true configuration and texture of such humours is unknown to us; yet in the way of practice, ‘tis sufficient that we have learn’d by experience the various progress, exit, and declension of their motions; for being excited and directed by nature, they unfold to us the true springs of indications, for the exhibiting or shifting of remedies.16

13 PM , bk. I, ch. 11, §7 (in Opera, 126). 14 Ibid. 15 PM, bk. I, ch. 11, §7 (in Opera, 126–127): “quicquid hac de re Medici asserere conantur, nil aliud vere sunt quam ignes fatui, qui rei corticem ne quidem attingunt.” 16 Ibid. (in Opera, 127): “Quamvis ignota nobis sit talium humorum vera configuratio, & textura: ad curationem tamen sufficiet, per experientiam nosse varios eorundem motuum progressus, exitus, & declinationes, qui utpote a natura excitati, & directi, veros indicationum fontes nobis adaperiunt, in exhibendis, mutandisque remediis.”

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‘Nature—Baglivi says—is more subtle than any mathematician’ (subtiliori quolibet mathematico, subtilior est natura): hence, it follows that medical practice can only progress through experience (solo usu, & exercitatione).17 In fact, what we hypothesise about diseases and remedies, and believe to be consistent and certain, turns out to be absurd or even impossible when implemented in clinical practice. Conversely, what seems useless and contrary to reason, because it does not fit our hypotheses or is impossible to fully explain, ultimately proves to be useful and reliable. At stake are also the gap between theory and practice and their role in medicine. Although this distinction is untenable, Baglivi recognises that the decline of medicine lies precisely in the fact that the purposes of theory and practice are not clearly separated: this happens whenever diseases and remedies are evaluated not by experience but only on the basis of theoretical assumptions and, reciprocally, whenever clinical practice totally ignores etiology by blindly following experience. If the theory of the ‘moderns’ has advanced beyond that of the ancients, the same is not observed in clinical practice. While ‘geometricmechanical principles’ and ‘physical–mechanical’ or chemical experiments help us to successfully explore the structure of the animate body, clinical practice shows us that nature eludes this kind of formalisation and axiomatisation. All the assumptions we make, which allow us to formulate hypotheses about how our bodies work, need to be verified by experience.

3 Analogical Reasoning and Quantification in Physiology Baglivi outlined his ‘fibre theory,’ which introduced a new element (the concept of ‘fibre’) in human physiology, in a short essay that appeared in Alessandro Pascoli’s Corpo umano in 1700. It was in fact a collection of short texts concerning experiments and observations on muscle contraction and the action and physical properties of some body fluids, such as blood, saliva and bile. He compiled them during his anatomy class at the new anatomical theatre in Rome, which opened in March 1700. Each essay corresponds to a different day or step of his public dissection, but supposedly includes data and observations dating back to the late 1690s. 17 Ibid.: “Haec cum vera sint, fatebimur sane, artem curandorum hominum, solo usu, & exercitatione comparari, adeoque praxim prae theoria […] curationi morborum magis conferre.”

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The explanation of muscle contraction given in De fibra motrice et morbosa is one of those topics in physiology where a mechanistic perspective sounds convincing. Baglivi first describes the observations that led him to distinguish two types of fibres, flesh and membranous. Next to an accurate preparation of the body tissue, these observations also benefited from the use of a four-lens microscope. Thus, Baglivi focuses mainly on the structure of flesh fibres, which are involved in the formation of muscles, tendons and bones: Niels Stensen’s geometrical theory of muscle contraction played a crucial role here. What enables the muscles to contract is the tomentum sanguineum, i.e. the blood which flows between the fibrils. Baglivi hypothesised that blood corpuscles act like many fixed pulleys (or trochlea), around which the fibrils slide like ropes (or levers). Muscles can therefore be considered as a combination of simple machines, i.e. as a compound machine, whose mechanical advantage is the product of the mechanical advantages of its component simple machines. In this case, since the number of blood corpuscles is almost incalculable, the force amplification due to tomentum sanguineum increases exponentially. However, this first hypothesis is untenable, because the fixed pulley does not adequately represent the motility of the blood corpuscles: Baglivi therefore compares the blood corpuscles to a part of the wheel and axle— the scytale—which is a kind of handle or radial lever that turns the wheel. In both cases, mechanical analogy serves as a heuristic tool through which Baglivi can identify the mechanism underlying muscle contraction and provide a new mechanistic explanation. Therefore, what makes muscle movement possible is primarily blood (and not, for example, animal spirits or nervous fluid), at a specific quantity and speed. Any deviation affects movement. Baglivi compares this mechanism to the spring of a watch18 : Two things seem to be necessary for the movement of muscles: first, a specific amount of blood in their fibres, and a specific speed of it. In fact, just as in a clock an excess or deficiency of weight prevents or slows down the movement of the clock, so an excess or deficiency of blood and speed in the muscles will be a great obstacle to their movement. Secondly, the due proportion of the movement of the resistance of each fluid flowing through its own channels, one of which, if perturbed, will give rise to an

18 Same analogy is used in his description of the dura mater.

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uneven and disturbed movement of the muscles. This is especially true of fever. […].19

The comparison with the clock shows us that the mechanism underlying the functioning of both machines and animate bodies is essentially the same. Moreover, these few lines suggest the importance of the concept of balance, i.e. proportion, which plays a key role in Baglivi’s pathophysiology. If equilibrium is disrupted, the clock does not work as well as muscle contraction does not occur. However, Baglivi does not give us any threshold value: how can we calculate or define this equilibrium condition? In fact, Baglivi alludes to the possibility of such a calculation: he believes that the laws of statics are fundamental to the solution of problems in the mechanics of motion. But as can be seen, these calculations are very demanding because many variables are involved: Obviously, no one can solve the problems of the mechanics of muscular movement without thoroughly investigating this proportion of motion and gravity between the smallest components of each fluid and between each fluid flowing in its channels, as well as the equilibrium between the flowing fluids of the animate body and the resisting solids, or, conversely, between those ones that push and those that resist, and finally between solids and solids that are both homogeneous, as between membranes or viscera made of membranes, and heterogeneous, as between fleshy fibers and membranous fibers.20

19 See Opera, 408: “Ad motum enim musculorum recte peragendum duo necessaria videntur esse, primum determinata sanguinis quantitas in ejus fibris, ejusdemque determinata velocitas. Nam sicuti in horologio excedens, vel deficiens appensum pondus horologij motum impedit, & retardat; ita deficiens, vel abundans sanguinis quantitas, velocitasque in musculis, illorum motui maximo erit impedimento. Alterum est proportio debita motus, & resistentiae singulorum liquidorum per canales suos currentium, quorum alterum si turbetur, musculorum quoque motus inaequalis, & turbatus inde orietur. Id magna ex parte experimur verum in febribus. […].” 20 See Opera, 408: “Certe nisi quis recte quaesiverit proportionem hanc motus, & gravitatis inter componentia minima cujuslibet liquidi, & inter singula liquida per canales suos currentia, nec non aequilibrium inter fluida corporis animati currentia, & solida quae resistunt, vel contra quae impellunt, & contranituntur; ac demum inter solida, & solida tum homogenea, ut membranas inter & membranas, & ex membranis compacta viscera, tum etherogenea ut inter fibras carneas, & membranosas, difficilem profecto problematum mechanices motus musculorum solutionem experietur.”

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Interestingly, we also note the evidence provided by fevers. As will become clearer in his treatise on fibre in 1702 (Specimen quatuor librorum de fibra motrice et morbosa),21 the impossibility of handling such complex variables forced Baglivi to find evidence in experience and thus in clinical observation. The search for ‘proportion,’ therefore, should be pursued first and foremost in nature: But here I see a doctor rising up against me, murmuring and inveighing with these words: How unacquainted with mathematics is this author of solids! How sparing he is in giving demonstrations and geometrical laws to illustrate the difficult field of solids! I reply that in this treatise on solids, whose sole purpose is to extend (medical) practice, I did not intend to use rigorous laws of demonstration, because the origin, course, and occurrence of diseases elude and deplore all speculative demonstrations of this kind: rather, I concentrated on general, well-considered rules and some principles of mathematics appropriate to this subject; I also decided to adapt the rules of geometry to the reliable observation of fibre affections, but not against observation. […].22

21 Baglivi thus provides a new interpretation of the Hippocratic concept of balance: it is about the forces and resistances between solids and fluids in the body, since the body is conceived as a bundle of closely interconnected fibres ( fasciculus fibrarum), which is crossed by a continuous oscillatory movement. That movement is exerted, first and foremost, by the dura mater of the brain, which serves as the central motor for the body. See Specimen, ch. 6. Luca Tonetti, ‘Bodies in Balance: Santorio’s Legacy in Baglivi’s Medicine’, in Santorio Santori and the Emergence of Quantified Medicine, 1614–1790, ed. by Jonathan Barry and Fabrizio Bigotti (Cham: Palgrave Macmillan, 2022), 289–315. 22 See Opera, 349–350: “Sed hic contra me obmurmurantem video medicum, & in me his verbis invehentem. Quam minime mathematice instructus est hic Autor solidorum? Quam parcus in afferendis geometricis demonstrationibus, ac legibus pro ardua solidorum provincia illustranda? Cui quidem respondeo, me in hoc de solidis specimine mere ad ampliandam praxim directo, non uti rigorosis legibus demonstrationum, quia morborum origo, progressus, & eventus omnes hujusmodi speculativas demonstrationes flocci faciunt ac spernunt; sed animo praeconceptis ac bene perceptis generalibus quibusdam Mathematices principiis ad hanc rem opportunis; regulas geometriae observationi certae affectionum fibrarum, non vero contra observationem geometriae accommodare in animo semper habuisse.”

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4

Blood, Saliva and Bile Matters: ‘Anatomising’ Body Fluids

Baglivi’s interest in body fluids was most likely influenced by Malpighi’s experiences with the nature of blood, bile and lymph. Malpighi’s description of human blood dates back to the very beginning of his career, in 1660: in his dissertation about the structure and action of lungs, De pulmonibus (1661), he described it as characterised by two different components, the white and red parts.23 A more detailed description is provided in De polypo cordis, which focuses on the nature of polyps, i.e. post-mortem blood clots that Malpighi occasionally had observed in cadavers.24 Malpighi adopted different techniques: he reported experiments with intravenous injections into dogs to test which conditions or substances were able to make the blood clot. However, he questioned this type of experimentation because an intravenous injection does not allow the physician to vividly see what is happening in the body. He therefore preferred ‘in vitro’ experiments, which involve taking blood from patients and observing any changes in its substance or colour when it is mixed with chemicals, such as vitriol oil or sulphur. In De recentiorum medicorum studio dissertatio epistolaris ad amicum (dated 1687, but possibly from 1689)—one of the core texts of the controversy with Malpighi—Giovanni Girolamo Sbaraglia (1641–1710) denied the importance of anatomical knowledge for medical practice— in particular, the one provided by comparative anatomy—, and believed that an over-emphasis on the study of solids in cadavers would ignore the role of fluids. Indeed, it would be quite illogical to study the affections of bodily solids without considering the actions that occur within fluids: In order to encourage the discovery and application of remedies, I would suggest rather that comparative anatomy should be undertaken between the humours of the healthy and the sick. The defects of the viscera in corpses are investigated, while the blood and the other humours are

23 On the use of colour as a tool of investigation, see: Domenico Bertoloni Meli, ‘The Color of Blood: Between Sensory Experience and Epistemic Significance’, in Histories of Scientific Observation, ed. by Lorraine Daston and Elizabeth Lunbeck (Chicago: The University of Chicago Press, 2011), 117–134. 24 See: Domenico Bertoloni Meli, ‘Blood, Monsters, and Necessity in Malpighi’s De polypo cordis ’, Medical History, 45 (2001), 511–512.

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ignored: which is precisely the same thing as looking at the effects in the solid parts, and blatantly omitting the causes hidden in the fluids.25

In his reply, Malpighi forcefully argues that, contrary to Sbaraglia’s claim, a thorough examination of bodily fluids was developed by the ‘moderns’: Malpighi mentions, for example, the experiments on pancreatic juice by Franciscus de le Boë, known as Sylvius (1614–1672), and Reinier de Graaf (1641–1673); on bile, by Johannes Bohn (1640–1718); on the aqueous humour of the eye, lymph and saliva by Antonius Nuck (1650–1692); on blood, by Robert Boyle (1627–1691), Antoni van Leeuwenhoek (1632– 1723) and Anton de Heyde (1646–1702).26 Furthermore, he maintains that he has collected several observations on fluids from both human and animal bodies, even in morbid conditions. Next to his already published research on blood (see De polypo cordis ), he also mentions unpublished observations on the serum of dropsy, the humour of the pericardium and the scrotum. In particular, he refers to the serum found in a woman who died of dropsy of the breast, and the chemical investigations carried out on this specific liquid by mixing it with four different substances: spirit of salt, spirit of vitriol, spirit of nitre, spirit of salt of ammonia. Similar analyses were performed on the lymph extracted from the vessels and thoracic

25 [Giovanni Girolamo Sbaraglia], De recentiorum medicorum studio dissertatio epistolaris ad amicum (Gottingae, 1687), 32: “[…] potius consulerem ad aliquam remediorum inventionem, & applicationem excitandam, ut Anatomia comparata inter fluida sana, & morbosa institueretur; quaeruntur in denatis viscerum labes, & sanguis caeterique humores negliguntur, quod est idem, ac investigare effectus in partibus solidis, & oscitanter praetermittere causas influidis latentes.” Sbaraglia uses the name “Aristides” as a pseudonym. The imprint Göttingen, 1687, is fictitious. 26 On Sylvius and de Graaf, see: Evan Ragland, ‘Experimenting with Chymical Bodies: Reinier de Graaf’s Investigations of the Pancreas’, Early Science and Medicine 13, 6 (2008), 615–664; id., ‘Chymistry and Taste in the Seventeenth Century: Franciscus dele Boë Sylvius as a Chymical Physician Between Galenism and Cartesianism’, Ambix 59, 1 (2012), 1–21. On Boyle, see: Harriet Knight and Michael Hunter, ‘Robert Boyle’s Memoirs for the Natural History of Human Blood (1684): Print, Manuscript and the Impact of Baconianism in Seventeenth-Century Medical Science’, Medical History 51, 2 (2007), 145–164. On 17th-century research into blood, see Robert G. Frank, Harvey and the Oxford Physiologists: Scientific Ideas and Social Interaction (Berkeley and London: University of California Press, 1980). On Leeuwenhoek, see: Lesley Robertson et al., Antoni van Leeuwenhoek: Master of the Minuscule (Leiden: Brill, 2016), esp. ch. 8; Ian M. Davis, ‘“Round, Red Globules Floating in a Crystalline Fluid”. Antoni van Leeuwenhoek’s Observations of Red Blood Cells and Hemocytes’, Micron 157 (2022): 103249. https:/ /doi.org/10.1016/j.micron.2022.103249.

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duct, on the serum found in the ventricles of the brain, on the fluid secreted by the cotyledons of the cow and so on. His unpublished notes preserved at Bologna University Library provide evidence for these observations, especially in the 1690s.27 A letter from Baglivi to Antonio Maria Valsalva describes further experiments on the nature of blood carried out with Malpighi through injections and ‘cantarella’ (a variation of arsenic or cantharidin powder): […] I am also making daily observations on corpses here [i.e. in Rome], and the other day, by order of Malpighi, we tried various experiments on human blood and serum with this physician from the Hospital of the Consolation, by pouring over them and mixing them with cantarella powder, and tomorrow we have decided to open the jugular of a dog and infuse it with a few portions of cantarella tincture, in order to see the effects that will follow, of which Your Excellency will be informed in due course.28

I assume that Sbaraglia’s claim that ‘modern’ medicine has largely ignored the role of fluids had prompted Malpighi to investigate further on bodily fluids. Inevitably, this dispute also influenced Baglivi’s early experiments 27 See, in particular, BUB, ms. 2085/II, which contains Malpighi’s “diarium”, a collection of unpublished notes. On this source, see: Domenico Bertoloni Meli, ‘The Archive and Consulti of Marcello Malpighi’, in Archives of the Scientific Revolution, ed. by Michael Hunter (Woodbridge: The Boydell Press, 1998), 109–120. 28 Letter from Giorgio Baglivi to Antonio Maria Valsalva, April 26, 1692, in BUB, ms. 4030 (see Ladislao Munster, ‘Nuovi contributi alla biografia di Giorgio Baglivi’, Archivio Storico Pugliese 3, 1–2 (1950): 120): “[…] del resto qui vado giornalmente facendo qualche osservazione ne’ cadaveri, e l’altro giorno per ordine del Signor Malpighi con questo Astante dell’Opsedale della Consolatione habbiamo tentato varii sperimenti sopra il sangue e siero humano con soprafonderli, e mischiarvi la polvere di cantarelle e dimani habbiamo determinato di aprire la jugulare d’un cane e d’infonderli qualche portione di tintura di cantarelle, per vederne gli effetti che ne susseguiranno, de’ quali V.S. Ecc.ma ne sarà partecipata a suo tempo […].” Remarkably enough, BUB, ms. 936, box II, folder A, fol. 2, includes a red chalk drawing of blood corpuscles from Malpighi’s observation on human blood in 1690 (“figurae obser: in sanguine humano 1690”). In 1691 Malpighi moved to Rome, following his appointment as archiater. In April 1692 Baglivi joined him. The physician (“astante”) from the Hospital of Consolation is presumably Antonio Pacchioni (1665–1726). On Pacchioni-Baglivi dispute, see Maria Conforti and Silvia de Renzi, ‘Sapere anatomico negli ospedali romani. Formazione dei chirurghi e pratiche sperimentali (1620–1720)’, in Rome et la science moderne: Entre Renaissance et Lumières [online] (Rome: Publications de l’École française de Rome, 2009), available at http:// books.openedition.org/efr/1951 .

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on this subject. In the third dissertation (Dissertatio III ) in De praxi medica, which collects many of these observations and experiences on blood, Baglivi emphasises all the issues related to the use of dissection in ‘biomedical’ research. In order to better understand the functioning of human physiology, he recommends the practice of ‘infusory surgery’— those procedures in which a solution is directly injected into the veins— since it preserves the relationship between fluids and solids in the body.29 Indeed, the action of certain fluids within the body would be lost in a dissected corpse. As we have seen from the letter to Valsalva, Baglivi’s first experiments on blood were mainly concerned with explaining the action of vesicants. ‘Vesicants’ are blistering agents that are able to induce or cause blisters to the skin for medical purposes. During the Renaissance a huge debate about the use of such drugs in medicine was raised due to their severe side effects. Interestingly, Baglivi’s essay in 1695 on the uses and misuses of vesicants (De usu et abusu vesicantium) tries to explain and identify precisely those conditions that make them useful or harmful.30 Experimentation on live animals, particularly on dogs, played a crucial role. The study of blood responses to different stimulant substances, like cantharides powder, was also decisive. Baglivi poured eight ounces of blood into two different vials, in one of which the blood was mixed with that powder. The other served as a control test, without any substances other than blood. Because the blood in the first vial clotted faster, Baglivi realised that drugs containing cantharides could accelerate coagulation.

29 See: Baglivi, Dissertatio III , Lectori (in Opera, 672): “Inter omnes investigationes, laboresque Anatomicorum, nihil utilius illustrandae morborum aetiologiae, structuraeque animati corporis duco, quam infusoriam liquorum in venas, viscerave Animalium vivorum; Quibus mortuis systema mutatur, tam solidarum, quam fluidarum partium, ita ut quandoque diversae appareant, quandoque vero abscondantur. Contra experientiae, quibus utimur in vivis, praecipue per infusoriam, ostendunt effectus inde profectos valde clare, ac sincere.” On ‘chirurgia infusoria’, see Silvia Marinozzi and Maria Conforti, ‘Dal sangue come terapia alla terapia attraverso il sangue nel XVII secolo,’ Medicina nei Secoli, 17, 3 (2005): 695–720. 30 See: Luca Tonetti, ‘Corpus fasciculus fibrarum: Teoria della fibra e pratica medica nel

De praxi medica di Giorgio Baglivi’, Physis. Rivista Internazionale di Storia della Scienza, 51, 1–2 (2016): 379–392; and id., ‘Stimulus and Fibre Theory in Giorgio Baglivi’s Medicine: A Reassessment’, in Mechanism, Life and Mind in Modern Natural Philosophy, edited by Charles Wolfe, Paolo Pecere, and Antonio Clericuzio (Cham: Springer, 2022), 67–82.

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Baglivi’s two essays on saliva and bile (De experimentis circa salivam, ejusdemque natura, usu & morbis, and De experimentis circa bilem, ejusdemque natura, usu & morbis ) both appeared in 1700, next to the De fibra motrice et morbosa. The second day of his anatomy class was in fact devoted to mouth, stomach and bowels—the digestive system. Surprisingly enough, he focused his dissertations on fluids, not organs: precisely, on saliva and bile. New anatomical discoveries had indeed revealed not only the nature, secretion mechanism and pathway of these fluids throughout the body—for example, the action of glands, or the role of the thoracic duct in the lymphatic circulation discovered by Jean Pecquet31 —but also their crucial role in several physiological and pathological processes, such as digestion. Baglivi complains that most physicians ignore how much the corruption of saliva and bile can severely affect human health. Like Malpighi, Baglivi replicated numerous chemical experiments aimed at making saliva and bile react with various substances, such as wine spirit, vitriol, nitric acids and even cantharid powder. For example, Baglivi maintained that saliva contains a nitrous salt whose action is crucial in fermentation and chylification. Bile, on the other hand, is composed of fixed salt, volatile salt, sulphur and phlegm, which provide it with a solvent and cleansing nature. Once mixed with the chyle, the bile preserves it from putrefaction, purifies it by dampening the acid that it contains, and predisposes it to the production of blood. In this sense, following Michael Ettmuller’s works, bile is a ‘vital balsam.’ Since many diseases result from a failed purification of the chyle, one can see how important it is to know the nature of bile and to realise what happens if its secretion in the body is altered. In De experimentis circa bilem, Baglivi provides a lot of information on the type of experiments and observations he collected, although the almost total absence of quantitative data makes them impossible to replicate. Most of these chemical experiments were performed in his private home: on March 20, 1700, he collected the bile of a gelding and poured it into numerous vials, each containing a different chemical. About fifteen

31 On Jean Pecquet’s experiments, see Domenico Bertoloni Meli, ‘The Collabora-

tion between Anatomists and Mathematicians in the mid-17th Century. With a Study of Images as Experiments and Galileo’s Role in Steno’s Myology’, Early Science and Medicine 13 (2008), 665–709. See also: Nuno Castel-Branco, ‘Physico-Mathematics and the Life Sciences: Experiencing the Mechanism of Venous Return, 1650 s–1680 s’, Annals of Science, 79, 4 (2022): 442–467.

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different substances are listed, of which Baglivi recorded the rate of reaction, fermentation, precipitation and any changes in colour, smell and taste over time. Other less detailed experiments on bile of a human cadaver, calf and ox were performed in the anatomical theater. All these findings were then compared with patients treated in Rome. From the way body fluids react to different chemicals, it would be possible to predict the occurrence of a disease (see, for example, the smell of breath, the cleanliness of the tongue and the condition of the teeth, all related to changes in saliva) and to figure out which remedy is the most appropriate to use. Indeed, Baglivi assumes that the reactions observed in the vials occur similarly within the body.32 Therefore, chemical analysis of body fluids, or ‘anatomia fluidorum,’ proves to be a valuable tool for understanding their physical properties and thus predicting how they might react with other substances. Just as injection experiments on live animals (chirurgia infusoria), the study of body fluids through the infusion of other liquids (investigatio anatomica humorum per multiplicem liquorum infusoriam) will also contribute to generating knowledge about diseases, particularly those originating in fluids.33

5

Conclusion

Body fluids pose a great challenge to the pathophysiology proposed by Baglivi. As I showed in my paper, while trying to bridge the gap between theory and practice through the formulation of a new methodology, Baglivi also realises that pathology seems to defy any geometrical-mechanistic axiomatisation. This does not mean that explanations cannot be given within this theoretical framework. But medical practice has other ‘concerns.’ Given the complexity of the variables involved in the study of fluids, medicine should find a different approach. Following a Baconian methodology, Baglivi strongly emphasises the role of experimentation. Although fluids escape calculation, they can still be 32 Baglivi, De experimentis circa bilem…, conclusio (in Opera, 441): “In decimo, & aliis experimentis, quae cum acidis facta sunt, bilis maximam mutationem in colore, & tota substantia subiit, quasi nihil magis inimicum sit bili, quam acidum. Et si haec exterius contingunt bili, cur negabimus etiam in humano corpore ab acidis peccantibus eadem fieri posse?”. 33 Ibid. (in Opera, 440): “Magna enim morborum pars cum sedem in fluidis habeat, examen, quod circa ipsa peragetur, chymia vel infusoria duce, fieri non potest, ut in curationis morborum utilitatem non redundet.”

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tested, accurately observed and mixed with other substances. What eludes geometric-mathematical formalisation can be recovered through observation. ‘Anatomy of fluids,’ like the traditional dissection of solid parts, is therefore a special tool for understanding the nature and action of body fluids that would otherwise elude investigation. Indeed, it can play a crucial role in the foundation of a new medical practice.

“The Human Body Should Be Investigated in All Its Details to the Most Precise Degree…”. Leibniz on the Quantification of Body in Medicine Osvaldo Ottaviani

J’avois coustume de dire à mes amis: sanitas sanitatum et omnia sanitas Leibniz to Nicaise, 1693, A II 2, N. 238, 736

This research was supported by Israel Science Foundation grant 399/20. The following abbreviations will be used: A = Sämtliche Schriften und Briefe, ed. Deutsche Akademie der Wissenschaften, 8 series, each divided into O. Ottaviani (B) Technion, Israel Institute of Technology, Department of Humanities and Arts, Haifa, Israel e-mail: [email protected]

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_8

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Leibniz’s interest in medicine was not a professional one, as he acknowledged on several occasions.1 Nonetheless, it was not just an occasional one, because he was particularly interested in the institutional aspects of medicine more than the content of its claims, but also devoted many methodological considerations to the foundations of medicine as an applied science, especially about the possibility of applying mathematics to it, as well as on the necessity of resorting on experiments and observations.2 On several occasions he expressed the wish that someone could finally write a scientific treatise containing the elements or the institutions of medical science, distinguishing what is certain from what is uncertain and more or less probable.3 Much of his efforts, however, were devoted to convincing the political authorities and the scientific institutions of his time of the need to promote the technical progress of medicine for the common good, especially as far as questions of public health were concerned. His suggestions about the importance of adopting a rigorous multiple volumes, Berlin, 1923-ongoing (Roman numbers indicate the series, Arabic numbers indicate the volume, and, in the case of the correspondence, also the number of the letter is given); D = G. G. Leibnitii Opera Omnia, ed. L. Dutens, 6 vols (Genevae 1768) (quoted by volume, tome, and page); GM = Leibnizens Mathematische Schriften, ed. C. I. Gerhardt, 7 vols (Berlin and Halle 1849-1863; reprint: Hildesheim, 1971); GP = Die Philosophischen Schriften, ed. C. I. Gerhardt, 7 vols (Berlin 1875-90; reprint: Hildesheim 1978); L = Philosophical Papers and Letters, ed. and trans. L. Loemker, 2nd edition (Dordrecht 1989); LBr = Der Briefwechsel des G. W. Leibniz in der königlichen öffentlichen Bibliothek zu Hannover, ed. E. Bodemann (Hannover 1889); LH = Die LeibnizHandschriften in der königlichen öffentlichen Bibliothek zu Hannover, ed. E. Bodemann (Hannover und Leipzig 1875); LSC = The Leibniz-Stahl Controversy, translated, edited and with an introduction by F. Duchesneau and J. E. H. Smith (New Haven and London 2016); NE = New Essays on Human Understanding, ed. and trans. J. Bennett and P. Remnant (Cambridge 1996). 1 Cf. De novo antidysinterico americano, 1695–1696, A IV 6, 586. 2 See Justin E. H. Smith, Divine Machines. Leibniz and the Sciences of Life (Princeton

and Oxford 2011), 28. Cf. A VI 4, 2755, and Leibniz to J. H. Burckhard, 11 October 1709: “Nulla enim scientia magis observationibus indiget quam Medica, cum nulla sit difficilior, et nulla tamen […] majoris momenti” (LBr 129, Bl. 5 r.). 3 “I am of the opinion that no one has yet written the Medical Institutions that I desire; yet I believe that today a learned doctor could easily write them” (De scribendis novis medicinae elementis, 1680–1682, edited in Enrico Pasini, Corpo e Funzioni cognitive in Leibniz, Milano, 1996, 212; translated in Smith, Divine Machines, 297). Cf. A II 12 , N. 156, 563; A III 8, N. 79, 239.

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quantitative approach to medicine were related to this more general project. Insisting on the importance of quantification to the advancement of medicine goes hand in hand with Leibniz’s defence of a mechanical approach to the study of the human body, which becomes apparent in his methodological texts and, even more, in the discussion with Georg Ernst Stahl (1659–1734) that took place between 1709 and 1711. Considering the human body as a mechanism, Leibniz justified the extension of quantitative methods to the domain of human physiology as well. At the same time, he noted that the human body is a mechanism of a particular kind: an infinitely more complex one than any human artifact whatsoever. Such an infinite complexity of the machines of nature poses many constraints to our efforts of explaining everything in a mechanical way, down to the innermost parts and functions of the human body. These limitations, though connected to our impossibility of grasping the infinity present everywhere in the natural world, can be partially mitigated by resorting to new methods of investigation and analysis as well as new instruments, which enhance the subtlety of our sense organs allowing us to proceed even further into the study of the inner parts of nature. In what follows, I will focus on Leibniz’s views, moving from a very early text in which his enthusiastic take to the quantification of life and health is immediately apparent, then showing how many of the issues at stake in that text will be recovered, rethought and further developed in his later writings.

1

Leibniz’s Directiones (1671). A Primer in Quantification?

Among Leibniz’s earlier texts, it is worth mentioning a series of annotations written in German (or, better, in a mix of both German and Latin), called Directiones ad rem medicam pertinentes, which, together with a follow-up entirely written in Latin, have been originally published by Fritz Hartmann and Matthias Krüger in 1976.4 The content of these notes is partially similar to that of a series of projects for the establishment of

4 See Fritz Hartmann, Mathias Krüger, ‘Directiones ad rem Medicam pertinentes. Ein Manuskript G. W. Leibnizens aus den Jahren 1671/72 über die Medizin’, Studia Leibnitiana, 8, 1, 1976, 40–68 (hereafter: Directiones ). The critical edition of these notes is in A VII, 2, 646–664. An English translation is in Smith, Divine Machines, 275–287.

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an Academy of Sciences drafted around 1671,5 and this suggests that all these texts belong to the same period, when a twenty-four years old Leibniz was still employed at the court of Mainz. The unsystematic character of the Directiones is undeniable, for they are a sort of wish list, a series of notes in which, sometimes in a rather haphazard way, Leibniz lists a series of desiderata for the establishment of a system of public health. It is easy to get impressed by the great variety of topics discussed there, as well as by the amount of medical literature the young savant refers to in these notes. Though belonging to a very early period of his thought, the Directiones prove to be very useful as a sort of leading thread through Leibniz’s reflections on medicine, physiology, and anatomy. From our perspective, however, the most striking feature of these notes is that they look like a sort of “primer” in the field of the quantitative approach to medicine. The passage I chose for the title of this paper is rather significant in this sense: “The human body should be investigated in all its details to the most precise degree, so as to always have, so to speak, a living anatomy in view”.6 These notes express the young Leibniz’s enthusiasm for the results already obtained by modern investigations as well as his hope that, if properly supported and well-oriented, medicine would be able to take unimaginable steps forward in a short period of time, coming out from its phase of childhood or adolescence.7 The possibility of improving medicine, however, is tightly connected to the improvement and amelioration of a strictly quantitative approach to all its branches. Following a suggestion by A. Trunk,8 the main issues discussed in the text can be traced back to the following headings: (1) the improvement of the health care system; (2) the institution of the “medical confession”; (3) empirical research and the collection of medical data; (4) new instruments 5 Cf. Grundriss eines Bedenkens von Aufrichtung einer Societät, and Bedenken von Aufrichtung einer Akademie oder Societät, A IV 1, respectively 530–543 and 543–552. 6 Directiones, 55 (Smith, Divine Machines, 277). 7 “Now, however, to the extent that physical reasoning is facilitated through mathe-

matics or mechanics, and experiments through microscopic observations and chemistry, it is hoped that physics [medicine is regarded as physica specialis ] will grow little by little and that it will be able in the end to abandon its children’s toys in order to reach adolesce” (LSC, 289–291). Cf. A IV 6, 586 and A II 2, N. 253, 779–780. 8 Achim Trunk, ‘An Early Concept of G. W. Leibniz Regarding Medicine’, in The Global and the Local. The History of Science and the Cultural Integration of Europe, ed. M. Kokowski (Krakau, 2007), 373–378.

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and methods; (5) the role of anatomy; (6) medicine an as an experimental science, and (7) knowledge of the inner structure of bodies. The first two points are apparently less relevant to the topics of this paper, so I will deal with them just in passing. Anyway, they concern the general framework of Leibniz’s thoughts on medical institutions, in which the idea of the quantification of the body plays a pivotal role and may be correctly assessed. At the bottom of Leibniz’s insistence on the establishment of academies and scientific institutions, there is the idea that the main goal of science is to improve human welfare as much as possible. When stressing the relevance of the scientific innovations of his time, Leibniz often emphasizes those concerning natural science, and medicine in particular, because they have an immediate impact on the welfare of the whole mankind. The practical strand of the scientific enterprise is stressed by Leibniz on many occasions. What is typical of his approach, however, is the fusion between the search for the improvement of human well-being through the progress of science and technology on the one hand, and the promotion of the glory of God on the other hand. The best way of honouring the majesty of God is the promoting of public utility, as he openly writes in a programmatic text composed at the end of the 1670s.9 This religious strand is also emphasized in the Directiones, where Leibniz proposes a reform of the medical institutions explicitly modelled on the organization of the religious orders: “As the Bartholomites have the convention of having their seminars and also their parishes, so similarly, should every village have two men, an old and a young one, who are physicians [physici] or doctors [Medici], and they should be changed regularly”.10 In addition to that, these doctors must be paid by the Republic alone, so that every man (no matter if wealthy or poor) can be

9 A IV 3, 875–876. Cf. A VI 4, 1994: “And what more beautiful hymn can we sing to [God] than one in which the witness of things themselves expresses his praise?” (L 280). The image of the hymn recalls the hymn of Galen in De usu partium corporis humani, extensively quoted in A IV 3, 850, and mentioned many times by Leibniz (e.g. in A II 12 , N. 162, 579). Cf. R. Andrault, “Divine Organs? Leibniz’s ‘Hymn to Galen’ and the Best of All Possible Bodies”, in Galen and the Early Moderns, ed. by M. Favaretti Camposampiero and E. Scribano (Dordrecht, 2022), 135–153. 10 Instead of the Bartholomites, the Capucins are mentioned in a letter to Huygens, June 1694: “I would like for some order, such as that of the Capucins, for example, to be associated with medicine by a principle of charity” (A III 6, N. 45, 125, transl. in Smith, Divine Machines, 43).

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treated in the same way: “For members of religious orders are disinterested. Orders that were founded for this reason would be the best means one could hope for of advancing the Christian religion”.11 Following the analogy between the physician and the priest, Leibniz introduces the idea of a “medical confession”: The institution of medicine should be organized in orders after the example of the church. A certain sort of confession should be required, which, however, people would do with pleasure. So that the confessions are more effective, and more general, lists of questions should be prescribed to people, just have we have confessional booklets that list a thousand different sins that could be imagined, so that no one forgets anything. There should be different times of year during which every person performs his medical confession, and says everything […].12

Formulated in this way, the idea of a medical confession may appear quite bizarre to us. Anyway, one must recall that it is grounded on a fundamental analogy between medicine and theology, emphasized by Leibniz in nearly all his remarks on medicine, from his very early years onward. The analogy is based on the duplicity of the word salus, which refers to the condition of the souls (as salus animarum) as well as to that of the bodies.13 The parallel between medicine, which aims at the health of the body, and theology, which aims at the health of the soul, mirrors the more general parallelism between body and soul involved in Leibniz’s pre-established harmony. The idea of the medical confession is clearly related to the necessity of collecting medical data in order to promote the advancement of medical science, as one can understand from the request that “lists of questions […] be prescribed to people”. Emphasis on the necessity of collecting medical data leads us to the first of the more substantial issues presented in this text. As summarized by Trunk: “In Leibniz’s concept,

11 Directiones, 59–60 (Smith, Divine Machines, 282). 12 Directiones, 60 (Smith, Divine Machines, 282). 13 Cf. Smith, Divine Machines, 26. See A I, 14, N. 470, 831–832, and A II 12 , N. 156, 563. See also A IV 3, 895 (ca. 1679), where Leibniz remarks that the most useful thing is the preservation of health, and that “health is as much a property of the body as a property of the soul”.

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health care and medical research are tightly interwoven, and an extensive health care system also allow to raise data in an extensive way”.14 Leibniz will always acknowledge collecting data and medical observations as the first and most important step toward a substantive advancement of medicine, and, as such, its importance will be highlighted in the New Essays: “As society becomes more civilized, it will eventually give more attention to the advancement of medicine than it has done so far […]; no sound observations will be left unrecorded; those who are engaged in this work will be helped; the art of making such observations will be highly developed”.15

2

Collecting Data

In the Directiones, this topic is introduced in the following way: One must procure all previously established cases and medico-physical observations. These should be brought together from all authors, and brought into order according to the degree of their plausibility. Then they should be tested as soon as possible. […] Thus it should be brought about that everywhere there is a catalogue of the patients in a given region, with all of the details of their illnesses.16 Leibniz also suggests following a sort of bottom-up approach, based on some sort of incentives: “whoever is in position to describe a remedy in more or less comprehensive detail, and to make this description plausible, shall be honored”. Every single physician should keep a diary or a register in which he takes notes of all his cases. Data can be collected also from popular sources: “those things that old ladies and market criers relate concerning medicinal plants should be brought together”.17 Once again, this reference to popular medical culture, like the old ladies healing secrets, may appear to be in contrast with the spirit of the new science of nature, but, despite its naivety, it has a rational ground in Leibniz’s overall approach. It is closely related to the necessity of reconciling together a 14 Trunk, ‘An Early Concept’, 375. 15 New Essays, IV, 3, 19, A VI 6, 387 (NE 387). 16 Directiones, 53 (Smith, Divine Machines, 276). Cf. also Leibniz’s letter to the Elec-

tress Sophie, May 1693: “Je suis asseuré par exemple, que dans un grand Hospital une seule année pourroit fournir un tresor de nouvelles observations, s’il y avoit des gens employés à les remarquer” (A I, 9, N. 33, 40). 17 Directiones, 52 (Smith, Divine Machines, 277).

