Empiricist Theories of Space: Space and Experience in Early Modern Philosophy [1st ed.] 9783030576196, 9783030576202

Table of contents :
Front Matter ....Pages i-ix
Introduction: Ideas of Space and Their Relation to Experience in Early Modern Philosophy (Laura Berchielli)....Pages 1-48
Hobbes on Space as Imaginary Space (Martine Pécharman)....Pages 49-78
Locke on Space and Substance (Martha Brandt Bolton)....Pages 79-93
Spacious Minds and Spatial Spirits: John Locke on Space and Thought (Philippe Hamou)....Pages 95-115
Berkeley’s Theological Challenge of Absolute Space in the Principles of Human Knowledge (Luc Peterschmitt)....Pages 117-129
The Consequences of the Consequences of the Principles for the Theory of the Principles (Margaret Atherton)....Pages 131-141
Berkeleian Instrumentalism: From Substance to Space (Robert Schwartz)....Pages 143-160
Berkeley’s Two Notions of Extension (Laura Berchielli)....Pages 161-186
The Ideality of Space in Enlightenment Empiricism: The Idéologues’ Contribution (Elisabeth Schwartz)....Pages 187-218

Citation preview

Studies in History and Philosophy of Science 54

Laura Berchielli  Editor

Empiricist Theories of Space

Space and Experience in Early Modern Philosophy

Studies in History and Philosophy of Science Volume 54

Series Editor Catherine Abou-Nemeh, History Programme, Victoria University of Wellington, Wellington, New Zealand Advisory Board Steven French, Department of Philosophy, University of Leeds, Leeds, UK Nicholas Rasmussen, University of New South Wales, NSW, Australia John Schuster, University of Sydney/Campion College, NSW, Australia Richard Yeo, Griffith University, Nathan, QLD, Australia Stephen Gaukroger, School of History & Philosophy of Science, University of Sydney, Sydney, NSW, Australia Rachel Ankeny, University of Adelaide, Adelaide SA, Australia Peter Anstey, School of Philosophical & Hist Inquiry, University of Sydney, Sydney, NSW, Australia Clemency Montelle, School of Mathematics & Statistics, University of Canterbury, Christchurch, New Zealand Ofer Gal, Unit for History and Philosophy of Science, University of Sydney, Sydney, Australia

Studies in the History and Philosophy of Science is devoted to the history of science and historically-informed philosophy of science. It includes monographs, edited collections, and translations of primary sources. The volumes cover the whole period of scientific investigation, from antiquity to recent developments. More information about this series at http://www.springer.com/series/5671

Laura Berchielli Editor

Empiricist Theories of Space Space and Experience in Early Modern Philosophy

Editor Laura Berchielli Department of Philosophy Université Clermont Auvergne Clermont-Ferrand, France

ISSN 0929-6425     ISSN 2215-1958 (electronic) Studies in History and Philosophy of Science ISBN 978-3-030-57619-6    ISBN 978-3-030-57620-2 (eBook) https://doi.org/10.1007/978-3-030-57620-2 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The idea for this volume comes from the discovery of the richness and articulation of the theories of space developed by empiricist philosophers together with the observation of the marginal place these kinds of theories occupy within secondary literature in early modern philosophy. In an oversimplified way, this literature may be divided into two broad categories: the first addresses the topic through the perspective of a history of the concept of space; the second takes a “monographic” perspective and deals with the way according to which an individual author, belonging to the empiricist tradition, tackles the issue. As regards the historical perspective, the classic studies of A.  Koyré (Koyré 1957), E. Grant (Grant 1981) and M. Jammer (Jammer 1993) deal with the notion of space from the angle of the concept change in physics and cosmology during the ‘scientific revolution’. Within this framework, they present the Newtonian concept of space and the critical discussion of it (i.e. Newton, Leibniz and their legacies) as the outcome of the reflection on space of this period.1 This perspective leads scholars not only to study the notion of space in its relation to the notions of body and void, but also to examine empiricist philosophers only if they had developed a critical reflection on the Newtonian concept of absolute space.2 Despite many differences among these approaches, they all give empiricist views a relatively marginal place. And accordingly, they usually discuss only one empiricist theory, deemed to represent the whole of the empiricist approach. In this way, they produce the illusion that a homogeneous theory of space, shared by all empiricist authors, exists. However, reality is quite different from this supposed

1  This physico-cosmological framework applies also to Grant 2016, even if the author mainly aims to highlight the presence of theological questions and of a scholastic legacy within the transformations that the notion of space undergoes during the early modern period. More recent and in the same physico-cosmological perspective is Miller 2014. For studies on conceptualizations of space and place in early modern natural philosophy that do not adopt the ‘Newtonian’, ‘physico-cosmological’ framework see Vermeir and Regier 2016. 2  An anthology on space open also to empiricist authors is Peterschmitt 2013.

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homogeneity: among empiricists, there is a wide variety both in the way of approaching the notion of space and in the resulting concept.3 The number of monographs on empiricist notions of space varies significantly according to the author studied. While Hume’s theories of space and, to a lesser extent, Berkeley’s have generated a large number of studies,4 what Hobbes, Locke or Condillac wrote about space has been of relatively low interest to scholars.5 However, this unequal interest is not the major obstacle to the reception of empiricist conceptions of space. The guiding principle of monographs is to focus on an author and on the relationships between their view on space and other parts of their work. This systematic approach, although legitimate, leads to the isolation of empiricist theories of space from one another and makes determining the relationship between the different concepts and approaches difficult. Since these critical studies treat, in general, only one author at a time, the literature on the empiricist concepts of space tends to be kaleidoscopic and fragmented. I was therefore led to believe that the relative marginalization of the theories of space developed by empiricist authors was linked to two inverse and complementary limits: the excessive compartmentalization of the by-author historiography, on the one hand, and the excessive homogenization of the historical approach, on the other. This volume aims to invite the reader to overcome these barriers and to discover empiricist theories of space in all their diversity and their problematic unity. A first consideration of this issue began when organizing the project Pneuma. The Space of Spirit: Theories of Space, Pneumatology and Physico-Theology in the Newtonian Age, funded by the French Agence Nationale de la Recherche (ANR), of which it formed one of the three main research axes. Within the framework of this project, two international conferences organized at the Université de Clermont-­ Ferrand allowed the discussion on this issue to develop. The first, organized in 2011, was entitled L’espace dans l’esprit. L’empirisme classique et la métaphysique de l’espace and the second was entitled Quantité/Qualité: perspectives croisées XVIIe/ XXe siècle and held in 2013. The papers collected here originate mainly from the lectures delivered during the first conference on the metaphysics of space. I would first like to thank all the authors for their valuable contributions and for their patience in completing the volume. I would also like to thank the Directors of Pneuma, Philippe Hamou and Laurent Jaffro, for giving me the opportunity to collaborate on this project and the Clermont-Ferrand Centre of Research Philosophies et rationalités (PHIER) for supporting part of the research. I feel particularly grateful to Sébastien Gandon, colleague, Director of the PHIER and friend, for all the 3  In a recently published book on the metaphysics of space, E. Slowik (Slowik 2016) appears to carve out a niche for empiricists and he entitles one of the last chapters: ‘The Rise of the Empiricist Approach to Space. Berkeley as Exemplar’. However, as Berkeley’s position is presented as representative of the whole tradition, he participates in the ‘homogenization’ of the empiricist concepts here at issue. 4  See, for example: Frasca-Spada 1998; Jacquette 2001; Jesseph 1993; Falkenstein 1994. A more extensive bibliography may be found in the first, introductory chapter of this volume. 5  See, for example: Slowik 2014, Gorham and Slowik 2014, Yolton 1983, 65–71.

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help he gave me and to Melissa Fox-Muraton for her generous linguistic revision of parts of the manuscript. Clermont-Ferrand, France  Laura Berchielli

References Falkenstein, L. 1994. Intuition and Construction in Berkeley’s Account of Visual Space. Journal of the History of Philosophy 32(1): 63–84. Frasca-Spada, M. 1998. Space and Self in Hume’s Treatise. Cambridge: Cambridge University Press. Gorham, G., and E. Slowik. 2014. Locke and Newton on Space and Time and Their Measures. In Newton and Empiricism, ed. Z.  Biener, and Schliesser, 119–137. Oxford: Oxford University Press. Grant, E. 1981. Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. Cambridge: Cambridge University Press. Jacquette, D. 2001. David Hume’s Critique of Infinity. Leiden/Boston/Köln: Brill. Jammer, M. 1993. Concepts of Space. The History of Theories of Space in Physics. Cambridge, MA: Cambridge University Press. Jesseph, D.M. 1993. Berkeley’s Philosophy of Mathematics. Chicago/London: University of Chicago Press. Koyré, A. 1957. From the Closed World to the Infinite Universe. Baltimore: The John Hopkins University Press. Peterschmitt, L., ed. 2013. Espace et métaphysique de Gassendi à Kant. Anthologie. Paris: Hermann. Slowik, E. 2014. Hobbes and the Phantasm of Space. Hobbes Studies 27: 61–79. Slowik, E. 2016. The Deep Metaphysics of Space. An Alternative History and Ontology Beyond Substantivailism and Relationism. Zurich: Springer. Vermeir, K., and J. Regier, eds. 2016. Boundaries, Extents and Circulations. Space and Spatiality in Early Modern Natural Philosophy. Zurich: Springer. Yolton, J.W. 1983. Thinking Matter. Materialism in Eighteenth-Century Britain. Chicago: Minnesota University.

Contents

1 Introduction: Ideas of Space and Their Relation to Experience in Early Modern Philosophy��������������������������������������������    1 Laura Berchielli 2 Hobbes on Space as Imaginary Space������������������������������������������������������   49 Martine Pécharman 3 Locke on Space and Substance ����������������������������������������������������������������   79 Martha Brandt Bolton 4 Spacious Minds and Spatial Spirits: John Locke on Space and Thought����������������������������������������������������������   95 Philippe Hamou 5 Berkeley’s Theological Challenge of Absolute Space in the Principles of Human Knowledge ����������������������������������������������������  117 Luc Peterschmitt 6 The Consequences of the Consequences of the Principles for the Theory of the Principles����������������������������������������������������������������  131 Margaret Atherton 7 Berkeleian Instrumentalism: From Substance to Space������������������������  143 Robert Schwartz 8 Berkeley’s Two Notions of Extension ������������������������������������������������������  161 Laura Berchielli 9 The Ideality of Space in Enlightenment Empiricism: The Idéologues’ Contribution ������������������������������������������������������������������  187 Elisabeth Schwartz

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Chapter 1

Introduction: Ideas of Space and Their Relation to Experience in Early Modern Philosophy Laura Berchielli

Abstract  This introduction has two aims. The first is to describe synthetically, for each author belonging to the tradition of classical empiricism, the main characteristics of his approach, the notion of space that results from it, and the place it occupies within his philosophy. The second is to show that, despite the individual particularities of each theory, there are some common features concerning both the content of the notion of space and the method adopted for its determination. This will lead us to an examination of the differences between varying conceptions of the contents of spatial experience, as well as of the diverse ways in which these are analysed by classical empiricists. We will provide a general framework in which to situate the more specific and in-depth discussions that will be developed in the following chapters, of which we will give a brief overview at the end of this introduction.