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rational and an empirical approach to the sciences of life, a task whose importance he stressed since his very early years, when he exhorted public bodies to “combine in a happy marriage both the theoretical investigators with the empiricist ones, and make up for the defects in one with the other […] in order to take advantage from singular incomplete observations”.18 Leibniz has always been interested in that great variety of practical skills and technical knowledge (typical of craftsmen, practitioners, etc.) which had not yet been codified into, nor acknowledged by the institutional science of his time. This kind of scattered knowledge is of the uttermost importance, especially in a field like medicine, where many results, both in the diagnosis of illness and therapeutics and pharmacology, come from the practice of singular physicians and doctors, or were also preserved by popular knowledge.19 Quoting Plinius, he observes that in ancient times multae gentes sine medicis vixere, non tamen sine medicina.20 Of course, Leibniz’s main worry was to find a way not just to collect all these particular knowledge into an encyclopaedic science, but also to check the validity of all these particular observations, remedies, etc., in order to see if they may be included or not within the corpus of the institutional science, or, alternatively, if they have to be rejected.21 For these reasons, Leibniz wants to understand in which way observations and empirical data may be integrated into the body of science, and a quantitative approach is his answer to this problem. Therefore, he looks with favour at the mathematization of medicine promoted by authors like Niels Stensen and Lorenzo Bellini.22 “Mathematizing in medicine” is the right way that allows to distinguish between sound theories and good 18 “Theoricos Empiricis felici connubio zu conjugiren und mit einem des andern defectus zu Suppliren” (Grundriss, ca. 1671, A IV 1, 538). 19 Cf. A VI 4, 432–433. See also A IV, 3, 875–876, and, especially, A VI 4, 959–960. On this topic see P. Rossi, I filosofi e le macchine. 1400–1700 (Milano, 1984), 136–142; A. Becchi, ‘Between Learned Science and Technical Knowledge: Leibniz, Leuweenhoek and the School for Microscopists’, in Tercentenary Essays on the Philosophy and Science of Leibniz, ed. L. Strickland, E. Vyncker, and J. Weckend (London, 2017), 47–79. 20 A IV 1, 552. 21 Cf. A VI 4, 1996. There is a genuine continuity between particular practices and

general theories, for the former constitute just pieces or parts of a theory which has not yet been codified. Cf. A VI 4, 961. 22 Cf. Directiones, 65. On the mathematization of medicine, see R. Andrault, ‘Mathématiser la médecine’: les enjeux de la position leibnizienne’, in Leibniz and the Empirical Sciences, ed. J. A. Nicholás, and S. Toledo (Granada, 2011), 17–34.

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practices on one hand, and pseudoscience on the other. In another place of these notes, he mentions the case of “medical chiromancy”, adding the following remark: “In order to determine whether there is something [of value] in the astrological tradition […], one must also inquire and set up experiments”.23

3

Anatomy

As far as the collection of data is concerned, Leibniz insists on two relevant case studies. The first concerns the progress made by anatomy and vivisection at his times. The topic of anatomy is introduced by resorting to the necessity of practising autopsies: All patients who die in the hospital should be anatomized, and it would be good if most people could be anatomized. All anatomies should be conducted in a different manner, as Steno prescribes in his Anatomica cerebri.24 As much as possible should be known about the “natural history” of the person who is anatomized […]. In the autopsy all the smallest details should be drawn, all the ducts and passages should be tested with coloured liquids poured into them, and all sorts of ligatures should be applied.25

Generally speaking, anatomy plays a considerable role in Leibniz’s reflections on medicine, as we can see from the late controversy with Georg

23 Directiones, 53–54 (Smith, Divine Machines, 277–278). A few lines above, Leibniz mentions an example of how to correctly set up an experiment, anticipating the idea of fingerprinting: “In order to determine whether the signs of the hand and so on have a certain power, one would have to make prints of the hands of many people whose actions are known to us. This could easily be done if their hands were covered in a liquid, with the prominent part being wiped off, printing that which lies beneath the lines” (Directiones, 53–54; Smith, Divine Machines, 277–278). Among Leibniz’s unpublished manuscripts, there is also a set of excepts from a German book on medical chiromancy, see LH III, 4, 8b, Bl.1–3. 24 Leibniz refers here to Stensen’s Dissertatio de cerebri anatome (1671, but the French edition was published in 1669). Steno’s text is available in English in Nicolaus Steno. Biography and Original Papers of a 17th Century Scientist, ed. by T. Kardel and P. Maquet, second edition (Dordrecht, 2013), 603–629. 25 Directiones, 52–53 (Smith, Divine Machines, 277).

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Ernst Stahl.26 In his tenth objection to the Theoria medica vera, Leibniz replies to Sthal’s claim that “the more recent anatomy is more fruitful in inquiries that have nothing to do with the scope of medicine”. As Duchesneau and Smith explain, Stahl questioned “the utility, for the treatment of wounds and surgical operations, of recent discoveries about the fine structure of muscles”, because “[c]uriosity-driven anatomy […] may advance our knowledge of the natural history of organic bodies, but it diverts our attention and efforts from the real scope of practical medicine”.27 On the contrary, Leibniz is sure that “in surgery more fine-grained anatomy is of great use; and I believe that when this art will be expanded […] men will arrive in time at certain cures that are hitherto dramatically lacking”.28 Leibniz’s passionate apology of anatomy is grounded on the presupposition that the advancements in physiology and medicine are made possible only by means of a mechanist approach, one aiming at discovering the operations of the machine of the body, operations which can be fully understood only in a mechanical way and not by resorting to principles of a different kind. Referring to Stahl’s scepticism about the fact that a complete and exact description of a clock would be sufficient to make sense of its functioning, Leibniz insists that “a comprehension of the reasons why and in what way a clock works follow from an exhaustive description of it”. The basis of all vital functions, consisting in the way in which “the living body perfects, nourishes, repairs, and propagates itself”, “follows from the very structure of the machine, even if everywhere the soul is conspiring”.29 Even if Leibniz is clearly committed to a mechanical approach to the study of living beings, this does not mean that he detaches mechanism from finalism. On the contrary, according to him, the description of the functions of a machine is part and parcel of the description of the machine

26 Leibniz’s two series of remarks on Stahl’s Theoria medica vera (1708) were published by Stahl himself in his Negotium Otiosum (1720). A complete edition of the latter, including Stahl’s own replies to Leibniz, is available in LSC, from which I quote. 27 LSC, 35 and, for the commentary, 422, fn. 24. On Stahl’s physiology, see Francesco Paolo de Ceglia, Introduzione alla fisiologia di Georg Ernst Stahl (Lecce, 2000); Id., I fari di Halle. Georg Ernst Stahl, Friedrich Hoffmann e la medicina europea del primo Settecento (Bologna, 2009). 28 LSC, 35, transl. mod. 29 LSC, 33 and 35.

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itself.30 In one of his most accomplished writings on medicine, Leibniz affirms that it is plainly evident “that the human body is a machine disposed of by its author or inventor to certain functions. And thus to write medicine is nothing other than to prescribe to a mechanical a method by which he will be able to conserve the machine that has been entrusted to his care”.31 And the same claim is repeated in the second set of replies to Stahl, when Leibniz comes to the apology of anatomy: “Since medicine certainly consists in the art of preserving the human body, a precise knowledge of the human body cannot be at all in excess with regard to the scope of medicine”, concluding that “[w]e will never be overrun by a surfeit of Stenos and Malpighis”.32

4

Medical Statistics

A second field in which one has to improve our collection of data is that of (what we would call) “medical statistics”: Bills of mortality must be brought to the greatest possible perfection and must be made not only in large cities, but also everywhere in the countryside. And the difference of climates, of the soils, of the air, etc., should be precisely noted: in this way, many admirable things will result.33

In addition to his well-known interests in the interrelations between probability and jurisprudence, Leibniz also developed a strong interest in the just-born discipline we call “statistics”, with particular emphasis on the calculation of life-rents or, as in this case, the application of statistics to the field of medicine, and of epidemiology in particular. The main upshots 30 “The human body, like the body of any animal, is a sort of machine. Any machine, however, is best defined in terms of its final cause, so that in the description of the parts it is therefore apparent in what way each of them is coordinated with the others for the intended use” (ca.1680–1682, ed. in Pasini, Corpo e funzioni cognitive, 217; Smith, Divine Machines, 290). The connection between mechanism and finalism is best understood if related to Leibniz’s understanding of living beings as machines having an infinity complexity. Cf. LSC, 19–25, and also A IV 3, 865. 31 De scribendis novis Medicinae Elementis, ca. 1680–1682, ed. in Pasini, Corpo e funzioni cognitive, 212 (transl. in Smith, Divine Machines, 297). This characterization of medicine is probably inspired to Steno’s views, cf. the text in Nicolaus Steno, 616–617. 32 LSC, 285 and 289. 33 Directiones, 54 (Smith, Divine Machines, 278).

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of Leibniz’s reflections on the calculation of life expectances and the estimates of mortality are reported in a series of texts, of which the Essay de quelques Raisonnements nouveaux sur la vie humaine et le nombre des hommes, ca.1680, is perhaps the most accomplished one.34 As the text above shows, since his early years Leibniz was attracted by the idea of using the bills of mortality to the improvement of medical knowledge. Later on, he will find a source of inspiration in this sense in the works on statistical epidemiology produced by the Italian physician Bernardino Ramazzini (1633–1714), considered the pioneer in the studying of occupational diseases (in his De morbis artificum diatriba, 1700). Leibniz met Ramazzini during his stay in Modena (from December 1689 to the beginning of February 1690), where Ramazzini was professor of medicine. The correspondence between the two covers the period from 1689 to 1700 when Ramazzini moved to the University of Padua.35 Leibniz’s core interest in Ramazzini’s compilation of “medical ephemerides”, as well as his enthusiasm for Ramazzini’s medical observations, is clearly expressed in a paper published in the Journal des sçavans in 1694, with the title Sur le manière de perfectionner la Médecine: I do not know if anyone in Paris is continuing the registers or lists of baptisms and funerals in this great city that were compiled in the time I was there. This project seemed very useful, as did the Bills of Mortality in London, from which able people have drawn important observations. Yet we could go further, by having an annual history of medicine drawn up for Paris and the Île-de-France, as well as for other provinces, on the plan given to us by Mr Ramazzini, able doctor of the Duke of Modena, with whom I met when I was staying in that region. I strongly urged him to execute and pursue such a laudable project. He was finally inclined to do so, and has already given us a few years, having even done me the honour of dedicating the second to me.36 […] This doctor [Ramazzini]

34 Edited in A IV 3, 456–467. Cf. Jean-Marc Rohrbasser and Jacques Véron, ‘Leibniz et la mortalité: Mesures des “apparences” et calcul de la voye Moyenne’, Population, French Edition, 53, 1–2 (1998), 29–44. 35 Leibniz’s correspondence with Ramazzini is carefully commented by James G. O’Hara in his forthcoming book, Leibniz’s Correspondence in Science, Technology and Medicine. Core Themes and Core Texts, to which I will refer in what follows. 36 Ramazzini published a series of annual “epidemic constitutions” on the territory of Modena, and the constitutions concerning 1691 were dedicated to Leibniz. The word

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spoke there first about the seasons and the constitution of the air that was observed during the course of the year in the region whose medical history he undertook to give […]. After that he relates how the grains and fruits prospered there, and the diseases which prevailed among the animals, and all this in few words. From there he comes to the chief matter, which is the health of human bodies, in which he observes not only epidemic diseases and symptoms, but also how other diseases have changed, since it is certain that there are great variations according to the constitutions of the times […] And there should be no doubt that years similar to the preceding ones often return, where the past would be of the greatest use to decide on this matter in the future, whereas now we are reduced to learning almost always from scratch at the expense of the sick. It’s easy to judge what a treasure trove of observations we would have if something similar had been done for a while now.37

Leibniz is concerned with the predictive utility of statistical research. From what he writes in the Directiones as well as elsewhere, it is clear that he is interested in a wide variety of statistical data, not just the bills of mortality. J. Smith has correctly remarked how Leibniz had clear in his mind that such measurements “should be brought together to produce a sort of meta-measurement”. Such records are not used for the diagnoses about individual cases, for, if the results of many individuals are compiled and collected together, “this would enable physicians to establish norms and averages for the human body and thereby gain a more thorough mastery of the distinction between the healthy and the pathological than had been possible in the era of medical reliance upon anecdotes”.38 In his writings, Leibniz also emphasizes the relevance of climatic factors to the insurgence of diseases and, thus, the importance of record-keeping about these and related epidemiological issues. In a German text, called Vorschlag zur Bildung einer Medizinalbehörde [Proposal for the Establishment of a Medical Board] (ca. 1680), Leibniz writes that it is necessary to present the doctors “with all kinds of questions for due investigations,

constitutio indicates the epidemic conditions of one year and was coined by Thomas Sydenham (1624–1689). Sydenham’s work is mentioned in De re medica augenda, see the appendix below. 37 D II, 2, 162/A IV 5, 661–662 (translated by L. Strickland: http://www.leibniz-tra nslations.com/medicine.htm). 38 Justin E. Smith, ‘Medicine’, in The Oxford Handbook of Leibniz, ed. by M. R. Antognazza (Oxford 2018), 485–497, esp. 491.

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but especially to direct their attentions on things like air, waters, soils, foods, local diseases, epidemic and endemic ones”. He also notes: The acts and archives of the [to be established] Collegium sanitatis could and should contain, among other things, [reports about] what happens from time to time in matters related to health and questions connected to the latter, especially how the weather changes in these and neighbouring places, and how the wind determines what one takes as degrees of heat and cold, dryness and moisture, how the weight of the air changes […] and whatever else can be detected by means of the new instruments, such as Thermometra, Hygroscopia, Anemia, Barometra and certain Compasses.39

Through the use of these instruments, it is possible to acknowledge the existing relationships between certain climatic conditions and the appearance and development of certain diseases with a much higher degree of exactness. As pointed out by J. O’Hara, the introduction of statistical reasoning in medicine produced a revolutionary change of approach, for “mortality, morbidity and population development could be quantitatively recorded for the first time. Demography, or the statistical study of population, in turn contributed to progress in medicine”. Accordingly, prevention became one of the principal tasks of the physicians, who “began to pay particular attention to the causes and circumstances of the occurrence of epidemics”.40 In a letter dated July 1691 to Johann G. Volckamer (1616–1693, then president of the Leopoldine Academy), Leibniz reported of his meetings with Ramazzini and insisted that the Academy should follow the example of the Italian physician in collecting medical statistics in Germany as well.41

39 A IV 3, 371 and 373–374. 40 O’Hara, Leibniz’s Correspondence in Science, Technology and Medicine (forthcoming).

Cf. De re medica augenda: “Observatis morborum moribus, mature praevidebuntur morbi mali moris, opportunisque remediis profligabuntur” (see Appendix). 41 A III 5, N. 30, 137–138. See the report drafted by Leibniz: Kurtze Anzeige des Grundes und Vortreflichen Nutzens der Observationum Metereologico-Epidemicarum, 1701, A IV 9, 923–934. For a thorough discussion of Leibniz’s interest in the works of Ramazzini, see François Duchesneau, ‘Leibniz, Ramazzini et le paramétrage des maladies épidémiques’, Studia Leibnitiana, 51, 2 (2019), 148–175.

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Instruments of Measure

Emphasis on measuring instruments is closely connected to the experimental nature of physical sciences. In a methodological text devoted to the analysis of bodies, Leibniz notes: “Bodies […] are to be examined by means of the instruments of experimentations [Organorum Empiricorum]—scales, thermometers, hygrometers, pneumatic pumps—and also by vision, whether naked or fortified, by smell, and by taste”.42 Right at the beginning of the Directiones, Leibniz claims that a great variety of different instruments must be employed in order to improve our knowledge of the human body and its operations: “One must have instruments for precisely investigating the urine and the pulse, since these are generally signs of a man’s condition”.43 Of course, scholars insisted a lot on the preponderant role played by the microscope in Leibniz’s conception of the natural world.44 The microscope is also the first instrument to be mentioned in the text of the Directiones, but not the only one, for what emerges from these notes is that the perfectioning of medicine requires the combination of a great variety of tests and testing devices. He also mentions the utility of thermometers: “To the observation of the pulse belongs the observation of the warmth and coldness of the hands by an exact, much improved thermometer”. About the observation of the pulse, in a later manuscript devoted to the causes of fevers, Leibniz suggests to improve the precision in our measuring both the frequency and the intensity of the pulse: the former by resorting to a pendulum, the latter by resorting to a sort of vesicle inflated of water which must be wrapped around the wrist.45 Leibniz also refers to the works of one of the ancestors of the quantitative approach to medicine, i.e., Santorio Santori (1561–1636) and his De statica medicina (1614): “Next a general examination of people should be established, by means of static medicine, as was put into a system 42 A VI 4, 1974 (L 175). 43 Directiones, 50 (Smith, Divine Machines, 275). 44 See C. Wilson, The Invisible World. Early Modern Philosophy and the Invention of the

Microscope (Princeton, 1997); A. Becchi, Arlecchino e il microscopio. Saggio sulla filosofia naturale di Leibniz (Milano–Udine, 2018). 45 Cf. De causis et curatione febrium, ca.1704–1705 (in Pasini, Corpo e funzioni cognitive, 225). The association between pulsation and oscillatory phenomena is recalled in the late correspondence with B. Zendrini. Cf. GM IV, 249–250, discussed in François Duchesneau, Leibniz, le vivant et l’organisme (Paris, 2010), 176–180.

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of rules by Sanctorius only after thirty years of experiments”.46 And in other texts, we also find references to Santori’s weighing chair, and to the phenomenon of “insensible transpiration” as well.47 One cannot but agree with J. Smith’s remark that the Directiones have to be read as a “manifesto” declaring the supreme importance of experiments in medical questions, especially as far as experiments are regarded as the most reliable gateway to the quantification of a great number of bodily functions. What these passages show, however, is that Leibniz is particularly interested in tests concerning bodily fluids and secretions, which is “in keeping with the much broader turn in experimental philosophy […] toward measurement of absolutely everything that can be measured”.48 But this attention to bodily fluids and secretions also hints at a more general philosophical problem. As noted by Smith, secretions are important because they come from the inside of the body and, therefore, can give us an idea of what is going on in certain parts of our body which are not directly accessible to us. In the Directiones Leibniz makes an impressive list of tests involving every sort of bodily fluid, from urine to sweat, vomit, arterial blood, as well as non-liquid parts which, in some way, help us in connecting the internal with the external. This impressive list of more or less invasive tests is not only required by the ideal of measuring “everything that can be measured”, but also responds to a major trend in Leibniz’s natural philosophy, which is already in place in these early notes: “One must, in particular, find, by reasoning, the communications of the external members [of the body] with the internal ones”. And, furthermore: “Ways should be found of arriving ever closer to the most interior parts of a living body”, either by making external what is internal (fluids like sweat, urine, vomit) or, the other way 46 Directiones, 51 (Smith, Divine Machines, 275). 47 Cf. A IV 3, 897, and a curious short note (ca. 1701): “If in a big city like London

or Paris one received a privilegium privativum in order to obtain a static chair like that of Santori, one could check his weight every day for a small amount [of money], and, in this way, one could know if the insensible transpiration, and, consequently, his health is still in good conditions” (A IV 9, 934–935). On Santorio’s chair, cf. Teresa Hollerbach, ‘The Weighing Chair of Sanctorius Sanctorius: A Replica’, NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin, 26 (2018), 121–149. 48 Smith, ‘Medicine’, 490. Animal secretion will always have a central role among Leibniz’s researches in physiology. See the unpublished manuscript, De secretione animali, LH III, 5, Bl. 17, as well as the late correspondence with Pietro Antonio Michelotti in 1715. Cf. Duchesneau, Leibniz, 180–184.

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around, by inserting something external into the internal parts of our body: “Through the injection of clysters, and through the ducts and the throat, certain means have already been found […] Now means should be found, further, of reaching the interior of man, as it happens with the scalpel”.49

6 The Interior of Nature and the Limits of Mechanization The image of the “most interior part” of a living body is just a variation on the theme of the “interior of nature”, which is dominant in Leibniz’s works from the very early years onward. Also in this case, Leibniz is following a tradition grounded on the idea of nature as the intima rerum,50 but, once again, what is peculiar to Leibniz is the way he appropriates this notion and the particular significance it acquires within his natural philosophy. A certain number of passages about the interior of nature have been commented on in connection to Leibniz’s promotion of microscope.51 The microscope, indeed, is the kind of instrument that, by artificially sharpening our sight, allows us to grasp the internal structures and textures of the natural world, which, otherwise, would be too small to be noticed. This contraposition between the internal and the external parts of nature has not to be hastily interpreted in metaphysical terms. On the contrary, Leibniz’s texts hint at the view that the dividing line between the external and the internal is never a fixed one, established once and for all, and that new observations and experiments are required (and should be encouraged) exactly because they allow us to arrive even closer to inner structures of the natural world which were previously unknown to us. As noted by P. Beeley, “like no other philosopher in his time, Leibniz recognized […] the need to take account of the growth of knowledge”,

49 Directiones, 58 and 64 (Smith, Divine Machines, 280 and 285. Transl. modified). 50 Cf. Thomas Leinkauf, ‘Der Natur-Begriff des 17. Jahrhunderts und zwei seiner Inter-

pretamente: “res extensa” und “intima rerum”, Berichte zur Wissenschaftsgeschichte, 23, 2000, 399–418. 51 Cf. Becchi, Arlecchino e il microscopio, 60–74.

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which means that “we can always push the limits of our analysis further, corresponding to the infinite actual division of everything in nature”.52 This assumption leads Leibniz to criticize the views of those who reduce the infinity complexity of the natural world (including human bodies) to the finite one of human artifacts, for they are “ignorant of the majesty of nature which is the same in the smallest as in the greatest things, and admits no elements”.53 In this line of criticism, Leibniz includes many different positions, from the atomists to Descartes’ theory of the first two elements of matter, for they all share one fundamental mistake, i.e. they pretend to arbitrarily fix limits to the level of complexity of reality, in order to make the latter corresponding to the limited capacity of our present knowledge. In September 1699, discussing with Friedrich Hoffmann (1660–1742) the project of building a rational medicine in accordance with the principle of the mechanist physiology, Leibniz notes: I wish that men who are experts in explaining the mechanism of nature could advance little by little, and pay attention not to reduce everything to the first principles (magnitude, figure, and motion) by a leap [per saltum], like the Cartesians do, for this cannot be achieved by us. But, rather, to proceed in a gradual way [per gradus ], by reducing composite things to those which are simpler and more proximate to the principles […]. Therefore, I am expecting from you certain elements of rational medicine, not relying too much on intellectual principles too far from the practice of art, as it is the case with Cartesian practitioners, and not too much attached to the illusions of the imagination, as is the case with Chemists; but which can bring about the intelligible causes of sensible things where this is allowed,

52 Philip Beeley, ‘De abstracto et concreto. Rationalism and Empirical Science in Leibniz’,

in Leibniz. What kind of Rationalist? ed. by M. Dascal (Dordrecht, 2008), 85–98, esp. 87. 53 De infinito, 1693–1697, LH XXXVII, 5, Bl. 188 v. A few lines below, he adds: “But every natural machine (which we call an organic body) consists in infinitely many organs coordinated with one another. For muscles too are resolved into other things beyond all our patience or capacity to investigate, and vessels are changed into filaments in turn conglomerated from other filaments, and we never arrive at ultimate degrees. And it is reasonable, I maintain, that there is no end of artifice in structure, nor can there be” (edited and transl. in R. T. W. Arthur and O. Ottaviani, Leibniz. Writings on the Metaphysics of the Infinite, Oxford, forthcoming). On the ‘machines of nature’, see Michel Fichant, ‘Leibniz et les machines de la nature’, Studia Leibnitiana, 35, 1 (2003), 1–28.

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or, when the former option is not allowed, can at least draw useful consequences from the effect of those things, which are certain to the senses even if they are not yet reduced to their causes.54

This matches pretty well with what he says in his late (September 1715) letter to Pietro Antonio Michelotti (1673–1740), where Leibniz discusses the latter’s mechanical account of animal secretion: “it seems likely to me that those things which take place insensibly in our bodies completely correspond to those which take place in sensible bodies”, and this is the place where one can detect the fundamental mistake made by the Cartesians: “because they try to bring back by a leap [per saltum] the insensible reasons of sensible things to the primary causes or the simplest elements themselves, from which, however, these are still very far removed”.55 These texts convey the idea that the limits of the Cartesian approach consist in the pretence to jump from the effects to the primary causes, thus imposing an arbitrary limitation on the possibility of further extending our knowledge by means of empirical observations. In other terms, the mistake consists in transforming the relative and empirical distinction between the exterior and the interior of nature (where the “exterior” is what is accessible to senses and observations, the “interior” what can only be grasped by the understanding) into an absolute one, fixed once for all.56 On the contrary, Leibniz favours a progressive, step-by-step approach from certain physiological phenomena to their mechanical causes, which have to be understood as explicitly provisional ones, given our impossibility to have direct access to the interior of nature (i.e., given the infinite complexity of natural bodies). Reference to insensible causes of sensible phenomena is the key element to understand Leibniz’s attitude toward the mechanization (and the mathematization) 54 A III 8, N. 79, 239. Friedrich Hoffmann was a German physician, professor of medicine in Halle, and main opponent of his colleague Stahl (cf. De Ceglia, I fari di Halle, esp. 269ff.). His main work, Medicina rationalis systematica, will appear in 4 volumes between 1718 and 1740. 55 D II, 2, 90. 56 A similar approach has been observed in Cartesian authors like La Forge, who,

according to Andrault, “emphasizes the clear separation between the invisible causes invoked by philosophers and the exterior figures observed by the anatomists”. Cf. Raphaële Andrault, ‘Anatomy, Mechanism and Anthropology: Nicolas Steno’s Reading of L’Homme’, in Descartes’s ‘Treatise on Man’ and Its Reception, ed. D. Antoine-Mahut and S. Gaukroger (Dordrecht, 2016), 175–192, esp. 187.

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of medicine. As he already noted in 1678, “the discovery of causes, without which we cannot hope for great advances in the most urgent field of physical science, namely medicine, can be obtained […] only through profound and almost geometrical reasonings”. Given the nature of our body—which is a machine containing fluids “which act not only by weight and in other ways manifest to the senses but also in certain hidden ways”, i.e., in many “processes in which composite things are dissolved into insensible parts”—then medicine should be based on geometrical and mechanical principles which “can be applied with equal ease to sensible and insensible things alike”, otherwise “nature in its subtlety will escape us”.57 The difficulty of establishing sound causal explanations in medicine was very clear to Leibniz’s mind right from the beginning, as the following passage (taken from a writing of 1671) shows very well: We are still not able to see the principia of medicine, i. e. the inner constitution of this so confused clock, and therefore its alterations and diseases are to a large extent known by us more effectu than definitione causali. The current methodus medendi is only a hypothesis, that one must resort to until one can find better individual remedies here and there.58

Many years later, in a letter (1711) to Friedrich Wilhelm Bierling (1676– 1728), Leibniz will explain that he is distinguishing between having a perfect knowledge of nature on the one hand, and the possibility of providing demonstrations in physics on the other hand. In the latter case, many natural phenomena can be explained even if we do not have a perfect knowledge of their nature (for instance, we have an explanation of the rainbow even without having a perfect knowledge of the nature of colours). In this sense, there are demonstrations in physics too, when “both mathematics and metaphysics are joined together with sensible observations”: Even if we are not allowed to know the interior of nature [intima naturae], because its subdivisions proceed to infinity, we can hope, however, to be able to penetrate more in the interior of things, as we 57 Praefatio ad libellum elementorum physicae, ca. 1678, A VI 4, 1998 (L 282–283). 58 A IV 1, 551.

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already begun to do, and that this would be extremely fruitful as far as [animal] economy and medicine are concerned. For there are degrees of inquiry [Sunt quidam in inquirendo gradus ]. […] In the meantime, we discover interior and invisible causes, but not therefore the innermost ones and not all causes.59

In this sense, in addition to the indispensable role of experiments in establishing medical knowledge, Leibniz is also advocating for what has been dubbed “provisional empiricism”, as a sort of middle way between the integral empiricism of practical medicine and a completely theorical approach to medicine, which is based on hypotheses and conjectures completely detached from any empirical ground.60 This contraposition is enlightened in the following passage contained in Leibniz’s reply (1702) to Pierre Bayle (1647–1706): In medicine, there is the sect of the Empiricists and the sects of Methodics and Rationals. The former allowed no search for causes or reasons, but are only satisfied with facts or experiences, so that they can just say: this [particular remedy] has been helpful or harmful [in this case], therefore it may be helpful or harmful also in similar cases. The simple Methodics are not

59 GP VII, 500. Leibniz was replying to Bierling’s claim (in his letter of 18 July, 1711): “Nondum tamen adduci possum, ut credam, dari demonstrationes de interioribus rerum, aut a priori cognosci posse caussas internas formatrices, prout eas […] appellavi. In cortice haeremus, ad nucleum penetrare concessum minime est” (D V, pp. 372–373). Friedrich Wilhelm Bierling was referring to what he said in his own work, Lineamenta methodi studiorum (Rinteln, 1711), 83. 60 Cf. Anne-Lise Rey, ‘The Status of Leibniz’ Medical Experiments: A Provisional Empiricism’, in Medical Empiricism and the Philosophy of Human Nature in the 17th and 18th Century, eds. C. Crignon, C. Zelle, and N. Allocca (Leiden-Boston, 2013), 34– 54. See also Mirko D. Grmek, ‘Leibniz et la médecine pratique’, in Leibniz 1646–1716. Aspects de l’homme et de l’oeuvre (Paris, 1968), 145–177.

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concerned with causes or reasons, for they believe they have reduced everything to causes or reasons.61 But the Rational physicians have attempted to improve experience by adding the search for causes to it.62

The necessity of joining together experiments and the search for causes, or, which is the same, induction and reasoning, is just another way of proposing the “happy marriage” between theoretical and practical investigators, mentioned above. Leibniz is not dismissing the mechanical and quantitative approach defended in the Directiones, as one can see from his discussion with Stahl.63 He is rather advocating for a better form of mechanization, one that really takes into account the (infinite) subtlety of nature and, therefore, cannot be satisfied with the too simplistic hypotheses of Cartesian physiology. In this sense, conjectures are essential in physical science, when they are intended not as a replacement for further empirical investigations, but, rather, as conjectures which help us in projecting new experiments, and, also, when they are employed following the rigorous criteria of the ars conjectandi.64 In this sense, given the status of our present knowledge, they are regarded as a sort of second-best option, which needs to be employed, especially when practical medicine is at stake, for “practice ought to be built up from the phenomena; and often, theories consist in

61 In a letter to Domenico Guglielmini (1655–1710), September 1697, Leibniz writes: “I must confess that many physicians who are commonly regarded as rational ones should be more properly regarded as barely conjectural, and sometimes, they impose very unlikely conjectures on us instead of plausible hypotheses” (A III 7, N. 142, 577). The distinction between empiricists, methodics and rationals is modelled on that proposed by Galen in De sectis ingredientibus. Cf. “On the Sects for Beginners”, in Id., Three Treatises on the Nature of Science, trans. by R. Walzer and M. Frede (Indianapolis-Cambridge, 1985), 1–20. Thanks to Simone Guidi for clarification on this point. 62 GP IV, 525–526. Cf. A VI 4, 1984, where ‘mixed truths’ are defined as those which derive partly from sensible principles and partly from intellectual ones. But see especially A VI 4, 1998, commented by Duchesneau, Leibniz, 66–70. Medicine is explicitly regarded as a scientia mixta in D VI, 1, 315. 63 See what Leibniz writes to Johann Bernoulli, May 6, 1712: “Some authors deny that all things are done mechanically in the actions of our bodies, among whom there is Stahl, who disputed with me by letters […]. Others, on the contrary, believe that all things may be explained mechanically by us. I agree with neither of them. For all things are done mechanically in these things, but we are not yet progressed so far as to be able to explain everything mechanically” (GM III/2, 884). 64 See A VI 4, 1985, and 1999–2000. Cf. also A IV 6, 586.

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hypotheses and conjectures”.65 Or, as he says in a preliminary draft of his letter to Bierling, “we must be content to have to do with principles which are plausible enough, especially in medicine”.66

Appendix: Leibniz “De re medica augenda” In this appendix, I give the critical edition of an unpublished text by Leibniz, which is closely related to the topics discussed in my paper above. It is a short note, which I called De re medica augenda (from its incipit), and belongs to that kind of texts which show Leibniz’s efforts for the promotion and advancement of medicine and public health. It is not possible to say exactly when this note has been drafted, but the content of the text shows some similarities with that of the German text Vorschlag zur Bildung einer Medizinalbehörde (A IV 3, 370–375), dated around 1680. Furthermore, the kind of paper matches with that of a series of texts drafted between 1684–1685 and 1687. I wish to thank Herma Kliege-Biller (Leibniz Forschungsstelle) and Paolo Rubini (BerlinBrandenburgische Akademie der Wissenschaften) for their help with the transcription and the dating of the manuscript. G. W. Leibniz, “De re medica augenda” Ms.: LH III, 5, Bl. 164 r.

De Re Medica augenda ad Generis humani bonum multa agitavi. Non parum conferre posset Societas Naturae Curiosorum.67 Sub Caesare 65 LSC, 313. Cf. also Leibniz’s letter to J. P. Bignon, May 26, 1714: “Il seroit à souhaiter qu’on prit soin un peu plus qu’on ne fait des avancemens de la Medecine practique en distinguant la simple hypothese d’une conjecture possible, la conjecture vraisemblable de la certitude des faits” (LBr. 374, Bl. 25 r.-v.). 66 LBr. 67, Bl. 48 r. “Interdum tamen cogimur verisimilibus contenta esse, praesertim in medicina. Quanquam non dubitem, etiam in ea mirifice posse profici, si satis studii et methodi adhiberetur. Sed ea rectorum reipublicae cura esse deberet, ut animarentur boni medici ad majorem animi applicationem”. A similar second-best approach is explicitly proposed in a text concerning botanics and the classification of plants: “Although, in advance of knowing the interior constitution of these machines of nature, no accurate method can be instituted, nonetheless a certain substitute method may be employed for the sake of our comprehension and progression in theory” (1701, A III 8, N. 253, 655; Smith, Divine Machines, 305). 67 Academy of Science founded in Halle in 1652, originally known as Societas Naturae Curiosorum. It was recognized by Emperor Leopold I who raised it to an academy in

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protector Minister scribatur tum ad societatem hanc, tum ad alios medicos doctos et intelligentes, ut suam sententiam dicant, et consilia conferant. Unusquisque Naturae curiosorum practicus ad exemplum Sydenhami68 quam minutissime annotet quae ipsi in praxi occurrunt, tam ea quae vulgo habentur notanda quam quae non habentur. Ut nempe etiam vulgatissimorum morborum varietates et mores, et status aeris, et quasi Historia sanitatis humanae ejus loci ubi agit et viciniae habeatur. Opus erit libro interrogatoriorum seu inquirendorum qui id praestet in Medicina quod Rutgerus Rulandus in Commissario 69 apud I[uris]C[consul]tos, et Frolichius70 et Zwingerus71 apud Geographos. Concinnatio talis operis plenissimi cum Medico insigni practico-theorico, docto et scribaci deleganda. Efficiendum apud proceres et civitates, qui Medicis salaria praebent, ut constituantur matronae quaedam piae, officiosae, experientia praeditae, quae etiam sine mercede aegris divitibus et pauperibus inserviant, et accuratissime observantes, quae vel ipsae vident, velut ab aegris aut domesticis intelligunt, ea Medicis narrent, vel etiam ipsae si possunt annotent, ut in Historiam sanitatis referantur. Eadem opera etiam exacte cognoscetur non tantum catalogus mortuorum, sed et quo quisque morbi genere, et ex quibus causis obierit. Cujus rei vel solius propemodum causa Londini certi homines habentur ubi religiosi erunt inprimis Capucini aut alii Franciscani, illi in partem hujus curaveniant. Observatis morborum moribus, mature praevidebuntur morbi mali moris, opportunisque remediis profligabuntur. Cum alias constet Medicos tardius malignitatem et artes mali occultas observantes, vix demum ubi multi jam initis auxiliis periere quid agendum sit cognoscere.

1677, and then declared it an Imperial Academy in 1687, allowing it to carry his name (Academia Leopoldina). 68 Thomas Sydenham (1624–1689), Observationes medicae, London 1676. 69 Rutger Ruland (1586–1630), De commissariis et commissionibus Camerae imperialis

probationis receptionem concernentibus libri quatuordecim, Frankfurt am Main 1597, also mentioned in A IV 1, 574, and especially A VI 4, 2755. 70 Dávid Frölich (1595–1648), Slovak naturalist and geographer, author of Medulla Geographiae Practicae (Barfta, 1639) and Cynosura seu Bibliotheca Viatorum (Ulm, 1644). Leibniz probably quoted his works after Bernhardt Varenius’ Geographia generalis (Cambridge, 1672), see A VIII 1, 570. 71 Theodor Zwinger (1533–1588), Swiss physician and humanist, author of the Theatrum vitae humanae (Basel, 1565), but also of Methodus apodemica in eorum gratia, qui cum fructu in quocunque tandem vitae genere peregrinari cupiunt (Basel, 1577).

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Critical apparatus 1 agitavi. (1) Multum (2) Non parum L 3 scribatur (1) medi (2) tum L 4 ut (1) quisque (2) suam (a) plurimi (b) sententiam L 6 occurrunt, (1) et (2) tam L 9 humanae (1) cui (2) ejus L 12 et Zwingerus add. L 14 Efficiendum (1) per (2) apud (a) principes et civ (b) proceres L 16 sine (1) salario (2) mercede L 19 referantur. (1) Accuratissima haec (2) Eadem L 21 solius (1) causa (2) propemodum L 23 veniant. (1) Etiam hac (2) Poterit etiam praevideri pestis (3) Cognitis (4) Observatis L 25 Medicos (1) non (2) tardius L

Data vs. Mathesis. Contrasting Epistemologies in Some Mechanizations and Quantifications of Medicine Simone Guidi

1

Introduction

It has recently been argued1 that early modern mathematization and quantification of nature was a complex and layered intellectual process, which cannot be reduced to the patterns imposed by grand narratives in the twentieth century. Indeed, even though it has often been portrayed as a unitary and monolithic movement, homogeneously opposed to the

1 Sophie Roux, ‘Forms of Mathematization (14th–17th Centuries)’, Early Science and Medicine, 15, 4/5 (2010), 319–337. For more specific aspects related to the mathematical background of some of the authors here addresses, see especially Douglas Jesseph, Ratios, Quotients, and the Language of Nature, in The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the 17th Century, ed. by G. Gorham, B. Hill, E. Slowik, and C. K. Waters (Minneapolis-London: University of Minnesota Press 2016), 160–177.

I am sincerely grateful to Anita Guerrini for her remarks on an earlier version of this chapter. I also thank Luca Tonetti, Andrea Strazzoni and Jip van Besouw for their helpful comments. All mistakes are my own.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_9

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Aristotelian qualitative conception of nature,2 the application of mathematics to natural science is a path studded with interruptions, conflicts, and different understandings of mathematics itself. On the other hand, the term “mathematization” refers to the application of concepts, procedures, and methods developed in mathematics to the objects of other disciplines or at least of other fields of knowledge. A definition of this kind seems to assume that there is an agreement, first, on what mathematics is, second, on the profits that various disciplines can make out of its application and, third, on the relevance of the very notion of application. But there are many good reasons to think that such an agreement might be difficult to achieve. There was never a working definition of mathematics in general; even at the time when the traditional definition of mathematics as the “science of quantities” or “magnitudes in general” emerged and was commonly accepted, there were different conceptions of quantities, and consequently different ways of conceiving of the unity of mathematics.3

The consequences of this picture are evident especially when addressing the application of mathematics to medicine and the quantitative understanding of physiology in the aftermath of Descartes and Newton. The historiographical category of “iatromechanics”4 indeed conceals contrasting views about how mathematics should be used in a medicine already reformed on the model of mechanics. S. Guidi (B) Institute for the European Intellectual Lexicon and History of Ideas, National Research Council, Rome, Italy e-mail: [email protected] 2 On the other hand, Daniel Garber, ‘Galileo, Newton and All That: If It Wasn’t a Scientific Revolution, What Was It? (A Manifesto)’, Circumscribere, 7 (2009), 9–18, notes that in the period of the so called ‘scientific revolution’ “there is opposition to Aristotelianism, but there is no single paradigm around which these novatores rally”. “Historians of philosophy and science often talk about the debate between traditional science (Aristotelian, etc.) and THE new science. But there isn’t any such things as THE new science; there are multiple new sciences, at least in the beginning, until things really get sorted out”. 3 Roux, ‘Forms of Mathematization’, 324. 4 See especially Antonio Clericuzio and Maria Conforti, ‘Iatrochemistry and Iatromech-

anism in the Early Modern Era’, in Encyclopedia of Early Modern Philosophy and the Sciences, ed. by Dana Jalobeanu and Charles Wolfe (Cham: Springer Nature, 2021).

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Such contrasts intrinsically reflect the puzzling status of early modern medicine itself, a practice-oriented knowledge, still placed between art and science, dependent upon other natural sciences and still conceived under the idea of the continuity between the macrocosmos and the microcosmos. In addition, those of mechanism, quantification, and mathematization are different, albeit interrelated, notions. They overlap with each other without ever becoming exactly the same, and their meanings are particularly sensitive to the overall epistemological debate about the ultimate method for finding the truth in science, which famously took place over the entire seventeenth century. Early modern iatromechanists—like early modern physicists—look at mathematics as the language through which the world is created, but also as a model of undisputable, certain knowledge.5 Yet, they wonder about how to conceive and apply such certainty to medicine,6 with respect both to theory and practice; and, secondly, they ask themselves where the exactness of mathematics should take place between the two segments of early modern scientific reasoning, i.e. logico-dialectical reasoning and observation. Many questions of more specific kinds arose from these two problems. Is mathematics just a model of ideal logical exactness, able to elevate medical reasoning (since Galen associated logical demonstration

5 Part of the debate presented here (particularly the positions of Gaukes) takes place, on the other hand, in the aftermath of the so-called Quaestio de certitudine mathematicarum. See especially Paolo Mancosu, ‘Aristotelian Logic and Euclidean Mathematics: Seventeenth-Century Developments in the Quaestio de Certitudine Mathematicarum’, Studies in History and Philosophy of Science, 23, 2 (1992); id., Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (Oxford: Oxford University Press, 1996). 6 Uncertainty is, on the other hand, a traditional characteristic of the epistemolog-

ical status of ancient and early modern medicine. See Geoffrey Ernest Richard Lloyd, The Revolutions of Wisdom (Berkeley-Los Angeles-London: University of California Press, 1987), 109–171: Stephen Pender, ‘Examples and Experience: On the Uncertainty of Medicine’, The British Journal for the History of Science, 39, 1 (2006), 1–28 (focusing on the years 1500–1680).

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and evidence)7 to the rank of a true science? Or does it constitute a technical instrument, allowing us to explore what is invisible to the human eye, and to theoretically dominate the functions of the human body, so as to cure it? The different replies to these and several similar questions, lead to as many different understandings about the role of quantification, the practice of “capturing in numerical form certain aspects of material things”.8 As for medicine, this re-understanding consists especially of the conjunction of mathematical physics with the path opened by early modern experimentalism, especially Santorio Santorio’s (1561–1636).9

7 As noted by Robert J. Hankinson, ‘Discovery, Method, and Justification Galen and the Determination of Therapy’, in Galen’s Epistemology: Experience, Reason, and Method in Ancient Medicine, ed. by R. J. Hankinson and M. Havrda (Cambridge: Cambridge University Press, 2022), 79–115, here 80, “Galen insists that genuine epistêmê, in the Aristotelian sense of securely founded scientific understanding, is available to the serious medical investigator. The foundations consist in propositions that are true, evidently so, and hence require no further support. There are two available criteria: things evident to the senses and things evident to reason, and these are ex heautôn pista, self-crediting, credible in virtue of themselves. On the basis of such propositions the diligent inquirer can erect a firmly founded structure of practical knowledge, a tekhnê, but one which is, none the less, in a genuine sense demonstrative”. 8 Roux, ‘Forms of Mathematization’, 325. 9 On Santorio see the many reconstructive essays collected in Santorio Santori and the

Emergence of Quantified Medicine, 1614–1790: Corpuscularianism, Technology and Experimentation, ed. by F. Bigotti and J. Barry (Cham: Palgrave Macmillan, 2022), and for the topics here addressed especially the ‘Introduction’ by Fabrizio Bigotti and Jonathan Barry (1–63), Fabrizio Bigotti, ‘“Gears of an Inner Clock’: Santorio’s Theory of Matter and Its Applications” (65–102); Fabiola Zurlini, ‘The Uncertainty of Medicine: Readings and Reactions to Santorio Between Tradition and Reformation (1615–1721)’ (103–117); Fabrizio Baldassarri, ‘Santorio, Regius, and Descartes: The Quantification and Mechanization of the Passions in Seventeenth-Century Medicine’ (165–190); Salvatore Ricciardo, ‘“An Inquisitive Man, Considering When and Where He Liv’d”: Robert Boyle on Santorio Santori and Insensible Perspiration’ (239–271); Luca Tonetti, ‘Bodies in Balance: Santorio’s Legacy in Baglivi’s Medicine’ (289–315). See also Fabrizio Bigotti, Physiology of the Soul. Mind, Body and Matter in the Galenic Tradition of the Late Renaissance (1550–1630) (Turnhout: Brepols, 2019), Chap. 6; id., ‘Mathematica Medica: Santorio and the Quest for Certainty in Medicine’, Journal of Healthcare Communications, 1, 4 (2016); Fabrizio Bigotti and David Taylor, ‘The Pulsilogium of Santorio: New Light on Technology and Measurement in Early Modern Medicine’, Soc Politica, 11, 2 (2017), 53–113; Edward Tobias Renbourn, ‘The Natural History of Insensible Perspiration: A Forgotten Doctrine of Health and Disease’, Medical History, 4, 2 (1960): 135–152; Jerome J. Bylebyl, ‘Nutrition, Quantification and Circulation’, Bulletin of the History of Medicine, 51, 3 (1977), 369–385; See also the paper by Jan Purnis in this volume and the many essays quoted in there.

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In this paper, I shall argue that in early modern iatromechanism conceptual differences arise about the use of mathematics and quantification. In particular, I here contend that contrasting understandings and uses of quantification in medicine correspond to different conceptions about the epistemological status of mathematics and especially of its conjunction with experience. These views sometimes trace back to major disagreements between the inspiring figures of early modern mechanism and experimentalism: René Descartes (1596–1650), Isaac Newton (1643–1727), Gottfried Wilhelm Leibniz (1646–1715), not to mention the influence of Francis Bacon (1561–1626) and notably of Robert Boyle (1627–1691). I will endeavour to point at these characters between the lines. In order to do that, I compare specific epistemological aspects of the work of some iatromechanists in the aftermath of Newton’s Principia. Hence I focus on physicians working in the late seventeenth and the early eighteenth centuries, at the time when the clash between Cartesian, Newtonian, and Leibnizian physics culminates. Since it is impossible to address the issue in the many European traditions, I concentrate especially on Scotland and Germany, as two areas extremely sensitive to these debates and in constant intellectual exchange. The authors I deal with for this survey are the Scottish Newtonians Archibald Pitcairne (1652– 1713) and James Keill (1673–1719), as well as their German colleagues Yvo Gaukes (ca. 1660–1738) and Friedrich Hoffman (1660–1742).

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2

Struggling for Certainty 2.1

Pitcairne and Keill

Thanks to the work of Guerrini,10 Brown,11 and Schaffer12 the ideas of the “Tory Newtonians” have come to the knowledge of today’s historian of medicine. Among them, Pitcairne is undoubtedly the forefather 10 See Anita Guerrini, ‘James Keill, George Cheyne, and Newtonian Physiology, 1690– 1740’, Journal of the History of Biology, 18 (1985), 247–226; ead., ‘The Tory Newtonians: Gregory, Pitcairne, and Their Circle’, Journal of British Studies, 25 (1986), 288–311; ead., ‘Archibald Pitcairne and Newtonian Medicine’, Medical History, 31 (1987), 70–83; ead., ‘Newtonian Medicine and Religion’, in Religio Medici: Religion and Medicine in Seventeenth Century England, ed. by O. P. Grell and A. Cunningham (London: Ashgate, 1996), 293–312; ead., ‘The Varieties of Mechanical Medicine: Borelli, Malpighi, Bellini, and Pitcairne’, in Marcello Malpighi. Anatomist and Physician, ed. by D. Bertoloni Meli (Florence: Leo Olschki, 1997), 111–128; ead., Obesity and Depression in the Enlightenment: The Life and Times of George Cheyne (Oklahoma: University of Oklahoma Press, 2000); ead., ‘Pitcairne, Archibald’, Oxford Dictionary of National Biography (Oxford: Oxford University Press, 2004), 44, 422–425; ead., ‘Scots in London Medicine in the Early Eighteenth Century’, in Scots in London in the Eighteenth Century, ed. by S. Nenadic (Lewisburg: Bucknell University Press, 2010), 165–185; ead., ‘Isaac Newton, George Cheyne, and the ‘Principia Medicinae’, in The Medical Revolution of the Seventeenth Century, ed. by R. French and A. Wear (Cambridge: Cambridge University Press, 2012), 222–245. 11 Theodore M. Brown, ‘Medicine in the Shadow of the Principia’, Journal of the History of Ideas, 48, 4 (1987), 629–648. By Brown see also ‘The College of Physicians and the Acceptance of Iatromechanism in England, 1665–1695’, Bulletin of the History of Medicine, 44, 1 (1970), 12–30 and the Ph.D. Dissertation, The Mechanical Philosophy and the Animal Oeconomy (New York: Princeton University, 1968). 12 Simon Schaffer, ‘The Glorious Revolution and Medicine in Britain and the Nether-

lands’, Notes and Records of the Royal Society of London, 43 (1989), 167–190. On Pitcairne see also Alsasdair Raffe, ‘Archibald Pitcairne and Scottish Heterodoxy, c. 1688–1713’, The Historical Journal, 60, 3 (2017), 633–657; and Michael Hunter Type, ‘Archibald Pitcairne Heterodoxy and Its Milieu in Late Seventeenth- and Early Eighteenth-Century Edinburgh’, in Early Modern Universities: Networks of Higher Learning, ed. by A.-S. Goeing, G. Parry, and M. Feingold (Leiden-Boston: Brill, 2021), 283–296. Pitcairne’s use of Huygens’ statistical mathematics is addressed by Stephen M. Stigler, ‘Apollo Mathematicus: A Story of Resistance to Quantification in the Seventeenth Century’, Proceedings of the American Philosophical Society, 136, 1 (1992), 93–126. See also Lester S. King, The Philosophy of Medicine: The Eighteenth Century (Cambridge, MA: Harvard University Press, 1978), 102–109; Margaret C. Jacob, The Newtonians and the English Revolution, 1680–1720 (Ithaca: Cornell University Press, 1976); Paul Wood ‘Science in the Scottish Enlightenment’, in A. Broadie, The Cambridge Companion to Scottish Enlightenment (Cambridge: Cambridge University Press, 2003), 94–116; Rienk Vermij, ‘The Formation of the Newtonian Philosophy: The Case of the Amsterdam Mathematical Amateurs’, British Journal of the History of Science, 36, 2 (2003), 183–200; and Jip van Besow

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of early Newtonian iatromechanics. His medicine welcomes the results of previous applications of mechanism to animal and human physiology— e.g. Giovanni Alfonso Borelli (1608–1679), Thomas Willis (1621–1675) and Lorenzo Bellini (1643–1704)—but simultaneously rejects, very critically, Descartes’s epistemology and natural philosophy. Pitcairne’s attack on Descartes, accused of being the leader of a hypothetical and anti-experimental sect of natural philosophers,13 might seem to mime Newton’s famous non fingo. Yet it is very significant since it reveals, even though negatively, Pitcairne’s specific understanding of what mechanism is. As is well-known, Pitcairne’s Newtonianism is portrayed by his Oratio of 1692,14 a short work where he promised “that he would liberate medicine from the thrall of philosophical sects by linking it to the true philosophy, the natural philosophy of Newton”.15 Pitcairne’s is in fact an anti-metaphysical experimentalism, marked by a pre-eminence of observations and epistemological pragmatism. His aim is indeed especially to free medicine from all “Patrons of Sects”, i.e. those philosophers who

and Steffen Ducheyne, ‘Characterisations in Britain of Isaac Newton’s Approach to Physical Inquiry in the Principia between 1687 and 1713’, Early Science and Medicine, 26 (2021), 341–372. 13 Pitcairne rejects all those “fictions” which traditionally affected medicine due to its subalternity to philosophy; i.e. notions like ‘vacuum’, ‘occult qualities’, and many conjectures infesting medical reasoning. But his critique extended not only to ancient and Renaissance philosophers, but also to the ‘father of modernity’, René Descartes, and from two different sides. On the one hand, indeed, Pitcairne portrays Cartesianism as the theory which, even banishing occult qualities and substantial forms from nature, has committed physics to new uncertain notions and explanations—especially via the theory of ‘subtle matter’, the target of many harsh criticisms by Pitcairne and his colleagues. On the other, Descartes is responsible for a model of science based—here the Scottish physician echoes Newton’s famous critique—upon fictions instead of the “Trials of Experience”. See Archibald Pitcairne, Oratio qua ostenditur Medicinam ab omni philosophorum secta esse liberam (Edinburgh: John Reid, 1696). English translation by Sewell with the title ‘Oration proving the Profession of Physic free from the Tyranny of any Sect of Philosopher’, in The Whole Works of Dr. Archibald Pitcairn (London: E. Curll, 1727 [second edition]), 5– 22, here especially 16. Pitcairne’s Oratio is published (in a slightly reworked version) also as an Introduction to his The Philosophical and Mathematical Elements of Physicks (London: Andrew Bell, 1718), a posthumous work collecting Pitcairne’s lectures in Leiden (1692– 1693) and a translation of Elementa medicina physico-mathematica (London: William Innys, 1717). 14 Pitcairne, Oratio. 15 Guerrini, ‘Pitcairne, Archibald’, 424a.

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sought “the Knowledge of the absolute Nature, and intimate Essences and Causes of Things, without any regard to the Discovery of their Properties”, so that they are “forced to make use of many Postulata’s, and but few Data’s, by which means they unavoidably fell into great Variety of Opinions”.16 In opposition to conjectural-metaphysical reasoning, Pitcairne’s epistemology appears to be strongly indebted to Bacon, here conciliated—according to a recurrent scheme—with Boyle’s “diffident” experimentalism and with a pragmatic understanding of Newton’s use of mathematics: It is evident to any one who has been a little more than ordinary conversant in the Mathematics, or the Practice of Physic, that our Knowledge of Things is confined to the Relations they bear to one another, the Laws and their Properties of Powers, which enable them to produce Changes in some Things, and to become altered by other Things: I speak of Corporeal Things. Now these Powers, and their Laws, are discovered by their mutual Action and Reaction upon each other: For Action and its Consequences are those Data that assist us in the Discovery of the Laws of their Powers; but a Physical Cause, and the Nature of Things which the Philosophers so much enquire after, is that unknown Something in Things from whence they will have all its Powers and Properties derived.17

As one can see, for Pitcairne all human science lies on such preliminary acknowledgement of the limits of human understanding, which is limited to the mutual relations between things, and cannot grasp the essence of the things themselves. Mathematics—i.e. mathematical physics—far from revealing any absolute truth, is among the elements persuading us that we are confined to these relations. Effectively, Pitcairne seems to understand the role of mathematics very pragmatically. According to a powerful analogy between macrocosmos and microcosmos,18 he thinks indeed of the specific applied mathematics he found in Newton’s Principia, where mathematics served essentially to draw extremely accurate models of phenomena, under the

16 Pitcairne, ‘Oration’ (English translation), 9. 17 Pitcairne, ‘Oration’, 9. 18 Ibid., 11–12.

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assumption that the physical world is written in mathematical language, even though mathematics does not reveal its ultimate truth.19 Just because of these structural limits of the human mind, scientists should settle for collecting data, i.e. goal-oriented information to use in natural histories of the relations of action and reaction. According to a still Baconian model,20 Pitcairne’s physician acts this way, pointing mainly at inferring from praxis powers and laws of natural things: The Business of a Physician is to weigh and consider the Powers of Medicines and Diseases as far as they are discoverable by their Operations, and to reduce them to Laws; and not lay out their Time and Pains in searching after Physical Causes, which can never be deduced till after the Laws of their Powers are found out; and when they are found out, will be of no Service to a Physician.21

Hence “data” are not, for Pitcairne, information about the essence of natural things. They are rather information about how things act and react to each other, so as to build medicine as a kind of logic22 of diseases and 19 Hence, for Pitcairne the physicians should imitate directly the way of recent astronomers, who “Never in the Explication of the Motion of the Planets, call in the Assistance of a Romantic Hypothesis concerning the Structure of the World”. 20 See especially Cesare Pastorino, ‘Weighing Experience: Experimental Histories and Francis Bacon’s Quantitative Program’, Early Science and Medicine, 16, 6 (2011), 524– 570, who stresses how Bacon’s “quantitative experimental program is always connected to an operative dimension, and to the possibility of producing opera and originate ‘Practice’. Accuracy and quantification are necessary conditions to reach such aims, and past histories are useless and fail in this respect because they lack such qualities”. On the issue of Bacon’s use of quantification and mathematics see Graham Rees, ‘Quantitative Reasoning in Francis Bacon’s Natural Philosophy’, News from the Republic of Letters, 2 (1985), 32–33; id., ‘Mathematics and Francis Bacon’s Natural Philosophy’, Revue Internationale de philosophie, 40, 159/4 (1986), 399–426; Dana Jalobeanu, “The Marriage of Physics with Mathematics”: Francis Bacon on Measurement, Mathematics, and the Construction of a Mathematical Physics’, in The Language of Nature: Reassessing the Mathematization of Natural Philosophy in the 17th Century, 51–80. See also Silvia Manzo’s paper in this volume. 21 Pitcairne, ‘Oration’, 10. 22 In the wake of Bacon’s epistemology. As is known, Paolo Rossi argued for the

derivation of Baconian espistemology from Ramist logic and dialectics. See Francis Bacon: From Magic to Science by Paolo Rossi (London: Routledge 2009), Chap. 4–6. See also id., Bacon’s Idea of Science, in M. Peltonen, The Cambridge Companion to Francis Bacon (Cambridge: Cambridge University Press, 1996), 25–45 and here also Brian Vickers, Bacon and Rhetoric, 200–231.

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remedies and constantly improve it. Accordingly, the physician should never point at the physical causes of what he has observed, but rather should collect these observations with the aim of medical intervention. At the same time, he can at best associate to this pragmatistic stance the seeking of “Mathematical” or “Medical” causes, but just for further clearness: I am satisfied with the Illustration of any one Property only of Diseases, which may be of Use in explaining their Phaenomenas, not pretend so much as to guess at a Physical Reason, being sufficiently assured no Man living is Master of one […]. But however, tho’ I know, nor am at all surprized, that the Physical Causes of these Symptom, and their intimate Natures, should escape the diligent Enquiry of Physicians, yet I think I have explained either the Mathematical or Medical Causes, that is, such as are most useful for a Physician to know.23

As is known, Pitcairne himself does not reject at all physico-mathematical reconstructions; but he effectively understands them only as “useful” for medical activity, and not as ultimate forms of understanding the nature of diseases and remedies. Disinterested in ultimate causes, and interested in pragmatic domination of phaenomena, this scientist pays attention to mathematics only as a way to accurately describe and account for certain natural happenings. This conception of mathematics appears to be quite different from that of other Newtonian iatromechanists who are often associated with Pitcairne. That is especially the case of James Keill,24 and a famous 23 Pitcairne, ‘Oration’, 21–22. 24 Keill’s masterpiece is his An Account of Animal Secretion, the Quantity of Blood in

the Humane Body, and Muscular Motion (London: George Strahan, 1708), republished many times with different titles. The second edition (1717), published by Keill himself and including two new essays, is entitled Essays on several Parts of the Animal Œconomy (London: George Strahan). The first Latin edition dates back to 1718, with the title Tentamina Medico-Physica. Quibus accessit Medicina statica Britannica (London: George Strahan & William and John Innys). This posthumous edition contains as an appendix the work Medicina statica Britannica, i.e. Keill’s reports of his own experiments on Santorio’s insensible perspiration. The Medicina statica Britannica would be published for the first time in English translation by John Quincy, in the second edition (London, 1720) of his translation of Santorio’s Medicina statica. A crucial source for the background of Keill’s view in natural philosophy is the work of his brother John Keill (1671–1721), est out especially in his lectures known as Introductio ad veram physicam (London: Thomas Bennet, 1702), collecting lectures at the University of Oxford in 1700. This work has

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physicist and physician, acquainted with David Gregory and Pitcairne himself,25 and a zealous Newtonian and anti-Cartesian. Keill shares with Pitcairne a radical scientific empiricism and the preeminence of data over postulates. At the same time, he is much less radical about settling for a mere Baconian pragmatism and about rejecting the seeking of physical causes in medicine. He points indeed at a progressive, experimental construction of knowledge, based instead on the discovery, offered by the new science, of the true forces of nature. In this view, “data” are yet not only pragmatic information about action-reaction relations but rather true information about aspects of natural phenomena, that make one able to understand them geometrically within the framework of Newtonian physics: many Phaenomena of the Animal Body which the Ages past thought inexplicable, have now by several been made the Subjects of Geometrical Demonstration. That many Things still remain undiscovered, is not, that of their own Nature they are less capable of Demonstrations; but that the Data are not sufficient, we are not yet fully apprised of all the Circumstances, which conduce to produce such Phaenomena.26

Unlike Pitcairne, Keill trusts not only in the cumulative work of medical natural histories, but also in the progressive construction of a coherent overall theory of the living, thought of as in strong continuity with the Newtonian revolution of physics. The core of this view is indeed the traditional notion of “Animal Oeconomy”, which Keill thinks of as the paradigm for the optimal functioning of an organism, understood as a “pure machine”.27 Yet, for him, “animal oeconomy” is a purely physical notion, and forces doctors to delve into purely physico-mathematical investigations.

been translated into English with the title An Introduction to Natural Philosophy (London: William and John Innys, 1720). 25 Especially through his brother John Keill, who followed David Gregory in Oxford

already in 1692 and was a major apologist for Newtonian science. See Guerrini, ‘James Keill, George Cheyne, and Newtonian Physiology, 1690–1740’; and ead., ‘The Tory Newtonians: Gregory, Pitcairne, and Their Circle’. 26 Keill, An Account of Animal Secretion, V. 27 And opposed to disease, meant as a loss of ‘oeconomy’. See Keill, An Account of

Animal Secretion, VI.

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In this regard, it is worth noting that in Keill’s epistemology accurate knowledge of “animal oeconomy” is something inseparable from experimentalism. The search for new data and observations indeed make sense only in the light of a deep physico-mathematical understanding of the animal mechanism (based, for instance, on deep knowledge laws of motion and hydraulics), which new observations constantly contribute to refining.28 Hence, only once modern physics has been reestablished, based on the new mechanical model and its laws, can medicine accordingly construct a mechanist model for animal and human physiology. And physicians should work, via experiments, to identify and explain the irregularities and the malfunctions causing the diseases.29 Due to this strong association between mathematical physics and experimentalism, Keill’s understanding of the role of mathematics in medicine is quite different from Pitcairne’s. For the latter, indeed, medicine can be built beside and in accordance with physics, whereas for the former medicine must be developed within mathematical physics. However, also Keill’s brother, John, affirmed his experimentalism with a harsh critique of Cartesianism, so devoid of experimental observations as to not even reach the status of a true mechanist philosophy.30 What is important is that these critiques (that might have influenced the work of James) still reveal much about the conception of mechanism which they lie upon. The older Keill even went so far as to portray Descartes 28 Keill, An Account of Animal Secretion, X: “If indeed Experiments are directed, by a Knowledge in the Animal Oeconomy, something may be hoped for from such a Method, and the greater the Skill is by which the Experiments are directed, the greater will be the Probability of Success; because by that we can aim more directly and certainly at the Irregularities of the Oeconomy, and he that knows the Disease is more likely to cure than he that is he that is wandring and dubious in his Mind, and uncertain what it is he ought to aim at. If he hits the Mark it is owing more to mere chance, than any good Skill. Experiments are the only Foundation upon which by a just reasoning we come at the Knowledge of any Phaenomenon of Nature”. 29 Note that just this specific dependence upon the physico-mechanical notion of ‘animal oeconomy’ makes scientific research different from random discovery. Indeed, for “a Man ignorant of the Structure of a Clock or Watch” it is impossible to be “able to put it in right Order, tho’ he had never so exact an History of its irregular Motions”. Likewise, “a Physician ignorant of the Animal Oeconomy, is ignorant of the Structure of the Machine he undertakes to regulate, and the best and exactest Histories of Disease can never suggest to him any Indication of Cure”. Nonetheless, “Natural Philosophy and the Histories of Diseases”, Keill stresses, “must go hand in hand in the improving the Art of curing” (Keill, An Account of Animal Secretion, XXIII). 30 Keill, An Introduction to Natural Philosophy, III.

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as the paradigmatic representative of those men “ignorant of Geometry”, that “presume to Philosophize, and to give the causes of Natural Things”, neglecting geometry “and being unacquainted with the Forces of Nature, which can only be estimated by the means of Geometry”31 : Though he [Descartes] was a famous Geometer, yet that he might accommodate himself to the idle and common Herd of Philosophers, made no use of Geometry in his Philosophy; and although he pretended to explain all things mechanically by Matter and Motion, yet he introduced a Philosophy, which was as contrary to the true Laws of Mechanicks, as was possible.32

This attack against Descartes, played on the very territory of the application of mathematics, was very significant. It was no accident that John Keill identified the main weak point of Cartesianism in a metaphysical conception and use of geometry, entirely disjointed from experiments, observations, and measurements, and hence limited to the setting up of fictional accounts for natural phenomena. The hidden side of John Keill’s critique was then his inflexible experimentalism. What the Scottish natural philosopher was pointing out is indeed that mathematics is not a way of thinking of the world, but rather something to “use” in natural philosophy. It is a technical instrument that the scientist should apply to things themselves in order to understand them physically, i.e. to “estimate” their properties “by the means of Geometry”. 2.2

Axiomatic Reasoning and Medicine: Gaukes and Hoffmann

Pitcairne’s and Keill’s attitude witness the mood of Newtonian Scottish iatromechanism. But the picture looks different when addressing the same problems in other regional contexts and traditions. That is the case of Germany, where we find specular attempts to put mechanical medicine in connection with epistemological principles borrowed from Descartes, Leibniz, and Wolff, especially axiomatic reasoning inspired by Euclidean geometry.33 31 Ibid., VIII. 32 Ibid. 33 This atmosphere is somehow present in the approach of Johann Jakob Waldschmidt’s Vademecum Wadschmidianum, hoc est Institutiones medicinae rationalis (Frankfurt:

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Here I shall focus only on two effective, albeit different, examples of this tendency in German iatromechanics. The first one is the work of Yvo Gaukes, today a quite neglected figure even if he was a prominent iatromechanist physician at his time.34 Gaukes is the author of several medical works, among which his Dissertatio de medicina as certitudinem mathematicam evehenda (1712).35 The second case is that of the— much better known—Friedrich Hoffman, and notably his understanding of medical reasoning especially in his Medicina rationalis systematica (1718–1734). Although he sometimes draws on Newton,36 Gaukes is strongly influenced by Descartes. He is indeed a iatromechanist, but against the

Friedrich Knoch, 1696), a work entirely articulated through analytic tables. Regarding the reception of Cartesianism in Germany, notably in German metaphysics and (via Regius) medicine, see Francesco Trevisani, Descartes in Germania. La ricezione del cartesianesimo nella Facoltà filosofica e medica di Duisburg (1652–1703) (Milano: FrancoAngeli, 1992), esp. 120–349. It is worth recalling that, in the Aristotelian tradition, mathematical reasoning is still classified as potissima demonstration, i.e. the most certain kind of demonstration and a scientific syllogism. See Mancosu, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, esp. 10–15, 17. 34 Besides the Dissertatio de medicina as certitudinem mathematicam evehenda (Amsterdam: R. & G. Vetstenios, 1712), Gaukes’s other relevant work are his Praxis chirurgico-medica rationalis (Groningen: Cornelium Barlink-Hof, 1700) and a defense of Descartes against Anthonius Driessen (1684–1748, the Sapientia hujus mundi quam Deus stultitiam fecit…, 1734) that presumably took place within the so-called ‘controversial Driessenio-Wittichiana’ (see Jonathan I. Israel, Radical Enlightenment: Philosophy and the Making of Modernity 1650–1750 [Oxford: Oxford University Press, 2001], 436–443). See Yvo Gaukes, Innocentia Cartesii defensa (Groningen: Jacob Sipkes, 1735). Some references to Gaukes can be found in Roger Kenneth French, Robert Whytt, the Soul, and Medicine (London: Wellcome Institute of the History of Medicine, 1969), 142– 143. A reaction against Gaukes’s Dissertatio could be the dissertation defended by the English physican Andreas Harley under the supervision of the Swiss Theodor Zwinger III (who, according to the process of the time, wrote the dissertation), and entitled Dubitatio medica de methodo docendi medicinam mathematica (Basel: ex tipijs Friedrici Lüdij, 1714). A medical work inspired by Descartes’ axiomatics, which has strong similarities with Gaukes’ is Niccolo Graniti’s Dell’antica, e moderna medicina teorica, e pratica (Venice: Domenico Occhi, 1739), 2 vols. I owe this reference to Luca Tonetti. 35 A telling title, and even more if considering the subtitle, where he associates Descartes and Newton. See Gaukes, Dissertatio de medicina, frontpage: “continens certa hujus artis principia; et quomodo ex iis omnia Mechanice, et methodo mathematica demonstrari possint. In ea quoque habentur diversae, cum aliorum, tum maxime cartesii & newtoni de rebus philosophicis sententiae sic…”. 36 Especially where he accepts his method on infinitesimals, see Gaukes, Dissertatio de medicina, 26, § 117.

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background of the full mechanization of the living, he pledges to refound reasoning in medicine upon the same degree of certainty as mathematics. A venture resulting in a radically axiomatic understanding of medical reasoning, which would have led Johann Bernoulli (1677–1748) to write that he found in Gaukes’ Dissertatio, “nothing mathematical save for the title”.37 Gaukes’s idea is indeed that medicine, on the model of mathematics, should find and prove a number of firm and basic (1) “indisputable principles”, which would then be the axioms of geometric-like demonstrations. They are as follows: (a) the remote causes of internal diseases and (b) the proximate [causes of internal diseases]; (c) the fluid causes of the external diseases; (d) those phenomena that, as they appear in all the bodies which medicine deals with, appear especially in diseases; (e) the variety of the remedies expelling the diseases, i.e. [the variety] of diets, medicaments, and instruments; (f) the natural powers of action, which make effective diets and medications.38

Note that these “principles” are actually classes of principles, and to meet Gaukes’s scientific ideal, medicine must get to know all the single instantiations existing for each class.39 Only once this mapping of the causes is complete, can medical reasoning attain the utmost degree of evidence (having eliminated everything that is confused and obscure). It thereby consists, like Euclidean geometry, just in making hypotheses and deductions. On the other hand, Gaukes reckons that every possible cause within each of these six principles, can be proved, i.e. deduced, from the overall principles of “physics” and “chemistry”40 (machinas invisibiles ).41 The same applies then to some other classes of principles, which Gaukes calls “actions”. They are:

37 Johann Bernoulli to John Arnold, 28 September 1713, MS Universitätsbibliothek Basel, L Ia 673:Bl.3–4, 3v. 38 Gaukes, Dissertatio de medicina, Praefatiuncula, no page numbers, 1–2. 39 E.g., one should know all the remote causes of all the internal diseases, or all the

remedies for each typology. 40 Gaukes, Dissertatio de medicina, Praefatiuncula, no page numbers, 2. 41 Ibid.

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(g) the usual, the undamaged and the damaged functions in our body, which are carried out by organic parts; (h) the permanent injuries due to external diseases; and (i) the surgeries that can be performed on our body and likewise, finally, (k) some varieties of actions.42

Anyway, Gaukes maintains that the “most suitable” principles from which to deduce first truths are those of “mechanics” and “hydraulics” (machinas visibiles ).43 As one can see, such new medical reasoning can be entirely reduced to, and deduced from, the principles of natural philosophy, i.e. of physics, and thereby of physico-mechanical chemistry, mechanics, and hydraulics, according to the Cartesian topography of the sciences.44 Besides these “indisputable principles” deduced from physics, the geometrization of medicine also entails epistemological premises, i.e. fundamental rules, most of which have an unmistakable Cartesian flavour.45

42 Ibid. 43 Ibid. 44 Gaukes, Dissertatio de medicina, 33, § 140. It is no accident that, in his treatise, Gaukes sets out a whole theory of these four sciences, in line with Descartes’ idea that all of them can be derived from “matter”, understood as extension, “movement”, meant as quantity of motion, and “form”, i.e. the shape of parts of matter with respect to others. These three elements, being able to grant the entire arbor scientiae, are also the ultimate foundation of medical knowledge, which is virtually contained in physics. See Gaukes, Dissertatio de medicina, 67–68, § 286: “Therefore, for so as from matter, due to motion, and form, by which the bodies are variously moved, and also are brought to rest, are produced infinite effects in all the corporeal nature, and hence in medicine, it is clear that these three [principles] are productive ( faeconda). And since everyone can clearly (clare) perceive those three, it is manifest that they are clear and evident. Thus, since productiveness and evidence are two of the required true principles, I therefore conclude that these three, i.e. matter, motion, and form, are true principles of medicine”. 45 They are: “(2) [that] all objects must be assumed as individual and certain. Thereby their truths must be deduced from those principles [i.e. (1) a–k)] (3) evidently, directly, and quickly. Which deductions are to be made by (4) the intellect, inasmuch as it always achieves the truths. And hence, for this to be done correctly, (5) the objects must be arranged in the natural order”. See Gaukes, Dissertatio de medicina, Praefatiuncula, no page numbers, 3. For Gaukes, medical reasoning should be an almost-ideal geometrical logic, exerted by the human intellect on individual and certain objects, for each of which we already know the entire set of possible causes. The entire process consists, indeed, in formulating hypotheses which are both consistent with those known principles and self-consistent, and then getting conclusions on the causes of single diseases and on their remedies.

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Yet, a crucial point threatens Gaukes’s transfer of axiomatic reasoning to medicine, i.e. what, as early as in Aristotelianism, has been dubbed as the problem of the “acquirement of the first principles”. Indeed, if Gaukes agrees with Descartes that God provided each intellect with innate ideas and definitions of geometrical beings,46 what about the medical principles mentioned above, whose causes and definitions are not innate, and which we must hence achieve inductively? The Saxon physician is aware of this problem and, as I will argue, he does not deny any role for natural history and sensory observation in this process of acquirement. Still, he remains a radical Cartesian in stressing the following: like physics, so medicine can also be seen either as a natural history of things (rerum historia), derived partially from appropriate observation and sensory experience, and partially from the report of others; or as a true science, which acquires truths by deducing them from the causes. And hence, it seems to me that medicine can get close to mathematics and benefit from mathematical certainty not inasmuch as a history of medical things, but insofar as it is a true science,47

namely as a kind of medical mathematics. Gaukes does not neglect that, “in medicine, we cannot use our intellect as purely as in mathematics”, but believes that, once our mind has been amended by a true “first philosophy”—able to establish new and true principles of science and to identify the rules of perfect reasoning—48 medicine can be finally taken to the degree of certainty of mathematics based on a simple and crucial principle, i.e. the absolute homogeneity of the physical world, and accordingly of the living body and its phenomena.49 Just because we can count on a stable physical notion of “human body”—and so on unchangeable relationships between the elements being the causes 46 Gaukes, Dissertatio de medicina, Praefatiuncula, no page numbers, 3, §§ 12–14. 47 Gaukes, Dissertatio de medicina, 31–32, §§ 135–136. 48 Gaukes, Dissertatio de medicina, 32, §§ 137–138. 49 Gaukes, Dissertatio de medicina, 32–33, § 139: “Thus, that medicine can be taken

up to the certainty of mathematics is clear; for the human body and its parts, both fluid and solid, have a stable and specific nature; for the rationale of the diseases that occurred in past centuries, today is still the same; for the causes of the diseases and phenomena produce them always in the same way; for the remedies, and likewise the machines, keep the same modes of working; and since all those things naturally depend upon each other, mutually”.

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of health and diseases—we can treat medical things abstractly from their individual instantiations, and from we get through sensory perception.50 The senses, in Gaukes’s view, are nonetheless the cause of many deceptions about several fundamental aspects, and overall they are not a preferred source of theoretical knowledge about things. Despite that, they remain the only way we have to know the an est of the many objects of medicine.51 Gaukes indeed applies a proto-occasionalistic understanding of the role played by the senses in knowledge.52 Although sensory perception is not a way of theoretical knowledge— but just a source of information used by the body-mind compound for practical purposes—it fulfils an important, although basic, function; that of giving us the chance to get knowledge about the existence of a given object of theoretical knowledge: I say that, through sensory perception, we get to know certain phenomena so that, by them [i.e. their perception], the intellect of our mind achieves the cognition of the nature or of the intrinsic and absolute truth of corporeal things, which escapes the senses. Indeed, the senses do not show us [such things], e.g. of what true figure or magnitude a body is; nor what is in them, which produced colours, smells, flavours, etc. Yet this is the intellect’s work, since its perceptions are innate ideas which show intrinsic and absolute truths of things, and even some images of truths. Thereby, mathematicians, detached from the sensible species of their object, contemplate the truths only by intellect.53

50 Gaukes, Dissertatio de medicina, 260, § 1002: “for demonstrations in medicine, insofar as it is a science, to be certain like those of mathematics, it is needed that physicians, like mathematicians, abstracting the mind from corporeal things, consider the nature of their objects [of study] also ideally, and operate the demonstrations by intellect, and not according to the precept of the senses”. 51 Gaukes, Dissertatio de medicina, 263, § 1014: “however, in no way do we reject at all the use of senses in mathematical demonstrations: indeed, they are needed to know the object of which the truths are to be demonstrated. So, thanks to their work […] we know the existence of the sensible objects to which our own body also pertains; [and so we know] the strict union of the mind with the body; and the senses, the appetite and the passions of the soul that rose from this union; the sensible causes of diseases existing outside our body; some phenomena; which remedies aid our body; and the effects in action of the natural powers, given that the powers themselves escape the senses”. 52 On Gaukes’ body-mind occasionalism see the precious remarks by French, Robert Whytt, 142–143. 53 Gaukes, Dissertatio de medicina, 263–264, § 1015–1016.