1.1  Introduction For the last 20 years or so, the existence and identification of a classical empiricist school has been the object of critical reflection and discussion. These discussions have shown that there is not a univocal theoretical frame shared by all the authors we usually call “empiricists” and that there is rather a variety of approaches and ways to accomplish the “empiricist project” taken in the large and vague sense of relating ideas and knowledge to experience and founding the former on the latter.1 Neither Locke nor Berkeley nor Hume employs the term “empiricism” to characterize their philosophy. In those days, there was no school or movement explicitly named “empiricist” and even in its subsequent use, the term “empiricism” is not 1  See Loeb 1981; Vanzo 2016; Anstey 2005; Wolfe 2010; Salter and Wolfe 2009; Biener and Schliesser 2014; Gaukroger 2010, 2014.

L. Berchielli (*) Université Clermont Auvergne, Clermont-Ferrand, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 L. Berchielli (ed.), Empiricist Theories of Space, Studies in History and Philosophy of Science 54, https://doi.org/10.1007/978-3-030-57620-2_1

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univocal; its use has different meanings depending on the context and the period to which it is applied. In what follows in this introduction, when we use the term “empiricism”, it is important to bear in mind that we refer to a set of authors (Locke, Berkeley, Hume, Condillac, and the Idéologues) and their texts rather than to a family of homogenous and well defined positions. This being said, when the aim is to study, not the general features of a supposed classical “empiricism”, but only the ways to tackle the notion of space and its empirical origin (through the senses or through the operations of the understanding), could we not try to discern, despite the variety of issues and theories, a common base that would provide insights concerning the perspective from which the issue of space is approached? Are there not a set of shared theses that could clarify – at least in a first approximation – on the one hand, the surfacing of certain common features, and, on the other, the peculiar difficulties that the issue of space may pose to them? Two features of the idea of space may explain why it represents a challenge when it is studied starting from the particular and sensible contents of experience. The first has to do with the content of spatial ideas, the second with the application of an analytical method to these ideas. 1. The idea of space is transparent in experience and it is given only when it is accompanied by other sensations that  – at least for some authors  – are not in themselves spatial. Our authors intend then to grasp the idea of space through different kinds of sensible contents, such as, for example, colour, tangible qualities, the sensations linked to pressure or to the movement of the proper body. However, the positions vary not only in relation to the kinds of sensation to which spatial sensations could be reduced, but also in relation to the starting point of this process of reduction, i.e. the particular spatial ideas. The authors differ in fact in the way of conceiving the sensible perceptions that instantiate spatial ideas. The variations between the particular ideas that should be counted as spatial are important. Locke, for example, claims that it is possible to perceive the idea of the distance between the parts of a concave surface either as a distance filled with matter or as a distance deprived of body, whereas Hume maintains that the perception of two luminous points in absolute darkness is not a perception of space. Also, according to Berkeley, the ideas perceived by sight are not spatial in the proper sense of the term, whereas according to Locke and to Hume, spatial ideas are equally perceived by sight and by touch. A wide variety of ways of conceiving can be found also in relation to the ways of conceiving the operations of the understanding involved in the grasp of the idea of space. According to the authors, the understanding has very different capacities and it cannot in every case form the same types of contents. In Locke, for instance, the understanding is capable of adding indefinitely any finite, determinate length, while this is impossible in Hume and in a sense also in Berkeley and Condillac. Similarly, Locke’s understanding has a capacity of abstraction that is rejected by Berkeley and Hume. And also if, following Locke, Berkeley, and Hume, the understanding does not need to learn to perceive the co-existence of sensible points, according to

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Condillac in the Traité des sensations, this capacity is not immediately given, and it is only when the subject has progressively developed his capacities of attention and memory that he will become able to perceive a co-existence, and, he will be able to perceive a co-existence of a larger number of parts only if he is endowed with the sense of touch and with the capacity of moving his own body. By virtue of these large variations concerning the content of spatial ideas and also the capacities of the understanding, there also exists a wide range of conceptions of the general idea of space. Locke thinks that the understanding may have the idea of an empty space, endowed with a kind of infinity and infinite divisibility. On the contrary, Berkeley and Hume claim that idea of space is always linked to the appearance of sensible qualities (colours or tactile qualities) and is not infinitely divisible. Finally Condillac maintains that there is no unique idea of space – there are different ideas of space whose richness and articulation are related to the structure of the different sensorial modalities, the capacity of reflection and the capacity of movement. 2. The second feature of the notion of space that challenges the empiricist project (taken in its broadest sense) is rather methodological and concerns the application of the analytical method to spatial ideas. Locke, Berkeley, Hume, and Condillac try to reduce ideas and knowledge to experience through one of the possible forms of analysis. Of course, according to the authors, the notion of analysis takes different forms. However, as an initial approximation, we can say that the analysis stands on a distinction between two sorts of ideas: simple (or simpler, elementary or constitutive) ideas and complex (more complex, non-­ elementary or derived) ones. The former originate in experience, while the latter may be actively created by the understanding. The analysis consists then, in this context, in decomposing complex (or more complex) ideas in simple (or simpler) ideas. Locke’s An Essay concerning Human Understanding is a quite clear example of this “analytical” model of empiricism.2 According to Locke, all simple ideas come from the senses or from reflection, and complex ideas are composed in different ways of simple ones. By virtue of the double source of ideas – they can be passively received or actively created by the understanding employing the materials of the first kind – Locke may develop the metaphor of the understanding as a “white paper, void of all characters, without any ideas” (Essay, II. i. 2) and receiving all its content (or ideas) from experience, that is from sensation and reflection. However, the Lockean model is not the only one. Empiricist authors have not all the same conception of the elementary and of the composed, and the analytical process takes, from author to author, extremely different and unexpected forms. Now, it seems that the idea of space is unsuited to the analytical method or at least requires some adjustments. In fact, it can be assumed that the idea of space is essentially composed of parts that in turn have parts, which is in tension with the

 Locke 1975, hereafter referred as Essay, followed by book, chapter and paragraph number.

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aim of a reduction to simple ideas. This difficulty will take a wide range of forms, according to the authors, and even within the same corpus. We might mention, among others, three aspects that may yield questions as to the application of the analytical method to space. First of all, there is the question of infinite regression. If the idea of space is composed of parts that are spatial, then, since the parts are in themselves spatial ideas, and therefore complex ones, it is impossible to find an end to the division process that continues ad infinitum. Aristotle and the Aristotelian tradition used arguments of this kind to show that a line cannot be made of points (Physics, VI I, 231a–233b). If this argument is accepted, the very idea of analysis become problematical. But this is not the only reason that makes space a challenge for empiricists. After all, it is possible to deny the idea that parts of space are always in themselves spatial. Hume, for example, maintains that space is composed of simple elements that are not extended. But another problem appears then immediately. This answer makes it difficult to understand the passage from simple, non-extended elements to space: if what constitute the idea of space is the mode of composition of simple elements, how should we conceive the relationship between these non-­ spatial elements and the spatial mode of their composition? Do we really analyse the idea of space when we reduce it to non-extended elements?3 Finally, and from the same perspective, it appears that the study of the notion of space suggests a strong solidarity between the totality and its parts. Although, it is possible to extract or isolate a constituent (simple or complex) from the complex idea in which it is inserted, in the case of the complex ideas of space, it appears problematical to extract or to isolate a part of space from the totality to which it is connected. Thus, it is possible to split a body into several parts, and it is possible to move it from one place to another. But, is it possible to split space itself into several parts? Is it possible to divide and move a part of space? Locke, for instance, defends the inseparability and immovability of parts of space (Essay, II. xiii. 13 and II. xiii. 14), while Hume describes a kind of disaggregation of sensible extension through the separation of simple non-extended elements.4 In this introduction, we present an overview of the ways the main classical empiricists use to approach the question of space, taking as a common thread the study of the way in which these authors analyze the idea of space. Section 1.2 is devoted to Locke, Sect. 1.3 to Berkeley, Sect. 1.4 to Hume and Sect. 1.5 to Condillac. This overview has several objectives. First of all, it aims to identify the main texts where the authors treat the issue of space, and to familiarize the reader with the problems addressed by each philosopher. The second objective is to give a condensed overview of the diversity of these approaches to space. Secondary literature on the issue of space in classical empiricism is scarce and above all, when it exists,

3  For instance, Hume’s analysis of space into a mode of disposition of unextended sensible points has been said to be circular because the concept of disposition includes the notion of space that it is supposed to reduce (or to analyse). See below note 38. 4  Hume 1978, 27 (Book I, Part ii, Section i) cited hereafter as T. followed by book, part, section and page numbers.

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fragmented.5 There are monographs on theories of space of some of the authors but, so far as we know, a complete and compact survey of theories of space of the main classical empiricists does not exist. The four following sections aim to fill this gap. It is a kind of tool for understanding how Locke, Berkeley, Hume and Condillac approach the issue of space, and also how their approaches are distinct and singular. In a certain way, the following text has been conceived as an initial map, a rough and revisable map, but one which we hope is useful in charting the more specific essays that compose this volume. The third objective of this introduction is to facilitate access to these essays, of which a presentation and summary is given in Sect. 1.6. Each of these essays addresses a specific question or a specific author. The general frame of Sects. 1.2, 1.3, 1.4 and 1.5 allows one to place them in their context. Although there is not a single empiricist theory of space, there is a common problem that cuts across all these theories: how to analyse the idea of space? What the following sections aim to show is that the reduction of the idea of space to simple ideas or to simpler elements is neither mechanical nor evident. It involves concepts of experience which are extremely different and rich, and also, at first, unexpected. The elements are in fact depicted in very diversified forms and in different domains: simple elements or simpler elements (lines into points, ideas of extension into ideas of pressure and movement, etc.), but also coordination between different sensorial modalities, etc.

1.2  Locke: The Source In the Essay concerning Human Understanding, Locke tackles ideas of space from different perspectives. Simplifying the intricate landscape, one can at least distinguish three main issues concerning the concept of space in the Essay: the first is related to the origin of the ideas of space; the second concerns the way ideas of space are composed; the third has to do with the distinction between body and extension (and in the frame of which are discussed the Newtonian problem relating to absolute versus relative space, the actual existence of empty space, and the actual infinity of space).6 But this list does not exhaust the various issues touched on by Locke. In his 5  Studies of space in the seventeenth and eighteenth century focus on the transformation of the concept of space in physics and cosmology and little or no attention is generally given to the authors we are studying in this introduction (for instance, Jammer 1993; Grant 1981; Koyré 1957; Casey 1997: Miller 2014). E.  Slowik (2016) devotes a section to “The Rise of the Empiricist Approach to Space”, but the section is only a few pages long. There are however monographs on the notion of space of eighteenth-century empiricists, but they concern exclusively Berkeley’s and Hume’s theories of space; see for instance, Frasca-Spada 1998; Jacquette 2001; Jesseph 1993. Less focused on “scientific revolution” is the 1930’s book of J.T.  Baker, entitled An Historical and Critical Examination of English Space and Time Theories from Henry More to Bishop Berkeley (Baker 1930). 6  Respectively in: 1) Essay, II. v., II. xiii. 1–6 and II. xv. 1–2; 2) Essay, II. xiii. 13–14 and II. xv. 9–10; 3) II. iv. 3; II. iv. 5 and II. xiii. 11–26.