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Hence, Gaukes locks up his entire model of science in the idea of Euclidean axiomatic reasoning, which coincides with the truest mathematization of medicine. Yet, this specific understanding of mathematics as a form of reasoning is not a specific peculiarity of Gaukes’s work, and after him other German iatromechanists keep traces of it. It is worth noticing that in the first volume of his Medicina rationalis systematica, Friedrich Hoffmann appears to agree with some of Gaukes’ positions: § I. Just as the mathematical method, which is in fact a logic, where it is used by geometers is excellent for finding and teaching all the truths in the demonstrations, so the physician and the philosopher should also arrange the demonstrations of the truths concerning their disciplines according to it [the method]. Just as in fact the geometers, from simple, easy and clear and manifest principles, and simple propositions, shape correct conclusions and connections by the due order and series, and thereby they explain difficult things, and they deduce and discover what is unknown: so also the physician and the philosopher should also collect and draw from clear principles the true conclusions and connections in all those things that, concerning the human body, occur by mutations.54

Hoffmann too understands the application of mathematics to medical reasoning as, essentially, the application of a certain kind of logic. It consists of a top-down movement ordered from causes to effects, and/ or from more general causes to more specific ones. In such a model, the physician should avoid taking into account the freedom of the soul (an undisputable, though metaphysical matter of fact), but neither should he ground his science on the senses: § VII. In order to explain medical things, we do not need any sensory principle, which would foresee the illness and the causes of illness, which would perceive them and would direct the movement to expel what is harmful. Effectively, where something can be explained by movement alone, which 54 Hoffmann, Medicina rationalis systematica, I (Halle: in Officina Rengeriana, 1729 [2nd edition]) c. 8, 41–42. On Hoffmann see especially François Duchesneau, ‘La physiologie mécaniste de Hoffmann’, Dix-Huitième Siècle, 23 (1991), 9–22; Ingo Wilhelm Müller, Iatromechanische Theorie und ärztliche Praxis im Vergleich zur galenistischen Medizin: Friedrich Hoffmann, Pieter van Foreest, Jan van Heurne (Stuttgart: Franz Steiner Verlag, 1991) and Francesco Paolo De Ceglia, I fari di Halle. Georg Ernst Stahl, Friedrich Hoffmann e la medicina europea del primo Settecento (Bologna: Il Mulino, 2009).

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is an operation of the bodies, we do not have to call for the help of a specific sense, or perception; indeed, if it is true that movement is different from perception of movement, thereby movements are produced based on laws and rules that in perceptions in no way are observed. § VIII. The physician, taking the effects back to the causes, and making up demonstrations, should be satisfied if he finds the proximate causes of the effects and phenomena, which, once the former are placed, the latter are placed, and when the former are removed, the latter are removed too; this since in contingent things the progression of the causes is infinite.55

Now, the body being entirely material and mechanical, the physician must seek such causes and principles just among material things.56 Having established this simple principle, one can easily claim that the subject of medicine is the body alone, insofar as it is a machine united with the soul.57 Besides that, it is not hard to notice that Hoffmann aligns himself here with the view that medicine should take from mathematics its axiomatic approach in particular. This attitude nonetheless reflects the traditional idea that medicine is divided into theory and practice, and that theory deals with universal notions.58 Of course, such theory cannot ignore physics, which provides the physician the core of his theoretical knowledge.59 Yet, for Hoffmann “true medical theory” is a “rational and demonstrative explanation” of what is known of illnesses by their natural history. And by “rational and demonstrative”, he understands exactly the Euclidean model of geometers:

55 Hoffmann, Medicina rationalis systematica, I, c. 8, 45. 56 Hoffmann, Medicina rationalis systematica, I, c. 8, 46, § IX. Hoffman here also

criticises those who reintroduce non-mechanical causes in mechanism, speaking of ‘forces’. 57 On Hoffmann’s conception of the body-soul union see especially Paul Hoffman, ‘La théorie de l’âme dans la “Medicina rationalis systematica”’, Revue de syntèse, 105, 113–114 (1984): 55–82. 58 Hoffmann, Medicina rationalis systematica, I, c. 1, 4–5, § VI: “In theory, the physician treats the most universal things; he explains the function of the parts, the causes of life and health, and what remedies, which proportion of food and which lifestyle one should comply with; then he deals with the causes and symptoms of specific illnesses, and by which remedies they should be cured. In praxis, instead, he discusses more specifically and with respect to individuals, and scrutinizes the very nature of the bodies themselves, whether they have a strong constitution, or a weak one, their age, their habits …”. 59 Hoffmann, Medicina rationalis systematica, I, c. 1, 5, § VIII.

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Scholion – An explanation of effects by causes is rational and demonstrative if one deduces [effects] from undisputable principles, as well as from first truths, by means of apt and syllogistic connection; [and so he] explains in the way, and by the method, of the geometers, who are used to employ it in their demonstrations. Indeed, the geometers, and even Euclid himself […] are used to no method, to demonstrate their truths, but the order of things and the series and connection of syllogisms.60

However, like Gaukes, Hoffmann cannot bypass the problem about how we can get to achieve those undisputable principles and first truths. And in this respect, his reply subscribes to inductivism rather than to innatism. Hoffman argues that medical truth depends on both experience and reason,61 but he coins his very concept of “experience” in contrast with that of experientia non intellecta, which has negative meaning.62 The latter is a hasty use of experience, which demands to induce general rules from one or a few experiences, or by impulsive reasoning. True experience, by contrast, [§ VI] springs out from many observations, great diligence, attention and the cure for remarkable things, which encompass the whole history of an illness, along with all circumstances relevant for things, from which the usefulness of medical observations becomes clear.63

This kind of experimentalism alone is still not enough to establish medical reasoning. Indeed, the physician’s reasoning must be led by reason, according to the geometric model exposed above. So, according to a very classical understanding of the “arch of knowledge”,64 the physician appeals to experience only to achieve these primary, more universal, principles, so that axiomatic reasoning can then be applied to the human body. Such a notion of experience includes also, and chiefly, the natural history 60 Hoffmann, Medicina rationalis systematica, I, c. 61 Hoffmann, Medicina rationalis systematica, I, c. 62 Hoffmann, Medicina rationalis systematica, I, c. 63 Hoffmann, Medicina rationalis systematica, I, c.

2, 10, § X, Scholion. 2, 8, § V. 2, 9, § VI. 1, 9, § VII.

64 On this notion see especially David R. Oldroyd, The Arch of Knowledge. An Introduc-

tory Study of the History of the Philosophy and Methodology of Science (New York-London: Methuen, 1986). See Carlo Cellucci, Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method (Cham: Springer, 2013), 37–155; and Simone Guidi, ‘Ipotesi e metodo. Osservazioni su Newton, Bacon e Descartes’, Syzetesis, 6, 1 (2019), 73–109.

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that allows us to infer the steady connections of elements characterizing a certain illness. Yet, besides natural history lies a strong previous knowledge of the structure of the human body, provided especially by anatomy. The good physician masters it according to a model which welds together theory and practice: None can claim for himself the sought cognition of the true medical theory, if not having exact and intimate cognition of the human body according to its structure; and thereby, if he has no tested and clear abilities about those things that can change it [the body]. And that is revealed by anatomy, by that physical doctrine which, as much as possible, is discovered by mechanical and chemical experiments; and [it is revealed] especially by all medical-practical annotated experiments.65

3

Quantifying Physiology: Contrasting Approaches

We have shown that among the iatromechanists here taken into consideration various understandings of the role of mathematics and experience medical reasoning circulated, which I referred to by the “data vs mathesis” opposition in the heading of this paper. One, pragmatic and physicscommitted (respectively Pitcairne’s and Keill’s), which already looks at medical knowledge as a data-driven science; and another, purely Euclidean (Gaukes’ and Hoffmann’s), inspired by the idea that mathematics is the most evident type of logic, and that experiments lead us at to seizing some evident principles or first truths, from which then to trigger geometric-like reasoning. I dwelled on these epistemological notions since they convey different ideas about the role of data in medicine, and are at stake when examining how these authors understand the quantification of physiological processes. In this paragraph, I shall argue that some of these medical systems inspired by the exactness of mathematics, even if arguing for a mathematization of medical reasoning, do not necessarily imply a true and genuine experimental or instrumental quantification of the body—i.e. a mathematical measurement of physiology and metabolism—in order to apply mathematics to them.

65 Hoffmann, Medicina rationalis systematica, I, c. 1, 11–12, § XV.

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Rather, these authors seem to part company along the line opposing divergent understandings of ‘quantification’ (as proportional ratio or as translation in numerical values), and hence of Santorio’s statics.66 On the one hand, those authors who understand mathematization in medicine according to the abstract sense of a reduction of the body to geometricomechanical relationships, without any specific need of measuring the phenomena. On the other hand, those who effectively think of quantification as measurement, i.e. the translation of natural phenomena into numerical magnitudes. 3.1

The Newtonians: From Ratios to Measurements

It has been noticed that Pitcairne’s “mathematical physick”—though it is pioneering in combining mathematical physics and medicine (and he would even provoke satirical attacks for that)67 followed Newton in describing a world that reified the ideal world of mathematics and was therefore not merely a hypothesis. […] The truth of Pitcairne’s conclusions was moreover guaranteed by God, who had created a world of geometrical proportion and symmetry.68

This way, Pitcairne settles for setting his “Newtonian, fully mathematized physiology of forces”69 in opposition to hypothetical reasoning, and for declaring that “his system had to be correct, because the terms from which it is constructed—fluids, velocities, dimensions of vessels—were all mechanical, mathematizable and, in principle, observable entities”.70 But besides that, he does not—and in a way cannot—pass from an idea of “quantification” still grounded on proportional relationships to one based on measurements expressed by numerical values, as keenly noted

66 These two understandings were already present in the Aristotelian notion of quantity: proportion and magnitude. 67 See Stephen M. Stigler, ‘Apollo Mathematicus’. 68 Guerrini, Obesity and Depression, 41. 69 Ibid., 40–41. 70 Brown, ‘Medicine in the Shadow of the Principia’, 632.

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by Guerrini about his account of secretion in his Dissertation Upon the Circulation of the Blood 71 : In his essay, Pitcairne demonstrated his mechanical theory of secretion with numerical proportions but not actual quantities. Had he adhered strictly to his own dictum – that only mathematical statements are possible about invisible entities – he could not have said anything about actual animal structure or function. He did not have, nor could he acquire, enough concrete, quantifiable data to fill in his new system of “iatromathematics.”72

As argued above, Pitcairne effectively understands the role of mathematics as though the latter would provide just an accurate descriptive language, able to bypass the problem of the unknowable ultimate nature of the phenomena. And he looks at mathematics essentially as the metaphysical code used by God in creating the world, which yet is ultimately inaccessible to us. Accordingly, he subscribes to the idea that to know something mathematically consists in grasping natural algebraic proportion between material things. Because of that, quantitative reasoning is for him nothing more than setting out explicative schemes based on ratios between these magnitudes, without trying to attribute numerical values to these via measurement practices or devices. A good example in this sense is the passage of his Elements where Pitcairne, speaking of the female body and its alleged tendency to be warmer than the male body, reasons as follows: in a lesser space of time they [the women] arrive at a determinate Bulk, by reason of a greater Quantity of Fluid, of which the solid Parts are form’d; whereby in a lesser time is supply’d an equal, or in an equal time a greater Quantity of Nourishment. But a greater Quantity of Lymph and Blood will produce a greater Heat…73

What Pitcairne pledges to do is to formulate a general principle about the relationships between quantity of fluids and bulk, as well as about the quantity of nourishment and heat. Yet, in no way does he dwell on 71 Originally published in Latin as Dissertatio de motu sanguinis per vasa minima (Leiden: Elsevier, 1693). English translation in The Whole Works. 72 Guerrini, Obesity and Depression, 41. Cf. also Guerrini, ‘Archibald Pitcairne and Newtonian Medicine’, 77–78. 73 Pitcairne, Elements of Physick, 19.

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capturing these quantities in numerical form by weighing or measuring specific cases. This, indeed, would entail a previous understanding of the mathematico-physical “animal oeconomy” as the very cause of the observed phenomenon, whereas Pitcairne, according to his pragmatistic stance, seeks only for stable associations between A (the bulk) and B (quantity of fluid), in order to establish that B → A. Here is another example, this time about digestion and animal economy: …the Parts of the Food, in some measure dissolved by the Motion of the Stomach, but not sufficiently separated from each other, through want of a due Quantity of Fluid, every one as yet being in some measure in contact with one another; are at length, by obtaining a greater Space in a greater Quantity of Fluid, much easier removed farther off from one another, and the lesser disengaged from the greater Particles: and when these greater or less digested Parcels cannot, by reason of their Magnitude, be strained in any considerable Quantity, into the Lacteals, they are yet thrust further into the intestinal Tube, and therein putrify….74

Broadly speaking, Pitcairne identifies quantification with the application of the models of hydraulics to the human body, which effectively represented a core practice in early modern iatromechanics. And in this sense, he continues and improves the work of early iatromechanists such as Borelli and Bellini and the seventeenth-century quantification of muscolar activity and fluids.75 Though, due to his specific epistemological approach, Pitcairne does not reason in numerical terms when conceiving these explanations, neither does he involve instrumentation in this process. An apparently contrasting example is, however, Pitcairne’s mathematical demonstration of Bellini’s theory that “the whole quantity of perspiration coming every minute from a shred, whose weight is a scruple, is 1200 part of a scruple”. Here Pitcairne delves into arithmetic calculation of the quantity of perspiration, but he grounds his entire demonstration on the numerical values he found in Santorio:

74 Pitcairne Elements of Physick, 24. 75 See Luca Tonetti’s paper in this volume and his ‘Bodies in Balance: Santorio’s Legacy

in Baglivi’s Medicine’.

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Sanctorius declares, that in the space of 24 Hours the Perspiration is 50 Ounces, which makes 1200 Scrup[les] that is, 50×24 Scrup[les]. Therefore we perspire in the space of an Hour 50 Scr[uples] and every Minute of an Hour there is perspir’d in the whole Body 5 six parts of a Scrup[le]. Since then the midle quantity of the weight of the Body of Man is 160 lib. which are equal to 60000 Scr[uple] or 50×1200 there is every Hour expir’d from the whole Body a quantity of Perspiration, which is 1200 part of the Body: And therefore from every part of the same there will expire the 1200 part, or in the space of an Hour there will go out of every Scrup[le] the 1/1200 of a Scrup[le]…76

76 Archibald Pitcairne, Apollo staticus. Or, The art of curing fevers by the staticks: invented by Dr. Pitcairn, and publish’d by him in Latine: now made English by a well-wisher to the mathematicks (Edinburgh: J. W. and Sold, 1695), 22–24; ‘The Whole Works’, 209–211. Pitcairne’s demonstration continues as follows: “…Therefore in that Man whose sum of the Shreds by which Perspiration is driven is 1/60 of his whole Body, that is (of a Man of midle weight) 3 lib. that sum will be at least 1000 Scrup. Therefore there behoves to sweat out by those 1000 Scrup. every Hour 50 Scrup: or by 1 Scrup. every Hour 50/1000 Scrup. must sweat out, that is 1/20 Scrup. And therefore in the space of a Minute, or 1/60 part of an Hour there will sweat out through 1 Scrup: 1/60 × 20 or 1/1200 Scrup: as Bellinus finds. And because the weight of Perspiration, all things being considered, is according to the weight of the Body perspiring. Therefore in a Body of 120 lib. or 45,000 Scrup. the Perspiration in 24 Hours will be equal to 900 Scrup: and Perspiration every Hour will be equal to the 37½ Scrup. Whence every Hour there perspires 1200 part of the Body, and so proportionably of every part and Scruple, because 45,000 Scrup: make 1200 × 37½ Scrup. Wherefore in that Body in whom the outmost Cuticle of the Uterus, Intestins, Lungs, Jaws, &c. made about 2 lib. the sum of the Shreds also by which Perspiration last went throw, was at the least 750 Scrup: or the 60 part of her Body. For she died of an immoderat Issue or Emoragy of Blood from the Womb, the third Day after Child-birth, but her Body was 106 lib. Now throw these 750 Scrup. there behoved every Hour to come out 37½ Sc. that is every Hour out of every Scruple to come out 37/750½ Scrup. that equals 1/20 Scru. seing 20 × 37½ equals 750: Therefore every Minute or 1/60 of an Hour, there will come out throw 1 Scr. 1/60 × 20 Scr. = 1/1200”. For some remarks about Pitcairne’s attempt at applying Huygens’ probability theory after this calculation see Stiegler, ‘Apollo mathematicus’, 110 (see also 105–109). Another contrasting case is what Pitcairne wrote to Robert Gray in 1694, and already reported by Guerrini (‘Archibald Pitcairne and Newtonian Medicine’, 81). Here Pitcairne effectively told of having “laid aside” a work (the De ictero) “till wee get some bodyes to look into […] I want the measure of the capacitie of some arteries without which all is conjecture” (Pitcairne to Robert Gray, 23 September 1694, in The best of our owne: letters of Archibald Pitcairne, 1652–1713, ed. by W. T. Johnston [Edinburgh: Saorsa Books, 1979], 19–20). However, Pitcairne’s letter witnesseses that he understood measurement as a strategy for testing and confirming his previously conceived mechanico-anatomical explanations.

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This aspect of Pitcairne’s medical thought perhaps shows that being a passionate Newtonian is not enough to understand the whole power of mathematics applied to medicine. Yet, as stressed aptly by Brown,77 Pitcairne’s efforts were later to be refined and improved in this sense by the whole generation of his Newtonian heirs in Scotland. It is worth noting, for instance, that in George Cheyne’s Theory of Acute and Slow Continu’d Fevers 78 —a work that famously takes up and reelaborates Pitcairne’s Newtonianism—one already finds a more explicit and specific acknowledgement that quantifying physiology consists essentially in collecting numeric dimensions: all the Distempers and Disorders of the Body of both [human beings and animals], are owing to a Vitiation of the Quantity, Quality, or Motion of the Fluids, or to a bad Disposition and Texture, a Distortion, Distention, Luxation, or Dilaceration of their Conduits, and the other solid Parts of their Bodies; and that Medicines operate by the Application and Mixtion of their Juices, or by a Communication of their Virtues to these. And seeing all these are the Modifications and Qualities of material Beings, which have the Dimensions of Bodies, and are therefore Quanta; it necessarily follows, that the only Method of examining the Effects and Causes of these Qualities, is by applying to them the Doctrine of Quantity, i.e. Geometry and Numbers.79

Here Cheyne subscribes to the idea that, since whatever body is by itself quantum, all bodies may immediately undergo the general “Doctrine of Quantity”—i.e. geometry, here associated with algebra (‘numbers’). Now, all the disorders of the body are due to changes in quantity, but also to the quality and the motion of fluids, which we can know just by means of

77 Brown, ‘Medicine in the Shadow of the Principia’. 78 Georges Cheyne, A New Theory of Continual Fevers (London: George Strahan,

1701). As of the 1702 edition which here I quote from (A New Theory of Acute and Slow Continu’d Fevers: 2d ed., with many additions [London: George Strahan, 1702]), this work contains a ‘Essay Concerning the Improvements of the Theory of Medicine’ where Cheyne defends his view about the usefulness of mathematics and mechanics in medicine. See also Cheyne’s brief essay Remarks on Two Late Pamphlets Written by Dr. Oliphant (Edinburgh, 1702), where Cheyne defends his and Pitcairne’s iatromechanism Against Charles Oliphant. See Guerrini, Obesity and Depression, 60–65. 79 Cheyne, A New Theory, 6.

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geometric reasoning. Indeed, this procedure makes us able to infer nonobservable qualitative changes in the material being by their observable, quantitative changes. However, within this conceptual framework, Cheyne still does not understand this quantification as based upon measurement but rather maintains that every material being is by itself a measurable magnitude, being everything that is material intrinsically subject to quantitative dimensions. It seems thus that measurement—here is another Baconian suggestion—acts for Cheyne just by making these dimensions immediately understandable for the mind, which draws all of its knowledge on the senses. Accordingly, in his reconstruction of the main stage in the evolution of modern medicine, Cheyne portrays Santorio as the one who invented various ways to bring to light, by measurement and proper instrumentation, what is invisible to the bare human senses: Sanctorius […], in his admirable Treatise of Statical Medicine, has obliged the World with many excellent Rules of Health, and many useful Observations of the Quantities and Proportions of the several Natural Evacuations, and the Effects of the Suppressions of these, whereby Men are enabled to talk more distinctly, and not left to guess at random about such things. It is to him likewise, we owe the Invention of what is now call’d the Thermometer, whereby we are not only enabled to distinguish the several Degrees of Heat and Cold, to a much greater Exactness than formerly, by our bare Senses.80

Through observations and technical instruments, one can effectively “capture in numerical form certain aspects of material things”, aspects that are already quantitative, although virtually or implicitly, in the physical dimensions of the bodies. Despite that, Cheyne does not take this numerical measurement as far as embracing a form of mathematically conceived experimentalism. He does not think that the physician must study the body by measuring its anatomic dimensions, but rather takes for granted the geometrico-quantiative nature of bodies, and still applies geometrico-algebraic models to medical problems (for instance, the relationship between fevers and quantity of blood), in order to accurately confirm his geometrico-hydraulic models.

80 Ibid., 15.

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As noted by Brown,81 a leap forward in this sense occurs only with Keill, also the greatest early modern commentator on Santorio.82 Compared to Pitcairne’s and Cheyne’s, Keill’s approach is—although in continuity with the iatromechanical tradition—quite peculiar, being extremely orientated towards a conjunction of experimentalism and instrument-driven quantification. Let us consider, for instance, this passage from his Account of Animal Secretion, already reported by Brown: I took a piece of the Intestine of a Dog, with part of the Mesentery and Pancreas Asellii, and having carefully emptied it of all its Contents, I weighed it exactly with all the Blood in the Vessels, its Weight was one Ounce and a half, one Drachm and eighteen Grains; then I injected Warm Water into the Artery, and having sufficiently washed out all the Blood; I blew it up and hung it to dry in the shade; after it had dried about a Week, I weighed it again, and its Weight was two Drachms, two Scruples, and eleven Grains: By which it appears, that it had lost six hundred and thirty seven Grains, and that there remained only one hundred and sixty one Grains. Now this loss could be only of Fluids, which being diluted with Warm Water, were the more easily evaporated.83

Keill’s experiment is not only well-conceived, but also “quantitatively conceived”84 from the very beginning. And his entire work is imbued with similar cases, the most relevant of which is his famous calculation of the force of the heart in driving the blood.85 Another effective example

81 Browne, ‘Medicine in the Shadow of Principia’. 82 As is known, Keill repeated Santorio’s experiments with the ‘weighing chair’,

reporting accurately all his results in his journals and improving Santorio’s calculations. See Keill, Medicina statica Britannica. For some observations about that see Barry and Bigotti, ‘Introduction’ and Renbourn, ‘The Natural History of Insensible Perspiration: A Forgotten Doctrine of Health and Disease’, 142–144, who notes that Keill did not accept especially Santorio’s idea “that obstruction of the insensible secretion was a cause of disease”, since “the effect of damp or cold was, in his opinion, not due to a block of what came out of the skin pores, but, rather, to an ingress of ‘frigorick’ particles, of a nitrous kind, capable of chilling, condensing and thickening the animal fluids”. 83 Keill, An Account of Animal Secretion, 116–117. 84 Brown, ‘Medicine in the Shadow of Principia’, 637. 85 Keill carries out this calculation based on principles of Newtonian dynamics and

hydraulics and the velocity of the blood measured on a dog’s cut artery. This way, Keill manages to correct Borelli’s previous calculation. See Essays on Several Parts of the Animal Œconomy, 79–87. See Brown, ‘Medicine in the Shadow of the Principia’, 639–642; and

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is the way he calculates the thickness of the coats of blood vessels in his Tentamina: Slit a piece of a Blood vessel, and reduce it to the Form of a Parallelogram, then weigh it in Water, and by that means find the Weight of Water equal to it in bulk. This weight reduced to decimal Parts of an Inch [i.e. a cubic inch] call, d, and suppose the length of the Parallelogram equal to e, and d = its breadth = c, its thickness f . Then d = e c f and consequently ec f the thickness of the Coat of the Vessel. Thus a piece of the Aorta of a Calf I found to be equal to 0,071897 parts of an Inch of Water, its length was 1,1, its breadth 1,28, and therefore its Thickness was 0,051. The Diameter of the Cavity of this Artery was 0,407 and consequently a 2 – 2 a b + b 2 equal to 0,165649, and 2 a b – b 2 equal to 0,093432, and therefore if the whole Body was composed of Arteries or Vessels which had the same Proportion to their Cavities, as the Arteries have to theirs, the Blood would be to the solid part of the Body, as 1,7 to 1, and a body weighing 160 Pound would have 100 Pound of blood.86

As one can see, Keill is led by the idea of taking this medical measurement by means of geometric tools. Yet, he does not settle for applying generic geometrical proportions, but concretely endeavours to get them by the actual measure of already-known dimensions. Conceiving the issue as a physico-geometric problem, he uses indeed the actual weight of some water, equivalent in bulk to the blood vessel, to get the volume of such correspondent water (an easy conversion from weight to cubic inch). Thus he manages to calculate the thickness of the vessel (of which he already knows the length and breadth) treating the water’s volume as if it was the vessel’s volume. Only then does he deduce proportional relationships between tissues and fluids, by algebraic work on these data. Hence Keill constructs experimentally and mathematically the very issue from below, i.e. by preliminarily measuring weights, heights, and other dimensions, and—by measurement —he imports the problem into

Frederic L. Holmes, ‘The Physical Sciences in the Life Sciences’, in The Cambridge History of Science. Volume 5—The Modern Physical and Mathematical Sciences, ed. by M. J. Nye (Cambridge: Cambridge University Press, 2002), 219–236, here 223. 86 Keill, An Account of Animal Secretion, 111–112.

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a geometrico-mathematical framework, where he can apply the power of geometry, algebra, and Newtonian physics.87 Of course—like Cheyne or any other good Newtonian—Keill too subscribes to the idea that the body is essentially quantum, so that one could directly treat bodies as based on geometrico-mathematical models, and as regulated by geometric proportions. Yet, measurement is for Keill’s experimentalism a preliminary and important phase of data collection, according to his understanding of “data”. Previous measuring allows us not only to rethink a given problem by analogy with geometricomathematical models, but to reduce concrete elements to geometricomathematical coordinates, so as to apply mathematical physics just to solve the issue. By quantifying the elements at stake in a problem, we can indeed translate every single element into numerical terms, then using algebra to necessarily and accurately infer their mutual relationships, i.e. ratios. 3.2

The Rationalists: Statics and Quantification

If Keill’s approach pushes the Newtonian conjunction of mathematization and experimentalism to its apex in medicine, what appears to be the role of quantification in those iatromechanists who conceived mathematics as a form of Euclidean logic, rejecting or limiting the role of observation in medical reasoning? The different approaches of Gaukes and Hoffmann seem to converge on the purpose of mechanizing—but not mathematizing—Galenic humoral medicine. They understand measurement in the light of the Sanctorian notion of ‘static medicine’, as a way of accurately monitoring some specific aspects of human physiology, related especially to fluids and to their overall balance (eucrasia). An excellent example of this stance is Gaukes’ definition of statica and hydrostatica: 87 One important aspects related with Keill’s work is that he is the first to acknowledge a role to short-scale attraction in his physico-medical reconstructions. See Guerrini ‘James Keill, George Cheyne, and Newtonian Physiology’, 258–259; and Browne, ‘Medicine in the Shadow of Principia’, 638. Also Cheyne speculated about attraction, even though in a spiritual-cosmological perspective. See Hélène Metzger, Attraction universelle et religion naturelle chez quelques commentateurs anglais de Newton (Paris: Hermann, 1938); Geoffrey Bowels, ‘Physical, Human and Divine Attraction in the Life and Thought of George Cheyne’, Annals of Science, 31, 6 (1974), 473–488; and Guerrini, ‘James Keill, George Cheyne, and Newtonian Physiology’, 260–265.

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816. Indeed, medical things can also be demonstrated by statics and hydrostatics, and nobody would go so far as to deny that: by them, indeed, we must demonstrate the weight (gravitatem) of physical bodies (gravium), and the balance (equilibrium) or equal weight of opposite bodies, which concerns it. 817. And so, as for the weight of physical bodies: where it is necessary to prepare some composition, e.g. as a mixture, an ointment, etc., it is necessary to demonstrate through statics the weight of the ingredients, so that is taken neither more nor less of them than what works. 818. So, also, in the name of statics, S. Sanctorius revealed the weight of the vapours ejected by our bodies, the body, and the things to be taken; [he did that] both weighing the greasy excretions, and subtracting their sum from the sum of the others.88

To understand this passage, we need to stress that balance is not a pivotal notion in Gaukes’s medicine, and does not correspond directly with health,89 as in the traditional Galenic view that he re-works mechanically. Also, for Gaukes, statics and hydraulics are connected with balance just as they concern the weight of remedies and other medical objects, given that “the weight and the balance of the things which are hidden in our body cannot be demonstrated in this way”.90 Indeed our organs cannot be weighed, and fluids can be partially and just indirectly. However, Gaukes understands the notion of balance twofold. On the one hand, he thinks of a balance of the solid parts, which is nothing but physical statics of the corpuscles making up the body. On the other hand, he rejects the idea of a specific balance of fluids (since they are a plurality and since such a balance is nothing but communicating vessels),91 and rather speaks of balance between solids and fluids. In both cases, Gaukes does not mean balance in strictly quantitative terms. The reason behind that is that for him mechanical philosophy alone, understood as a geometrical modelization of the living functions, is enough to reduce the body to something immediately evident for our mind. This way, and according to the occasionalist approach recalled above, one can easily transfer the bodily functions onto the level of

88 Gaukes, Dissertatio de medicina, 215. 89 Ibid., 215ff. 90 Ibid., 216, § 822. 91 Ibid., 218, § 829.

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mathesis, where they are objects of geometrico-mathematical abstract reasoning. Yet one might guess another (admittedly quite bizarre, albeit congruent with similar problems already present in Aristotle92 ) reason why Gaukes does not keep a specific place for measuring. It is suggested by what he claims about the shape of material things, including our body and medical instrumentation, which for Gaukes are no perfect geometrical things, so they can be reduced to geometry only by abstraction by the mind: 774. After all, we can easily know that in our body there are no parts which have a perfect mathematical shape, in view of the account given [above] of particles and molecules […]. 775. Likewise, outside of our body there are not surgical instruments having perfect mathematical shape, since by art they [these shapes] cannot be induced in natural things […] 776. Yet the mathematical shapes are attributed both to the parts of our body, and to the surgical instruments, by mental abstraction, which cause the demonstrations made by it [i.e. mental abstraction] to be more accurate.93

92 See Met. III, 2, 997b 25–8a 19: “If geometry is to differ from mensuration only in

this, that the latter of these deals with things that we perceive, and the former with things that are not perceptible, evidently there will be a science other than medicine, intermediate between medical-science-in-itself and this individual medical science, and so with each of the other sciences. Yet how is this possible? There would have to be also healthy things besides the perceptible healthy things and the healthy-in-itself. And at the same time not even this is true, that mensuration deals with perceptible and perishable magnitudes; for then it would have perished, when they perished. And astronomy also cannot be dealing with perceptible magnitudes nor with this heaven above us. For neither are perceptible lines such lines as the geometer speaks of (for no perceptible thing is straight or curved in this way; for a hoop touches a straight edge not at a point, but as Protagoras said it did, in his refutation of the geometers), nor are the movements and complex orbits in the heavens like those of which astronomy treats, nor have geometrical points the same nature as the actual stars. Now there are some who say that these so-called intermediates between the Forms and the perceptible things exist, not apart from the perceptible things, however, but in these”. Cf. Henry Mendell, ‘Aristotle and Mathematics’, in The Stanford Encyclopedia of Philosophy (Fall 2019 Edition), ed. by E. N. Zalta, s. 6, who speaks of ‘problem of precision’: “The physical straight lines we draw are not straight; a physical tangent line does not really touch a circle at a point. In other words, physical objects fail to have the mathematical properties we study”. 93 Gaukes, 204, § 774–776. Here Gaukes seems to subscribe to a abstractionist/ fictionalist account of mathematical beings, which is traditionally attributed to Aristotle. See Mendell, ‘Aristotle and Mathematics’.

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No material being is a purely geometrical one, if not by an approximation made by virtue of mental abstraction. Hence, no medical instrumentation might capture pure geometrical data (in the ideal sense of mathesis), and so elevate medicine up to the degree of certainty of mathematics, which instead is still guaranteed by the mental operation of abstraction. On the other hand, Gaukes seems to maintain that mathematics (here understood as applied mathematics, opposed to more geometrico reasoning) intervenes in medical demonstrations only when hydraulic and purely mechanical models overlap into the same issue. This overlap indeed makes the problem become mathematical, since mathematics belongs to both, and a demonstration performed per objecta mathematica unifies them into a single problem.94 Gaukes enumerates several of these mathematical objects one can resort to in medical demonstrations, which are: Numbers, the magnitude of dimensions, mathematical shapes, and movements executed according to certain lines: and also, when something is demonstrated by means of their truths.95

As one can notice, Gaukes sticks very precisely to the tree of sciences of his time. Mathematical truths are, strictly speaking, neither medical truths, nor physical ones. They belong to different fields, corresponding to as many different truths. Yet the truths of mathematical objects can be employed to solve mechanico-hydraulic problems by a sort of analogical reasoning made possible by abstraction. However, Gaukes proposes some examples of these applications, for instance, the arithmetical demonstration of the volume of air breathed by a lung through a glass cylinder96 ; or the calculation of the dimensions of secretions in arteries based on the diameter of the arteries,97 among others. Gaukes thus shows in these cases an opening towards physicomathematical reasoning that assumes preliminary quantification of the dimensions of a given problem. But he also reasons at best like Pitcairne, not acknowledging for measuring a pivotal role in formulating the issue. His idea of mathematics applied to medicine indeed does not include any

94 Gaukes, Dissertatio de medicina, 202, § 765. 95 Ibid., 202, § 766. 96 Ibid., 202, § 767. 97 Ibid., 202–203, § 768.

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kind of experimentalism based on the preliminary quantification of living functions, and the role of measurement seems to be, for him, only to make intelligible to the mind physiological relationships that are hidden to the senses. Finally, to continue this epistemological comparison, it is worth making a few remarks about Hoffmann. As seen, the Halle doctor also understands mathematics as a kind of Euclidean logic; but—unlike Gaukes—he does not reject at all experience, stressing especially the role of rational experience, i.e. experimentalism. Famously, this stace is associated with to an alchemico-chemical understanding of quantification, which draws from Boyle’s ideas rather than from Newtonian mechanical philosophy. Let us consider what he argues about Santorio: § XXII. Sanctorius, nonetheless a loyal follower and commentator of Galen, in his beautifully written book De medicina statica; nobody prescribed us more righlty and accurately the foundations and the laws of dietetics, and of excretions, and above all of perspiration, and taught and confirmed, by multiple static experiments, the highest necessity [of these things] for taking care of health, and the healthiness of taking precautions against illnesses.98

Within this more traditional perspective, Hoffmann embraces a kind of quantification that effectively captures aspects of living functions in numerical form, yet not applying mathematical reasoning to them. Likely, this specific approach is intentional and stems from his overall stance. Hoffmann, for instance, is aware of Keill’s work—especially his effort at establishing the quantity of circulating blood—which he quotes several times,99 and at the same time he shows a deep knowledge of his contemporary iatromechanics. Hoffmann’s understanding of quantification is nonetheless still conceived within the Galenic idea of a natural, medical semiotics100 of the ill body, which includes quantitative and qualitative aspects, taken simultaneously together. Accordingly, the elements that for him should undergo

98 Hoffmann, Medicina rationalis systematica, I, c. 6, 37, § XII. 99 For instance, Hoffmann, Dissertatio medica de vera perpetui mobilis in homine vivo

idea, § 51, in Friedrich Hoffmann, Operum omnium physico-medicorum supplementum (Genevae: Fratres de Tournes, 1749–175), 5 vols., V, 220. 100 See Hoffmann, Fundamenta medicinae, c. 1.

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these procedures are—following a solid seventeenth-century tradition— in particular fluids (blood, urine, saliva) and the pulse,101 all being signa morborum. Let us examine, for instance, this passage of Fundamenta medicinae touching on urine inspection: 32. In inspecting urine, one should pay attention to the quantity, the quality, the color, the smell, the consistency and what is contained in it. / 33. The augmented quantity of urine indicates a separation of the serum from the blood, or suppressed perspiration or obstructed transpiration. / 34. In acute and malignant illnesses urine often is copious and flows feebly, and this is a bad sign. / 35. Few urine reveals either that urinary tracts are obstructed, or that the mixture and the circulation of the body is upset […] / 36. The urine’s weight, which must be investigated through a static instrument, shows fixed earthy saline contents according to its quantity.102

As one can see, weight, quantity, and other quantitative aspects are just some of the many things a good physician should note when inspecting fluids, but they are surely important elements. Hoffmann insists especially on quantitative aspects related to the weight and the density (specific gravity) of blood and urine, which he usually inspects via proper instrumentation: And now some things should be added about the different ways to examine human blood. There are several, and the first is certainly to investigate its specific gravity, compared with that of simple water. This is executed by a static instrument, through which I usually evaluate urine, milk, as well as springs of salt water and medical water.103

The mentioned instrument is a “static cylinder”, i.e. a hydrometer, whose use was already very much appreciated by Robert Boyle.104 It is

101 See Friedrich Hoffmann, Dissertatio inauguralis pulsuum theoriam et praxin examinat, in id., Opera omnia, 6 vols. (Genevae: Fratres de Tournes, 1740), VI, 237–244. 102 Friedrich Hoffmann, Operum omnium physico-medicorum supplementum, II, 27b. 103 Hoffmann, Medicina rationalis systematica, III, s. 1, c. 12, 282, § XI. 104 See Robert Boyle, The Works of Robert Boyle, ed. by M. Hunter and E. Davis, vol. 8 (London: Pickering & Chatto, 1999–2000), 532–540 (Philosophical Transactions, 10 [1675]). See Ricciardo, ‘An Inquisitive Man’, 259. Hoffmann mentions several times in his works this instrument (not rarely claiming to be the one who perfected this instrument for this medical use).

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worth reading a passage of the same work, where Hoffmann defends the doctrine of a specific proportion of solid matter in urine: to a more accurate understanding of this doctrine pertains also, so that the physician has a clear view: how much solid matter is contained in one pound of urine of a healthy person. For instance, actually, for investigating the specific gravity of fluids, or the quantity of solid matter contained in a fluid, nothing is more apt than of a static cylinder, proficiently prepared for use for this aim; and so the physician can employ very easily such an instrument not only on the contents of the ingested liquids, such as are those of beer, wine, water, and milk, but also on urine; however, hardly anyone thought about that until these days.105

Starting from an idea of mathematics as the purest form of logical reasoning—but not as an actual part of experimentation—Hoffmann’s experimentalism quantifies, even via proper instruments, observable aspects of physiology without feeling compelled to convert them into numerical values. He rather seems to think of quantification as a way for collecting more precise data about a certain phenomenon, and reading in these numerical relationships the signs of healthy or ill conditions. (Iatro)mechanism, understood this way, is nothing more than a theory of proximate causality, which can be disconnected from purely mathematical aspects.

4

Conclusion

Reworking a famous Galenic distinction,106 in 1702 Leibniz commented on Bayle’s Dictionnaire writing that in medicine there are three sects: “the sect of the Empiricists and that of Methodics [Methodiques ] and Rationals”, i.e. those who “are only satisfied with facts or experiences”, those who “do not care about observations and experiences, and believe they have reduced everything to causes or reasons”, and those “who

105 Hoffmann, Medicina rationalis systematica, III, s. 1, c. 13, 288–289, § VI. See also De elementis aquarum mineralium, § VI, in id., Opera omnia, V, 133a. 106 Galen, De sectis ingredientibus, in id., Opera omnia, I, 64–107. English translation On the Sects for Beginners, in id., Three Treatises on the Nature of Science, trans. by R. Walzer and M. Frede (Indianapolis-Cambridge: Hackett, 1985), 1–20. See Lloyd, The Revolutions of Wisdom, 158–167.