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chapters on space, Locke follows many directions and multiplies the angles from which he tackles the subject of space. This feature distinguishes Locke’s treatment from Berkeley’s, Hume’s, and Condillac’s more unified conceptions of space. In this presentation, I won’t attempt the difficult task of articulating in one unified theory the various remarks and considerations Locke devoted to the notion of space.7 I also won’t try to describe in detail the themes, problems, and theses in Locke’s writings. My more modest aim is to survey and to highlight the topics that will play a central role in the subsequent empiricist theories of space. I will first discuss the relationship between ideas of space and their sensible origin (1.2.1). The two subsequent sections will be devoted to Locke’s very intricate analysis of the parts of the idea of space. We will first study Locke’s most common way of conceiving of the nature of the simplicity and complexity of space (1.2.2). We will then focus on an alternative conception that Locke presents in a cursory way and underline the tensions it generates within his thought (1.2.3).

1.2.1  Origin of the Idea of Space: Sensation and Imagination One of Locke’s fundamental claims about space is that the idea of space has its source in human experience. In holding this thesis, Locke distanced himself from Descartes’ idea that humans have an innate, clear and distinct idea of extension.8 But if the target is plain, Locke’s positive account is intricate. Locke mainly holds three different theses: first, we receive the idea of space by the senses; second, even if one can perceive by the senses only a limited portion of space, the understanding provides us with the means to generate an idea of immensity; third, the idea of space is independent of the idea of solidity (and therefore of matter). In chapter II. v., Locke claims that we get the particular ideas of space from two senses that are sight and touch. Locke repeats this claim at the beginning of the chapter II, xiii, on the simple modes of space (Essay, II. xiii. 2, 4 and 10). However, perception (sight and touch) provides the understanding only with ideas of limited parts of space. How then is it possible to pass from these ideas to a concept of unlimited space? According to Locke, men can form the idea of immensity – i.e., the idea of a space that is unlimited, or more precisely, that can be enlarged as much as we want. But how can one generate this idea of immensity from ideas of limited portions of space? In explaining this, Locke proposes to examine the ideas of space that the mind is able “to make within it  self, without the help of any extrinsical 7  In the secondary literature on Locke’s Essay, the chapters on space (Essay, II. xiii and II. xv, Of simple Modes; and first, of the simple Modes of Space, and Of Duration and Expansion, considered together) are rarely discussed and even less the sections on the parts of space on which we will focus our presentation. For general presentations on Locke’s theory of space see Yolton (1983, 65–71); Ayers (1991, vol. 1, 223–236); Hamou 2012. On the question of Locke and the notion of absolute space see Gorham and Slowik 2014. 8  Descartes 1996, vol. VII, 63–65 (Meditationes de prima philosophia, Meditatio quinta).

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Object, or any foreign Suggestion” (II, xiii, 1) and claims that the mind is capable of adding and multiplying indefinitely any finite idea of distance: Men, for the use and by the custom of measuring, settle in their minds the Ideas of certain stated lengths, such as are an Inch, Foot, Yard, Fathom, Mile, Diameter of the Earth, etc., which are so many distinct Ideas made up only of Space. When any such stated lengths or measures of Space are made familiar to Men’s Thoughts, they can, in their Minds, repeat them as often as they will, without mixing or joining to them the Idea of Body, or any thing else; […] This Power of repeating or doubling any Idea we have of any distance and adding it to the former as often as we will, without being ever able to come to any stop or stint, let us enlarge it as much as we will, is that which gives us the Idea of Immensity.9

I will come back to the notion of mental unity of measure later. One finds thus two basic ideas in Locke’s analysis of the origin of our idea of space: the idea of space has a sensible origin and the understanding has the power of repeating any idea of a stated length. In this way, the understanding may go beyond the limits of particular ideas actually received by the senses and Locke may claim that it is possible to link the idea of immensity to experience. This has as a consequence that we can have an idea of the infinity of space. Therefore, since Locke believes that ideas of the senses and ideas produced by the imagination are equally produced by experience, he can claim that all ideas of space – immensity included – have their origin in experience (internal and external). Thirdly, as we said, in developing his thought, Locke opposes Descartes’ conception of space. Not only does he object to the Cartesian view that extension is an innate, clear and distinct idea, but he also criticizes his identification of space and matter (and the consequent impossibility of the void). Locke claims in fact that, even if ideas of space are generally perceived in relation to bodies, they are completely distinct and independent of the idea of solidity or matter. Thus, according to Locke, the idea of the distance between the opposite parts of a concave surface is “equally as clear, without, as with the Idea of any solid Parts between: […]” (Essay, II. iv. 5). To rigidify the distinction between space and matter (or solidity), Locke even proposes a new terminology according to which the term “extension” should be applied only to the distance of the extremities of particular bodies, whereas the term “expansion” applies “to Space in general, with or without solid Matter possessing it, – so as to say Space is Expanded and Body extended.” (Essay, II. xiii. 26) However, if from one side it is evident that several of the sections on space are attacks on Descartes’ clear and distinct ideas of extension and the identity of extension and matter, Locke appears here to distance himself also from another kind of position, claiming that ideas of space may be derived from experience by way of abstracting from the perception of bodies.10 Locke’s anti-abstractionist approach and the claim of the independence of ideas of space from ideas of bodies or solidity may also explain why the ideas of the simple modes of space are discussed by  Essay, II. xiii. 4. See also Essay, II. xiii. 1, II. xiii. 5 (on figures) et II. xvii. 3 and 22.  Something of this kind may be associated, for instance, with Suarez’ notion of spatium imaginarium (Suarez 2001, sec. 4, §7; see also Disputatio LI). Hobbes’ notion of spatium imaginarium and its relation to abstraction is discussed in Pécharman in this volume.

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Locke within book II “Of Ideas”, and not in book III “Of Words” where he presents general terms and the general abstract ideas that constitute their meaning. The choice of this place in the general economy of the Essay is important because it shows that Locke approaches the nature of space at the level of particular ideas (and their variations by the imagination), rather than at the level of abstract ones. In the first part of chapter xiii, Locke is concerned with all possible ideas of space as they are received by the senses or produced by the understanding and he acknowledges that “our Ideas are not always Proofs of the Existence of Things; […]” (Essay, II. xvii. 4) or, in other words, that the possession of the idea, for instance of an infinite space, is not a guarantee for the actual existence of such a boundless space. However, in the second part of the chapter Locke argues in favour of the actual existence of infinite and of empty spaces (Essay, II. xiii. 13). Locke, in fact, argues not only that we possess the idea of immensity, but also that “Space in it self is actually boundless, […]”.11 In a similar way, he argues, from one side, not only that we can have the idea of an empty space, but also that empty spaces should actually exist (Essay, II. xiii. 21., 21bis, 22, 23) and, finally that the continuity of space cannot be separated “neither really, nor mentally” (Essay, II. xiii. 13). The shift from claims concerning ideas to claims concerning space as actually existing is founded on a series of physical and theological arguments. It is then important to realize that even if Locke’s starting point on space are ideas and their contents, the impact of his considerations may spread outside the universe of ideas and concern the “actual” existence of space “in it self” (Essay, II. xvii. 4).12

1.2.2  Simplicity and Complexity of Space That the idea of space comes from experience is not the only claim Locke wants to make in the Essay. An important part of his effort is devoted to the analysis of the way space is composed. In chapter II. xv., Locke proposes to clarify the nature of

 Essay, II. xvii. 4; Locke pursues some arguments in favour of the claim that “Space in it self is actually boundless, […]” restating, for the essential, the physical and theological arguments in favour of the infinity of space already developed in the chapter on the simple modes of space. See also II. xiii. 21 where the existence of a boundless space is linked to the possibility of movement at the limits of the universe. However, Locke’s position concerning “space in itself” and its infinity is controversial: Gorham and Slowik (2014, 119–137) maintain that Locke defends an absolutist notion of space in the Essay, at least in part linked to Newton; a similar opinion is held by M. Ayers (Ayers 1991, vol. 1, 234–236). G. A. Rogers claims the mutual independence and the conceptual difference between Locke’s concept of space “in itself” and Newton concept of absolute space (Rogers 1978). We agree with G. A. Rogers concerning both the existence of a realistic concept of space in Locke, and its independence from Newton’s notion of absolute space. Indeed, Locke always defends very clearly a relational notion of place (Essay, II. xiii. 7–10). See also Thomas 2018. 12  To distinguish the two domains of his discourse, Locke uses opposite qualifications, such as “actual” versus “mental” (Essay, II. xiii. 13), “in thought” versus “in reality” (Essay, II. xiii. 13), “real existence” versus “idea” (Essay, II. xiii. 23). 11

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the ideas of space and time, considering them together. In this perspective, he deals at length with the parts of space and makes two apparently contradictory claims: ideas of space (as ideas of time) always have parts that have in turn parts; and, all ideas of space, immensity included, are simple. How can Locke hold these two theses at the same time? How can an idea of space be simple, and at the same time be composed of parts? This contradiction disappears when one takes into account the very peculiar use Locke made of the notion of simplicity, defining simplicity in terms of uniformity. Spatial ideas are uniform precisely because all spatial parts have in turn parts. This means that, as uniformity is the criterion for simplicity, spatial ideas may be said to be “simple” because they are uniform in the sense that they all have parts that have in turn parts (Essay, II. xv. 9). In order to clarify this point, Locke describes the way in which ideas of space diverge from the ideas of number: in the case of numbers, there exists an idea, the unity, which is different from any other idea of number because it has no parts. Therefore, in the case of numbers there exists only one simple idea, that is the unity, and all the others  – that are obtained by the addition of the unity  – are complex (Essay, II. xv. 9). On the contrary, in the case of space every part has parts and in this sense they are all of the same type, or uniform – and thus, can be characterised as simple. The lack of a spatial unity also explains why, in order to get the idea of immensity, Locke proposed to add the idea of some unity of measure we learned by habit to have, even if this idea has in fact parts (Essay, II. xiii. 4 and II. xv. 9). Behind Locke’s claims about the parts of space, one can recognize the Aristotelian characterization of space as a continuum. At different places in the Essay, in fact, Locke presents continuity as a fundamental property of space.13 Locke’s analysis of continuity, however, is quite original and is connected to the claim that the parts of the simple idea of space are at the same time inseparable and unmovable.14 I will leave this feature aside; indeed, what is important for us here is that, for Locke, space cannot be composed of indivisible spatial atoms.15 Note however that Locke underlines that the claim that all spatial parts have in turn spatial parts should not to be taken as a definition of space. In fact, explains Locke, to say that spatial parts have “partes extra partes” cannot amount to a definition because it neither captures nor defines what makes these parts spatial ones (Essay, II. xiii. 15).

 See Essay, II. v. 9. and II. xiii. 13.  Essay, II. xiii. 13 and 14. At Essay, II. xiii. 13, for instance, Locke writes that “The Parts of pure Space are inseparable one from the other; so that the Continuity cannot be separated, neither really, nor mentally”. In a parallel way, in Essay, II. iv. 5, Locke describes the extension of space as “the continuity of unsolid, inseparable, and immovable Parts” whereas the extension of bodies is said to be “the cohesion or continuity of solid, separable, and movable Parts”. Space therefore is a continuum with parts that are inseparable and unmovable. On the infinite divisibility of the idea of space, see also Essay, II. xvii. 12. On the tradition leading to Locke’s position on the parts of space, see Grant 1981, 232–240. 15  On this point, see, however, the next section. 13 14

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1.2.3  Sensible Points and Space as Complex However, the relative coherence of Locke’s account of ideas of space, and his efforts to keep together simplicity, parts and continuity are interrupted, when at the end of II, xv, 9, he suggests that, instead of taking all spatial ideas as simple, perhaps it would have been more correct to consider as simple only the idea of the smallest spatial extension we are able to perceive: But the least Portions of either of them [i.e. ideas of space and time], whereof we have clear and distinct Ideas, may perhaps be fittest to be considered by us, as the simple Ideas of that kind out of which our complex modes of Space, Extension, and Duration are made up, and into which they can again be distinctly resolved. (Essay, II. xv. 9)

In order to give an empirical foundation to this new hypothesis, Locke refers to a particular idea of space, actually existing in experience that would be the perfect candidate to the role of spatial “unity”. This idea, Locke writes, is “the least Particle of Matter or Space we can discern, which is ordinarily about a Minute, and to the sharpest eyes seldom less than thirty Seconds of a Circle, whereof the Eye is the centre” (Essay, II. xv. 9). If we follow this hypothesis, ideas of space and ideas of number would partake the same structure of complex ideas composed by the addition of a certain number of simple unities. Therefore, if such a spatial unity – or atom of space – exists, not all ideas of space may be thought as having parts and therefore as being uniform and simple. With the hypothesis of the sensible points, Locke introduces a simple idea of space that (1) has no parts at all and therefore cannot represent a continuum; (2) is the constitutive part of complex ideas of space and then (3) could be taken as the elementary part of a discrete geometry. Now, Locke appears unaware that this hypothesis along with transforming the simple spatial ideas into complex ones, could also have consequences for the assertion of the continuity of space he strenuously defends in the rest of the chapter. Things are even more complicated if we take into account a note added to the fifth edition of the essay, which Locke would have dictated to Pierre Coste – the French translator of the Essay – in answer to an objection by M. Barbeyrac on the simplicity of the idea of space.16 In this note, Locke restates almost point by point what he said before about the uniformity and simplicity of spatial ideas and about the alternative hypothesis of the smallest perceivable part of space as the simple elementary part starting from which all ideas of space would be composed. However, things become more complicated here because, at the end of the note, we read “[…] it is not the Design of Mr. Locke, in this Place, to discourse of any thing but concerning the Ideas of the Mind. […]” (II, xv, 9, note).17 This remark is problematic because it suggests that, according to Locke, it would be possible to maintain, on the  On Pierre Coste and his translation of the Essay, see Hamou 2009.  The distinction between two domains of discourse is even more explicit in the French version of the note, that is: “Car l’affaire de M. Locke n’est pas de discourir en cet endroit de la réalité des choses mais des idées de l’esprit.” 16 17

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one hand, that ideas of space have indivisible minima and, on the other, that space has parts that have parts and therefore is continuous. If this is true, Locke appears to consider the statements concerning the nature of ultimate parts of the idea of space as being independent of claims concerning the parts of space. This suggestion is odd. Indeed, all the chapters on space are explicitly supposed to be about our ideas of space. Locke could not then pretend by contrasting our atomistic idea of space with the continuous objective space! More precisely, there are at least two reasons for doubting that Locke can defend the independence of the two domains of discourse. The first is a problem of foundation. How can Locke, in the context of his enquiry on ideas in the second book of the Essay, claim that his statement concerning sensible points applies to ideas of space but not to space in itself? Secondly, let’s suppose that Locke could justify the asymmetry between space and the idea of space; how then could he maintain that, in the case of space, the ideas of the senses are a reliable source of knowledge of the object represented by the ideas? Malebranche, for instance, employed precisely this difference between the “sensible” space perceived by the senses and the “real” space, the one conceived by reason, to disqualify the senses as a reliable source of knowledge and limit genuine knowledge to ideas given by reason and perceived in God.18 Now, given the tensions introduced by the hypothesis of sensible points, it is worthwhile to raise the following question: Why does Locke want to leave a place for the sensible points hypothesis notwithstanding the tensions it engenders and of which he cannot be completely ignorant when – in the fifth edition of the Essay – he decides to add a note on this subject? The difficulty is to explain why the peculiar feature of our experience of sensible points appeared to him particularly important and worth consideration. A possible way to explain the existence and persistence of the sensible points hypothesis is to remember that Locke’s aim – even in treating space – is to describe the actual content of our ideas, and from this perspective, it is quite natural to describe the content of certain spatial ideas that appear to be in a sense simpler than the others because no part may be sensibly detected (or perceived) in them. Moreover, and more importantly, as Locke presents it, the idea of “the least Particle of Matter or Space we can discern” is the same – or at least similar – in all human beings and, as such, it can provide us with a unit of measure and can confer a measurable, objective dimension to the subjective contents of experience. In other words, what the existence of sensible points appears to make clear is that ideas, despite their private character, may, in some cases, be compared and measured. The interest that Locke shows in the objective comparison of ideas is also made evident by the very last section of chapter II, xiii, which Locke summarizes in the following terms: “Men differ little in clear simple Ideas.”

 See Malebranche 1979–1992 vol. 1, 54–66; 320–347; 900–916; (La recherche de la vérité, respectively Livre I, chap. vi.; Livre III, Part II, chap. I–VI and X Eclaircissement) and Malebranche 1979–1992, vol. 2, 675–683 and 713 (Entretiens sur la métaphysique et sur la religion).

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Note that something analogous to this “objectivation of experience” comes again in the Essay in chapters IV, iv (“Of the Reality of our Knowledge”) and IV, xi (“Of our Knowledge of the Existence of other Things”) where Locke, trying to assess the conformity between ideas and reality, appeals to the correspondence between ideas of different sensorial modalities (as the ideas of movements tracing letters on paper and the letters seen afterwards) and, more importantly, ideas belonging to different senses and to different individuals (as when someone reads aloud the letters written by someone else). It is then likely that Locke’s claim that there are natural spatial unities of measure (which attracted the ironical and harsh criticisms of Leibniz in the Nouveaux Essais)19 should be put in the general context of Locke’s thought on the meaning of intermodal and inter-subjective sensorial conformity. These positive-objective perceptual features may then justify Locke’s inclusion of the hypothesis on sensible points, notwithstanding the difficulties it generates within Locke’s overall conception of space. As we said above, space in Locke is less an object for a theoretical unified treatment than a crossroads where many different conceptual threads, coming from very distinct parts of Locke’s thought, intersect. The tension observed between the claim that space is made of spatial parts and the claim that there are atomistic sensible points should be understood in this wider context – it witnesses a collision between a broadly Aristotelian analysis of spatial continuity and a reflection on the relation between ideas and the external world based on conformity of ideas. A last remark, which owes its importance to what happens in Berkeley: in these chapters on space, Locke treats sight and touch as senses that are equally capable of receiving distinct ideas of space. In the Essay, the only place where Locke appears to refer to an asymmetry between sight and touch is the chapter II. ix. On Perception, where he claims that often in perception and especially in the case of vision, a judgement intervenes and modifies the ideas immediately perceived. To illustrate this claim, Locke decides to insert – in the second edition of the Essay – the discussion of Molyneux’s question and to quote with approval the answer of Molyneux himself who assesses that only experience may teach the blind man newly made to see: “[…], that what affects his touch so or so, must affect his sight so or so; or that a protuberant angle in the cube, that pressed his hand unequally, shall appear to his eye as it does in the cube” (Essay, II. ix. 8). We are not going to discuss these sections here because they focus on the processes of perception without any apparent consequences on the subject we discussed here, i.e. the nature of the ideas of space, their empirical origin, and the structure of their parts. We will limit ourselves to remembering that, in the chapter on space, each time that Locke refers to the particular sensible ideas of space received by the senses he does not refer to any asymmetry between sight and touch, not even on the number of perceivable dimensions. In other words, in the chapters

 See Leibniz 1965, II. xiii. 6. M.  Ayers (1991 1:229–230) discusses the questions opened by Locke’s mental unity of measure.

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on space, sight and touch are put on the same plan without reference to any difference between a visual and a tactile space.20

1.2.4  Conclusion As we said at the beginning, we did not try to unify the various considerations Locke elaborates about space. Many divergent lines meet in Locke’s writings on space (the anti-Cartesian development, the Aristotelian analysis of continuity, the defense of the existence of sensible points, the anti-Newtonian claim of the relativity of place, etc.), and this variety and proliferating character is precisely, in our opinion, what confers on Locke’s Essay its unique importance. As we will see below, Berkeley’s, Hume’s, Condillac’s (very distinct) approaches of space can all be traced back to Locke’s reflections on the topic. Locke’s accounts of space in the Essay are intricate, but they set the stage for the ideas of later empiricists. Berkeley, Hume, and Condillac will resume the issue raised by Locke. They will try to solve or at least smooth the tensions present in Locke’s account, they will extend and deepen some of Locke’s insights, they will articulate in a new way the loose strands contained in Locke’s writings. In this respect, Locke’s thought can be regarded as the source of the empiricist conception of space. In what follows, we will see how Berkeley, Hume and Condillac, each in their own way, build upon this important legacy.