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attempted to improve experience adding the search for causes to it”.107 Comparing the positions of Pitcairne, Keill, Gaukes, and Hoffman, I have endeavoured to show that, at the turn of the seventeenth and eighteenth centuries, the picture is much more tangled, especially when one looks at how these authors understand the role of quantification and mathematization and their connection with the search for causes of medical phenomena. Different forms of quantification depend on as many different combinations between the understanding of the role of mathematics in scientific reasoning and the role attributed to experience in medicine. These four authors overlap and simultaneously distinguish themselves from each other, showing unexpected contrasts and affinities. However, some final comparative remarks can be put forward. Pitcairne, Keill, and Hoffmann share an overall experimental approach, while Gaukes confines himself to a rigorous Euclidean, axiomatic model, even denying any role for observation. Pitcairne and Keill understand experimentalism more sceptically and pragmatically than Hoffmann, who thinks instead, nearer to Gaukes, that experience provides to the mind some relationships from which it can move towards a sort of Euclidean reasoning. Despite that, Pitcairne, Hoffmann, and also Gaukes understand the quantification of bodies and living processes in light of a mechanization of Galenism, which concerns especially fluids, or the relationship between liquid and solid parts of bodies. This kind of quantification is inspired by statics and looks especially at establishing proportions between various components of the body, sometimes reading them within the concept of medical semiotics. Otherwise, it aims at reducing certain phenomena to the geometrical laws of hydraulics or mechanics, in order to show that they are purely mechanical. Yet, these conceptions of quantification are quantifications only in a broader sense, since they do not point at capturing physiological elements by converting them into numerical values. This latter aspect marks, by contrast, the approach taken by Keill alone, at least among the authors we have considered. Unlike his iatromechanist colleagues, Keill conceives his experimentalism as intrinsically mathematical, so he moves just from the previous measurement of the phenomena he deals with. What he constantly tries to do is notably to transfer to medicine the methodology employed by Newton in other contexts. Keill’s 107 Gottfried Wilhelm Leibniz, Die Philosophischen Schriften, ed. by C. I. Gerhardt, 7 vols. (Berlin: Weidmann, 1875–1890), IV, 525–526.

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idea is indeed that one must treat the living based on the physico-medical notion of “animal oeconomy”, which is strictly committed to mechanical physics, but also to mathematico-mechanical physics. The whole process of medical experimentation and reasoning is strictly related to this mathematico-mechanical core. For Keill, the physician’s work consists first of all in accessing numerically, and then mathematically, the physiological aspects he wants to understand. Hence mathematics, as well as its role in medicine, is far from being understood univocally over the decades we have addressed, and actually, it undergoes multiple conceptualizations of its epistemological status. Keill’s specific stance is just a specific outcome of Newton’s understanding of the role of mathematics contrasting with axiomatic views and with the widespread idea that mathematics exemplifies to the highest degree a form of knowledge grounded on self-evidence and necessary deduction. Yet, as for the quantification of the living function, we can confirm that “it was a readily understandable historical development but not one, like Newton’s science itself, that marked a fundamental turning point on the road to modern science”.108 As is known, this model—despite its technical effectiveness—would be abandoned, or at least suspended for centuries, since medicine was yet to discover its proper subject matter, and it seemed clearer and clearer as the eighteenth century progressed that the subject matter of medicine could only be discovered by careful attention at the bedside rather than by mathematical or even experimental excursions. […] Physicians, it seems, had to aspire more to Bacon than to Newton if they wished to advance their art and their science.109

Nonetheless, within less than 150 years the triumphs and the successes of the application of mathematical physics to medicine would be described as the attempt of superbes mathématiciens to bring into medicine something which has a “very secondary use” and in general “to have done more harm than good”: Let us see where it [mathematics] has led Borelli, Malpighi, Kell [sic], Bernoulli, Bellini, Pitcarn [sic], Senac and so many others, and we will 108 Brown, ‘Medicine in the Shadow of the Principia’, 648. 109 Ibid.

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remain convinced that their contribution has been rather harmful or disastrous than useful or beneficial to medicine; but this shall not prevent mathematicians from repeating unceasingly that their science alone has the exclusive privilege of forming judgment, and of bestowing on our reason the first habit and the first folds of truth.110

110 Théophile-Charles-Emmanuel-Edouard Auber, Traité de philosophie médicale: ou, Exposition des vérités générales et fondamentales de la médecine (Paris: Baillière, 1839), 88–89.

The Pulse Watch and the Physician’s Senses: John Floyer on the Quantification of the Body Marco Storni

1

Introduction

Sphygmology, together with uroscopy, has been one of the main diagnostic techniques for centuries. This holds true not only of Western medicine, but also of non-Western traditions. In China, accounts of pulse diagnosis appeared as early as the Han dynasty (206 BC–220 AD), while in India the art of sensing the pulse was extremely popular as of the fifth century AD.1 In Greco-Roman antiquity, Galen wrote several treatises on the pulse which had a long-lasting influence on the European medical tradition.2 Galen stressed the importance of the arteries in the 1 See D. Evan Bedford, ‘The Ancient Art of Feeling the Pulse’, British Heart Journal, 13, 4 (1951), 423–437. 2 The first complete English edition of Galen’s treatises on the pulse has been published in 2023 under the title: Galen on the Pulses (Ian Johnston, and Niki Papavramidou, Galen on the Pulses. Medico-historical Analysis, Textual Tradition, Translation [Berlin-Boston: De Gruyter, 2023]).

This work was supported by the Swiss National Science Foundation (SNSF) as part of the research project Mesure du temps, chimie et cuisine: Formalisation des pratiques au XVII e et au XVIII e siècle (grant number 100011_184856).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_10

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phenomenon of the pulse, as motion (or “power”) was communicated from the heart to arteries, and through the arteries’ pores into the “outer skin”.3 Moreover, Galen classified several types of pulses which could be sensed with a finely trained touch, as well as possible alterations of the pulse, due to natural causes (season, place, temperament) or non-natural causes (gymnastics, cold baths, meals). Up to early modern times, sphygmology remained essentially qualitative, and did not involve any attempt at exact measurement. One interesting testimony to this fact is found in the iconography of medical practice. The Dutch Golden Age painter Jan Steen portrayed a physician visiting an old patient, whose critical health condition was underlined by a weeping man standing between the doctor and the patient (Fig. 1). The physician, elegantly dressed, examines the patient’s urine contained in a flask, while delicately sensing the old man’s wrist with the other hand. The same pattern was reproduced in coeval paintings: one might consider the work of another Dutch Golden Age painter, Matthijs Naiveu (1647– 1726), who represented the medical examination of a noblewoman, taking place in a richly decorated room (Fig. 2). Again, Naiveu’s medical practitioner holds in one hand the woman’s wrist to sense her pulse, and in the other hand a flask filled with her urine. Over the eighteenth century, however, the iconography of clinical practice underwent a change. Sphygmology was increasingly associated with a new technical device, the pocket watch, which contributed to introduce measurement into medical practice, and progressively became an attribute of the medical profession. An instance of this phenomenon is to be found in the famous engravings representing the experiments on respiration carried out between 1777 and 1790 by the French chemist Antoine-Laurent Lavoisier (1743–1794), and portrayed by his wife Marie Anne Paulze (1758–1836) (Fig. 3). In these experiments, Lavoisier isolates a subject (his collaborator Armand Séguin) and lets him breathe through a copper mask, which is connected to a device that controls the quantity and quality of the inspired and expired air. In the engravings, one can see Lavoisier standing and dictating M. Storni (B) University of Neuchâtel, Neuchâtel, Switzerland e-mail: [email protected] 3 See Michael Boylan, ‘Galen: On Blood, the Pulse, and the Arteries’, Journal of the History of Biology, 40 (2007), 207–230.

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the observations to his wife, who sits at the desk; among the experimental assistants, the Scottish physician Hugh Gillan is portrayed in the act of measuring the pulse with a pocket watch.4 The association between the pulse and the pocket watch became commonplace over the nineteenth century, when illustrations of medical visits often portray a physician holding a watch in one hand and the patient’s pulse in the other. A midnineteenth-century engraving by J. H. Barker features a physician taking the pulse of a young woman lying on the bed (Fig. 4). The doctor is focused on his pocket watch, with which he measures the patient’s pulse rate. The young woman’s mother is seated opposite the physician, looking concerned for her daughter’s health; a servant stands in the background, with a preparation in her hands. The penetration of the mechanical watch into medical practice displayed by the iconography finds confirmation in the increasing number of treatises published as of the mid-eighteenth century where the exact quantification of the pulse rate held a central place. The works of British and Irish physicians such as Bryan Robinson (A Treatise of the Animal Oeconomy, 1734), William Heberden (Remarks on the Pulse, 1768), William Falconer (Observations Respecting the Pulse, 1796), and Robert Graves (Clinical Lectures on the Practice of Medicine, fourth lecture, 1848) were in this respect emblematic.5 On the Continent, the quantification of the pulse was systematically practiced by prominent figures such as Jean Senac and Albrecht von Haller.6 It goes without saying that the pulse quantification through the mechanical clock encountered the resistance of a few medical schools. Vitalist physicians, such as those affiliated with the Faculty of Medicine at the University of Montpellier, criticized the excessive interest of modern physicians in pulse quantification, since this could be the prodrome of the reduction of human physiology to pure mechanism. A major figure of this school, Théophile

4 See Marco Storni, ‘Clocks and Timekeeping in Lavoisier’s Experiments on Animal Respiration. The Chemical Revolution, Its Material Culture and Taken-for-Granted Knowledge’, in Material Histories of Time: Objects and Practices, 14th–19th Centuries, ed. by G. Bernasconi and S. Thürigen (Berlin-Boston: De Gruyter 2020), 187–200. 5 See Gary L. Townsend, ‘Sir John Floyer (1649–1734) and His Study of Pulse and Respiration’, Journal of the History of Medicine and Allied Sciences, 22, 3 (1967), 286– 316. 6 See Werner F. Kümmel, ‘Der Puls und das Problem der Zeitmessung in der Geschichte der Medizin’, Medizinhistorisches Journal, 9, 1 (1974), 1–22.

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Fig. 1 Jan Steen (and school), A medical practitioner examining the urine and taking the pulse of an elderly man (Source Wellcome Collection, London. Attribution 4.0 International [CC BY 4.0])

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Fig. 2 Matthijs Naiveu, A physician feeling the pulse of a seated woman patient (Source Wellcome Collection, London. Attribution 4.0 International [CC BY 4.0])

de Bordeu, explained in his Recherches sur le pouls that pendulums and pocket watches could be useful in determining the pulse rate. However, other elements were to be considered in order to obtain a suitable knowledge of the pulse, namely whether it was “free, dilated, supple, soft […], intense, hard, dry, compressed […], salient, full, strong”.7 All these notions could not be derived from measuring instruments, but must be acquired “by experience, without any pocket watch, without any pendulum”.8 More generally, Bordeu suggested that medicine should adopt a

7 Théophile de Bordeu, Recherches sur le pouls, par rapport aux crises (Paris: De Bure, 1756), 17. 8 Bordeu, Recherches sur le pouls, 13.

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Fig. 3 Lavoisier in his laboratory conducting an experiment on the respiration of a man at work (Source Wellcome Collection, London. Attribution 4.0 International [CC BY 4.0])

“holistic” approach, namely that it should examine the body as a relational system of living parts, in sympathetic cooperation.9 Still, in the late nineteenth century, several physicians considered it vulgar to measure the pulse rate with a mechanical watch, as part of a general skepticism toward the introduction of quantification in medicine. As Hermann von Helmholtz recalled in the discourse Das Denken in der Medizin (1877), although at the beginning of the century “counting [the pulse] with the second watch was already common, the old gentlemen considered it to be a method of not very good taste,” since it “disparaged the patient, who is a human being, degrading them to a machine”.10 Alongside the mechanical watch, other technical instruments generated

9 Charles T. Wolfe, La philosophie de la biologie avant la biologie. Une histoire du vitalisme (Paris: Classiques Garnier, 2019), 225–262. 10 Hermann von Helmholtz, Vorträge und Reden (Braunschweig: Friedrich Vieweg und Sohn, 1896), 2, 179.

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Fig. 4 J. H. Barker, A physician taking the pulse of a young woman, her concerned mother is seated opposite him, with a servant in the background (Source Wellcome Collection, London. Attribution 4.0 International [CC BY 4.0])

suspicion, such as the ophthalmoscope, which a practitioner in conversation with Helmholtz declared “useful for doctors with bad eyes, while he had very good eyes and did not need it”.11 Between the eighteenth and the nineteenth century, the practice of measuring the pulse with a mechanical watch thus became the symbol of the search for accuracy and objectivity in medicine, embraced by physicians who looked up to the hard sciences, and rejected by others in the name of anti-reductionism and of the primacy of sensory experience. In

11 Ibid.

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the late seventeenth and early eighteenth centuries, however, this polarization was not yet fully established, and the two opposite approaches—the “mechanist” and the “holistic”—could be combined in original ways. An emblematic instance of a hybrid system, which fostered the emergence of a mechanist approach to the pulse, while remaining close to the Galenic paradigm and a qualitative study of pulse, was that of the English physician John Floyer (1649–1734), to which this chapter is dedicated. Floyer was among the first physicians to support the methodical introduction of the mechanical watch into medical practice, and to provide a mechanist framework for this practice. Yet Floyer did not embrace a mechanist reduction of physiology, and often stuck to traditional views, while emphasizing the role of the senses and direct experience as more reliable than philosophical theories in guiding medical practice. The study of Floyer’s views will provide new insights to assess the relationship between the early modern practitioner’s body and the technological apparatus, which is rarely discussed in reference to medical work. Floyer considered technology, notably the pulse watch, as an extension of human sensibility, which could correct the vagueness and inaccuracy of perceptive data, and contributed to codify the practical knowledge of medicine.12 Moreover, the analysis of Floyer’s eclectic natural philosophy will make it possible to reflect upon the frailty of doctrinal boundaries when one’s main concern was of a practical nature, such as patient care. Practitioners like Floyer hybridized different if not incompatible theories, insofar as it was functional to make sense of the phenomena encountered in the practice. There was no attachment to the esprit de système, namely the logic for which the acceptance of certain ideas dogmatically implied the acceptance of the whole system to which such ideas belonged.13

12 On the role of technological innovation in the codification of practical knowledge, see Matteo Valleriani, ‘The Epistemology of Practical Knowledge’, The Structures of Practical Knowledge, ed. by M. Valleriani (Cham: Springer, 2017), 1–19: 3–14; and Marco Storni, ‘Denis Papin’s Digester and Its Eighteenth-Century European Circulation’, The British Journal for the History of Science, 54 (2021), 443–463, here 444–446. 13 The notion of “esprit de système” as synonymous with formalism and dogmatism is typical of the French Enlightenment authors, who opposed it to the more positive notion of “esprit systématique” (Claude Grignon, ‘L’esprit scientifique et l’esprit de système’, Revue européenne des sciences sociales, 46, 3 (2008), 11–33, here 14–17; Élodie Cassan,

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The Pulse Watch and the Mechanist View

Born in Staffordshire, Floyer studied at Queen’s College, Oxford, between 1668 and 1680. In 1680, he returned to Staffordshire and settled in Lichfield, where he spent the rest of his life. Besides his professional activity as a physician, Floyer had a successful career in politics, which eventually led to a knighthood (1684). Throughout his life, Floyer wrote on a variety of medical topics, including asthma, cold bathing, and gerontology. Among his major works was the treatise The Physician’s Pulse-Watch, published in two volumes between 1707 and 1710.14 Floyer aimed to improve the ancient technique of pulse measurement, building on the preparatory studies accomplished by sixteenth and seventeenthcentury physicians, particularly the Padua professor Santorio Santorio (1561–1636).15 Santorio invented a device, the pulsilogium, to measure the pulse by using the results of Galileo Galilei’s studies on the pendulum. The pulsilogium required the experimenter to change the pendulum’s length until its oscillation was synchronized with the patient’s pulse. The patient’s pulse corresponded then to a unit of length, obtained by measuring the pendulum cord with a ruler.16 Further versions of this tool were realized by the Jesuit polymath Atanasius Kircher and the Bohemian physician Jan Marek Marci; the latter also conceived a portable version of the pulsilogium, which was described in his 1639 treatise De proportione motus.17 ‘Esprit systématique et esprit de système’, Labyrinthe, 34, 1 (2010), 11–14; Sophie Marchand and Élise Pavy-Guilbert, ‘Introduction’, in L’Esprit de système au XVIII e siècle, ed. by S. Marchand and É. Pavy-Guilbert (Paris: Hermann, 2017, 5–30). 14 In all quotations from Floyer’s texts, I have respected the original spelling. 15 John Floyer, The Physician’s Pulse-Watch, vol. 1 (London: Printed for Samuel Smith

and Benjamin Walford 1707); and John Floyer, The Physician’s Pulse-Watch, vol. 2 (London: Printed for J. Nicholson, 1710). Floyer owned a copy of Santorio’s 1614 Statica medicina (in the 1701 edition), and was inspired by Santorio’s “weighing chair” as he kept track of his weight variations between 1699 and 1703 (Mark S. Jenner, ‘Tasting Lichfield, Touching China: Sir John Floyer’s Senses’, The Historical Journal, 53, 3 [2010], 647–670: 661–662). 16 Fabrizio Bigotti, David Taylor, and Joanne Welsman, ‘Recreating the Pulsilogium of Santorio: Outlines for a Historically-Engaged Endeavour’, Bulletin of the Scientific Instrument Society, 133 (2017), 30–35. 17 Fabrizio Bigotti and David Taylor, ‘The Pulsilogium of Santorio: New Light on Technology and Measurement in Early Modern Medicine’, Societate si politica, 11, 2 (2017), 53–113.

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In approaching the issue of pulse measurement, Floyer designed a technical instrument to help this practice, trying to make it easier to use and more accurate than Santorio’s. In collaboration with a renowned watchmaker, the Englishman Samuel Watson, Floyer elaborated a special model of a pocket watch, two exemplars of which are still extant in collections. The one preserved at the International Museum of Horology in La Chaux-de-Fonds, Switzerland (Fig. 5), presents a quadrant with only one hand, indicating both the minutes (marked on the outside, in Arabic numerals) and the hours (marked on the inside, in Roman numerals). Its period is of 6 hours. Interestingly, the watch also presents a smaller quadrant with a hand that runs 60 seconds, which is an extremely rare feature for a watch of the early eighteenth century. Moreover, Watson’s watch is endowed with a lever to stop the mechanism, and with a button to open the case of the watch with only one hand.18 These technical features made it possible to manipulate the watch with only one hand, while the other hand was free to touch the patient’s pulse.19 Watson’s innovative pulse watch, however, could not be trusted blindly because technical problems sometimes occurred: as Floyer noted, “since the watch does run unequally, rather too fast” he had to regulate it using a portable hourglass.20 The core of Floyer’s medical practice consisted in finding a method to “know the natural pulse” of a patient, namely the pulse rate of any subject in a state of perfect health. The knowledge of the natural pulse would allow us to define disease in terms of “excesses and defects” of pulse rate, and draw from these data “indications for the use of diet and medicines” to bring the pulse rate back to normal.21 How could the natural pulse be determined? “The method […] – Floyer explained – is to observe what number of pulses every one has in his perfect health, by observing

18 Jean-Michel Piguet, ‘Une curieuse montre anglaise destinée à mesurer le pouls (Pulse-Watch)’, Chronométrophilia, 62 (2007), 95–102. Another pocket watch made by Watson, with technical features similar to those of the watch preserved in La Chaux-deFonds, was acquired by Theodore P. Camerer Cuss for his collection, and is described in the Camerer Cuss Book of Antique Watches (Denis Gibbs, ‘The Physician’s Pulse Watch’, Medical History, 15, 2 (1971), 187–190). 19 Gianenrico Bernasconi, ‘Pour une archéologie des pratiques’, Socio-anthropologie, 40 (2019), 247–262: 251–253. 20 Floyer, The Physician’s Pulse-Watch, 1, The Preface. 21 Ibid., 1, 13.

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Fig. 5 Musée International d’Horlogerie, La Chaux-de-Fonds, INV I-1183. By kind permission of the head of the Museum

the morning-pulses, before eating, exercise, or other external accidents disturb it”.22 Measurements should be constantly repeated, day after day, and then the average number should be calculated. Floyer presented the example of the work he had done to determine his own natural pulse: “I find my pulse […] run in one minute this latitude from 66 to 86 in perfect health; I therefore take the middle number for my most moderate and healthful pulse, which is 76”.23 The operation was simple enough for anybody to measure their own natural pulse, to help the physician’s work (see below, Sect. 4). Once found, any significant alteration of the natural pulse represented a sign of disease, or of an unhealthy humoral constitution.24 The task of the physician was to correct the unhealthy

22 Ibid., 1, 148. 23 Ibid. 24 In the Galenic tradition, bodily fluids or “humors”—blood, phlegm, yellow bile and black bile—were the basic components of the human body, combined in various ways to yield different “temperaments” (Jim R. Hankinson, ‘Humours and Humoral Theory’, in

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pulse and bring the pulse rate back to its natural state. The key principle was that a quick pulse must be slowed down with a cold diet or cold remedies (food, baths, etc.), and a slow pulse must be accelerated with a hot diet or hot remedies. As Floyer put it, “the blood and spirits are either too much rarifi’d and mov’d, or too much condens’d and slow in their motion: for the first we prescribe contraries, such is [sic] the cold regimen; and for condens’d humours, and obstructed motion, the hot regimen”.25 Floyer presented his work as most innovative, as it provided a “rule or measure” much needed in medicine to formulate diagnoses and therapies upon “certain and obvious” signs.26 Through his method, “all fine hypotheses will be excluded from practice, and a more certain and sensible foundation will be laid for it”: the art of medicine, as Floyer argued, once based merely on “conjecture,” was now made more accurate and efficient “by my measure”.27 The accuracy of quantification was also enhanced by the contextual use of other instruments, especially a thermometer and a barometer, which helped rationalize the impact of climatic factors on medical practice.28 The reliability of Floyer’s approach was also grounded on the systematic nature of its measurements. The first volume of The Physician’s Pulse-Watch features several tables where Floyer displays the results of his research on pulse rates among people of different age and sex, in different seasons and in different health conditions. He notably conducted research on several patients at the Lichfield hospital.29 On a theoretical level, Floyer often presented his medical approach in mechanist terms. In the preface, for instance, the task of the physician was described as follows: “The physician’s business is to regulate the circulation, and to keep it in a moderate degree, suppose once in three minutes: if it run oftner or slower, our mechanism is out of order”.30 Here, Floyer

The Routledge History of Disease, ed. by Mark Jackson (London-New York: Routledge, 2016), 21–37. 25 Floyer, The Physician’s Pulse-Watch, 1, The Preface. 26 Ibid. 27 Ibid. 28 Ibid., 1, 317. 29 Ibid., 1, 185, 308–310; see also Denis Gibbs, ‘The Almshouses of Lichfield: Cradles

of Pulse-Timing’, Journal of Medical Biography, 2 (1994), 89–93. 30 Ibid., 1, The Preface.

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described the human body as a machine, a metaphor that recurred in other of his works. In the 1702 treatise Psychrolousia: Or, The History of Cold Bathing, Floyer adopted the same mechanical vocabulary while discussing impotence: When all other remedies have fail’d, nay, and after some years standing, (cry mercy, not standing, I mean) when the case has been old, and no hopes of cure ever expected where the cremaster’s, the muscles of their testimonies, has been weak, and the clock-weights of their hearts sunk and hung low, etc. there I say, in more than twenty such cases the cold water […] has wound up their watch, and set their pendulum in statu quo, etc.31

As a matter of fact, the pocket watch was for Floyer not only a technical device expected to revolutionize medical practice, but also a metaphor for the human body, whose diseases were seen as mechanical issues that could be quantified and consequently fixed as easily as resetting a clock. In this sense, Floyer defined the therapeutic method based on the pulse watch as “a new mechanical method for curing the diseases”.32 Therapies could indeed be established on precise information, such that “the effects of medicines [were] certain and sensible, […] and we shall not hereafter impute cures to chance”.33 Floyer’s quantifying approach to human physiology was to inspire the following proponents of the “mechanist approach,” as emerges clearly from the polemical statements of eighteenth-century anti-mechanists. In the article “Pouls” of the Encyclopédie, the Montpellier physician JeanJoseph Ménuret de Chambaud criticized Friedrich Hoffmann’s mechanist theory of the pulse, attributing to him positions almost identical with those one could find in Floyer’s work: Doctrine of the mechanists on the pulse […]. Since the pulse is the most immediate effect of blood circulation, it must also be its most distinctive sign and indicate all its variations. The pulse, therefore, must necessarily become the most universal and clear sign of any trouble of the animal

31 John Floyer, Psychrolousia: Or, the History of Cold Bathing (London: Printed for Samuel Smith and Benjamin Walford, 1702), 278. 32 Floyer, The Physician’s Pulse-Watch, 1, 188. 33 Ibid., 1, 195.

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economy. As Friedrich Hoffmann claims, along with all the other mechanists or partisans of circulation [circulateurs ], it is unquestionable that on the circulation of blood “depend life and health. Circulation governs the human machine: one might consider it as the good nature and provident mother which preserves health and cures diseases. Therefore, the more the pulse is moderate and regular, the more nature tends directly and victoriously to its end; the more the pulse deviates from this perfect state, the weaker the body is, the more one should worry that it succumbs to the obstacles that oppress it. The pulse does not only express the trouble or force of the whole body, but also the constitution and nature of blood, and the state of secretions; it is like a pendulum, whose even and uniform motion is clear evidence of the good state of the clock of which it is part […]”.34

As a matter of fact, Floyer and Hoffmann agreed on the crucial role of pulse measurement for assessing the health condition of a subject, and both employed the metaphor of the clock to describe human physiology.35 Floyer, however, despite the adoption of mechanist concepts and of a mechanist vocabulary, did not aim to build a full-fledged system of iatromechanics. Rather, he often insisted on the limits of the mechanist view. On the one hand, he claimed that traditional—both Western and non-Western—medicine was not obsolete, but rather complementary to the modern medical approach. On the other hand, he underscored the primacy of sensory experience over philosophical arguments and remained skeptical toward abstract reasoning not rooted in clinical practice.

3

Floyer on the Limits of the Mechanist View

Let us first consider Floyer’s relationship with traditional medicine. In various passages of The Physician’s Pulse-Watch, Floyer relied on the Galenic theory of humors to account for altered health conditions. While the measurement of pulse rate remained the main diagnostic method, the 34 Jean-Joseph Ménuret de Chambaud, ‘Pouls’, in Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, ed. by D. Diderot and J. Le Rond d’Alembert (Neuchâtel: Samuel Faulche, 1765), 13, 205b–240b: 217–218. 35 For Hoffmann’s use of the metaphor of the clock, see Johann Deodatus Blumentrost’s doctoral dissertation Dissertatio inauguralis pulsuum theoriam et praxin examinat, supervised—and in fact written—by Hoffmann himself (Friedrich Hoffmann, Dissertatio inauguralis pulsuum theoriam et praxin examinat [Halle: Christoph Andreas Zeitler, 1714], 17–18).

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altered numbers of the pulse could in fact be the sign of many different diseases. The correct diagnosis could only be formulated by considering the alterations in the balance between the humors composing the patient’s body. Floyer’s medical philosophy, therefore, was not strictly mechanist, but rather eclectic, as it mixed a quantitative and a qualitative approach: “According to these several degrees of choler and phlegm, I have noted such degrees of numbers as I found most frequent in several constitutions; but this adjusting the numbers of the pulse to the several qualities of our humours, perhaps is no less difficult than useful”.36 Alongside the Greco-Roman tradition, Floyer made several references to Chinese medicine, which he considered superior to Western medicine in many respects. Most notably, the Chinese gave centrality to the pulse not only in the detection of diseases, but also in the choice of an appropriate therapy: “The Greeks used their ars Σϕυγμικη´ [sphigmik¯e] for prognostications chiefly, and also a part of the semiotica; but the Chinese also have made that a part of their therapeutics, as well as of the other; for from the pulse they take their indications for cure, in which they excell’d the Greeks”.37 By his own account, Floyer was deeply inspired by the Chinese tradition since it considered the practice of sensing the pulse as the most important medical technique: “I will first prove that they [the Chinese] have a real great knowledge in that practice [of feeling the pulse], and that they may well build a practice of physick on their art of feeling of the pulse”.38 Floyer’s eclecticism, therefore, did not merely consist in the combination of the Galenic and the mechanist approaches, but was also open to non-Western traditions, which were considered just as worthy as the Western: “I may vindicate the Chinese way of practice, and find as much natural philosophy in their writings, as was in Hippocrates in Plato’s and Aristotle’s time, and their anatomy was not more exact than the Chinese”.39 While for Floyer the acceptance of the mechanist view did not imply the dismissal of alternative medical traditions, there was another reason that led him to insist on the limits of iatromechanics. Floyer was in fact skeptical about natural-philosophical discourses of a speculative kind, not

36 Floyer, The Physician’s Pulse-Watch, 1, 68–69; my emphasis. 37 Ibid., 1, The Preface. 38 Ibid.,1, 227. 39 Ibid., 1, 231–232.

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grounded in experience. The chief aim of his work was to formulate useful indications to improve clinical practice. This explains Floyer’s statement that the mechanical method based on pulse measurement could be adopted even “without knowing the mechanism of it [the pulse]”: ’Tis not necessary for us to understand the motions of the particles in the blood, nor the texture of the viscera and organs; ’tis enough that I know by a hot regimen and hot tastes I can raise deficient pulses, and by a cold regimen and medicines of a cool taste, I can depress and sink the number of exceeding pulses.40

Leaning too much into natural-philosophical reasonings, far from the actual medical work, could dangerously lead to building imaginary systems, inconsistent with reality. In the Directions by Sir John Floyer for the Education of His Grandson as a Physician, a manuscript to be dated around 1714–1720, Floyer discussed this point in detail. As he argued in the section on “the difficulty of applying mathematicall principles to animall bodyes”: I doe not question the mathematicall principles or demonstrations, but cannot believe they are truly applied to the bodyes of animals […]; thus wee may prove noe animal has the sense of feeleing: noe demonstration against the evidence of our senses can bee true.41

Floyer stressed that if one reasoned a priori any proposition could be demonstrated, even those in patent contradiction with the most evident facts of experience. He saw a prominent example of such absurd a priori reasoning in the claim formulated by several physicians that blood particles attract each other without mutual contact: The notion of attraction of particles of our blood is onely a conjecture, not perceptible by any sense not agreable to phylosophy that one particle can act upon another without a contact: but its more agreable to be assert that a long circulation will project particles of different gravityes to different glands, which are placed att different distances, and those who have the

40 Ibid., 1, The Preface. 41 Queen’s College, Oxford, Ms. 559, f. 47r.

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same weight and viscidity or tonicity in health will meet all the same glands.42

This passage criticizes the intellectual approach of the so-called “medical Newtonians,” such as Archibald Pitcairne and James Keill.43 In his Account of Animal Secretion (1708), Keill contended that “this power, by which the particles of the blood attract one another, is the same with that which is the cause of the cohesion of the parts of matter”.44 The whole organism of animals could thus “depend upon this attractive power,” which had analogies with “that other attractive principle […] first discovered by the incomparable Sir Isaac Newton”.45 Floyer considered claims such as Keill’s to be purely speculative, insofar as not grounded on any available empirical evidence. In opposition to the physiology of attraction, Floyer stuck to the traditional view—also appropriated by mechanist philosophers—that body–body interactions solely occur by means of contact action. Further on in the same manuscript, Floyer insisted again on the hiatus between theoretical and practical knowledge, with reference this time to the mechanist view: [H]ee that nicely studyes the laws of motion in mechanics and hydrostatics and applyes them to human bodyes may reason like a phylosopher very well upon the animal oeconomy but knows nothing more than the common anatomist of the morbific causes of diseases, and their cure.46

42 Queen’s College, Oxford, Ms. 559, f. 47v. 43 See Charles T. Wolfe, ‘On the Role of Newtonian Analogies in Eighteenth-Century

Life Science: Vitalism and Provisionally Inexplicable Explicative Devices’, in Newton and Empiricism, ed. by Z. Biener and E. Schliesser (Oxford and New York: Oxford University Press, 2014), 223–261. According to the (unfinished) catalogue of Floyer’s library completed by Denis Gibbs in 2006, Floyer had a copy of Pitcairne’s Dissertationes medicae (1701). I am thankful to Yijie Huang for providing me with a copy of the Gibbs catalogue. 44 James Keill, An Account of Animal Secretion, the Quantity of Blood in the Humane Body, and Muscular Motion (London: George Strahan, 1708), 7. 45 Keill, An Account of Animal Secretion, 8; see also Anita Guerrini, ‘James Keill, George Cheyne, and Newtonian physiology, 1690–1740’, Journal of the History of Biology, 18 (1985), 247–266. 46 Queen’s College, Oxford, Ms. 559, f. 48r.

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Mechanical models are fruitful heuristic methods in natural philosophy, but they do tell little or nothing on how to recognize a disease and treat it conveniently. In sum, Floyer did by no means reject the validity of mechanical models—and more generally of speculative knowledge— as such, but stressed that they should be subordinated to the evidence derived from the senses. The primacy of sensory data over abstract thinking was a central theme of Floyer’s whole work, starting from his first treatise, Pharmako-basanos: Or, the Touch-Stone of Medicines (1687–1690). Here, Floyer described taste and smell as the best guides to medical practice.47 If medicine was to be defended “from the common scandal of being conjectural” (Floyer 1687, The Epistle Dedicatory), therapies needed to be elaborated “by describing the tastes and odors of medicines, and also of animal humours”.48 Floyer’s project was to classify remedies and bodily constitutions based on their sensible qualities—the taste and smell of medicines (plants, minerals) and those of bodily secretions—to then correct unhealthy states of the body with a remedy of a contrary quality. This method could lead to the “true fundamental rules of physick, built on the testimony of our senses, and not on the whims of chymists, or the fanaticisms of occult qualities”.49 The notions of “Aristotle’s philosophy,” and the discoveries made by chemists such as “the learn’d Mr. Boyl” could still be useful to understand the principles of medicine; however, the “chief business of a physician” was not to make philosophical distinctions but “to chuse, and apply tastes”.50 While addressing the readers of The Physician’s Pulse-Watch, Floyer presented this treatise in strong continuity with the Pharmako-basanos. The Pulse-Watch could indeed be considered as a work on the role of touch in medical practice: I have formerly shewn the usefulness of tasting and smelling for discerning the nature of animal humours, and the qualities of our medicines which we

47 See Jenner, ‘Tasting Lichfield, Touching China: Sir John Floyer’s Senses’. 48 John Floyer, Pharmako-basanos: Or, the Touch-Stone of Medicines, vol. 1 (London:

Printed for Michael Johnson, 1687), The Epistle Dedicatory. 49 Ibid. 50 Ibid., 1, To the Reader.

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use in curing of them: but in these papers my design is to discover what advantages physicians may have by a right use of the sense of feeling.51

In Floyer’s view, a good physician needed to develop a fine-grained sensibility, since medicine was first and foremost an activity performed through the body.52 The physicians had to be trained to identify diseases and therapies by using the natural faculties given to them by nature, which were more reliable than any formal education one could acquire through lectures and books. In this sense, medical practice could be less improved by developing one’s erudition than by exercising one’s own body, and by confronting one’s own impressions with those of other people, including patients themselves. As Floyer wrote in the Pharmako-basanos: I have not wholly trusted to my own taste, in the description of our country herbs, but have consulted the tastes of all sorts of persons; and for that am oblig’d to divers divines, apothecaries, chyrurgeons, gentlewomen, and young persons, who have been my patients; whose judgments, as Galen says, is uncorrupt and unprejudic’d. I must needs acknowledge, that the palats of women are more critical than men’s, who generally dull it by intemperance and tobacco.53

Floyer’s work presents the reader with a tension between the insistence on sensory experience, which implied the proximity to a qualitative paradigm and traditional medicine, and the suggestion to base clinical work on the mechanical watch, which pushed Floyer toward a quantifying approach and a mechanist view. As I have claimed above, the reason why Floyer refused to fully adhere to a mechanist approach was his skepticism about philosophical speculations, which could by no means replace knowledge directly derived from the body. However, it still needs to be clarified why, if the medical practice was primarily a bodily exercise based on the physician’s sensibility, one must introduce a mechanical device, external 51 Floyer, The Physician’s Pulse-Watch, 1, The Preface. 52 On the importance of bodily knowledge in early modern science, see Pamela H.

Smith, The Body of the Artisan: Art and Experience in the Scientific Revolution (ChicagoLondon: The University of Chicago Press, 2004); and Lissa Roberts, Simon Schaffer, and Peter Dear (eds.), The Mindful Hand: Inquiry and Invention from the Late Renaissance to Early Industrialisation (Amsterdam: Royal Netherlands Academy of Arts and Sciences, 2007). 53 Floyer, Pharmako-basanos, To the Reader.

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to the practitioner’s body, into medical practice. Why could one not simply stick to the traditional qualitative paradigm, and ground medicine on unmediated sensory experience? Why was it necessary to use a pulse watch?

4

The Necessity of the Pulse Watch

Despite the primacy of evidence derived from the senses in the understanding of medical issues, there were several compelling reasons for introducing the pulse watch into practice. The first was the accuracy that the instrument could afford. Whereas smelling and tasting could not be improved by any technical tool, touching could in fact be made more accurate with the help of a watch. One should not forget that, before creating the new pulse watch, Floyer was already using other timekeeping devices to help his practice, namely “common watches, and pendulum clocks,” and when he started to use Watson’s watch he did not stop carrying with him a “half minute [hour]glass” and also using a “minute [hour]glass, which I always kept at home as my standard”.54 Despite some technical problems with the pulse watch that made it impossible to always trust it blindly (see above, Sect. 2), the method based on the employment of mechanical timepieces could in principle lay “a more certain and sensible foundation”55 for medical practice, contributing to clarifying the directions provided by the medical tradition through quantification: “All the old method of practice and rules for cure by contraries, will be comprehended under these two general indications of stopping the pulse or circulation when they run too fast, or promoting them when they move too slow”.56 Accuracy, however, was not the only (nor the main) reason why, in Floyer’s opinion, the introduction of the pulse watch was necessary for the improvement of medicine. The second reason had to do with the difficulty of measuring the pulse without the help of a technical tool: pulse measurement, as Floyer put it, “requires a great nicety of feeling”.57 The difficulty of this operation could easily lead to errors, which would

54 Floyer, The Physician’s Pulse-Watch, 1, The Preface. 55 Ibid. 56 Ibid. 57 Ibid., 1, 153.

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ultimately jeopardize the whole diagnostic process. The introduction of the pulse watch made pulse measurement much quicker and easier: The art of feeling the pulse, which I have propos’d for distinction sake, I will call mechanical; ’tis short, easie, and more certain than the Galenical or Chinese art, because it requires no more than counting of the pulse, and observing the time by the pulse-watch; […] and he who knows and can best regulate the excesses or defects in the pulse, and circulation (as I conjecture) in the learned ages which are to come, will be esteemed the best physician.58

The importance of this simplification of the physician’s work needs to be understood in the cultural and social context to which Floyer belonged. Floyer considered himself as a “country physician” and conceived his work not only as a contribution to the general advancement of medical science, but also as a useful textbook for ordinary practitioners, including those who worked in a provincial setting. The interest in the education of country practitioners is a concern that characterized the whole of Floyer’s work. One might consider the unpublished materials Floyer left, that are now preserved at Queen’s College, Oxford. Among these, one finds a series of Directions for the Education of His Grandson as a Physician 59 — which were never of use due to the early death of the boy—the draft of a treatise entitled Advise to a Young Student in Physicke,60 as well as several papers in which Floyer described and classified medical remedies “for the use of countrey physicians and apothecairyes”.61 The insistence on the pocket watch is also to be read in light of the attempt to make medical work within everyone’s reach. By the early eighteenth century, the pocket watch was widespread in European society, as clarified by research conducted on early modern probate inventories in England and France.62 Mechanical timekeepers became popular

58 Ibid., 1, 425. 59 Queen’s College, Oxford, Ms. 559. 60 Queen’s College, Oxford, Ms. 558, partially edited in Denis Gibbs, Philip K.