1.3  Berkeley: Space and Movement Berkeley’s analysis of the notion of space has the unity and systematic character that lacked in Locke’s treatment of the topic. Berkeley follows Locke’s basic anti-­ Cartesian inspiration according to which the content of the idea of space comes from the content of particular sensible ideas. Starting from this background, Berkeley however goes very far in directions that are only hinted at in Locke. The conclusions of Berkeley’s analysis are profoundly different from the ones highlighted by Locke. To say that Berkeley, unlike Locke, has a more unified theory of space is not to say that one does not find evolutions and tensions in Berkeley’s account of spatial ideas.21 One of the hallmarks of Berkeley’s discussion however is the attention he draws to the consequences (metaphysical, but also scientific) of his  See, for instance, Essay, II. xiii, 2, 5 and 10. I do not agree with the mainstream interpretation of Locke’s discussion of Molyneux’s question in Essay, II, ix, viii et ix. The theme of the heterogeneity between spatial ideas perceived by sight and by touch is never actually discussed by Locke. On this subject see Berchielli 2002. 21  See Atherton 1990, 2008a, b; Paukommen 2014; Grush 2007; Storrie 2012; Schumacher 2007; Schwartz 2006, 11–89; Jesseph 1993; Raynor 1980. 20

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claims. As we will see, it is sometimes the ongoing and systematic exploration of those consequences that led him to back down on this issue. In this short presentation, we have chosen to highlight the connection Berkeley draws between the idea of space and the notion of movement of one’s own body – i.e., what we could call the pragmatic conception of space. This idea is central to many developments in Berkeley’s philosophy of space. It is not, however, the sole line Berkeley proposes. In the first paragraph, we focus on Berkeley’s famous heterogeneity thesis, and on the primacy given by Berkeley to the tactile over the visual perception of space. In the second section, we connect this analysis with the idea that space is intimately related to movement and action. The last paragraph has a different purpose. There we focus on an unpublished early manuscript where Berkeley toys with the idea that concepts of extension and figures are composed of sensible points, or minima. Berkeley never makes explicit this hypothesis in published texts, but a short synthesis of this research is useful both for showing the kind of conceptual exploration Berkeley engaged in, and for articulating his thought vis-­ à-­vis Locke and Hume.22

1.3.1  Space and Touch Berkeley describes the basis of his theory of space in the Essay towards a New Theory of Vision. This may at first appear surprising because Berkeley presents the Essay essentially as a new explanation of vision – not as a work on the metaphysics of space. However, Berkeley devotes the fourth part of his book to the question of the existence of ideas common to (in the sense of “equally perceptible by”) sight and touch. It is in order to answer this question that Berkeley proceeds to an examination of what is actually “spatial” in the particular ideas perceived by sight and touch. Berkeley concludes his examination with the notorious heterogeneity thesis, according to which there are no ideas that are equally perceived by sight and by touch. In order to prove his claim, he makes use of the results of the analysis of the complex contents present in the mind when we ordinarily believe that we are seeing the distance, magnitude, figure or situation of an object, an analysis that he has developed in the first parts of his essay. Berkeley inserts then his analysis of space in the context of a discussion of the claim (which Locke considered “needless to prove”) that space and extension were ideas perceivable by both sight and touch.

22  All references to Berkeley are from Berkeley 1979. The following abbreviations are employed: “PC” for Philosophical Commentaries (Berkeley 1979a) followed by entry number; “NTV” for An Essay toward a New Theory of Vision (Berkeley 1979b) followed by section number; “PHK” for A Treatise Concerning the Principles of Human Knowledge, (Berkeley 1979c) followed by section number; “3D” for Three Dialogues between Hylas and Philonous (Berkeley 1979d) followed by page number.

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At the very beginning of the Essay towards a New Theory of Vision, Berkeley maintains that distance cannot be perceived by sight because distance is a line directed into the eye that projects itself only onto a point on the retina; and a point cannot inform one about the length of the projected line (NTV, 2). But then, Berkeley asks, what does it mean to see something at a distance? Proceeding to a detailed analysis of the ideas actually perceived, Berkeley shows that there is no visual idea of distance and that what we see (the visual idea) works as a sign for a complex of tactile ideas actually corresponding to distance. According to Berkeley, when we “see” something at a distance, we see merely visual signs for some tactile ideas suggested by the imagination: […] So that in truth, and strictness of Speech, I neither see distance it self, nor any thing that I take to be at a distance. I say, neither distance, nor things placed at a Distance are themselves, or their ideas, truly perceived by sight. This I am persuaded of, as to what concerns my self. And I believe whoever will look narrowly into his own thoughts, and examine what he means by saying, he sees this, or that thing at a distance, will agree with me that, what he sees only suggests to his understanding, that after having passed a certain distance, to be measured by the motion of his body, which is perceivable by touch, he shall come to perceive such, and such tangible ideas which have been usually connected with such and such visible ideas. (NTV, 45)

Berkeley develops the same kind of analysis for the other spatial features such as the size, situation, figure, etc. For each of them he shows, first of all, that the ideas perceived by sight are not of the same kind as the ideas perceived by touch and, secondly, that ideas immediately perceived by sight work as signs of the (heterogeneous) tactile ideas, by virtue of an association steadily established by habit. Berkeley’s account of the idea of space has then two ingredients. The first one is the distinction and separation between the ideas of sight and the ideas of touch. The second component of Berkeley’s account is the primacy given to touch in the perception of space. Indeed, the ideas of sight are in themselves not spatial: for Berkeley then  – unlike what happens in Locke  – only touch can immediately grasp spatial ideas.

1.3.2  Space and Activity One could wonder why touch should be regarded as the spatial sense par excellence. Why would it be not possible for a mind endowed only with a visual sense to form a spatial idea? In an important passage of the Essay (NTV, 153–159), Berkeley considers precisely this question and more particularly, he raises the following: to what extent could a mind able to see but lacking the sense of touch (a disembodied or a pure spirit, as he calls him) understand geometry? Berkeley explains that this “disembodied spirit” could grasp neither solid nor plane geometry because, lacking the sense of touch and the notion of distance, it could manipulate neither three-­ dimensional nor plane figures. First of all, this mind, being without body, would not be able to continue a line, to rotate or translate a figure, to draw a circle starting from

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a given point, etc. Moreover and more dramatically, Berkeley goes on to claim that such a “spirit” would not even be able to see plane figures, because such a perception requires following the edges of the perceived figure, and then the capacity of moving in an ordinate way, which is something that a subject missing the sense of touch is incapable of. According to Berkeley, the disembodied mind would have access only to some patches of colour differently distributed rather than to figures because the distribution of the coloured patches would be too fleeting to make a plane figure with steady and fixed contours (NTV, 156–158). From this discussion and from other sections of the New Theory of Vision, it appears that the essential components of the ideas of space are the ideas of movement and protrusion and thus presuppose a subject capable of progressing in space, applying pressure and grasping objects.23 Therefore, not only is it that these ideas may be perceived exclusively by touch, but also it implies an active, pragmatic subject which, in a way, constitutes space through his actions. This connection between space and movement surfaces again in the arguments Berkeley uses in Principles (and afterwards in De Motu) against Newton’s theory of absolute space. Berkeley claims that only relative space, time, and movement are actually conceivable to us and also that, precisely these “relative” notions (and not the absolute ones) are actually at work in Newtonian physics. However, a closer look at Berkeley’s notion of relative movement reveals that it has some features that make it profoundly different from Newton’s notion of relative movement and make it conceptually close to Newton’s notion of absolute movement. Berkeley starts his analysis with the experience of movement that anyone has when, for instance, walking in the street. He then extends this analysis to movements of inanimate bodies (PHK I, 113–115). At first, he says that the perception of movement is always the perception of the changing relation between two bodies’ positions (carrying on  – with Locke  – the Newtonian concept of relative movement). But then he adds that the idea of movement cannot be reduced to the mere idea of a change in relative position. In fact, if this was the case, when we are walking in the street, it should be equally possible to say that our body is moving or that the stones of street are moving. However, it is always the body of the subject that is perceived as moving while the street is at rest (PHK I, 113). According to Berkeley, this suggests that the idea of movement contains also a second component that explains why the choice of the reference system and of the moving body is not an arbitrary one. This second component consists in conceiving that a “force” – or as Berkeley adds in the second edition of the Principles (1734) an “action” – is applied to the body that is actually moving and not to the bodies representing the reference system (in this case the street): moving body and reference system are not interchangeable (PHK I, 113). At the same time, “when I speak of pure or empty space, it is not to be supposed, that the word space stands for an idea distinct from, or

 In Samuel Johnson’s Dictionary of the English Language of 1785, the term protrusion is defined as “the act of thrusting forward; thrust; push”.

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conceivable without body and motion” (PHK I, 116). Note that it is only in the case of the movement of his proper body that it is possible to experience the second component of movement, the one by virtue of which we distinguish the mobile from the unmoving reference system. Then Berkeley applies this analysis to the movements of inanimate bodies that are said to be moving when (1) they change position in relation to others and (2) we consider that some force or action is applied to them. Thus, it is because men have the capacity to move themselves that they can build a notion of actual or real motion richer than the mere perception of a change in position in relation to a system of reference. Therefore, that Berkeley links the notion of a space to activity and movement is not only shown by the role he assigns to the movement of one’s own body for the constitution of the ideas of movement and space, but also – as we have seen before – by the primacy he gives to touch over sight in his concept of space, the connection of the capacity of grasping a figure to the movement of one’s own body, to the capacity of pressing and following the contours of an object. The discovery of these pragmatic components is essential to Berkeley’s analysis of space.

1.3.3  Minima Sensibilia and the Theory of Abstraction In NTV, 3D and PHK, Berkeley refers to a notion of visible and tactile point or minimum. In NTV and 3D, the notion is employed to account for the comparisons in magnitude of visual or tactile ideas,24 whereas in PHK a sensible point is seen as the ultimate limit for any actual division of a finite line (PHK I, 132). In all cases, the admission of minima sensibilia goes against the possibility of the infinite division of a finite line. What is important, however, is that, except in one difficult passage of NTV, which is suppressed in the third edition (see below), the admission of minima (visible or tactile) does not threaten the legitimacy of Euclidean geometry. In other words, in NTV and PHK, Berkeley makes both the existence of ultimate parts of the division of finite space and Euclidean geometry coexist. How is it possible for Berkeley to claim at the same time both that a segment has a finite amount of sensible points and that Euclidean geometry – that appears to require continuity and infinite divisibility – is valid? Berkeley’s theory of generalization, which is presented in the Introduction of the PHK, dating from 1710, provides this riddle with its solution. According to Berkeley, any particular idea may be universal “in its meaning”, when it is made to represent innumerable other ideas of the same kind. As applied to geometry, this theory implies that a line of (let’s say) one inch long, having a determinate finite number of parts, may represent an innumerable amount of other lines of any size, and may thus represent a line which has “ten thousands parts or more”.25 By virtue of this relation

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 NTV 54 and 79–83; 3D, 188 (First Dialogue).  PHK, Introduction, 126.

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of sign to meaning, any line in a diagram may be taken as representing properties it does not instantiate: Because there is no number of parts so great, but it is possible there may be a line containing more, the inch-line is said to contain parts more than any assignable number; which is true, not of the inch taken absolutely, but only for the things signified by it. (PHK I, 127)26

Therefore, the possibility of dividing a segment in any number of parts results not from the “absolute” possibility of dividing a particular idea of a line, but rather from the relation in meaning between the actual particular line and the lines it signifies. In PHK, then, the admission of minima peacefully coexists with the endorsement of Euclidean geometrical truths. Although it is not made explicit, in NTV, Berkeley appears to know already at least the first elements of his theory of generalization, and therefore to have the means to understand the validity and universality of Euclidean geometry. However, in a section that appears only in the two first editions of NTV (both dating from 1709), Berkeley acknowledges a tension between his “thoughts” and the “common road of geometry”: 160. Sure I am, that somewhat relating thereto has occurred to my thoughts, which, tho’ after the most anxious and repeated examination I am forced to think it true, doth, nevertheless, seem so far out of the common road of geometry, that I know not, whether it may be not be thought presumption, if I should make it public in an age, wherein that science hath received such mighty improvements by new methods; great part whereof, as well as of the ancient discoveries, may perhaps lose their reputation, and much of that ardour, with which men study the abstruse and fine geometry be abated, if what to me, and those few to whom I have imparted it, seems evidently true, should really prove so.

It is likely that Berkeley is here referring to an alternative heterodox geometry grounded precisely in the notion of minima.27 Indeed, in some unpublished notes, currently known as Philosophical Commentaries, dating to early in Berkeley’s career (the precise dating is uncertain but it is usually situated between 1707 and 1708), Berkeley explores the consequences for geometry of the rejection of the infinite divisibility of the line. About a third of the notes deals with geometry and part of them with the destructive impact that admission of minima (not being tempered by the theory of generalization) has on Euclidean geometry. In order to illustrate these consequences, in order also to show that Berkeley knew about them, I will briefly explain some aspects of these exploratory notes.

 See also PHK I, 128: “From what hath been said the reason is plain why, to the end any theorem may become universal in its use, it is necessary we speak of the lines described on paper, as though they contained Parts which really they do not. […] And that when we say a line is infinitely divisible, we must mean a line which is infinitely great […]”. See also PHK Introduction, 15–16 and I, 124–132. 27  S. Storrie (2012) defends in a convincing way the thesis, that I endorse here, according to which Berkeley, when writing NTV, was engaged in two distinct geometrical projects: the first, to develop ex nihilo a non-Euclidean geometry of minima; the second, to account for the validity and universality of Euclidean geometry. See also PHK 131. 26

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In PC, Berkeley maintains that it is impossible to conceive spatial ideas independently from sensible qualities. A spatial idea has to be endowed with a particular sensible content (i.e., with colour or some tactile quality).28 The Euclidean point as the Euclidean line have no sensible content and should then be discarded. This means that all the basic notions of Euclidean geometry, far from being intuitive, are pure nothing and should be replaced by concepts which do not make room for the basic Euclidean operations – especially, the division at infinity. This approach has of course devastating consequences that the young Berkeley recognizes and seems to endorse, as for instance the falsity of Pythagoras’ theorem, or the fact that circles of different radius are not similar: 340. X It seems all Circles are not similar figures there not being the same proportion betwixt all circumferences & their diameters. 500 X One square cannot be double of another. Hence the Pythagoric Theorem is false.

Two things are interesting in these exploratory developments. The first is that, claiming that the figures of different dimensions are not similar ones, Berkeley rejects in one block the possibility of geometrical thought.29 The second is that it draws in outline the crucial role played by Berkeley’s theory of general non-abstract ideas, which alone can explain how the admission of minima does not lead to a costly rejection of Euclidean geometry. As we will see soon, the notion of minima sensibile is taken over by Hume in his theory of space, where it plays a central role. However, since Berkeley’s and Hume’s general theoretical frameworks are different, the role played by the minima in the two philosophies also diverges significantly (see below Sect. 1.4). The occurrence and persistence of the notion of sensible points or minima in the empiricist tradition from Locke to Hume seems nevertheless to indicate the existence of a conceptual connection between this notion and the epistemological choice of taking the content of particular sensible ideas and its parts as the starting point for the understanding of the notion of space.

1.3.4  Conclusion To summarize, Berkeley links the idea of space to a set of ideas of movement, action, operations and activity, connecting in this way the idea of space to sensible experience. This conception of space succeeds an alternative notion explored mostly in some unpublished notes according to which spatial ideas are essentially constituted of sensible minima and Euclidean geometry cannot account of the properties of its figures. The theoretical importance accorded to sensible minima is  PC 18, 21, 330, 373, 466.  For more on Berkeley’s attempts see Jesseph 1993, 53–69. See also White 1992 for an analysis of atomistic criticism of Euclidean geometry in the Hellenistic period.

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progressively reduced in Berkeley’s more mature philosophy. In PHK, the theory of general non-abstract ideas allows Berkeley, on the one hand, to use points, lines and surfaces in a way that is compatible with an important part of classical geometry and, on the other, to criticize the legitimacy of the notion of the infinitesimal, considering the minima as the smallest, indivisible parts of extension. At the same time, in PHK and later in the De Motu, Berkeley puts forward his dynamical conception of space. What is interesting for us here is that Berkeley’s analysis of sensible contents, leads to a notion of space centered on certain operations or activities: the idea of space cannot be derived by abstraction from these operations and activities but may be conceived as a complex idea composed by these kinds of sensible (and according to Berkeley simpler) ideas of sensations.30

1.4  Hume: Minima and Mode of Disposition In the last 20  years, Hume’s theory of space has known  – after a long period of neglect or of heavy criticism – an important resurgence of interest and many positive accounts.31 In our presentation, we are not going to explore all the different aspects of this theory. We will instead focus on the relationship between the concept of space and the contents of particular sensible perceptions. Moreover, we will not discuss the actual historical genesis of his theory,32 though we will occasionally indicate the most important differences from and common points with Locke and Berkeley. In the Treatise, I.  II. iii., Hume presents the idea of space as an abstract idea derived from particular ideas of visual and spatial extension (T.  I. ii. iii, 34). Concerning the process of abstraction, Hume explicitly says that he endorses Berkeley’s theory of representative generalization according to which general “abstract” ideas are nothing but particular ones taken as representative of a whole set. This means that what holds for the abstract idea of space should also hold for particular ideas of space and that the fundamental notions of space (fundamental in the sense of logical dependence) are the particular ideas of space (T. I. i. vii, 17–18 and I. ii. iii, 34). In the part entitled Of the ideas of space and time (I. II. ii), Hume gives a positive description of particular ideas of space, as ideas composed of sensible, indivisible  For more, see R. Schwartz’ paper and mine, in this volume.  For the critical accounts see Kemp Smith 1941; Newman 1981; Fogelin 1988; for some of the more sympathetic ones, see Falkenstein 2006; Frasca Spada 1998; Holden 2002; Jacquette 2001; Waxmann 1994. 32  On the independence of Hume’s theory from Berkeley’s and on the influence of Bayle on both of them, see Bracken 1977. The actual influence on Hume of Bayle’s claims about the aporetic nature of space thought as existing outside the mind is largely admitted. On this issue, see Jacquette 2001, 22–28. 30 31

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points attacking straightaway the possibility of their infinite divisibility. What singles out Hume’s theory in the Treatise is the importance he gives to the atomistic claim: for him, finite ideas of space are always composed of a finite amount of sensible points, and any conception which confers to space an infinite divisibility is rejected at the outset.33 The defence of this radical claim does not exhaust Hume’s conception, however. He claims that ideas of space are the copy of some impressions of points and of the manner of their appearance or disposition (T.  I, ii, iii, 34–35). Indeed, Hume should explain how the perception of a set of simple sensible points becomes the perception of sensible extension. That is, he should give an account of what imparts to a manner of arranging sensible points the status of spatial disposition. I will tackle the issue of the minimal sensible points in the first section, and the issue of the modes of disposition in the second section.

1.4.1  Visible and Tangible Minima In order to explain Hume’s notion of space, it is useful to remember the very first principles of his philosophy. Hume presents his Treatise as an application of the experimental method to the study of human nature.34 Two distinctions and two principles play a very important role within this “new science”, both of which provide a very clear basis for Hume’s analysis of the idea of space. The first distinction is the division of all perceptions into “impressions” and “ideas” according to their degree of vivacity: the more vivid perceptions are said to be “impressions”, the less vivid ones are said to be “ideas”. The second division is between simple and complex perceptions: simple perceptions are uniform and indivisible, whereas complex perceptions are composed of simple ones. In the first pages of the Treatise (just after having introduced these two distinctions), Hume establishes two important principles. First, that every simple idea has always been preceded by the correspondent impression of which they are a weakened copy (copy principle). Second, that all complex perceptions may be separated into their simple components (separability principle).35 These two principles make the general framework of Humean empiricism more rigid than the one we found in Locke. In particular, they play a central role in

 In an interesting way, T. Holden (in Holden 2002) underlines the importance of the metaphysical dimension of Hume’s argument against infinite divisibility and its a priori nature. According to Holden, the “purely mathematical reading” is responsible for the dismissive attitude towards Hume’s theory of space. 34  See T. Introduction, xvi. 35  For the copy principle, see T. I. i. i, 4 “That all our simple ideas in their first appearance are deriv’d from simple impressions, which are correspondent to them, and which they exactly represent; for the separability principle, see T 1.1.7, 18 “whatever objects are different are distinguishable, and whatever objects are distinguishable are separable by the thought and imagination”. 33

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Hume’s rejection of the infinite divisibility of space that, as we have seen, Locke tried at any price to conserve. At the beginning of Part II on space, Hume states that the capacity of the mind is finite, that it can never attain an adequate conception of infinity and that “whatever is capable of being divided in infinitum, must consists in an infinite number of parts” (T. I. II. i, 27). From these claims, Hume derives as a consequence that any finite extension may be divided only a finite number of times before attaining some simple, indivisible part (T. I. II. i, 26–27). Now, unlike Locke, Hume claims that the ideas of imagination, exactly as the impressions of the senses, cannot be infinitely divided and their division leads to some last, indivisible parts of extension. Taking as an example of an idea of imagination the division of a grain of sand he writes: […] What consists of parts is distinguishable into them, and what is distinguishable is separable. But whatever we may imagine of the thing, the idea of a grain of sand is not distinguishable, nor separable into twenty, much less into a thousand, ten thousand, or an infinite number of different ideas. ‘Tis the same case with the impressions of the senses as with the ideas of the imagination. Put a spot of ink upon paper, fix your eye upon that spot, and retire to such a distance, that at last you lose sight of it; ‘tis plain, that the moment before it vanish’d the image or impression was perfectly indivisible. […] (T. I. II. i, 27)

Thus, any finite extension – imagined or sensed – has parts and therefore is divisible, but its division ends necessarily with a simple sensible point (T. I. II. iii, 34). On the side of impressions, the description of the ink spot observed from a constantly increasing distance allows an experimental determination of the “minimal” nature of these points. According to Hume, in this case, it is possible to detect a precise moment which marks the limit where – if the distance is even very slightly increased – the ink spot would no longer be perceptible (and then would cease to exist) (T. I. II. iii, 34). All visible points as they appear just before disappearing, are not only the smallest, they are also, and more importantly, simple. They are simple because any subtraction of parts leads to their disappearance, whereas if they had parts, it should be possible, thanks to the “separability principle”, to subtract at least one part from the whole. According to Hume, this simple idea represents not only the simplest and most minute parts of our ideas of space, but also the most minute parts of space itself because nothing can be smaller than what is “perfectly simple and indivisible” (T. I. II. i, 28). By virtue of this correspondence, he claims that these simple ideas are adequate representations of the simple parts of extension and that “whatever appears impossible and contradictory upon the comparison of these ideas, must be really impossible and contradictory, without any farther excuse or evasion” (T. I. II. ii, 29). The establishment of adequacy between parts of space and parts of the ideas of space at this stage of his development is an important step because it allows him to reject any attempt to introduce, as Locke in his answer to Barbeyrac, an asymmetry between ideas of extension and extension. This adequacy is then what allows him to develop from the beginning his enquiry exclusively at the level of ideas of space, their parts and their relations. The restriction of the domain of