Wilson, ‘Advice to a Young Physician’ by Sir John Floyer MD (1649–1734) of Lichfield in Staffordshire (York: The Ebor Press, 2007). 61 Queen’s College, Oxford, Ms. 562, Ms. 563 and Ms. 564/1–2. 62 Paul Glennie and Nigel Thrift, Shaping the Day: A History of Timekeeping in England

and Wales 1300–1800 (Oxford-New York: Oxford University Press, 2009); Marie-Agnès

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even beyond the scientific elites and the upper social classes, and were widespread among the members of the middle class. Watches came to circulate widely as they grew more affordable and more portable in size. The large diffusion of timepieces also contributed to their becoming fashionable accessories, employed not only to measure the duration of everyday life activities but also to display the social status of their owners.63 The watch was therefore halfway between scientific practice and everyday routine: it was the subject of various scientific inquiries, and was used for specific technical operations (such as the determination of longitude), but was also an object of consumption, familiar to everybody, used to measure the duration of quotidian activities or even just displayed as a status symbol.64 The popularization of the pocket watch that took place at the turn of the eighteenth century was a counterpart to the update of medical practice which Floyer envisaged. In his view, medical practitioners had to become “artisans of healthcare,” with a modest theoretical background but capable of using their senses as well as simple measuring instruments, notably the pulse watch. At the same time, patients themselves were to collaborate with physicians, thus playing an active part in the diagnostic process: It is requisite that every intelligent patient should thus try his pulse in a morning in his health, that he may inform his physician what number of pulses he has in a perfect health, by which a physician may judge of his natural constitution; and the physician may know how far the diseas’d pulse receeds from the natural numbers; […] and all this the patient himself may discern by the pulse; and then he will intirely acquiesce in his physician’s judgment and method, when he hears that both correspond with the pulse; and the patient will have this father [sic] satisfaction, to try by his pulse how the medicine and method alter his pulse toward its natural state, by its returning to its natural numbers […].65

Dequidt, Horlogers des Lumières. Temps et société à Paris au XVIII e siècle (Paris: Éditions du comité des travaux historiques et scientifiques, 2014). 63 John Styles, The Dress of the People: Everyday Fashion in Eighteenth-Century England (New Haven-London: Yale University Press, 2007), 97–107. 64 Storni, ‘Clocks and Timekeeping in Lavoisier’s Experiments on Animal Respiration’, 194–196. 65 Floyer, The Physician’s Pulse-Watch, 1, 149–150.

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The method based on the pulse watch was easy enough for any “intelligent patient” to adopt, that which allowed anyone to observe the effectiveness of Floyer’s method. The advice of a professional physician, however, could not be eluded as the average patient did not possess the required knowledge to establish correspondences between altered pulse rates and their causes (be they humoral, environmental, etc.).

5

Conclusion

In this chapter, I have shown that the late eighteenth-century polarization of the “mechanist” and “holistic” approaches to the practice of measuring the pulse did not yet exist earlier in the century, at the moment when the mechanical watch was introduced into medicine. I have focused on the figure of John Floyer, one of the first physicians to suggest the systematic employment of the pocket watch in medical practice. Floyer’s work challenged the abovementioned polarization as it borrowed key concepts from the modern mechanist tradition, but did not ipso facto abandon a qualitative approach, inspired by Galen. I have argued that Floyer was original as he combined the ancient and the modern approaches in an eclectic fashion. Floyer’s originality, however, also lay in arguing for the primacy of unmediated sensory evidence as the touchstone of any scientific truth, while pleading for the introduction of measuring technologies into medicine—notably the pulse watch—to ease diagnoses and enhance the effectiveness of therapies. The tensions characterizing Floyer’s non-orthodox approach to medical practice are also to be understood in the cultural and social context where he belonged. As a Staffordshire country physician, Floyer’s main interest was not to intervene in scholarly disputes, but rather to “preserve the lives of […] country-men”66 as well as to instruct other physicians working in the same environment. Ultimately, the physician was for Floyer an “artisan of healthcare,” well educated but not too concerned with natural-philosophical distinctions, who relied massively on evidence derived from their senses, and always had their pulse watch at hand.

66 Ibid., 1, 187.

Against the Quantification of the Living: Hegel’s Critique of Romantic Naturphilosophie in the Phenomenology of Spirit Gaetano Basileo

In the chapter in the Phenomenology of Spirit on Observing Reason, Georg Wilhelm Friedrich Hegel (1770–1831) provides a historically and systematically remarkable analysis of the conceptual structure of the living organism and the relationship between individuality and its physical body. Hegel does not expound his theory dogmatically, but rather compares it to those of the science and Naturphilosophie of his time, both of which latter were characterized by the attempt to express the essential characteristics of the organic (the living world) by means of quantitative correlations. In this paper, I will try to highlight the key elements of Hegel’s critiques of these approaches and to show why Hegel believes that the arguments and explanatory strategies they develop are non-informative and incapable of articulating necessary laws.

G. Basileo (B) University of L’Aquila, L’Aquila, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_11

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In the first part, I outline the Hegelian conception of the organic and I show why he claims that only dialectic can adequately express the relationship between the “inner” and “outer” that characterizes the living organism, namely the immanence of purposiveness to the organism’s process of self-realization. The second part highlights the general methodological and ontological assumptions that define what Hegel calls “Observing Reason.”1 With this in view, I will then try to show the kind of conceptual difficulties that, according to Hegel, belong to every attempt to express the connection between the conceptual interior of the organism and its external structure by means of quantitative laws. It emerges that Observing Reason undergoes a necessary evolution when it faces these difficulties and this results in the cognitive position typical of the romantic Naturphilosohie. In the third part, I will consider the main features of Hegel’s confrontation with romantic Naturphilosophie. It is necessary to consider the following points in this context: (a) the attempts of thencontemporary natural philosophers to express the connection between the conceptual interior of the organism and its external configuration (Gestaltung ) by means of quantitative laws; (b) Franz Joseph Gall (1758–1828)’s attempt in his phrenology to deduce the specific mental characteristics of the individual subject from the measurable characteristics of the skull; and (c) the Schelling-inspired project of a Naturphilosophie that reconstructs the natural history of the Earth, itself understood as a single living organism.

1

Hegel’s Conception of the Living Organism

The entire development of Hegelian thought is characterized by its interest in the problem of the living organism. This is motivated by the fact that for Hegel the organism shows in its very existence that special unity of subjectivity and objectivity, thought and being that speculative philosophy must produce as the crowning achievement of its systematic 1 Observing Reason is thematized in Georg W. F. Hegel, The Phenomenology of Spirit, trans. Terry Pinkard (Cambridge, 2018), 142–203. In the following, Hegel’s Phenomenology of Spirit is abbreviated as “PhS”. For a thorough introduction to this chapter of Phenomenology, see Michael Quante, ‘Die Vernunft unvernünftig aufgefasst. Hegels Kritik der beobachtenden Vernunft’, in Hegels Phänomenologie des Geistes: Ein kooperativer Kommentar zu einem Schlüsselwerk der Moderne, ed. Klaus Vieweg and Wolfgang Welsch (Frankfurt am Main, 2008), 325–349.

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development. Life, the mark of the organism for Hegel, is conceived as a peculiar logical structure which overcomes the originally Platonic problem of the relationship between logical form and concrete content and reconciles the metaphysical opposition between thought and being.2 While traditional logic opposes concept and being, form and content, Hegel shows with reference to the organic that there is rather a dialectical relationship between these determinations. And because of this dialectical relationship, their differences must be thought of as at the same time a unity and their unity as a difference. According to Hegel, the logical structure of the living takes thus the form of a “pure flux” of identity and difference, that is, the form of an immanent nexus of mutually opposed determinations.3 This immanent nexus, however, does not replace the opposition of the determinations with the idea of their immediate unity—for it would then be impossible to preserve the moment of their logical difference—but rather with the idea of their procedural identity. According to Hegel, this procedural identity is the result of the Aufhebung-process of difference and at the same time its origin. When conceived in this way, the structure of the organism turns out to be the movement of its “estrangement” (Entzweiung ) into shapes and groupings and at the same time the “dissolution of this estrangement” or, as Hegel describes it, the movement of “the whole developing itself, then dissolving its development, and, in this movement, being the simple self-sustaining whole.”4 The category of “inner purposiveness” is used to clarify the structure of the organic. Hegel illustrates this by referring to a simple unity of determinations, by virtue of which these determinations are not comprehensible as mutually independent—i.e., as “rigid determinations,” connected by an external physical or chemical link—but only as organs of a living individuality. He draws on traditional philosophical terminology to interpret the immediacy of this connection between concept and reality, speaking of the omnipresence of the soul in the different organs and limbs of the

2 For more on this see Angelica Nuzzo, ‘Idee bei Kant und Hegel’, in Das Recht der Vernünft. Kant und Hegel über Denken, Erkennen und Handeln, ed. Christel Frike, Peter König, and Thomas Petersen (Stuttgart-Bad Cannstatt, 1995), 81–120. See also Alison Stone, Petrified Intelligence: Nature in Hegel’s Philosophy (Albany, 2004), 29ff. 3 See PhS, 97. 4 PhS, 106.

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body.5 The central point that Hegel tries to highlight is that this unity of soul and body, conceptual inner and external body structure—which is the condition of life—is not to be understood as a static unity in which the logical distinction of the different moments is lost. Life is rather a relationship that unifies differences and at the same time preserves the distinction between the relationship and the relata. The purposive structure of the organic is conceived as a dialectical relationship of unity and difference through which the soul (the moment of unity) is connected to the organs of the body and so obtains reality and objectivity. At the same time, the activity of the organs of the body reconstitutes the whole that includes them in its unity, thus enabling the overcoming of the otherwise abstract opposition of unity and difference and transforming it into a logical moment in the vital process of the organism itself.6 In the speculative understanding of the living being, the organism is constituted in such a way that it shows itself as originally distinct in the different limbs or organs. These certainly have the impulse to realize themselves and to posit themselves as independent of their original unity. However, the realization of each organ has immediately the opposite meaning of overcoming its independence, since that process of affirmation is at the same time the means for the realization of the other organs and the whole. This is because each organ in the living being can perform its function only by using the other organs, which are then transformed into a means of its realization. The realization of a single organ also means allowing the other organs and the whole to be realized. Hegel believes he can identify the negation of the opposition of the multiplicity of organs with respect to their primitive ideal unity in this process in which, as Kant had already shown, each organ is both the means and the end. The result of the reciprocal relationship of the various organs is their involvement in a single movement through which the work of the individual organs aims at the preservation of their whole.7 The organism itself is produced by the different organs exercising their functions and shows itself to be the final cause of the entire movement 5 See Georg W. F. Hegel, The Encyclopaedia Logic, with the Zusätze: Part I of the Encyclopaedia of Philosophical Sciences, trans. Theodore F. Geraets, Wallis A. Suchting, and Henry S. Harris (Indianapolis, 1991), § 216. 6 See Hegel, Encyclopedia, § 218. 7 Hegel, Encyclopaedia, § 216 and § 218.

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that constitutes its life. The organic whole is therefore structured as a movement in which “what is first” or the beginning “only […] comes back round to itself in the very result of its doing” (PhS, 153). Hegel adds that precisely for this reason what is first in the organism “proves itself to be the kind of thing which has itself as its end, and therefore, as what is first, it has already come back round to itself, or it is in and for itself ” (PhS, 153). The life of the organism is precisely the whole of this movement, the becoming of what had already become. It is therefore not a rigid and static unity of concept and reality that is somehow already given, but a logical process in which the soul or the structural principle is the foundation of the organic limbs and at the same time the totality resulting from the process itself.

2

Observing Reason and the Phenomenological Genesis of Romantic Naturphilosophie

According to Hegel, speculative thinking’s ability to express the necessary connection of inner and outer, concepts and being as it takes place in life is not the result of the work of a brilliant thinker nor is it something that can be externally opposed to alternative theories. This capacity is instead understood as a particular moment within the process in which discussion, refutation, and overcoming, in a word, the progressive sublation (Aufhebung ) of the main currents in the philosophy and natural science of his time takes place. In the Phenomenology of Spirit, this process, which according to Hegel must fulfill the general function of systematically introducing finite subjectivity to speculative knowledge, is conceived as a particular idealistic history of self-consciousness and, more specifically, as a skeptical examination of concrete forms of knowledge and specific truth claims that consciousness raises in relation to what constitutes the essence of objectivity for it or its relationship to objectivity.8 The term “history” takes on the meaning of a systematic and ideal genesis of shapes and modes of consciousness in this context, while “consciousness” indicates 8 For more on the characterization of the Phenomenology of Spirit as an introduction to speculative knowledge and an idealistic history of self-consciousness, see Klaus Düsing, ‘Theorie der Subjektivität und Geschichte des Selbstbewusstseins im Frühidealismus und in Hegels Phänomenologie’, in Geist und Psyche: Klassische Modelle von Platon bis Freud und Damasio, ed. Edith Düsing and Hans D. Klein (Würzburg, 2008), 178–191.

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the common subject of all the different forms of knowledge revealed in the Phenomenology (finite Consciousness, Self-Consciousness, Reason and Spirit)—a subject which gradually develops itself through these forms until it reaches its definitive shape, which is for Hegel the pure self-consciousness of absolute subjectivity. Hegel’s confrontation with the sciences and Naturphilosophie of his time takes place mainly in the chapter of Phenomenology dedicated to Observing Reason and so as part of the introduction to speculative knowledge. Hegel first tries to explain that the scientific attitude of knowing subjectivity toward objectivity has a historical and procedural character. At the same time, he wants to isolate the constitutive characteristics of the Observing Reason that had led the various sciences following its methodology to look for laws of nature (and even biological laws) that consist of quantitative relationships. Secondly, Hegel shows that the clarification of those constitutive characteristics enables a contextual, progressive enrichment of the logical means by which the sciences and the philosophy of nature in the different stages of their development try to account for the structure of the living. By virtue of this progressive enrichment, it finally becomes possible to overcome the cognitive attitude proper to the Observing Reason itself. In order to clarify the procedural and historical character which is proper to the scientific attitude toward nature, Hegel emphasizes that this attitude presupposes that knowing subjectivity shares the fundamental idea of Reason, according to which thought and being “are the same essence, or the same not in comparison with each other, but rather the same in and for itself” (PhS, 139). This conviction is mirrored by consciousness’s immediate and unconscious adhesion to the heuristic presupposition that nature is fundamentally knowable. This underlies the sort of “curiosity” that enables the subject’s “positive relation” to the world. The subject’s confidence in its capacity to investigate nature and grasp its laws express this on the theoretical level.9 Nevertheless, in the Hegelian conception of an idealistic history of self-consciousness that determines itself completely, the immediacy which initially characterizes Observing Reason’s presupposition represents a form of mediation of thought and being that is yet incomplete. It is only a particular stage in a more comprehensive process from out of which

9 See PhS, 136.

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the different scientific systems of Hegel’s time gradually developed. To use the terminology of the Phenomenology, Observing Reason is only the certainty of being all reality and it consequently grasps the idea of a unity of thought and being only in the form of a presupposition that is not yet adequately thematized.10 However, the development of the sciences and naturalistic investigations carried out by Observing Reason in progressively more refined forms is a process in which it tries to confirm its starting hypothesis about the identity of thought and being and thus to raise its certainty into truth.11 In order to explain how this process of gradually enriching the relationship between knowledge and objectivity takes place, Hegel emphasizes some fundamental characteristics of Observing Reason and shows that the latter is essentially affected by limits that lead it to identify the essence of its knowledge of objectivity in quantitative laws on the one hand and to continually experience the inadequacy of the theories it comes up with on the other. These characteristics and limits are both epistemological and methodological. From an epistemological point of view, they can be identified in the abstract analyticity of the knowledge that characterizes Observing Reason or, stated differently, in the fact that Reason in all its forms presupposes that the contents it considers must be independent of each other and have their conditions of identity within themselves. From a methodological point of view, the limit can be identified in an attitude of pure passivity that the consciousness maintains during its investigations.12 Although Observing Reason engages experience and almost tries to extort the answers it seeks from nature, it nevertheless always presupposes that its search is aimed at something that must be given and experienced on the empirical level.13 It is due to these fundamental characteristics that Observing Reason and the natural sciences that share its methodology go toward what could be defined as the negative dialectical side of their experience of objectivity: in all their forms, they end up subverting the initial assumption of identity

10 See PhS, 137–138. For a more detailed discussion of this passage in the Phenomenology see Michael Quante, ‘Die Vernunft unvernünftig aufgefasst’, 328. 11 See PhS, 142. 12 See PhS, 143. 13 See PhS, 146.

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of thought and being and inadvertently producing an opposition between them.14 This happens as soon as Observing Reason attempts to grasp the contents of knowledge not just in their singularity and independence, but also seeks to unify them by means of a necessary relation. Since even in this research consciousness is conditioned by the assumption of the givenness and reciprocal independence of the terms it considers, it reifies the unifying relation itself both when this is sought or understood as a common universal quality of a series of determinations and when Observing Reason, considering the idea of a necessary existence of their connection, enunciates natural laws. In other words, since Observing Reason presupposes on the one hand that a law is “in experience in the way that sensuous being is for it ” (PhS, 147), and on the other hand that all the terms it considers, although necessarily connected to each other, are mutually independent, this means that the world of laws, i.e., the conceptual and universal dimension of the logos, is understood as something that exists for itself on a level of reality beyond that of the particular phenomenal world. Yet this world is also understood as an extreme utterly opposed to its own (external) phenomenal manifestation as well as to the observing consciousness itself.15 According to Hegel, Observing Reason can only posit a superficial relation such as that expressed by proportionality or, more generally, by quantitative correlations between these extremes that are assumed to be mutually independent, stable determinations. However, these relations cannot offer an adequate understanding of the natural phenomena

14 In the Introduction to the Phenomenology, Hegel makes it clear that consciousness,

understood as the general subject of the different forms of knowledge, discovers at every stage of its development that the opposite of what it had believed to be true proves to be the truth: for example, sensuous-certainty believes that truth is something immediately given to its senses, but the skeptical examination of this belief shows that its truth is rather the sensible universal. The experience of every further shape of consciousness takes place in a similar way: precisely because of this negative-dialectical aspect of its experience and the related annihilation of what it believed to be true, consciousness must always fall prey to doubt and even despair (see PhS, 52). 15 Hegel explains the origin of this metaphysical opposition between the supersensible world of laws and the phenomenal world from an abstract theoretical point of view in the chapter on “Force and Understanding.” For this, see PhS, 88–90.

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they set out to explain because they do not define their identity conditions.16 For this reason, the various forms of scientific research in which Observing Reason articulates itself are condemned to fail in their attempt to adequately understand the relationship between the two planes that they inadvertently separate. Philosophy, however, can interpret the conceptual structures developed by the natural sciences and arrange them in a dialectical progression by means of a speculative logic.17 We can distinguish three main phases in this progression: In the first phase, whose concrete instantiation can be found in the Newtonian scientific tradition, Hegel identifies the main result of scientific research as the progressive organization and universalization of immediate and naive data of experience by means of increasingly efficient criteria of methodological functionality.18 As Hegel put it, since the order in nature is initially supposed to be expressed through descriptions and classifications, Observing Reason first tries to find universal determinations and common features it can utilize. But since the natural systems thus

16 In a problematic passage in the Preface to the Phenomenology where mathematical knowledge is discussed in a rather vague way, Hegel states that “Magnitude”, i.e. quantitative ratio, is a “relationship which is non-essential and devoid of the concept.” In mathematics, Hegel adds, “the movement of knowing […] takes place only on the surface; it does not touch on the thing that really matters, does not touch on the essence, or the concept, and hence it does not constitute any kind of comprehension of what is at stake” (PhS, 27). Significantly, Hegel brings this character of mathematical knowledge back to the fact that it presupposes fixed, dead determinations. “Precisely because it does not move itself, what is lifeless does not make it all the way to the differences of essence, nor to essential opposition, or to inequality, nor to the transition of one opposition into its opposite, nor to qualitative, immanent self-movement” (ibid.). 17 The conceptual justification for this Hegelian claim is found in the Introduction to the Phenomenology, where Hegel brings back the possibility of systematically ordering the various shapes of consciousness to the capacity of the speculative philosopher to recognize that the negation of an “untrue” belief is not a simple abstract negation, which only has a pure nothing as its result, but is rather a determinate negation, which has a positive outcome (see PhS, 52–53). 18 For the association of this phase of the development of Observing Reason with the sciences of the Newtonian tradition, see Luca Illetterati, ‘Hegels Kritik der Metaphysik der Naturwissenschaften’, in Hegel als Schlüsseldenker der modernen Welt. Beiträge zur Deutung der Phänomenologie des Geistes aus Anlass ihres 200-Jahr-Jubiläums, ed. Thomas S. Hoffman (Bonn, 2009), 178–205, here 181.

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obtained turn out to be arbitrary and incomplete, the scientific investigation then tries to find the true essence of the observed things in the relations existing between them, i.e., in natural laws.19 However, Observing Reason does not thereby step out of the process of raising phenomena to the level of an increasingly universal and abstract conceptuality. According to Hegel, it ultimately arrives at a totally abstract and indeterminate unity. Observing Reason is then faced with the problem of how the relationship between the universal dimension of principles and the concrete and multiform dimension of observable things can be expressed in conceptual terms.20 As Hegel clarifies elsewhere in the Phenomenology, Newton’s theory of universal gravitation provides the best exemplification of these difficulties. In this theory “the law according to which a stone falls and the law according to which the heavenly spheres move have been conceptually grasped as one law.”21 In Hegel’s opinion, the law of universal gravitation simply states that “everything has a constant difference with regard to everything else” (ibid.), that is, it only posits a quantitative relation between the universal level, understood as conceptus communis, and particular laws and objects. However, such a relationship is not able to overcome the reciprocal heterogeneity between the two levels. Instead, 19 See PhS, 146–147. 20 To explain the origin of these metaphysical and philosophical difficulties, Hegel

mentions that the distinguishing marks and laws sought by Observing Reason, which aims at the universal behind the phenomena, also represents the product of the subject’s cognitive activity. However, since Observing Reason understands itself as purely receptive, it neglects its own cognitive activity and its intervention on the data of the experience. For example, Observing Reason, describing and cataloging things, affirms that the objectivity of its knowledge is guaranteed by the merely passive and receptive character of its experience to which it adds nothing subjective. But Hegel points out that it is impossible to describe something without introducing criteria and priorities and, above all, that in this process the “sensuous-this” (which as such always has the status of a particularity) is immediately converted into a universal determination, that is, into words and names that can be communicated linguistically (see PhS, 143–147). In a similar way, Observing Reason believes that the objectivity of the laws it enunciates is based only in its empirical experience. Hence it prepares experiments and uses analogical and inductive procedures to justify its knowledge. In reality, however, the experiments which were to provide the justification for the objectivity of the laws turn out to be the process by which laws definitively lose their reference to the data of the sensible experience while induction and analogy turn out to be insufficient in establishing the necessity characterizing a true law of nature and can only establish its “probability” (See PhS, 147–149). 21 PhS, 90.

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in the Newtonian cosmological model, “universal attraction, or the pure concept of law, stands over and against determinate laws.”22 But if unity is thought of as a law that neglects the determinacy of particular laws, then this unity itself turns out to be a moment of logical opposition, which means that it is impossible to explain “how difference or otherness is supposed to come out of this pure essence.”23 According to Hegel, the need to adequately express the relationship between the universal and the particular leads Observing Reason to go through a second phase in its development that is characterized by an interest in the organic and the living. Hegel here focuses on the rationalization and ordering of the organic world that was carried out in the philosophy of nature and biological sciences of the late eighteenth century and especially in their attempt to prepare and legitimate a conceptual apparatus capable of overcoming the difficulties that characterized the mechanistic approach.24 Hegel claims that this attempt culminates in the Critique of Judgment where Kant reintroduces inner purposiveness into the history of philosophy and thus came to foreshadow a style of thought capable of expressing the structure of the concept (the

22 Ibid. 23 PhS, 100. 24 In his Metaphysical Foundations of Natural Science, Kant questioned the epistemo-

logical and ontological foundations of the mechanism of the Newtonian tradition, which was characterized by both the atomistic hypothesis concerning the constitution of inert matter and the reduction of any model of causality to adequately explain physical events to that of efficient causation. Taking up the results of naturalists and philosophers of nature who were his contemporaries, such as Bichat and Blumenbach, Kant proposed to limit the validity of the mechanical laws of motion, according to which change in matter “must always have an external cause” to inorganic matter alone, which can therefore be understood according to the model of efficient causality. For organic substances do not present themselves as a set of material points on which external forces can be applied, but as endowed with life, i.e. “the faculty of a substance to determine itself to act from an internal principle.” Immanuel Kant, Metaphysical Foundations of Natural Science, trans. Michael Friedman (Cambridge, 2004), 88. In the Critique of Judgement, Kant explains further that “an organized being is […] not a mere machine. For a machine has solely motive power, whereas an organized being possesses inherent formative power, and such, moreover, as it can impart to material devoid of it—material which it organizes. This, therefore, is a self-propagating formative power, which cannot be explained by the capacity of movement alone, that is to say, by mechanism.” Immanuel Kant, Critique of Judgement, trans. James C. Meredith (Oxford, 2007), 202.

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Hegelian Begriff ).25 On the other hand, however, Hegel emphasizes that Kantian philosophy, because of the distinction made by consciousness between knowledge and object, is instinctively induced to transform the concept of inner purposiveness into a reflection that the subject brings to bear on experience. Observing Reason (in its Kantian version) accordingly falls into a new form—which we could define as subjective—of the separation between the logical plane of principles and the concrete one of being (now identified in the concrete organism) and it is therefore unable to express their necessary relation. As Hegel points out, in the (Kantian) Observing Reason the connection between means and purpose, as expressed by inner teleology, occurs only at a conceptual and abstract level, which means that purpose is not conceived as the immanent principle of determination or as the essence of the organism, but as something which “falls outside the bounds of the thing that presents itself as a purpose”26 —thus either within the bounds of consciousness itself (where it is considered to be a subjective principle that directs the investigation of organic nature) or within the bounds of “another understanding,”27 the divine one. In both cases, however, the (Kantian) Observing Reason proves itself incapable of providing a truly systematic and necessary knowledge of the objects it addresses. And while Kant himself had been forced to recognize the unscientific nature of biology, Hegel observes that in Kantian philosophy the organism turns out to be “fully lawless” and exposed to randomness, that is, its “efficaciousness” is considered to be even lower than that of a machine, “for a machine has a purpose [although an external one], and its efficaciousness thereby has a determinate content.”28

25 Hegel writes that the organic, whose logical structure the Kantian philosophy seeks to express, is an object “which in itself contains the process in the simplicity of the concept” (PhS, 150). As we tried to show in the first part of this paper, Hegel understands the concept as the relationship that expresses the dynamic and processual unity of opposite determinations or as the movement in which each logical moment shows itself as inseparable from its opposite one. 26 PhS, 153. 27 PhS, 154. 28 PhS, 155.

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When Observing Reason becomes aware of the necessity of overcoming the Kantian position, it then goes through a third moment in its development, which according to Hegel coincides with the Naturphilosophie and the romantic sciences of his time.

3

The Controversy Concerning Romantic Naturphilosophie

Despite its merely subjective character, the Kantian conception of the living organism played a key role in transmitting to the next generation of thinkers the fundamental features of a vision of the world that seemed capable of overcoming the intellectualism and the metaphysics of the given which characterize the sciences of the Newtonian tradition.29 For German Naturphilosphen, this overcoming became possible through interpreting the Kantian maxim of knowledge, which commands understanding every determination of the living organism as if it had a constitutive relationship to the whole, on an ontological level and so placing it within a dynamic and procedural conception of the organic itself and even of nature in general.30 This kind of biocentric conception of nature conceived the main task of the sciences as attempting to investigate the fundamental unity and intimate vitality that were supposed to inform living organisms and the whole of natural processes. For romantic scientists and philosophers, however, this holistic knowledge of reality could not be ensured by merely assuming an atomistic and mechanical point of view centered on the consideration of universal determinations (common features) and their extrinsic

29 For a more detailed discussion of the relationship between Kantian philosophy

and romantic Naturphilosophie see Timothy Lenoir, The Strategy of Life: Teleology and Mechanics in Eighteenth-Century German Biology (Riedel, 1989) and, from a different point of view, John Zammito, ‘The Lenoir Thesis Revisited: Blumenbach and Kant’, Studies in History of Biological and Biomedical Sciences, 43 (2012), 120–132. 30 According to Stefano Poggi, Kant’s reflection on inner teleology, together with the controversy concerning the atomistic hypothesis in explaining physical processes, made possible a different conception of temporality, and one that no longer seemed to be connected to the typical temporal schema of physical and mechanistic causality—that of the post hoc, ergo propter hoc—but was rather a circular movement internal to the organism that makes its preservation and its life possible. Stefano Poggi, Il genio e l’unità della natura. La scienza della Germania romantica (1790–1839) (Bologna, 2000), 85–87.

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relationships (the laws of dynamics). Rather, they claimed that the understanding of living organisms was only possible by adopting a dynamic point of view that focuses on the analysis of the forces at work in the processes of conservation and reproduction of the living and which would make it possible to “consider the intertwining of the spatial and the temporal dimension in which life takes place in its reality […] and to follow step by step the becoming of the living in the multiplicity of its internal and external interrelations.”31 In Hegel’s view, the biocentrism and dynamism that characterize Naturphilosophie represent a conceptual advancement in comparison to the previous phases of scientific development. Nonetheless, the thinkers and scientists of this time were unable to express the organization of the whole of life in its necessity.32 The romantic thinkers were accordingly seen by Hegel as conditioned by an unconscious adherence to the perspective of Observing Reason, which meant that they were induced to distinguish between a conceptual interior of the organic (its inner forces) and its external, physical Gestaltung. However, the various forms of the quantitative relationship they posit between these relata are repeatedly shown to be without any necessity. 3.1

The Inner-Outer Relationship in Romantic Naturphilosophie

Romantic Naturphilosophie fundamentally aspires, first, to identify the set of forces that are at work in every living thing and to characterize it as such and in contrast to the inorganic world. Starting with the works of Johann Georg Zimmermann (1728–1795) and Albrecht von Haller (1708–1777), these forces were identified as sensitivity, irritability, and reproduction while their outer manifestation was found respectively in the

31 Poggi, Il genio e l’unità della natura, 39 (my translation). Poggi points out that the spread of a biocentric conception of nature is connected with a renewed interest on the part of the romantic Naturphilosophen in some fundamental aspects of the German philosophical and scientific tradition of the eighteenth century. This tradition, strongly influenced by Leibniz, had been characterized by the importance it assigned to the study of the phenomena of generation and transformation of (living) matter. Romantic Naturphilosophie could also draw on the natural notions summarized by alchemical tradition, as well as on scientific investigations carried out by French authors such as Buffon, Bonnet, Robinet or Diderot (see Poggi, Il genio e l’unità della natura, 129–130). See also Stefania Achella, Pensare la vita. Saggio su Hegel (Bologna, 2019), 81ff. 32 On this point see Illetterati, ‘Hegels Kritik’, 181.

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nervous system, in the muscular system and in the reproductive organs. Secondly, Naturphilosophen tried to account for the development and evolution which, in their opinion, affects the entire sphere of living and so to define the place of every single organism and species within the whole of nature. Carl August Kielmeyer (1765–1844) formulated such a research program in the clearest way. He maintained Naturphilosophie had to search for the relationships between (organic) forces in the different forms of organization and to identify the laws that explain how these relationships change in different organisms.33 For Hegel, however, in pursuing its research, Naturphilosophie must necessarily run into a sort of category error that predetermines its efforts to fail. He claims Naturphilosophie unconsciously follows the methodology and the metaphysical presuppositions typical of Observing Reason and it is accordingly unable to conceive the moments of the organic in their constitutive processuality. Instead, it bases its investigations of living nature on the opposition between the inner concept of organic life— “the simple soul , the pure concept of purpose, or […] the universal ”—on the one hand and on the other hand that same life as it appears “in the motionless being of the organic” body (PhS, 156), namely as outer Gestaltung and anatomical parts. Hegel explains that because Naturphilosophie follows the methodology of Observing Reason, it reifies and considers the two sides of the organic as immediately given. It thus conceives their relationship in terms of quantitative laws that regulate (1) the “relation among universal organic activities”34 of the inner and (2) the correspondence between an interior function or capacity and its external effectuality. In this case, Observing Reason seeks the “law which would express the true outer as the imprint of the inner.”35 In a clear reference to Kielmeyer’s work, Hegel states that an example of a law of the first type is the one in which “sensibility and irritability stand in inverse relations of magnitude, so that as the one increases, the other diminishes” (PhS, 159). An example of a law of the second type 33 See Karl F. Kielmeyer, Über die Verhältnisse der organischen Kräfte untereinander in der Reihe der verschiedenen Organisationen, und die Gesetze und Folgen dieser Verhältnisse, in Kielmeyer, Karl F. Gesammelte Schriften, ed. by F. H. Holler (Berlin, 1938), 59–101, here 67–100. 34 PhS, 158. 35 PhS, 161.

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is the one that determines “an animal with strong muscles” as being “an animal organism of higher irritability,”36 and so on.37 Laws of this sort, however, prove to have no truth at all. What Hegel radically questions is the procedure implicitly adopted by Kielmeyer. He claims that Kielmeyer first tries to identify and distinguish the fundamental forces of the organism and the anatomical parts—or determine them as “something restricted, like a thing”—and only at a later logical moment does he search for the laws that regulate their mutual relations.38 Because of this approach, which abstracts from the constitutive relation between the forces and the whole organism, both the moments of the inner and those of the outer are conceived as “given things.” Consequently, “sensibility, irritability, and reproduction subside into being ordinary properties, which are universals that are just as indifferent towards one another as are specific weight, color, hardness, and so on” (PhS, 161). The attempt to find regularities among such rigidified determinations and to then claim that they have the necessity of a law of nature is equally unsuccessful. This does not mean that it is not possible to observe that “one organic being could be said to be more sensitive or more irritable, or to have a greater reproductive power than another” (PhS, 161), but that these regularities only express a relationship existing between determinations that are indifferent to each other, without thereby defining their conditions of identity. For Hegel, however, true necessity characterizes a dynamic relational structure that produces from itself relations and relata. The failure of Kielmeyer’s research is ultimately due to his inability to adequately understand and to express the dialectical nature of the logical relationship which binds the determinations of the living organism.39 As Hegel put it in the Phenomenology, this relationship is only present and 36 PhS, 164. 37 Kielmeyer, who is not expressly mentioned by Hegel, had enunciated the laws of

the organic in a similar way (see Kielmeyer, Über die Verhältnisse der organischen Kräfte, 80). We cannot exclude that the real target of Hegel’s polemic was Schelling. Schelling, who was influenced by Kielmeyer, had adopted these laws in his natural philosophical works; see Friedrich Wilhelm Joseph Schelling, First Outline of a System of the Philosophy of Nature, trans. Keith R. Peterson (Albany, 2004), 135ff. 38 See PhS, 158. 39 Hegel writes that it is necessary to distinguish between sensibility, irritability and

reproduction. In his opinion, however, their distinction is “qualitative” and so it should be made “according to their concept” (PhS, 159). Hence Naturphilosophie attempt to

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conceivable as “a movement that runs throughout the various parts of the shaping, and within which what is torn out and rigidly set up as a singular system is shown to be essentially a flowing moment, so that what can be counted as their reality is not the former actuality in the way anatomy finds it; rather, what counts as their reality is only that actuality as a process, within which alone even the anatomical parts have a sense.”40 Because it is unable to express such a movement, Naturphilosophie remains confined to an empty game of legislating and because of its reification of the parts of the organism it only understands the living being “according to the abstract side of dead existence; taken in that way, in fact, its moments belong to anatomy and to the cadaver, not to cognition and the living organism.”41 3.2

Hegel’s Criticism of Phrenology

The limits to Naturphilosophie’s attempt to find quantitative laws capable of expressing the necessary relationship between inner and outer become even more evident when we analyze some of the studies conducted in this period on the human body and on the relation they claimed existed between psychology, understood as the theory of the faculties of the human soul, and anatomy, understood as the study of the physical and therefore measurable features of the body. Hegel’s criticism of physiognomy and especially of phrenology is particularly interesting here.42

express their relationship by means of quantitative correlations would “generally rest on a lack of acquaintance with the logical nature of these oppositions” (PhS, 160). 40 PhS, 162. Hegel will explain his own conception of the relationship between organic inner and its outer shaping (Gestaltung ) only in the Encyclopedia where he shows that the three systems of irritability, sensitivity and reproduction and their respective anatomical concretions must be developed in a speculative and syllogistic way according to the conceptual determinations of universality, particularity and singularity. For this, see Georg W. F. Hegel, Hegel’s Philosophy of Nature: Being Part Two of the Encyclopedia of the Philosophical Sciences (1830) Translated from Nicolin and Pöggeler Edition (1959) and from the Zusätze in Michelet’s Text (1847), trans. Arnold W. Miller (Oxford, 2004), § 353. 41 PhS, 612. 42 Here we can abstract from the argumentative organization of the Phenomenology of

Spirit, according to which the exposition of phrenology does not take place after that of Kielmeyer’s philosophy of nature, but only at the end of the analysis of the theoretical experiences of Reason. According to Hegel, the analysis of phrenology makes possible the

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According to the fundamental assumption of phrenology, it is possible to detect in the immediate physical existence of the skull a series of observable phenomena that allow us to access the most hidden character traits of an individual. The founder of phrenology, the German neuroanatomist Franz Joseph Gall, posited that there was a certain number of spiritual faculties in an equally determinate number of brain organs and areas. He believed that every mode of spirit was located on a determinate part of the skull and that the shape of the skull indicated particular modes of spirit. Gall claimed that a disposition towards murder, theft, poetry, and even the most hidden and as yet unconscious intentions of any individual could be recognized by an external observer through the particular “mark” they leave on the skull.43 For Hegel, however, when phrenology seeks to enunciate the laws that supposedly govern the correspondence between an individual’s psychological faculties and the conformation of his skull, it only produces a new form of the relationship between inner and outer that predetermines the deceptive outcome of the ‘knowledge’ it attains. He points out that the investigations conducted by phrenology presuppose the isolation of the observed determinations, which are once again considered to be mutually indifferent universalities and not fluid moments of the concept.44 But Hegel’s view is that such a cataloging of the human spirit reflects the anthropological presupposition, implicitly adopted by phrenology, that each individual has a peculiar original essence, stable and equal to itself, i.e. a defined character that can be expressed by determined

conceptual transition to the exposition of the practical experiences of Reason. As is wellknown, this is because in the chapter on phrenology consciousness comes to consider the logical structure of the infinite judgement, which is exemplified in the proposition: “the being of spirit is a bone” (PhS, 201). For the purposes of this article, however, the logical transition to the practical experiences of Reason is not relevant, while it is important to highlight the argumentative affinities between the “knowledge” achieved by phrenology and the conception of the relationship between inner and outer. On the infinite judgement in phrenology and the related transition to the practical part of Reason, see Ludwig Siep, Hegel’s Phenomenology of Spirit, trans. Daniel Smyth (Cambridge, 2014), 130–132. 43 Supported by Goethe, Gall had lectured on his theories in Jena, where Hegel lived, in 1801. For more on Gall’s phrenology, see John van Wyhe, ‘The Authority of Human Nature: The Schädellehre of Franz Joseph Gall’, British Journal for the History of Science, 35 (2002), 17–42. 44 See PhS, 195.