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discourse to ideas will find new justifications in the course of the Treatise and already in the last section of the part devoted to space (the section is entitled Of the idea of existence and of external existence) Hume states that the only kind of existence we can conceive of is the one of our perceptions (T. I. II. vi, 67–68). At the end of this very section, Hume announces that the same subject will be developed later in Part IV, sect. II (Of the scepticism to regard to the senses), and there he explains how the opinions about the continued and distinct existence of objects are produced by a kind of natural movement of the understanding, which, starting from particular features of impressions (as their coherency and constancy), reinforces them, making the perceived uniformity as complete as possible. Unlike Locke, Hume considers that the belief in the external (i.e. distinct and continued) existence of objects is nothing else than a fiction that men are led to elaborate starting from their sensible ideas.36 The notion of “fiction” – which plays a very important role in the general economy of the Treatise – is here given in its technical sense as not only a complex idea produced by the imagination and for which we have never received a correspondent impression, but more precisely as a combination of inconsistent ideas that we believe to be compatible by virtue of a confusion between one of the component ideas and some similar, but distinct and related, one. Because of their internal inconsistency, fictions are not ideas in the proper sense of the term. The Lockean problem concerning the relation – and asymmetry – between space and the ideas of space is thus deflated.

1.4.2  Space and Manner of Disposition In addition to the claim concerning the simple nature of sensible (visual and tactile) points, Hume maintains that one of the essential features of the idea of extension is the fact that it has parts. The other features of the idea of extension are derived from the examination of the content of impressions of extension and of the ideas that are their weakened copies: The table before me is alone sufficient by its view to give me the idea of extension. This idea, then is borrow’d from, and represents some impression, which this moment appears to the senses. But my senses convey to me only the impressions of colour’d points, dispos’d in a certain manner. If the eye is sensible of any thing further, I desire it may be pointed out to me. But if it be impossible to shew any thing farther, we may conclude with certainty, that the idea of extension is nothing but a copy of these colour’d points, and of the manner of their appearance. (T. I. II. iii, 34)

The nature of spatial impressions and ideas may then be described through two essential features. The first consists in the composition of a certain number of points

36

 T. I. iv. ii, 187–218, see more particularly 205, 208, 209.

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endowed with sensible qualities (colour or tactile qualities). The second consists in the manner of disposition of the points. An immediate consequence of this claim is that points being simple are not extended, and thus that a space cannot consists in only one point. Another related consequence is that colour and solidity are not necessarily extended (T. I. II. iii, 34). If any particular idea of extension is sensible (coloured or solid), the converse is false: it is possible – as it is the case of visual points – to be coloured or solid without being extended. This tight connection made between space and composition places a heavy burden on the concept of “manner of disposition”, which is charged with explaining how a set of sensible points can form an extended space. Note first that this notion is a thorny one because there is not an obvious place for it within the reduced Humean metaphysics of simple and complex impressions and ideas. Actually every particular spatial idea does not appear to be merely an idea composed (as a pure addition or combination) of a certain number of sensible points, but rather as the arrangement or disposition of these points. This appears to imply that in the world of perceptions we should count not only simple and complex perceptions, but also the modes of disposition of simple perceptions.37 Moreover the analysis of the impression of extension in terms of modes of disposition may appear to be circular because the notion of “manner of disposition” to which space is reduced – being actually a manner of disposition in space – may appear to include the very notion of space that it is supposed to explain.38 There is a lot of literature on these issues, but we are not going to deal with these questions in detail.39 I will enlarge on this difficult point here, only to focus on the internal features of the notion of “manner of disposition” or “way of appearance” that confers on it the status of a spatial manner of disposition. Indeed, if an extended impression is a set of sensible points, it is not the case that any set of points forms an extended space. The points should be appropriately arranged. What are the structural properties that give to a certain number of simple unextended points the character of being a space? Unfortunately, Hume does not directly address this decisive issue, and his ideas on the topic have to be inferred from what Hume writes on the impossibility of the idea of a void, i.e. of an idea of extension deprived of any sensible quality. The first premise of Hume reasoning is that where there are no sensible qualities (as when looking at the most obscure darkness), there is no perception of space at all. He then examines whether it is possible to have some perception of space when

 T. I. II. iii, 33–34.  A.  Rosenberg denounces such circularity: “[…] the manner of appearance of these coloured points has them either to the left or, to the right of, above, or below one another. But where do these ideas come from? They presuppose space. If so, […], the “manner of appearance” of extended minima must be spatial itself, […]” (Rosenberg 1993, 83). 39  Many authors consider the notion of “manner of disposition” as a problematic one introducing a tension into the distinction between a simple and complex idea, the distinction between impression and ideas, and the copy principle. For an insightful description of the questions relative to the status of the notion of “manner of disposition” in Hume philosophy, see Falkenstein 1997. 37 38

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only two distinct and distant luminous bodies are made to appear in the middle of darkness: The sole difference betwixt an absolute darkness and the appearance of two or more visible luminous objects consists, as I said, in the objects themselves, and in the manner they affect our senses. The Angles, which the rays of light flowing from them, form with each other; the motion that is required in the eye, in its passage from one to the other; and the different parts of the organs, which are affected by them; these produce the only perceptions, from which we can judge of the distance. But as these perceptions are each of them simple and indivisible, they can never give us the idea of extension.40

Hume claims then that the perceptions of the two luminous points and of their distance (perceived by “the different parts of the organs, which are affected by them”) are not enough to give rise to a complex idea of space. According to Hume, the only difference between the perception of the luminous points and the previous absolute darkness consists in the distinct perceptions of the two luminous points. Something more is required to perceive space – but what exactly? Two facts may explain why Hume does not consider the perception of two luminous points against a dark background as a perception of an extended space. First of all, according to Hume, the two isolated points are perceived as having a determinate location in the visual field – and this, independently from any kind of action or movement on our part, as if the visual field were endowed with some kind of constituted topology. Secondly, the perception of the movement from one point to a distant one is presented as a simple (and therefore unextended) perception. In the case discussed by Hume then, the perception of the two sensible points are not the perception of a space either because the “gap” between the two points are not filled with intermediate sensible points, or because the movement allowing us to switch from one to the other is not regarded as made of sensible parts. In both cases, the simple sensible points do not give rise to a perceptual continuum. One can thus conclude that, for the perception of two punctual lights to be the perception of an extended space, the two lights should be either related by a series of contiguous sensible points, or connected by a movement passing in a continuous way through one to the other, as it is the case with the illuminated sky presented by Hume just before the discussion devoted to the two luminous bodies in complete darkness.41 In other words, a manner of disposition of several simple ideas is a spatial one, if the

 T. I. II. v, 57–58. In the Appendix, Hume confesses that he discovered an error where he claims that “the distance betwixt two bodies is known, among other things, by the angles, which the rays of light flowing from the bodies make with each other.” In fact he says “‘Tis certain that these angles are not known to the mind, and consequently can never discover the distance” (T Appendix, 636). This sentence is very similar in form and content to sections 12 and 13 of Berkeley’s NTV. It is possible to explain Hume’s “more mature reflexion” on the perception of distance through angles supposing that he actually read the Essay toward a New Theory of Vision, only after the publication of the first and second book of the Treatise. 41  T. I. II. v, 56: “When I hold up my hand before me, and spread my fingers, they are separated as perfectly by the blue colour of the firmament, as they cou’d be by any visible object, which I cou’d place betwixt them.” 40

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perceived points are contiguous, or, at least, if the distance between the different points is perceived by a movement having perceivable parts. In sum, according to Hume, ideas of space are complex ideas composed of a set of sensible qualities forming a sensible (visual or tactile) continuum and being divisible only a limited number of times. In T. I. ii. 4., Hume connects his criticism of infinite divisibility to a fundamental question concerning the criterium of equality in geometry. According to Hume, geometry – working on comparisons of spatial magnitudes – presupposes a precise definition of equality, but the criterium for equality is never made explicit (T. I. ii. 4, 45). Further, he claims that our sensible (or intuitive) judgements of spatial equality are imprecise, and that in many cases we can make them a step more precise through measures and juxta-position in no case attaining a perfect and exact measure. However, even if by these improved measurements it is not possible to know the exact proportion among figures, we are led to believe, by a natural movement of our understanding, in the fiction of the possibility of improving them ad infinitum attaining in this way a perfect and exact proportion of extension: […], we therefore suppose some imaginary standard of equality, by which the appearances and measuring are exactly corrected, and the figures reduc’d entirely to that proportion. This standard is plainly imaginary. For as the very idea of equality is that of such a particular appearance corrected by juxta-position or a common measure, the notion of any correction beyond what we have instruments and art to make, is a mere fiction of the mind, and useless as well as incomprehensible. But tho’ this standard be only imaginary, the fiction however is very natural; nor is any thing more usual, than for the mind to proceed after this manner with any action, even after the reason has ceas’d, which first determin’d it to begin. (T. I. ii. 4, 43)

As we have seen above, fictions are combinations of inconsistent ideas. In this case, the imagination combines the idea of a perfect standard of equality with the idea that this perfect standard cannot actually be applied to spatial magnitude, because it goes “beyond what we have instruments and art to make”. This combination of ideas is a fiction because a standard that cannot be applied contradicts the very nature of a standard. What is interesting on this point is that Hume explicitly connects standard of equality and actual practice of measure. (I. ii. 4, 48). Notwithstanding his criticism of infinite divisibility and of the criterium for equality in geometry, Hume does not propose either to reform classical geometry (as Berkeley in PC) or to use the theory of generalization in order to make compatible the sensible finite divisibility of our ideas with the principle of infinite divisibility of Euclidean geometry (as Berkeley in the Principles). However, it is not an easy task to determine the consequences of Hume’s criticism of infinite divisibility and of the standard of equality on the status of geometrical knowledge in the Treatise. Secondary literature is quite divided on this critical point.42

 Fogelin (1988, 56–57) claims that Hume, in the Treatise, defends a sensible notion of equality and therefore a kind of sensible, approximative, geometry. D. Jacquette, on the contrary, maintains that “Hume wisely maintains that his indivisibles confer the idea of equality only for purposes of reasoning, and do not provide a practical basis for determinations of geometrical equality and