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conceptual marks. Anthropometric characteristics and more specifically the shape of the skull can be taken as a revealing indication of an individual’s heart only because of this assumption. However, phrenology thereby ignores the individual’s ability to influence and modify not only his own exteriority, but also his own character.45 In short, it misunderstands the essence of individual freedom and the structural interaction between the organic inner, its external configuration and the living environment— an interaction, which makes possible endless gradations of the universal determinations phrenology seeks.46 Because of the infinite richness and versatility of the human soul, its physical constitution cannot have the “value of a sign,” and cannot be indicative of the invisible interior of the organism. The alleged laws of phrenology remain thus completely arbitrary. According to Hegel, even if it were conceded that the spiritual movements and determinate modes of the brain display their external actuality in the skull, it still would be impossible to establish “whether a spiritual moment, depending on whether it was originally stronger or weaker, would in the former case either have to possess a more expanded brain-organ, or in the latter case a more contracted brain-organ, or else just the other way around.”47 In the same way, it would be impossible to determine whether the brain’s training enlarges or reduces the organ or whether it makes it thicker or finer.48 It is important to note that Hegel did not intend to exclude either a theory of brain localization or the existence of causal correlations between mind and body for conceptual reasons. Hegel certainly does not deny that each one of us necessarily lives in a body and in an external environment that we have not chosen. As I tried to show above, the reference of the soul to bodily organs remains fundamental in the Hegelian theory of the organism. However, he maintains it is not possible to achieve certain knowledge nor to identify the fundamental characteristics of the mental by following the descriptive approach of the Observing Reason. For Hegel, the lack of a qualitative distinction between the functional activities of the brain and the brain itself as a physical organ lies at the

45 See PhS, 178–179. 46 See PhS, 195. 47 PhS, 193. 48 See PhS, 193.

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root of an irremediable ambiguity. The cataloging of the faculties of the soul that phrenology presupposes is, he claims, first and foremost the result of the psychological analysis of a given era.49 Phrenology’s aspiration to justify the division of the soul through cerebral localizations that were only made possible by psychological analysis itself inevitably turns out to be a circulus in probandum. In order to overcome this difficulty, this (pseudo)science has no other option than to postulate a sort of “pre-established harmony.”50 For a “disenchanted” researcher, however, the use of pre-established harmony only betrays the inability to articulate binding laws capable of regulating the relationship between mind and body. 3.3

Hegel’s Criticism of the Schelling-Inspired Naturphilosophie

The dynamic and biocentric conception of the natural world culminates conceptually, on Hegel’s interpretation, in the attempts of Friedrich Wilhelm Joseph von Schelling (1775–1854) and his followers to develop from a few fundamental principles “the system of life differentiating itself in the element of being.”51 Schelling claimed it was necessary to go beyond the Newtonian conception of inert matter and conceive the whole of nature as a single living organism, endowed with a capacity for action and creation.52 His philosophical program intended to show the a priori construction of the particular levels and laws of nature, i.e. the genesis and development of a (non-continuous) series of natural entities from the simplest (the inorganic elements) to the most complex (the human being, capable of intellectual intuition).

49 See PhS, 195. 50 PhS, 192 and 195. 51 PhS, 166. 52 In this way Schelling referred to some elements of the Kantian philosophy of nature,

which, however, were understood on a dogmatic-metaphysical level. For an overview of the relationship between Kant’s and Schelling’s philosophy of nature see Klaus Düsing, ‘Teleologie der Natur. Eine Kant-Interpretation mit Ausblicken auf Schelling’, in Natur und Subjektivität. Zur Auseinandersetzung mit der Naturphilosophie des jungen Schelling, ed. Reinhard Heckmann, Hermann Krings, and Rudolph W. Meyer (Stuttgart/Bad Cannstatt, 1985), 187–210.

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This chain of the living being was conceived as a manifestation of a single and identical universal life. In On the World Soul Schelling tries to show that a fundamental organizing principle that gives the world the form of a system is immanent in nature. This unitary principle, which Schelling determines as an absolute identity, nonetheless develops into an opposition: “The foundation (Grund) of life is contained in opposite principles, of which one (the positive) must be sought outside the living individual, the other (the negative) in the individual itself.”53 The positive principle is understood as the common substance (or soul) of the many living forms and natural entities or, in Schelling’s words, as something “spread throughout creation and permeating, like a breath of nature, each individual being.”54 Individual beings, however, are distinguished from each other according to their different degrees of realization and therefore by virtue of a further (negative) principle that, by limiting the first, causes the general principle of life to be individualized in every single living being. If taken separately, the two principles are actually “false principles”: the possibility of life is grasped only if one can think of productivity and product together, that is, think of the union of the two principles. Only then is it possible to understand how individual natural entities have their identical matrix in the Absolute of which they are the symbols or individualizations.55 These Schellingian speculations influenced an entire generation of German Naturphilosophen, who not only recognized themselves in these

53 Friedrich W. J. Schelling, Von der Weltseele – Eine Hypothese der höhern Physik zur Erklärung des allgemeinen Organismus. Vol. 6 of F.W.J. Schelling Werke, ed. Jorg Jantzen and Thomas Kisser (Stuttgart/Bad Cannstatt, 2000), 192 (my translation). 54 Ibid. 55 Schelling grounds the systematic organization of the different productions in which

the infinite activity of living nature is articulated in their teleological structure: in the introduction to the System of Transcendental Idealism Schelling, when discussing the possibility of realizing the coincidence of objectivity and subjectivity starting from the objectivity (the path of the philosophy of Nature, which is the alternative to that of transcendental philosophy), states that, from this point of view, “Nature’s highest goal, to become wholly an object to herself, is achieved only through the last and highest order of reflection, which is none other than man; or, more generally, it is what we call reason, whereby nature first returns into herself, and by which it becomes apparent that nature is identical from the first with what we recognize in ourselves as the intelligent and conscious.” Friedrich Wilhelm Joseph Schelling, System of Transcendental Idealism, trans. Peter Heath (Charlottesville, 1978), 6.

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ideas, but also radicalized them. The Norwegian Henryk Steffens (1773– 1845), to whose work Hegel refers at length in the Phenomenology of Spirit, is of particular interest in this context. Drawing on Schelling’s work, Steffens tried on the one hand to reduce the processes in which the history of the Earth takes place to necessary laws and on the other hand to explain how the fundamental force of nature individualizes (or determines) itself in the series of natural beings— a series which he conceives as teleologically oriented to the achievement of that being in which organization and self-consciousness reach the highest level. In his reconstruction of Steffens’ philosophy of nature, Hegel points out that the Norwegian Naturphilosoph had identified the guideline for the systematization of natural entities in the numerical quantity that expresses the relationship between some of the observable properties of these entities. For example, Steffens identified the interior of natural entities in their “cohesion” or in their “specific gravity:” the different values of these properties were used to order the different natural substances by way of graduation.56 Hegel, however, thinks Steffens’ philosophy of nature is open to the same kind of difficulties that had beset the aforementioned search for laws of the inner-outer relationship. Steffens too (and indirectly also Schelling) necessarily reifies the determinations he considers and, purporting to grasp their connections in the form of quantitative relations, fails to articulate necessary laws. On the one hand, Hegel claims this form of Observing Reason is incapable of justifying the essential importance it attributes to the observable properties that are used to understand the development of the series of natural entities.57 On the other hand, he points out again that a simple relationship of proportionality is not capable of expressing a necessary relationship between the moments of the inner and those of the outer. On the contrary: since the quantitative relationship between the observed determinations, as exhibited by a number, “does not contain the principle of movement” and does not “express a relation and a transition of 56 See PhS, 167ff. Probably, Hegel refers here to Henrik Steffens, Beyträge zur inneren Naturgeschichte der Erde (Freyberg, 1801), 14–15. 57 According to Hegel, cohesion or specific gravity are, along with others, individual properties of a being. Every one of them could be “selected equally correctly, i.e., equally wrongly, to be chosen as the representative of all the other aspects” (PhS, 170).

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these properties to each other,” it can accordingly only be considered as a “simple […] property” or as “the expression of determinateness as non-essential.”58 Precisely for this reason, the system of nature conceived by Steffens (and, more generally, by all Schelling’s followers) does not take the form of an animated and rationally organized whole, but of a “a system of indifferently posited differences”59 which are supposed to be immediately given to human knowledge. As Hegel shows in the final part of his confrontation with Naturphilosophie, these conceptual difficulties cannot even be solved by resorting to the theory of intellectual intuition that Schelling and his followers purported to be both the epistemological and ontological condition for the immanence of the infinite principle of life in all its finite realizations, i.e., in individual beings. According to Schelling, this mysterious ability made possible the notion that “the whole—the infinite—mirrors itself in each individual being in Nature” and that “just for this reason each individual intuition is only apparently individual ” whereas “actually the intuition of the whole universe is contained in every individual [intuition].”60 Taking up these ideas, Steffens speaks in the second part of his work of “an infinite, holy, mysterious abyss (Abgrund) of forms,” which would be the foundation of life’s individualizations and into which we can only gaze in an inspired intuition.61 According to Hegel, however, such speculations have only the semblance of a compelling argument and this semblance is produced by a superficial imitation of the characteristic sign of rationality itself, i.e. syllogistic development. As he puts it, in Steffens’ Naturphilosophie “we see a syllogism, in which one extreme term is the universal life as universal, or as genus […], the other extreme term is that same life as singular, or as a universal individual […], the middle term is composed out of both.”62

58 PhS, 169. 59 PhS, 172. 60 Friedrich W. J. Schelling, First Outline of a System of the Philosophy of Nature, 18–19. 61 See Steffens, Beyträge zur inneren Naturgeschichte der Erde, 306. For more on

this see Cinzia Ferrini, ‘Reason Observing Nature’, in The Blackwell Guide to Hegel’s Phenomenology of Spirit, ed. Kenneth R. Westphal (Chichester, 2009), 109–111. 62 PhS, 172.

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However, this Schelling-inspired Naturphilosophie does not place a “genuine mediation existing-for-itself”63 among the moments of syllogism. This means it not only abandons the previously stated model of gradual development of natural entities from the simplest to the most complex, but also proves itself incapable of truly explaining the integration of knowledge and being. In Hegel’s view, in fact, this kind of Naturphilosophie limits itself to recognizing the immediate presence of the whole in every single observed being. Consequentially, it does not go beyond the concept of Reason as “life in general,” which “immediately descend […] into the singularity of existence”64 and therefore does not contain its immanent specification. For this reason, the unification of “simple determinateness and singular liveliness” remains a contingent movement “within which the whole is preserved” and through which it “is not present […] for itself as a whole,”65 but only for the knowledge (the intellectual intuition) able to grasp the relationship of identity between the two moments of the universal and the particular and yet remains different and separated from that immediate identity. As is clarified in the “Preface” to the Phenomenology, this means that the entire explanation of natural reality proposed in this form of knowledge ends up being a “monochrome formalism,” that is, “the shapeless repetition of one and the same thing which is only externally applied to diverse material and which contains only the tedious semblance of diversity.”66 This is because here “the knowing subject only applies the one unmoved form to whatever just happens to be present and then externally dips the material into this motionless element.”67 The lack of a necessary mediation between the abstract universal and the multiplicity of natural beings soon reveals itself to Observing Reason itself, which becomes aware that its empirical experience “cannot get any further than… mak[ing] charming remarks, bring out interesting connections, and make friendly concessions to the concept ” (PhS, 174). These, however, are not a knowing of necessity nor a knowledge of the vital 63 PhG, 174. 64 PhS, 173. 65 PhS, 173. 66 PhS, 11. 67 PhS, 11.

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relationship that binds universal and particular in the unity of the concept (Begriff ).68 In Hegel’s opinion, only a knowledge that exceeds the limits of Observing Reason and its constitutive tendency to reify the contents it considers is able to conceive the authentic movement of life which “in its differentiation has […] a rational sequence and demarcation and is […] a system of shapes grounded within itself.”69 He is alluding with this to his own conception of a progressive self-determination and self-generation of the absolute, which is dialectically organized and characterized by the ability to understand absolute self-knowledge as the culminating moment of its own development. The exposition (and the foundation) of this “system,” which unfolds throughout the totality of the “shapes of consciousness as a life of spirit ordering itself into a whole,” is the task Hegel assigns to the Phenomenology of Spirit in its entirety.70

4

Conclusion

In this essay, I tried to show that in the Phenomenology Hegel provides a conceptual interpretation of the genesis and development of the Naturphilosophie of his time. He can do this because he understands the development of the natural sciences as a particular moment, that of Observing Reason, of a more comprehensive idealistic history of self-consciousness whose exposition is the main task of Phenomenology. Hegel proves himself capable not only of individuating the fundamental evolutionary lines of the science of his time in his reconstruction, but also of highlighting both the conceptual depth and the inconsistencies of Naturphilosophie. As he points out, on the one hand Naturphilosophie is able to grasp the unity of thought and being, but on the other hand, it

68 PhS, 174. 69 PhS, 173. 70 See PhS, 173. According to Hegel, this “system” also has a syllogistic form. However, it differs from Steffen’s apparent syllogism because the middle term is correctly conceived in this case as having “in its own self the extreme terms of inner universality and universal individuality.” The so conceived middle term is precisely the consciousness whose idealistic history (its “self-systematizing development” as Hegel here says) is explained in Phenomenology as the mediation process between “the universal spirit and its singularity, or sensuous consciousness” (PhS, 173).

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cannot go beyond the consideration of reified determinations and reduces its search for the laws of life to the statement of quantitative correlations that always turns out to express the necessary connection of conceptual inner and physical outer inadequately. Admittedly, the contemporary interpreter can only regard with suspicion Hegel’s aversion to the search for quantitative correlations and the hostility with which, at least in the Phenomenology, he judges mathematical knowledge itself. From this contemporary point of view, it must be recognized that Hegel’s criticisms are only valid in relation to the Naturphilosophie of his time.71 From another point of view, however, Hegel’s criticism of Naturphilosophie is also of interest for today’s readers. By explaining the development of Naturphilosophie on the basis of its having implicitly assumed the main characteristics of the Observing Reason, Hegel anticipated a fundamental trend in contemporary thinking and showed that philosophy can relate to empirical sciences without pretending to delegitimize them and without offering an alternative access to knowledge of nature. Rather, according to the Phenomenology, the task philosophy reserves for itself is to bring to light (and critically discuss) the metaphysical and epistemological premises implicitly assumed by science, with the ultimate aim of showing their conceptual connections and highlighting the sense of their becoming. Significantly, Hegel also believes that the emergence of an authentic philosophical vision of reality, that is, one capable of speculatively understanding the whole of human experience, has as one of its necessary preconditions the sciences and their organization of the knowledge of nature.72 71 Obviously, while writing the Phenomenology Hegel could not know what impressive developments were about to take place in mathematics and in the physical and chemical sciences nor that precisely these developments would have brought a quick end to the romantic Naturphilosophie. In defense of Hegel, it can be added that his attitude towards mathematics will change in the Encyclopedia, where he will recognize the role mathematics plays in the foundation of scientific knowledge of nature. For more on this development, see Poggi, Il genio e l’unità della natura, 52–54. 72 At the end of the Phenomenology of Spirit Hegel explains that the idealistic history of self-consciousness is coordinated with, and even based on, a parallel development of logical categories, i.e. that an abstract moment of Science (i.e. Hegelian speculative science) corresponds to each “shape of appearing spirit per se” (PhS, 465). With reference to the chapter on Observing Reason, this implies that the development of the empirical sciences and philosophy of nature, which was here explained, constitutes a moment in the process of self-determination of the concept (Begriff ). To be sure, this should not be understood

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To be sure, Hegel was still convinced of the substantial superiority of philosophy over the empirical sciences and this is mirrored by the extremely high cognitive expectations of his philosophical system. However, as was shown in the examination of a seemingly outdated part of Phenomenology—that which treats romantic Naturphilosophie—Hegel abides in the dimension proper to the philosophical classics, which are characterized by their inexhaustible ability to stimulate the thought of every age and to provide orientation in the ongoing search for answers to the persistent questions of humanity.

as implying that Hegel wanted to deduce the conceptual determinations of nature from its logic, but rather that the development of the metaphysical assumptions which are implicit in sciences can only be adequately understood and founded by means of dialectical logic. The adequate exposition of the latter and of the movement of self-determination of the concept is, however, a primary task of philosophy and it finds its complete elaboration in the Science of Logic. On this point, see also Illetterati, ‘Hegels Kritik’, 204–205.

Measuring the Mind: The French Debate on Fechner’s Psychophysics in the Late Nineteenth Century Denise Vincenti

1

Introduction

When it comes to psychophysics, one particular image recurs in the works of its proponents: that of a monumental building and its implacable ruin. In fact, the project of determining, on mathematical bases, the relationship between outer excitements and inner sensations is indeed a rather monumental one, leading to what has been defined as the “quantitative revolution” in psychology.1 The paternity of such a project is primarily attributed to the work of German physicist and philosopher Gustav Theodor Fechner (1801–1887), who first coined the term “psychophysics” (Psychophysik) to indicate the exact science regarding the

1 See: Edwin G. Boring, ‘The Beginning and Growth of Measurement in Psychology’, Isis, 52, 2 (1961), 238–257; Donald Laming, The Measurement of Sensation (Oxford, 1997); Riccardo Martinelli, Misurare l’anima (Macerata, 1999); Verena Zudini, I numeri della mente (Trieste, 2009).

D. Vincenti (B) University of Milano-Bicocca, Milan, Italy e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7_12

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mind–body relation.2 Yet, the extent of this endeavor is much wider. Like every monumental edifice that builds upon well-established foundations, the introduction of measure into psychology had deep roots. Although it is fairly common to put Fechner’s name next to that of the physiologist Ernst Heinrich Weber (1795–1878), the project of applying quantitative methods to psychological matters had characterized German psychology from its very beginnings, as exemplified paradigmatically by Johann Friedrich Herbart’s (1776–1841) theory.3 In addition, from its first formulation in Fechner’s doctrine, psychophysics developed different forms over time, gradually becoming a multifaceted discipline, though one always grounded in the quantitative approach.4 Sometimes, however, with exponential growth comes decline. A monumental building, having attained a peak of prosperity, can fall into ruin. Indeed, as early as 1877, the Belgian psychophysicist Joseph Delboeuf did not hesitate to report such a fate for Fechner’s doctrine: “I do not know if there is a more painful feeling for a man than to see a vast edifice, erected by him at the cost of his greater efforts and destined to be his main title of glory for posterity, falling down one day before his eyes.”5 Fechner, in the very same year, indirectly replied to this remark with a suggestive allegory: Just as the Tower of Babel could not be finished because the workmen who were supposed to build it could not understand each other anymore, the psychophysical monument which I have attempted to raise might well

2 Gustav Theodor Fechner, Elements of Psychophysics (1860), trans. Helmut E. Adler, vol. 1 (New York, 1966), xxvii. A selected bibliography on Fechner would include: Edwin G. Boring, A History of Experimental Psychology (New York, 1950); Joseph Brožek, and Horst Gundlach, eds, G.T. Fechner and Psychology (Passau, 1988); Marilyn Marshall, ‘The Theme of Quantification and the Hidden Weber in the Early Work of Gustav Theodor Fechner’, Canadian Psychology, 31 (1990), 45–53; Isabelle Dupéron, G.T. Fechner: le parallélisme psychophysiologique (Paris, 2000); Michael Heidelberger, Nature from Within: Gustav Theodor Fechner and His Psychophysical Worldview (Pittsburgh, 2004). 3 See Johann Friedrich Herbart, Psychologie als Wissenschaft (Königsberg, 1824–1825). 4 Consider, for example, the Belgian Joseph Plateau (1801–1883) and Joseph Delboeuf

(1831–1896), who advanced a bisectional method for scaling sensory measurements. See: Serge Nicolas, and David J. Murray, ‘The Psychophysics of J-R-L Delboeuf’, Perception, 26 (1997), 1297–1315. 5 Joseph Delboeuf, ‘La loi philosophique, 3 (1877), 225.

psycho-physique:

Hering

contre

Fechner’,

Revue

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continue to remain standing because those who desired to pull it down could not come to any final agreement among themselves.6

The study of the quantitative relations between sensations and physical events was indeed either a pioneering or a persnickety project. The introduction of measurement and quantitative methods to the psychological sphere would have achieved the prayed-for arrival of psychology into its scientific phase, along with its definitive emancipation from philosophy. The final years of the nineteenth century saw the proliferation of different approaches aimed at fulfilling a similar goal. In Germany, Johannes Peter Müller’s (1801–1858) research on specific nerve energies and Hermann von Helmholtz’s (1821–1894) physiological studies on perception had made major contributions to the process of the “naturalization” of the mind. The possibility of treating sensations in terms of quantities and magnitudes, and hence of employing mathematical tools to evaluate them, could only represent a step forward in the scientific appraisal of psychic phenomena. This is not to say that the project was sheltered from pitfalls. On the contrary, as seductive as it was, psychophysics soon encountered several criticisms regarding both its mathematical and philosophical implications. The aim of this paper is to assess the theoretical consequences of this project of mathematization of the mind by relying on a specific debate, namely, the late nineteenth-century French7 debate on psychophysics. Although this discipline was attacked by thinkers and scientists from all over the world, the French discussion seems to display a peculiarity: a profound concern about the reduction of internal facts to quantities and mathematical unities—in other words, the quantification of the mind. A similar worry can be grasped in both the scientific and the philosophical-academical environment, which appears to prove the existence of a common front regarding what form psychology should acquire once it had attained its scientific status.

6 Gustav Theodor Fechner, In Sachen der Psychophysik (Leipzig, 1877), 215; trans. in Nicolas, and Murray, ‘The Psychophysics of J-R-L Delboeuf’, 1307. 7 With the term ‘French’, I refer more generally to the francophone context.

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2 Fechner’s Psychophysics and Its Introduction into France The “deed of foundation” of psychophysics is notoriously identified with the publication of Fechner’s Elements of psychophysics in 1860. This theoretical project, however, is older and can be dated to Fechner’s early metaphysical works.8 Deeply fascinated by Schelling’s and Spinoza’s philosophies, in his earlier writings Fechner defined spirit and matter as two sides of the same absolute reality. In this view, spirit and matter are the very same phenomenon, seen from two different angles—much like a circle, which is both concave and convex depending on the perspective adopted.9 Philosophical monism is thus the bedrock and the inferential outcome of psychophysical parallelism. Thanks to the fact that there is a tight relation of covariance between the two, observation directed toward the external side of reality can present us with inner reality as well. Yet, this observation, in order to be scientifically rigorous, has to be conducted through the means of mathematics. It is a matter of drawing out the equation underlying the parallelism both between psychological and physiological facts (inner psychophysics), and between psychological and physical facts (outer psychophysics).10 In Fechner’s view, inner psychophysics had to be conceived as the ultimate goal of his doctrine.11 Nevertheless, in order to achieve that, it was paramount to find a way to measure the inner side. This was the purpose of outer psychophysics. Even though Fechner’s main goal was to outline a scientific way to investigate the mind–body relation, it was his outer psychophysics that entered the international debate and ultimately won his acclaim. In francophone areas, Fechner’s doctrine penetrated quite late, yet aroused

8 Gustav Theodor Fechner, Nanna oder über das Seelenleben der Pflanzen (Leipzig, 1848); id., Zend Avesta (Leipzig, 1851). See: Marilyn Marshall, ‘Physics, Metaphysics, and Fechner’s Psychophysics’, in The Problematic Science: Psychology in Nineteenth-Century Thought, ed. by William R. Woodward, and Mitchell G. Ash (New York, 1982), 65–87; Serge Nicolas, ‘La fondation de la psychophysique de Fechner’, L’année psychologique, 102, 2 (2002), 255–298. 9 Fechner, Elements of Psychophysics, 2. 10 Ibid., 12. 11 Gustav Theodor Fechner, Revision der Hauptpunkte der Psychophysik (Leipzig, 1882),

262.

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great interest.12 The first account of psychophysics emerged thanks to a supporter of this new science, Delboeuf, who published in 1873 a text presenting and revising the Weber–Fechner law.13 However, it was only in 1874 that an article by Théodule-Armand Ribot (1839–1916) introduced French audiences to this new science and contributed to its dissemination.14 As Ribot acknowledges, German works on psychology of sensations were “very little known in France. Yet, they deserve to be known, since they represent the first attempt at subjecting psychic phenomena to measurement, namely to exact and rigorous knowledge.”15 Like every science based on the experimental method, Ribot recalls in a later text, German psychology had grounded its processes in the principle of causality, in the possibility of determining the effects by their causes, that is, by measuring sensations through external stimuli (method of indirect measurement).16 It is in fact commonly accepted that an increase in the magnitude of a stimulus produces a concomitant increase in our sensations: there is a huge difference between a sensation of brightness produced by a candle and the one produced by ten of them. Fechner translated this relationship into a mathematical formula.17 Sensations, according to Fechner, can be both intensive (sensations of brightness, heat, weight, etc.) or extensive (perception of an extension via sight or touch). Psychophysics deals mostly with the former, but only as far as their quantitative side is concerned. Intensive sensations can indeed be considered according to two aspects: their magnitude (or strength), and their form (or quality). And though the quality of a sensation is invariable—a sensation of red cannot become, let’s say, blue—its quantitative side can vary depending on the magnitude of the stimulus.18 Usually, we 12 On Fechner’s reception in France, see: Serge Nicolas, ‘Les débuts de la psychophysique en France’, Teorie e modelli, 6/2 (2001), 5–28; Larry S. McGrath, Making Spirit Matter. Neurology, Psychology, and Selfhood in Modern France (Chicago 2020), 47–76. 13 Joseph Delboeuf, Étude psychophysique (Bruxelles, 1873). 14 Théodule-Armand Ribot, ‘La psychologie physiologique en Allemagne: la mesure des

sensations’, La revue scientifique, 24 (1874), 553–563. 15 Ibid., 553. 16 Théodule-Armand Ribot, La psychologie allemande contemporaine (Paris, 1879), xix–

xx. 17 Ribot, ‘La psychologie physiologique en Allemagne’, 553–554. 18 Fechner, Elements of Psychophysics, 14–16.

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are able to acknowledge that a sensation has increased or diminished. A more complex task is determining by how much it has done so. In order to do that, Fechner relied on the experimental research on tactile sensitivity led some years before by Ernst Weber.19 In his studies, Weber had wondered how to measure the sensory domain and answered that it consisted in the smallest perceptible difference occurring between two stimuli of the same kind, but with different magnitudes. Let’s consider, for example, our sensitivity to pressure: such sensitivity will be determined by the smallest difference, between for example two weights placed on our hands, required for us to be aware that the initial stimulus has changed. Hence, what we feel is not the weights, but the relation between differences; a relation of differences that is revealed when a certain level of sensory stimulation has been attained, that is, a certain differential threshold.20 Beneath a certain threshold, our sensitivity is numb; beyond it, we feel a change in our sensory sphere. Weber also found out that there exists a constant—different for each sensory modality—between changes of the same stimulus and the aforementioned sensory differences. As for sensations of pressure, that constant is roughly 1/8, which means that if I have in my hand a weight of 30 grams, in order to feel a difference, it is necessary to add 3.75 grams; whereas if I have 60 grams, I need 7.5 grams more to feel that the stimulus has changed. As we can see, the more we increase the magnitude of the stimulus, the more we need a much stronger excitation in order to become aware of a change. Yet, this difference is always felt as the same by the subject.21 In terms of internal perception, there is no difference in passing from 30 to 33.75 grams or from 1000 to 1125 grams. Weber’s observations provided Fechner with a useful tool for developing his own psychophysical doctrine. Fechner’s objective was nevertheless wider and theoretically more challenging: to measure sensations, not only the sensory domain. This passage is crucial because it amounts to the introduction of quantitative methods to psychology. In Fechner’s view, it was possible to consider sensations in turn as measurable

19 Ernst Heinrich Weber, The Sense of Touch (1834), trans. Helen E. Ross, and David J. Murray (New York, 1978). See also: Horst Gundlach, Entstehung und Gegenstand der Psychophysik (Berlin, 1992). 20 Weber, The Sense of Touch, 172. 21 Ibid., 91–92.

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magnitudes, though not in a direct way. Sensations were after all irreducible and undecomposable entities, and as measurement only applies to fractionable objects,22 the only solution was to measure them indirectly, comparatively. In lieu of measuring sensations per se, Fechner intended to measure them through their differences, namely through the smallest difference occurring between two sensations, that is, just-noticeable differences (JND).23 JNDs are thus psychological units corresponding, but not equating, to Weber’s differential thresholds, which are instead physical units. Let’s consider a sensation of weight (S 1 ) given by 3 grams placed in my hand. If 2 grams are added, the sensation I experience (S 2 ) is not the same as the one before. Its strength has increased. But by how much? Now, the strength cannot be obtained by summing up S 1 and S 2 , as sensations are non-directly measurable entities. Nor can we simply say that S 2 is 2 grams heavier than S 1 . That would be nonsensical. It is necessary to find another unit of measurement, a psychological one. What Fechner does is take JNDs as psychological units of measurement. Indeed, as shown by Weber, differences between sensations are always felt in the same way. Fechner deduces that they have, psychologically speaking, the same magnitude and can be used as homogenous and well-defined units. The idea of relying on JNDs to quantify the increase of strength of S 1 and S 2 is fascinating but must be defined. Firstly, we have to pinpoint where these sensations position themselves within a graduated scale of sensations of the same kind. As for sensations of pressure, we will have a scale that begins at ground zero (i.e., the minimum perceptible threshold; the first sensation we are aware of) that corresponds, according to some experiments, to roughly 1/20 of a gram (0.05 grams) in the palm.24 Secondly, we have to understand how this graduated scale develops from zero onward. As shown by Weber, our ability to detect a difference between two stimuli is inversely proportional to the physical magnitude of the first stimulus, which amounts to saying that sensations do not proportionally increase with the increase of external stimuli, but do so much more slowly. Hence, from a mathematical viewpoint, we can say that the 22 On Fechner’s mathematical approach: Verena Zudini, ‘The Euclidean Model of Measurement in Fechner’s Psychophysics’, Journal of the History of Behavioral Sciences, 47, 1 (2011), 70–87. 23 Fechner, Elements of Psychophysics, 60–108. 24 Ribot, ‘La psychologie physiologique en Allemagne’, 558.

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strength of a sensation increases in proportion to the logarithm of the corresponding stimulus strength. That is the well-known Weber–Fechner law, formulated by Fechner as follows25 : S = K log I S indicates the strength of sensation; K is a constant (a.k.a. Weber constant; in sensations of pressure, various research has established that the constant is 1/3, instead of 1/8)26 ; I the physical intensity of the stimulus. With all these elements, it is finally possible to draw a diagram of the relation between sensations and outer stimuli (Fig. 1). The diagram and the law show that sensations, albeit changing in jumps (as Weber’s work had shown through the concept of differential thresholds), actually display a certain continuity. The logarithmic formula, illustrated by the curve connecting one sensation to another, reveals that there is a continuum in the increase of sensations. This was possible only

Fig. 1 Illustration Weber-Fechner

25 In fact, Fechner gave various mathematical formulations of the law. The one displayed here is the simpler. 26 For a table of each sensory modality’s constants, see Wilhelm Wundt, Vorlesungen über Menschen- und Thierseele (Leipzig, 1864), 98.

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by returning to infinitesimal calculus.27 Whereas Weber conceived of the passage between sensations as a difference (Δ), Fechner preferred instead to think of it as a differential (d). The implication is that when we feel a difference between two sensations, as a matter of fact it is always the same sensation that has changed, increasing or decreasing its magnitude. Returning to our previous example, in this graduated scale, S 1 can be placed between the points indicating stimuli of 2.77 and 3.69 grams, whereas S 2 can be placed between the points indicating stimuli of 4.92 and 6.56 grams. Hence, S 2 is greater than S 1 of 2 JNDs. All these reflections are summed up by Ribot in his 1874 article. At this point in time, Ribot seems to have been seduced by this new science, considering it the main road toward the constitution of psychology as a science: The importance of the psychophysical law rests in what it promises: thanks to it, exact measure is applied for the first time to psychic phenomena. […] The problem of sensations is, after all, paramount, since everything depends on it. If the exact science seizes [this question], it will make a breach in the mysterious palace and one day will access it.28

Ribot’s judgment was, nevertheless, destined to change. In his first encounter with psychophysics, enthusiasm prevailed and dimmed his capacity to evaluate it in its fullness. The pitfalls hidden beneath this project of quantification of the mind soon became clear to the French intellectual milieu, influencing Ribot himself, who later wrote: “[psychophysics], although ingenious, does not represent the soundest part of German psychology.”29 Interestingly enough, the first criticisms pertained almost exclusively to the validity of Fechner’s mathematical formulas, and not the possibility itself of applying quantitative methods to psychology. The latter concern appeared only in a later phase of the discussion, thanks, especially to the sharp insights of Henri Bergson (1859–1941).

27 Fechner, Elements of Psychophysics, 51ff. 28 Ribot, ‘La psychologie physiologique en Allemagne’, 563. 29 Ribot, La psychologie allemande contemporaine, xxi.

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3

Mathematical Issues of Fechner’s Law

Ribot’s article had a deep impact on French culture and managed to popularize a discipline that had remained, until this point, unknown to the majority. Yet, such significant exposure also produced an unforeseen backlash. Soon after the issue of Ribot’s text, an anonymous mathematician—who ten years later turned out to be the French mathematician Jules Tannery (1848–1910)30 —published an acrimonious article aimed at demonstrating the inconsistency of the Weber–Fechner law: Since we cannot take the logarithm but of a number, and since the logarithm of a number is a number, it is necessary, for Fechner’s law to be logical, that sensation and excitation are there replaced by numbers. It would be useful to say how we arrive at these numbers, which measure they are expressions of, through which unity we obtain them.31

The point—the anonymous writer continues—is that we measure only through lengths, and to relate sensations to lengths is utterly problematic. This would ideally be possible if physiology could discover a function capable of evaluating the movements produced in the nerves through the influence of outer stimuli. But, until then, the relation has to be taken as purely hypothetical.32 The main mistake of Fechner’s psychophysics consisted thus in the ambiguous status attributed to sensations. Although considered nondirectly measurable entities, they were surreptitiously treated as numbers in the logarithmic formula. Fechner tried to disguise this fact by introducing differentials: it is the dS that counts as a number, not the sensations per se. But, in the anonymous writer’s view, it is absurd to introduce a d if we are not even capable of determining what the difference is between two sensations (Δ). To obtain a Δ from two unknown quantities is, indeed, unwarranted. We can say that this Δ corresponds to our awareness that something has changed in the sensory sphere. However, the statement is preposterous. No parallel is granted between

30 See: Émile Picard, ‘Un géomètre philosophe: Jules Tannery’, Revue des Deux Mondes, 31, 4 (1926), 858–884. 31 Anonymous [Jules Tannery], ‘À propos du logarithme des sensations’, Revue scientifique, 8 (1875), 876. 32 Ibid., 877.

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a mathematical Δ and an introspective comparison. Instead, we should acknowledge that sensations are not discreet units, have no clear borders and cannot represent comparable terms. Otherwise put, sensations are qualitative, not quantitative, phenomena.33 Various responses followed the publication of this article.34 Ribot delivered a somewhat weak answer.35 Wilhelm Wundt (1832–1920) also took part in the discussion.36 But Delboeuf’s reply proved altogether more interesting. It is worth mentioning that Delboeuf had already criticized the Weber–Fechner law from a mathematical viewpoint in his 1873 text Étude psychophysique. Such criticisms were not meant to prove the inconsistency of Fechner’s project, but rather to provide it with sounder foundations.37 There again, he strongly believed in the fact that “as long as a phenomenon, physic or moral, is not translated into numbers, it always leaves in the mind something mysterious.”38 Delboeuf’s response to Tannery is rather fierce, and notes that once one admits, as Tannery does, that sensations can be more or less vivid, it is unwarranted to state that they have no magnitudes. The act of saying “more or less” already contains a certain quantification, albeit still unspecified.39 Here, Delboeuf agrees with Fechner, who had transformed Herbart’s conception of intensive magnitude into an extensive notion. The problem is rather to do with defining this quantity. In this regard, Tannery’s belief that the only way to measure sensations would be to rely on physiology is, according to Delboeuf, absurd. There is no such thing as an exterior side of sensation—not even its neurophysiological process. Instead, sensations have to be measured from sensations, which can be

33 Ibid., 876. 34 The editor of Revue scientifique published in the same issue Ribot’s, Wundt’s and

Delboeuf’s replies. 35 Théodule-Armand Ribot, ‘Réponse à propos du logarithme des sensations’, Revue scientifique, 8 (1875), 877–878. 36 Wilhelm Wundt, ‘La mesure des sensations’, Revue scientifique, 8 (1875), 1017– 1018. 37 Delboeuf, Étude psychophysique, 21–26. See also Nicolas, and Murray, ‘The Psychophysics of J-R-L Delboeuf’, 1298–1299. 38 Joseph Delboeuf, ‘La mesure des sensations’, Revue scientifique, 8 (1875), 1015. 39 Ibid., 1016.

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done indirectly, namely via their relations with physical stimuli.40 The covariation between sensations and stimuli has thus to be preferred to the alleged identity between sensation and neural paths. It is, after all, peculiar to positive sciences that they consider two orders of facts, linked by a cause–effect relation, and measure one to quantify the other.41 Upon closer inspection, Delboeuf’s reply seems to miss the real point of discussion. Tannery had in fact struck a much more powerful blow. The actual goal of his article was to show that the method of indirect measurement cannot be adopted by psychophysics, since it did not compare two facts of the same order. It is one thing to compare heat—considered as the sum of forces given by molecular vibrations—and the mercury column, but quite another to compare sensations and stimuli. In the first case, we are juxtaposing two physical phenomena; in the second case, two different phenomena, one psychological, one physical. Such a difference becomes even more patent when we see that the relation heat-mercury column is indeed 1:1, whereas the relation sensations-stimuli is logarithmic. This is not a secondary matter. Some years later, the neocriticist Charles Renouvier (1815–1903) published an article advocating the correctness of Tannery’s objections.42 Renouvier actually went further. He claimed that the problem did not lie in the invalidity of the method of indirect measurement, but rather in the fact that psychophysicists, while officially adopting this method, did nothing but measure sensations through sensations, in a direct way. Renouvier reported, to this end, Delboeuf’s counterintuitive example of heat measurement: we think we measure heat using a thermometer, but in reality, we initially measured heat through heat, by making it successively increase in identical units. Later on, we represented it with a number and measured the dilatation of mercury in a thermometric tube; we saw that there was a proportionality between the increase of heat and the increase

40 It is worth mentioning that Delboeuf’s psychophysics, unlike Fechner’s, relied on a method of direct measurement of sensations. Here, he is simply addressing Tannery’s criticisms, stressing the correctness of Fechner’s methodology. 41 Ibid. 42 Charles Renouvier, ‘La psychophysique appréciée d’après la doctrine mathématique

de la mesure des grandeurs’, La critique philosophique, 1 (1878), 179–188.

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of volume, and that is why we can now substitute one measurement with another.43 The implicit target of this example was actually Fechner’s psychophysics—specifically, his notion of JND. As noted above, the fact that the difference between two sensations is always felt as the same allowed him to transform a feeling into an absolute unit of measurement. This proves that the starting point of psychophysics was a direct measurement of sensations. We obtain the unit of measurement from an introspective observation, and only at a later stage do we connect, from a mathematical viewpoint, this unit of measurement with the variation of external stimuli. How could this be logical? Renouvier asked. Are we really able to tell when two sensations are equal?44 We can suppose at best that we feel the same difference between sensations, but it is nothing more than pure conjecture, deprived of any scientific value. Sensations are, by their very nature, vague and unquantifiable. Hence, they cannot represent the bedrock of a science.45 In addition, psychophysics is also based on an unacceptable philosophical stance, namely the continuity of mental fact—a continuity which is mathematically expressed by Fechner through the integration of infinitesimal differences.46 For Renouvier, to affirm that there are mathematical infinitesimals in nature is nonsensical. Of course, it is essentially possible to apply this calculus to outer stimuli, but the same cannot be said for sensations, which “are given in their discreet and discontinuous status when compared to one another, and they are produced in the sensory domain only for finished intervals of excitation.”47 These remarks fit perfectly with Renouvier’s philosophical system,48 wherein representations (sensations included) are always discontinuous elements of the mind. That does not 43 Ibid., 185. Joseph Delboeuf, ‘La loi psychophysique et le nouveau livre de Fechner’,

Revue philosophique, 5 (1878), 61. As mentioned, Delboeuf employed a method of direct measurement of sensations; according to Renouvier, this is also Fechner’s modus operandi. 44 A widespread criticism against Fechner was that equality is not the same as equally perceptible. 45 Renouvier, ‘La psychophysique’, 182. 46 Ibid., 179–181. 47 Ibid., 181. 48 See Laurent Fedi, Le Problème de la connaissance dans la philosophie de Charles Renou-

vier (Paris, 1998); Warren Schmaus, Liberty and the Pursuit of Knowledge (Pittsburgh, 2018).

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mean that sensations are not quantifiable, yet their increase or decrease is purely intensive, not extensive. It is a matter of more or less, not of how much. Moreover, since Renouvier’s philosophy builds upon a rejection of the mathematical infinite, sensations are conceived as limited and finished. This entails, if anything, that we can agree with Weber’s law and say that sensations increase in intensity within certain limits, but not with Fechner’s logarithmic law, which ends up being general, transcendental and limitless.49 Tannery’s article strongly impacted subsequent French debates on psychophysics,50 and also provided them with a set of theoretical and mathematical tools with which to oppose this new science from Germany. Indeed, the mainstay of subsequent criticisms would have been how one could compare two orders of phenomena that were substantially different. On the one hand, there were physical stimuli, which are homogeneous, continuous, and extensive; on the other, sensations, which are heterogenous, discontinuous, and intensive. The endeavor appeared to many thinkers unachievable. Yet, the physiognomy of the debate was destined to take on a different guise. Bergson would relocate the battlefield from mathematics to philosophy.

4

Bergson and Fechner: Quality or Quantity?

Despite the lively debate surrounding the mathematical implications of Fechner’s psychophysics, curiously enough this new science of quantification of the mind hardly caught the interest of the philosophical set. Philosophical responses to this novel conception were indeed few and quite weak. A meaningful example of this is the spiritualist thinker Paul Janet (1823–1899), uncle of Pierre Janet (1859–1947) and head of the psychological courses in the French academy. In an 1888 article,

49 Renouvier (‘La psychophysique’, 179–80) here exaggerates the mathematical implications of Fechner’s law by stating that it can be ideally applied to infinite values. 50 Lionel Dauriac, ‘De la notion de nombre’, La critique philosophique, 1 (1882),

321–325; Paul Tannery, ‘Critique de la loi de Weber’, Revue philosophique, 17 (1884), 15–35; Idem, ‘À propos de la loi de Weber’, Revue philosophique, 21 (1886), 386– 387; Georges Sorel, ‘La psychophysique’, Revue philosophique, 25 (1888), 462–463; Paul Tannery, ‘Philosophie mathématique et psychophysique’, Revue philosophique, 27 (1889), 73–82.

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Janet, describing the psychophysical project, defined it as rich in positive outcomes.51 This was a rather bizarre move for a philosopher who belonged to a tradition (spiritualism) that advocated the irreducibility of mind to physiological or physical elements. The impression is that philosophers struggled at first to grasp what was at stake in such a mathematization of the mind, or simply underestimated its theoretical outcomes. Bergson’s doctrine represents an exception.52 Bergson’s first work, Time and Free Will, which in French is Essai sur les données immédiates de la conscience, is a text written for his doctoral dissertation at the Sorbonne in 1889. Less known is that the original title was Qualité et quantité, with Essai sur les données immédiates de la conscience as a subtitle.53 This is interesting, as it demonstrates that the reflection on quantity and quality in psychology, as well as the confrontation with psychophysics, was not a secondary matter for Bergson. It is worth remembering that the thesis was destined to be discussed in front of a jury composed of elder spiritualists, chief among whom was Émile Boutroux (1845–1921), who had not only been reflecting on the problem of quality/quantity, but was also a close friend of Jules Tannery.54 The latter, in synergy with Boutroux, had coined the notion of heterogenous magnitudes, namely those magnitudes that apply to phenomena that are more than a simple addition of units—like, for example, aesthetic objects.55 Boutroux, in turn, had affirmed that qualities differ from quantities in that they cannot be placed externally alongside one another, they have no start or end, they are complex and fluid, and they are the immediate contents of the mind.56 Such reflections undoubtedly impacted the composition of Time and Free Will, to the point that, according to some interpreters, the dedication of the

51 Paul Janet, ‘Une chaire de psychologie expérimentale et comparée au Collège de France’, Revue des Deux Mondes, 86/58 (1888), 535. 52 On Bergson, see, among others: Albert Thibaudet, Le bergsonisme (Paris: 1923); Jacques Chevalier, Bergson (Paris, 1926); Jean-Louis Vieillard-Baron, Bergson (Paris, 1991); Arnaud François, Bergson (Paris, 2008); Mark Sinclair, Bergson (London, 2019). 53 See: Jorge Martin, ‘Récit sur la soutenance des thèses d’Henri Bergson’, Ideas, 3 (2017), 27–38. 54 McGrath, Making Spirit Matter, 62–64. 55 Jules Tannery, Science et philosophie (Paris, 1912), 6, 139. 56 Émile Boutroux, De la contingence des lois de la nature (Paris, 1874), 70–73.

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thesis to spiritualist philosopher Jules Lachelier (1832–1918) was actually a disguised homage paid to Boutroux himself.57 In addition, we should recall that, during the discussion, Boutroux demonstrated a strong interest in the chapter devoted to psychophysics, paying almost no attention to the chapter on durée (duration), which represented in Bergson’s view the most original part of the work.58 The problem of quality and quantity was evidently felt by Boutroux to be predominant. Besides the debts to Boutroux’s and Tannery’s theorizations, Bergson’s text represents an unprecedented attempt to philosophically confront Fechner’s project. The mainstay of the entire analysis is the following: there is no such thing as an intensive quantity. Philosophers had often discriminated between an extensive quantity, which can be accurately measured, and an intensive one, which is susceptible to a certain variation in magnitude, vaguely expressed as “more or less.”59 Now, according to Bergson, this second notion is nonsensical. We always measure through lengths, and lengths are, by their very nature, extensive things. Hence, when measuring the intensive, what we are doing is nothing more than translating it into an extensive notion.60 Usually, we define the intensity of a sensation through the magnitude of the external causes that trigger it: we reckon, for instance, a sensation of brightness to be more intense the more luminous the source is. The problem is precisely how to explain this application of an external criterion to the inner sphere, and to justify the irruption of a quantitative measurement into a nonextensive phenomenon. That is the provocation for which psychophysics must account.61 According to Bergson, there is nothing wrong in what is claimed by Weber’s law, namely that, in order for consciousness to perceive a change in the stimulation, the quantity of excitation added to the initial excitation is always in constant relation with the latter. In fact, Weber limited his analysis to a measurement of external stimuli, with very little involvement

57 Laurent Fedi, ‘Bergson et Boutroux’, Revue de métaphysique et de morale, 2 (2001),

98. 58 Martin, ‘Récit’. 59 Henri Bergson, Time and Free Will (1889), trans. Frank L. Pogson (New York,

2001), 3. 60 Ibid., 4. 61 Ibid., 42.

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of the inner sphere: it is only a matter for the subject to acknowledge a certain change in the sensory domain. Much more problematic is Fechner’s pretension to measure the mind.62 Fechner realized very early on that, in order to introduce measure to psychology, it was first necessary to establish the equality of two sensations.63 The problem—Bergson highlights—is that the only way for sensations to be equal is for them to be identical. Now, identity and equality are very different concepts. Whereas equality applies to things with the same extension, identity applies instead to things with the same quality. When dealing with an external object, we put aside its qualitative element and measure it through its extension. In psychology we are faced with a very different situation. Sensations are only qualitative things, and putting aside their qualitative element is not a viable option.64 There is, then, something highly paradoxical in what psychophysics attempts to do; Fechner himself seems to have sensed that when, defining sensations as irreducible and simple elements, he returned to their minimum differences (JND) as units of measurement. But, Bergson asks, what is a JND? Where does it get its validity from? Assume that I experience a sensation S, and that, increasing the stimulus continuously, I perceive this increase after a certain time. I am now notified of the increase of the cause: but why should I call this notification an arithmetical difference? […] the transition from S to S1 could only be called an arithmetical difference if I were conscious, so to speak, of an interval between S and S1 , and if my sensation were felt to rise from S to S1 by the addition of something.65

The real issue here is that, by giving this transition a name, ΔS, we make it first a reality and then a quantity. Both inferences are unwarranted. ΔS is not a reality, since we only experience two separate states, not the passage from one to another. Nor is ΔS a quantity, given that we are unable to tell what this interval consists of. We could determine it only if S and S 1 were numbers, which is not what Fechner’s psychophysics postulates.66 62 Ibid., 61. 63 Ibid., 63. 64 Ibid., 63–64. 65 Ibid., 65–66. 66 Ibid., 66.

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Delboeuf’s psychophysics encounters the same issue. Instead of integrating minimum differences, he preferred to compare sensations to one another. It was the method of direct measurement of sensations. He placed an observer in front of three concentric rings varying in brightness and caused each of these rings to pass through all the shades intermediate between white and black. When two hues of gray were simultaneously produced on two of the rings (A and B), Delboeuf altered the brightness of ring C and asked the observer to say when the contrast AB was equal to the contrast BC. The aim was to construct a scale of luminous intensities where we pass from one sensation to the next by equal sensible contrasts.67 Now, instead of relying on arithmetical differences, Delboeuf relied on contrast; he substituted the idea of transition with the idea of simultaneity. Still, this contrast is not a reality. Whether we adopt a Δ or a contrast as the unit of measurement, we are providing a mental fact (qualitative, irreducible) with a quantitative value.68 Hence, psychophysics proves to be nothing but a symbolic interpretation of quality in quantitative terms.69 To apply quantitative methods to the unquantifiable is, for Bergson, the result of what we would call today a cognitive bias. Yet, it is a bias that is highly rational. We are indeed naturally inclined to believe that a certain sensation can increase or decrease in intensity; that there exist intensive quantities. However, one thing is a natural inclination— albeit useful—while the other is a reality. As Bergson shows, our reflective consciousness (intelligence) is based on an unconscious spatialization of the world, with space as the prerequisite for discriminating, counting, and ultimately making use of the surrounding objects. Reflective consciousness is first and foremost a utilitarian faculty, directed at facilitating our relationship with the world. Because of a spontaneous inclination, our mind is drawn to apply the same criterion to the inner sphere. That is why sensations are so frequently considered magnitudes and therefore treated as external objects.70 Psychophysics has done nothing but convert such a psychological tendency into a scientific truth.

67 Ibid., 58–59. 68 Ibid., 67–68. 69 Ibid., 69. 70 Ibid., 90–91.

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In a sort of dualist fashion, Bergson stresses the gap between the physical-physiological and the psychological, the former being considered in terms of spatial conditions, the latter in terms of pure duration. Contrary to a longstanding and well-consolidated tradition, Bergson claims that real time cannot be reduced to spatial elements.71 Normally, when considering the very essence of time, succession, we think of an object substituted by another object, substituted by another object, and so on and so forth. Succession is thus the sequential presentation of different things, not juxtaposed in the same space. But then, forced by the utilitarian nature of our mind, we are drawn to count the passing of time; we want to give this succession a magnitude. Therefore, we tend to retain the successive images of the objects in the same space, to the point that juxtaposition overtakes succession.72 Time becomes a juxtaposition of elements into an ideal space. And this space is the homogeneous ground from which we can discriminate, count and abstract all the elements composing it.73 However, imagine a being deprived of any concept of space, one that has not yet acquired any knowledge whatsoever. A being plunged into pure duration. What this being will see is not a homogenous plan, whose parts are exterior to one another, coexistent and simultaneous; instead, she will be faced with the reign of pure heterogeneity. Heterogeneity is the actual immediate datum of consciousness. Our inner life is populated by irreducible and qualitatively different states.74 It is what Bergson calls—not without an implicit reference to Boutroux and Tannery—a “qualitative multiplicity”.75 This reconceptualization of the mind helps us to understand his rejection of psychophysics. Ultimately, the problem is that it conceives the transition from a sensation to another as an increase in magnitude. On the contrary, Bergson claims, it is a qualitative change. Look closer at a sheet of paper lighted e.g., by four candles, and put out in succession one, two, three of them. You say that the surface remains white

71 Ibid., 99–100. 72 Ibid., 77. 73 Ibid., 95–99. 74 Ibid., 95, 97, 104. 75 Ibid., 224–226.

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and that its brightness diminishes. […] Put aside what you remember of your past experiences […]; you will find that what you really perceive is not a diminished illumination of the white surface, it is a layer of shadow passing over this surface […]. If you call this surface in all its brilliancy white, you will have to give another name to what you now see, for it is a different thing: it is, if we may say so, a new shade of white.76

The passage between S and S 1 is not a ceaseless decrease in intensity of the same sensation, but rather the transition from a sensation to a qualitatively different one. There is no continuity from the point of view of intensity or quantity. We have thus two different sensations, a shadow of white and a shadow of gray. How could it be possible to treat them as comparable terms and arithmetically define their difference? One could say, though, that it is undoubtable that there has been a decrease of a certain kind between S and S 1 . Why were we able to tell that the sensation had dimmed, even without knowing that three candles had been extinguished? It is, according to Bergson, because we interpret the shadow of gray in relation to our past experiences concerning the decrease of the number of luminous sources. In the course of our lives, we have learned to put these two things in relation to one another, and we keep on projecting our knowledge about the external world onto our inner one.77 It entails that the scale of sensations postulated by Fechner is, in turn, neither a mathematical truth nor a reality. This question invites Bergson to dissolve an ambiguity that still lies at the center of Fechner’s psychophysics: are sensations continuous or discontinuous? Indeed, following Weber, Fechner acknowledged that sensations always increase by jumps, but at the same time implied, with the logarithmic formula, that between two sensations there was a fundamental continuity. As for Bergson, if we consider psychological facts heterogenous, we would be tempted to believe that these facts are discontinuous—similar to Renouvier. Yet, heterogeneity in Bergson’s text does not read as an absence of unity. Again, it is the reflective consciousness that conceives sensations as discontinuous, due to its recourse to the notion of space. Instead, from the perspective of pure duration, psychological states are not exterior, but rather permeate one another

76 Ibid., 53. 77 Ibid.

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and organize each other as a whole.78 An image to which Bergson often returns is the idea of a melody, where every single note is perceived as a living part of the entire piece.79 The transition from a sensation to another is thus a sort of metamorphosis, displaying no breaks or discontinuities, characterized by progression and synthesis. It is a metamorphosis that does not depend on a variation in magnitude, but rather on a continuous stream of qualitative elements.80

5

Conclusion

The early French reception of Fechner’s psychophysics, if an exception is made for its few supporters, was rather lukewarm and sometimes even hostile. Initially focused on the scientific limits and naiveties of Fechner’s logarithmic law, interpreters soon realized that the main problem of this doctrine was first and foremost theoretical. The process of the theoretical reappraisal of psychophysics first advanced thanks to thinkers who were determined to assess the consistency of notions like “intensive magnitudes” or “quantitative sensations”. Tannery’s and Boutroux’s reflections had no other end than to demonstrate the inadequacy of such concepts, yet their analyses only scratched the surface and did not result in a novel psychological project. That was instead the objective of Bergson’s philosophy, wherein criticisms against Fechner’s psychophysics went hand in hand with the urge to drastically rephrase long-standing and outdated conceptions of the mind. The need to draw a line of demarcation between the outer and the inner world, by rethinking the problem in terms of dualities (quantity/quality, space/duration), lies at the center of Bergson’s text. It would not be unreasonable to say that this very need was ultimately prompted by challenges from emerging mind sciences, not least from psychophysics.

78 Ibid., 110. 79 Ibid., 35, 132, 146, 168. 80 This conception also explains the intellectual proximity between Bergson and William

James.

Index

A Addison, Joseph, 129 age, 4, 7, 9, 11, 12, 14, 16, 26, 37, 40, 42, 45, 51, 53, 57, 58, 60–62, 67, 70, 76, 100, 101, 107, 117, 119, 122, 125, 161, 220, 252, 261, 291 ageing/senility, 53 Agency, 130 air, 26, 32, 36, 53, 104, 105, 115, 123, 127, 185, 187, 188, 234, 242 Alembert, Jean le Rond de, 4–6, 40, 41, 254 Alpetragius, 91 anatomy, 13, 30, 44, 47, 48, 77, 164, 168, 172, 178, 179, 183–185, 222, 255, 281 anger, 125–127 animal economy, 36, 39, 225, 254 anthropometry, 21, 283 appetite, 70, 91, 95, 97, 98, 104, 107, 109, 218

Aquinas, Thomas, 11, 12 Arévalo, Rodrigo Sanchez de, 76 Aristotle/Aristotelianism, 6–9, 11, 18, 23, 25, 64, 71, 72, 87, 146, 151, 202, 217, 233, 255 mathematization of, 201 notion of quantity, 10, 223 attraction (force of gravity), 107

B Bacon, Francis, 29, 34, 35, 46, 66, 90, 91, 93–108, 205, 239 Baglivi, Giorgio, 37, 47, 123, 157–168, 170–173, 204, 225 balance, 16, 31, 46, 51, 112, 113, 115, 116, 118, 128, 160, 166, 231, 232, 255 Barrow, Isaac, 11, 36 Bayle, Pierre, 195, 237 Bellini, Lorenzo, 37, 182, 206, 207, 225, 239 Bellinus, Laurentius, 121, 226

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. Guidi and J. Braga (eds.), The Quantification of Life and Health from the Sixteenth to the Nineteenth Century, Palgrave Studies in Medieval and Early Modern Medicine, https://doi.org/10.1007/978-3-031-15725-7

315

316

INDEX

Bergson, Henri, 50, 301, 306–308, 310–313 Bernoulli, Daniel, 42 Bernoulli, Johann, 37, 196, 215 Bierling, Friedrich Wilhelm, 194, 195, 197 Boë, Franciscus de le (Sylvius), 169 Boethius, Severinus Manlius, Torquatus, 9 Bohn, Johannes, 169 Bordeu, Théophile de, 245 Borelli, Giovanni Alfonso, 36, 37, 40, 159, 206, 207, 225, 229, 239 Botallo, Leonardo, 28 Boutroux, Émile, 307, 308, 311, 313 Boyle, Robert, 2, 169, 204, 205, 208, 235, 236 brain, 37, 44, 100, 124, 146, 167, 170, 282, 283 Bridgman, Percy Williams, 29 Buridan, Jean, 25 C cadaver, 168, 173, 281 Cardano, Girolamo, 19, 23, 26, 28 Carnap, Rudolph, 3–5, 8, 12 certainty/uncertainty, 3, 17, 131, 203, 215, 217, 271 demonstrative/demonstration, 131, 234 evidence, 204 historical, 131 of mathematics, 217, 234 moral, 131 character (individual), 80, 282, 283 chemistry/alchemy chemicals, 47, 163 iatrochemistry, 2, 38, 47, 157, 159, 202 quantification of, 17, 42 Cheyne, George, 206, 211, 227–229, 231, 257

Chinese medicine, 255 circulation, 36, 64, 172, 236, 252–254, 256, 260, 261 climate, 33, 85, 128, 185 clocks. See time analogy with the human body, 112 cold, 12, 17, 33, 81–83, 100, 134, 188, 229, 242, 249, 252, 253, 256 Cole, William, 129 complexity, 31, 34, 43, 44, 48, 70, 95, 137, 141, 152, 173, 177, 185, 192, 193 Comte, Auguste, 43, 44 Conimbricenses (Coimbra Jesuits), 21 consumption, 56, 58, 100, 103, 112, 262 Cornaro, Alvise (Luigi), 18, 44, 45, 52–67, 100 Counter-Reformation, 54, 70 Cusa, Nicholas of (Cusanus), 19, 21–24 D data, 32, 37, 48, 99, 164, 172, 180, 181, 183, 187, 208, 209, 211, 212, 222, 230, 231, 237, 250, 273, 274 death, 56, 65, 66, 81, 137, 261 De Chambaud, Jean-Joseph Menuret, 39, 40, 253, 254 degrees (distances), 25, 26, 106 Delboeuf, Joseph, 294, 297, 303–305, 310 density (specific gravity), 97, 236 Descartes, René/Cartesianism, 33, 35, 41, 47, 112, 131, 133–142, 146, 149, 150, 153–155, 202, 204, 205, 207, 212–214, 216, 217 De Villa Nova, Arnaldus, 25 De Witt, Jan, 38 Diderot, Denis, 254, 278

INDEX

diet, 26, 45, 51, 57, 59, 60, 62–65, 107, 115, 215, 250, 252 digestion, 37, 42, 58, 61, 115, 123, 126, 135, 172, 225 intestine, 229 stomach, 172 Driessen, Anthonius, 214 dry, 61, 73, 81–83, 229, 245 Ducheyne, Steffen, 207 Düsing, 269 E education, 45, 69, 70, 72–74, 76–80, 85, 129, 163, 259, 261 Enlightenment, 6, 248 Erasistratus, 28, 116 ethics, 2, 80 Euclid, 9, 19, 221 evidence. See certainty/uncertainty excretion, 112, 232, 235 exercise, 79, 103, 115, 124, 125, 129, 251, 259 experience/empiricism, 34, 35, 38, 48, 51, 56, 61, 64, 79, 116, 120, 122, 123, 126, 128, 131, 132, 143, 159, 160, 162, 164, 167, 195, 205, 211, 221, 247, 256, 259, 271, 272, 274, 282, 290, 312 experimentalism/experimentations, 13, 30, 31, 92, 112, 168, 171, 173, 205, 207, 212, 213, 228, 231, 235, 237–239 explanation, 42, 47, 104, 112, 113, 125, 127, 138, 139, 141, 151, 155, 159, 165, 194, 207, 220, 225, 226, 288 extension. See space F Falconer, William, 243

317

fear, 46, 125–127, 129 Fechner, Gustav Theodor, 42, 44, 50, 293, 294, 296–305, 308, 309, 312, 313 fibers, 160, 166, 167 Fick, Adolf Eugen Fick, 42 flesh, 64, 71, 82, 83, 104, 136, 165 Floyer, John, 37, 48, 49, 248–250, 252–256, 258–263 fluids blood, 36, 136, 164, 168, 190, 236, 251. See also Humors quantity of, 36 saliva, 164, 169, 172, 173, 236 Fonseca, Pedro da, 147 foods promote or hinder perspiration, 126 quality, 57 quantity, 28, 56, 58, 118 Formey, Jean-Henri-Samuel, 6

G Galen, 13, 15–18, 51, 57, 74, 80, 82, 86, 111, 237, 241, 242 Galilei, Galileo, 31, 249 Gall, Franz Joseph, 43, 266, 282 Gassendi, Pierre, 137–139, 148 Gaukes, Yvo, 203, 205, 214–219, 222, 231–235, 238 Gavarret, Luis-Denis-Jules, 42 gender, 81, 136, 146, 252 female, 81 male, 81 generation, 47, 136, 137, 139, 141, 142, 146, 152, 153, 227, 277, 278, 285, 289 God, 19, 22, 47, 66, 91, 135, 138–140, 144, 146–148, 152–155, 179, 217, 223, 224 Graaf, Reinier de, 169 Graniti, Niccolò, 214

318

INDEX

Graunt, John, 38 Graves, Robert, 243 growth, 73, 145, 191, 294 Gruman, Gerald, 62

H Hales, Stephen, 37 Haller, Albrecht von, 41, 243, 278 Harley, Andreas, 214 Harvey, William, 17, 24, 36 health definition, 28 preservation, 117, 180 standard, 118–120 health-care system, 178, 181 heart blood pressure, 37 circulation, 36 force of, 229 mechanization of, 36 quantification, 132 heat, 10, 17, 73, 75, 83, 100, 104, 134, 152, 188, 228, 297, 304 Heberden, William, 243 Hegel, Georg Wilhelm Friedrich, 49, 265–273, 275, 276, 278, 280–284, 286, 289–291 Helmholtz, Hermann von, 42, 44, 246, 247, 295 Helmont, Jean Baptiste van, 2, 23, 24, 116 Herbart, Friedrich, 294, 303 Herophilus of Alexandria, 14 Heyde, Anton de, 169 Hippocrates of Kos, 13 historical phenomenology, 128 Hoffmann, Friedrich, 192, 219–222, 235–238, 254 Holyday, Barten, 111, 112, 120, 130 homo clausus , 131 hospital, 170, 181, 183, 252

Huarte de San Juan, Juan, 45, 71, 78 Hudde, Jan, 38 humid, 81, 83 Humors, 16, 45, 73, 102, 251, 254 humours/humoralism black bile, 115, 251 blood, 115, 136 phlegm, 107, 115, 251, 255 yellow bile, 115, 251 Huygens, Christiaan, 38, 179, 206, 226 hydrometer, 236 Hypothesis, 92, 146, 163, 165, 209, 223, 271, 275, 277, 280

I illness/sickness, 3, 23, 26, 39, 58, 66, 75, 117, 130, 181, 182, 219, 220, 222, 236 imagination, 81, 86, 143, 192 inertia, 49, 153, 284 ingenium/wit/talents, 71, 74, 76–79, 81, 83–87 inner-outer, 286 insensible perspiration, 112, 115–118, 120, 124, 128, 132, 210 irritability, 41, 278–281

J Janet, Paul, 306, 307 joy, 46, 55, 126

K Kant, Immanuel/Kantism, 139, 268, 275–277 Keill, James, 36, 205, 206, 210, 211, 231, 257 Keill, John, 210, 211, 213 Kepler, Johannes, 19, 24 Kielmeyer, Carl August, 279

INDEX

Kircher, Atanasius, 249 Koyré, Alexandre, 5, 13 Kuhn, Thomas S., 30, 99

L Lachelier, Jules, 308 latitudo sanitatis , 16, 26, 32 Lavoisier, Antoine, 42, 242, 246 Leeuwenhoek, Antoni van, 169 Leibniz, Gottfried Wilhelm, 48, 49, 140, 177–197, 213, 237, 278 Leonardo da Vinci, 19 Lessius, Leonard, 45, 52, 53, 64, 65 life, 2, 3, 18, 30, 36–39, 42, 45, 52–57, 59, 60, 62, 65–67, 70, 72, 73, 80, 90, 93, 100, 109, 112, 128, 132, 136, 137, 139, 146, 148, 150–152, 177, 182, 185, 220, 249, 254, 262, 268, 269, 275, 277–279, 284, 285, 287–290, 311 animal, 146, 152 dialectical understanding, 43 Galenic definition, 59 lifestyle, 56, 59, 220 mechanical definition, 39, 43, 139 of plants, 146, 151, 152 prolongation, 90, 100 liver, 28, 103, 115 Locke, John, 131 logic, 7, 16, 21, 22, 25, 149, 209, 216, 219, 222, 231, 235, 248, 267, 273, 291 and mathematics, 203, 219, 221, 231, 235 and medical reasoning, 203, 216, 219, 231 Louis, Pierre Charles Alexandre, 42 Lower, Richard, 37 lungs, 158, 168, 226, 234

319

M macrocosmos and microcosmos, 21, 30, 203, 208 magnitude, 3, 4, 7–11, 15, 18, 22, 25, 218, 223, 224, 228, 233, 279, 295, 297–299, 301, 303, 308, 310, 311, 313 Malebranche, Nicolas, 47, 133, 139–143, 145, 147–149, 151–153, 155 Malpighi, Marcello, 142, 149, 160, 168–170, 239 maniac, 123 Marci, Jan Marek, 249 Mathematics/mathematical algebra, 224, 231 geometry, 9, 30, 35, 92, 213, 231 and nature, 17, 35 knowledge, 7, 10, 30, 43, 49, 202, 212, 273, 290 ratios, 35, 273 and reasoning, 37, 239 matter/natural bodies atomism, 192 continuity, 92 corpuscularianism, 31 inorganic, 275 motion, 92, 97, 147–149, 151, 213 organic, 275 powers, 106, 148, 257 res extensa, 47 measurement ponderation, 130 unit of measure, 6, 19, 26, 305 weighing, 46, 230 mechanism/mechanization, 5, 36–38, 42, 47, 49, 137, 139, 141, 147, 151, 153, 155, 165, 172, 177, 185, 192, 193, 203, 205, 207, 212, 215, 220, 238, 243, 256, 275

320

INDEX

iatromechanics, 37, 47, 158, 207, 225 limits of, 191 Melanchthon, 77 membranes, 166 Mersenne, Marin, 19, 154 metabolism, 31, 32, 34, 222 metaphysics, 2, 6, 149, 194, 214, 277 Michelotti, Pietro Antonio, 190, 193 microscope, 48, 142, 145, 165, 189, 191 mind, 21, 22, 34, 38, 43, 44, 46, 48, 50, 53, 55, 70, 75, 76, 87, 91, 98, 113, 115, 125, 131, 140, 144, 147, 154, 155, 187, 194, 209, 217, 218, 228, 232, 235, 238, 283, 284, 295, 301, 303, 305–307, 309–311, 313 measurement of, 309 mind-body relationship, 113 moderation (temperance), 18, 45, 51, 55, 58, 115, 119, 125 Montaigne, Michel de, 58 Montpellier school, 39 morality, 97, 123 Mullen, Allan, 120, 121 Müller, Johannes Peter, 295 muscles, 159, 160, 164–166, 192, 253, 280 quantification, 252 music, 15, 54, 63, 93 N Naiveu, Matthijs, 242, 245 natural history, 37, 92, 96, 108, 183, 184, 209, 211, 217, 221, 266 nature human, 18, 22, 37, 40, 79, 90, 94 natural temperament, 18, 58, 79 second nature, 57, 58 Nebrija, Elio Antonio de, 76 nervous system, 37, 44, 279

neurophysiology, 303 Newton, Isaac/Newtonianism, 35, 47, 139, 205, 207, 227, 238, 239 non-naturals, 53, 115, 117, 118, 121, 242 Nuck, Antonius, 169 nutrition, 45, 53, 136 O Obizzi, Ippolito, 24, 113 Observing Reason, 49, 265, 266, 270–279, 283, 286, 288–290 Occasionalism, 141, 145, 147, 148, 154, 218 operationalism/operationalization, 29, 32 operational physics, 94 Oresme, Nicolas, 25 organism, 16, 40, 41, 43, 46, 112, 135, 211, 257, 266–269, 276, 277, 279–281, 283, 284 Ortiz, Alonso, 76 P Pascoli, Alessandro, 164 Passavant, Daniel, 42 passions, 34, 53, 67, 74, 80, 84, 100, 115, 124–127, 129, 218 affections, 125 emotions, 125, 126 pathology, 1, 42, 47, 158, 159, 173 Paulze, Marie Anne, 242 Pecquet, Jean, 36, 172 Petty, William, 38 pharmacology, 17, 25, 182 pharmacopoeias, 103 quantification, 16 phrenology, 49, 266, 281–284 physics (mathematical physics), 13, 48, 204, 208, 212, 223, 231, 239

INDEX

laws of motion, 212 laws of physics, 163 physiognomy, 19, 49, 281, 306 Pinel, Philippe, 42 Pitcairne, Archibald, 36, 37, 205–211, 213, 223–227, 234, 238, 257 plants, 136–138, 144, 146, 150–152, 181, 197, 258 life of. See life Plinius, 182 Plutarch, 72, 73, 75 Poisseuille, Jean-Léonard Marie, 42 Possevino, Antonio, 77 preformation/encapsulation theory, 47, 139, 141, 143–145, 150, 151 proportions and quantity, 64 food, 57, 58, 63–65, 127, 220 geometrical, 18, 223, 230 human body, 18, 20, 21 humors, 16, 26 Protestantism, 53, 54, 66, 70 psychology experimental, 44, 297 psychophysiology, 115 quantification of, 50 pulse/sphygmology, 13–16, 23, 24, 28, 33, 37, 49, 99, 189, 241–245, 248, 250–252, 254–256, 260–262 pulsilogium, 24, 33, 112, 249 purgatives, 46, 101–103, 105–107, 109, 129

Q quality, 12, 17, 57, 65, 82, 83, 101, 102, 105, 107, 108, 119, 148, 209, 227, 236, 242, 258, 272, 297, 307–310, 313 qualitative conception of nature, 202

321

Quincy, John, 113, 117–119, 122–128, 131, 210 R Ramazzini, Bernardino, 186, 188 rationalism, 159 reasoning analogical reasoning, 46, 159, 234 axiomatism, 213, 217, 219, 221 induction, 196 inference, 309 syllogisms, 214 Redi, Francesco, 149 Régis, Pierre-Sylvain, 47, 139, 140, 149–153, 155 registers, 46, 98, 99, 181, 186 records, 46 Regius, Henricus, 33, 113, 204, 214 Renouvier, Charles, 304–306, 312 respiration, 37, 42, 117, 135, 159, 242, 246 rest, 53, 58, 78, 103, 117, 216, 249, 281, 301 Rhetorics, 7 Ribot, Théodule-Armand, 297, 301–303 Robinson, Bryan, 37, 243 rules, 23, 51, 57, 66, 67, 70, 92, 97, 104, 127, 140, 190, 217, 221, 258, 260 S Santorio, Santorio (Sanctorius), 24, 31–34, 38, 46, 48, 111–113, 116–120, 122–128, 130–132, 204, 225, 228, 229, 235, 249, 250 Schelling, Friedrich Wilhelm Joseph, 266, 280, 284–287, 296 Sclano, Salvo, 26 seasons, 76, 117, 119, 187, 242, 252

322

INDEX

semiotic, 45, 235, 238 Senac, Jean, 239, 243 sensation, 30, 44, 50, 293, 295, 297–306, 308–313 sensibility, 41, 118, 248, 259, 279, 280 Sensory knowledge, 218 sleep, 53, 119, 129, 132 sorrow (melancholy), 59, 62, 115, 125–127 soul, 34, 45, 54, 63, 66, 70, 73, 75, 80, 85–87, 125, 135, 136, 142, 148, 150–153, 180, 184, 218–220, 267–269, 279, 281, 283–285 distinction from the body, 86, 268, 283 powers/faculties, 86, 124, 131, 281, 284 space, 8, 21, 24, 35, 46, 96–98, 104, 106, 108, 117, 118, 121, 134, 155, 224, 226, 310–313 extension, 134, 155 Speroni, Sperone, 60, 61 Spinoza, Baruch, 296 Spirit, 4, 40, 46, 49, 66, 86, 100, 102, 104, 115, 123–126, 136, 146, 165, 169, 252, 270, 282, 289 Stahl, Georg Ernst, 177, 184, 185, 196 statical medicine (statics), 32, 113, 128, 166, 223, 232, 238 statistics, 38, 42, 185, 188 Steffens, Henryk, 286, 287 Steno, Nicolas, 37, 183, 185, 193 stomach. See digestion structure, 29, 32, 43, 49, 77, 81, 84, 153, 164, 165, 168, 179, 184, 191, 192, 204, 222, 265, 267, 268, 270, 275, 276, 280, 282, 285

Suárez, Francisco, 6, 147 surgery, 171, 184 Swammerdam, Jan, 142, 143 Sylvanius, Bartholomeus, 80 Sympathy, 53, 107–109

T Tannery, Jules, 302, 307 Tartaglia, Niccolò, 10 teeth, 158, 173 teleology, 275–277 finalism, 139 inner purposiveness, 267 temperaments, 3, 18, 45, 77, 78, 81, 82, 84–86, 242, 251 temperature, 10, 16, 33, 99, 101, 109, 126, 135 Temple, William, 66 thermometer, 10, 30, 48, 112, 129, 189, 252, 304 time/duration, 2, 5, 7, 8, 10, 13, 15, 16, 22–24, 26, 28–31, 33–36, 41, 44, 46–50, 56, 60, 65, 76, 77, 79, 80, 82, 93, 96–101, 103, 105, 106, 108, 109, 115, 117, 119, 120, 122, 123, 126, 135, 136, 140, 144, 146–149, 151–153, 155, 161, 162, 173, 176–179, 182, 184, 186, 188, 191, 202, 205, 210, 211, 214, 224, 225, 233–235, 255, 257, 261, 262, 265, 267–271, 277, 278, 289, 290, 294, 301, 308, 309, 311–313 Aristotelian definition, 135 instrumentum acolingen, 28 measurement of, 97, 108 mechanical clocks, 243 water-clocks, 16, 22 tongue, 173

INDEX

U urine/uroscopy, 13, 23, 102, 112, 115, 117, 189, 190, 236, 237, 241, 242, 244 V Valsalva, Antonio Maria, 170, 171 van Besouw, Jip, 201 Veronese, Guarino, 71, 72, 75 Vesalius, Andreas, 19, 30 vessels, 6, 28, 36, 138, 158, 169, 192, 223, 229, 230, 232 vitalism, 41, 151 Vitruvius, 19, 20, 22 Voit, Carl von, 42 Volckamer, Johann G., 188

323

body weight, 46, 119–121, 123 changes, 31, 104, 109 deficiency of, 165 metaphysics of, 24 scale, 121 weighing chair, 120, 249 weight and age, 26 weight and food, 28 weight and health, 22, 28, 46, 119, 120, 257 weight and humors, 26 weight of fluids, 194 Wharton, Thomas, 37 Wolff, Christian, 213 Wundt, Wilhelm, 303 Y youth, 73, 78

W water-clock, 16, 22 Weber, Ernst Heinrich, 7, 22, 294, 298–300, 306, 308, 312 weight

Z Zimmermann, Johann Georg, 7, 278 Zwinger, Theodor II, 198