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One important consequence of Hume’s analysis of the idea of space is the rejection of the notion of empty space. Actually, since the ideas of space consist in a certain mode of disposition of sensible points, they necessarily imply qualities, and cannot be given without them. As a consequence, the mere conception of empty space – being the mode of disposition of sensible qualities without sensible qualities – is inconsistent and therefore impossible.43 At this stage, one could complain about the very counter-intuitive consequence of Hume’s claim. How can we really believe that it is impossible to form an idea of the distance between two luminous bodies appearing against a dark background? According to Hume, when we imagine an empty space, what we really conceive of is the idea of a sensible extension that could replace mere darkness without any modification of the surrounding objects.44 We believe in the conceivability of an empty space because we confuse space (that is necessarily sensible) with what is not space but may be replaced by it. Thus, the idea of an empty space, as the idea of a standard for exact equality or the idea of external existence, should be classed as a fiction.45 Finally, I would like to emphasize that Hume, in his account of the notion of space, does not make any place for the difference between visual and tactile ideas of space. Thus, very regularly, when Hume presents a case concerning sight, he gives (not without introducing some kind of pedantic heaviness) also a corresponding explanation for touch. This allows him to treat space as an abstract idea derived equally from the particular perceptions of extension of sight and of touch.46

proportion.” (Jacquette 2001, 178; see also 168–180 for a general discussion of this point). Whether Hume’s position on the status of geometry as an empirical or as a deductive science in the Treatise and in the First Enquiry are essentially the same or if they radically diverge is another claim which is a subject of debate in secondary literature (see Newman 1981, 57–58; Fogelin 1988, 57–58). In an interesting way, W. Waxmann (in Waxmann 1994, 115–127 and especially 123–125) connects the question of the (impossible) exactness of the standard of equality to the use of language. 43  Hume’s criticism of empty, insensible space is a criticism of Newton’s insensible, absolute space. Nevertheless, Hume thinks that this key concept of Newtonian physics can be “rightly understood”, that is, it can be rendered compatible with a correct (empiricist) conceptual analysis of space. See T. Appendix, A note to Book I, line 19, p. 64, 639: “If the Newtonian philosophy be rightly understood, it will be found to mean no more. A vacuum is asserted: That is, bodies are said to be plac’d after such a manner, as to receive bodies betwixt them, without impulsion or penetration. The real nature of this position of bodies is unknown. ...” 44  T. I. II. v., 59. 45  T. I. II. v., 60. 46  T. I. II. iii., 34 and 38; several times in relation to empty spaces at T. I. II. v., 56–59. It is possible that Hume takes care on the symmetry between sight and touch on this point because he dreads the heavy theological consequences that Berkeley collects from his heterogeneity thesis that is taken as an essential part of the thesis of vision as the language that God speaks to men. However, it is also possible that when writing the first book of his Treatise, Hume was not yet familiar with Berkeley’s NTV (see above note 40). For a different point of view on Hume’s conception of the heterogeneity of visual and spatial ideas of space, see Waxman 2008.

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1.4.3  Conclusion I have focused my presentation of Hume’s theory of space on his description of the content of particular spatial ideas. Hume’s theory of sensible space can be seen as a development of some ideas already present in Locke. In particular, his analysis of space in terms of un-extended minima can be traced back to Locke’s discussions of “the least Particle of Matter or Space we can discern” (see Sect. 1.2.3). But Hume breaks completely with Locke’s Aristotelian conception of space as a continuous medium and pushes the atomistic thesis towards its ultimate consequences. In this respect, one point deserves to be underlined: while Locke, when discussing infinite divisibility refers to an asymmetry within spatial sensation, on the one hand, and both, ideas of imagination and space in itself, on the other, Hume stresses the fact that no asymmetry may be invoked among these three domains of discourse.

1.5  Condillac Condillac presents his philosophical project as an extension of Locke’s, namely, as a program of foundation of our knowledge in experience.47 However he believes that, concerning at least two points, his philosophy improves on Locke’s. First, for Condillac, not only our ideas but also our faculties are generated from sensations. Second, he emphasizes more than Locke the role played by signs and language in the development of knowledge.48 Condillac deals with space mainly in two works: the Essai sur l’origine des connaissances humaines, dating from 1743, and, more at length, in the Traité des sensations, from 1754. In both books, he relates the concept of space to its sensorial origin, but the Essai and the Traité differ in the way of linking the idea of space to the senses. Condillac is conscious of this change and, in the introduction to the Traité, he presents his new position concerning the perception of space as the most significant difference between the two texts. The difference is roughly that in the Essai, he maintains that sight and touch receive directly and immediately the idea of three-dimensional extension, whereas, in the Traité, he claims that the senses need to develop and structure themselves progressively through experience before being able to perceive an idea of a full-fledged, three-dimensional space. The main theme of the Traité is in fact that “we have learned to see, hear, taste, smell and touch”  References to Condillac 1947a (Essai sur l’origine des connaissances humaines) are indicated as Essai, followed by part, section, chapter, paragraph and page number. The reference of the English translation (Condillac 2001) is indicated as E transl., followed by the page number. References to Condillac 1947b (Traités des sensations) are indicated as Traité, followed by part, chapter and page number. The reference of the English translation (Condillac 1982) is indicated as T transl followed by the page number. On this point: Essai, Introduction, 4–5; E transl. 5; and in relation to the discussion of the senses: Traité, Dessein de cet ouvrage, 221–223, T transl. 155–158. 48  See Essai, Introduction, 3–5; E transl. 5–8. 47

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(Traité, Dessein de cet ouvrage, 221b, T transl. 170). Notwithstanding this difference, in both texts Condillac tackles the question of space at the level of the content of sensible experience and he develops his enquiry within the domain of ideas.49 In this section, I will first present Condillac’s conception of the relation between the idea of space and the sensible perception in the Essai sur l’origine des connaissances humaines (1.5.1). I will then pass to the Traité des sensations, where Condillac introduces two different, alternative ways of constructing an idea of extension. I will first describe the features of the most elementary notion of space as perceived by sight (1.5.2), and second, I will present the connection existing between the idea of extension perceived by touch and the capacity of movement (1.5.3). Finally, I will explain in which way Condillac’s view of the “analysis” of spatial ideas represents an alternative to the description of the most elementary components of the idea of space that we found in Berkeley and Hume (1.5.4).

1.5.1  S  pace in the Essai sur l’origine des connaissances humaines Condillac thinks that “analysis” is the method to examine and to establish our knowledge. This method: … merely consists in composing and decomposing our ideas to create new combinations and to discover, by this means, their mutual relations and the new ideas they can produce. This analysis is the true secret of discoveries because it always makes us go back to the origin of things. (Essai, Part I, Sect. II, ch. vii, § 66, 26b, E transl. 48)50

According to Condillac, analysis is first and foremost a process that nature taught us in order to acquire all our ideas and to develop our faculties. It can become a method for science and for the critics of knowledge only once ideas and faculties are acquired.51 Condillac’s analysis is not the simple decomposition of ideas into their simple components; rather, it consists of a double process: first, the process of reducing the complex idea into simpler ones that compose it and, second, the process of generating the complex idea by following the steps by which it has actually been created from simpler ones. The relevant aspect of analysis as conceived by Condillac is not the traditional decomposition into simple parts, but rather the description of the actual, sensible genesis of the idea. Thus, in describing his method, Condillac  Essai, Part I, Sect. I, ch. I, §1, 6a, E transl. 11; and more precisely concerning extension Traité, Part IV, ch. v, §1, 306a note, T transl. 323 38n. 50  See also Essai, Part II, sect. II, ch. iii, §36, 11a); E transl. 212. On Condillac’s notion of “analysis”, see Charrak 2003, 124–128. 51  This is explicit in the title of the first part of the Logique (Condillac 1947–1951, II: 372) that is: Comment la nature même nous enseigne l’analyse; et comment d’après cette méthode, on explique l’origine et la génération, soit des idées, soit des facultés de l’âme. Logique, ou les premiers développemens de l’art de penser. 49

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points out that we have to start not from the simplest ideas but rather from the simplest ideas transmitted by the senses. (Essai, Part II, Sect. II, ch. iii, §34, 112b; E transl. 211). As we saw, the distinction between simple and complex ideas is crucial to both Locke’s and Hume’s discussions of space. Condillac as well, in the Essai, uses this distinction in order to clarify the nature of the idea of space. He introduces the distinction quoting Locke’s Essay at length. He describes a complex idea as “the union or the collection of several perceptions” and a simple idea as “a perception considered distinct by itself [in French: “une perception considérée toute seule”]” (Essai, Part I, Sect. III, §. 1, 37b-38a; E transl. 71). However, applying this framework to the case of space, Condillac, exactly as Locke did before him, is led to relax the criteria of this division. At first, the idea of extension is classed within complex ideas and more precisely within ideas that “are compounded of uniform perceptions, or rather they are merely the same perception repeated several times” (Essai, Part I, Sect. III, §4, 38a; E transl. 72). This class is further subdivided into two subclasses: first, ideas for which the number of the composing perceptions is undetermined (as in the abstract idea of extension), and second, ideas for which the number of composing perception is determined (as in the case of a foot that is nothing but the perception of an inch taken twelve times) (Ibidem). Immediately after this statement however, Condillac considers simple and complex ideas from an epistemological point of view and claims that simple ideas  – being nothing else than our own perceptions – are known exclusively by reflection on the content of our perceptions, while to know complex ideas we have to reduce them to the simple ideas that compose them and to follow the very generation of the thing. Thus we must reduce them to “the simple ideas they are made from and follow their generation” (Essai, Part I, Sect. III, §9, 38b; E transl. 73). Now (and here is the clever bit), Condillac claims that all complex ideas that – as the idea of space – are the indeterminate repetition of uniform perceptions, despite their complexity, are known, as the simple ones, by reflection on the content of our perception (Part I, Sect. III, §6, 7). Therefore, even if these ideas are ontologically complex, from an epistemological point of view, they behave as simple ones. Indeed, Condillac claims that since he looks “at ideas only in regard to the manner in which we come to know them”, in the following, when speaking about “complex ideas”, he has to be understood as referring only to ideas formed by different perception or by the same perception repeated in a determinate manner, in this way excluding from the range of complex ideas the ideas of indeterminate extension (Essai, Part I, Sect. III, §.8, 38b; E transl., 73). For Condillac as for Locke, one of the most important truths is that many ideas, not being composed, cannot be defined. Ideas of space – despite their complexity – share with simple ideas the property of not being reducible into simpler components. Therefore, ideas of space may be known only through their sensible contents that are perceived immediately by sight and by touch. This may explain why

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Condillac neither develops the concept of sensible point conceived as the smallest perceivable parts of extension (as Locke, Berkeley and Hume do) nor defines space as a “manner of disposition of sensible points” (as Hume does).52 Alongside the claim that the idea of space cannot be known by the separation and enumeration of its components, Condillac also develops a criticism against the “genetical” description of spatial concepts endorsed by geometry. Condillac targets more precisely the usual definitions of geometricians who, starting from the definition of the point as “that which terminates itself on all sides’‘, characterize the line as what is generated by the movement of a point, the surface as what is generated by the movement of a line, etc. According to Condillac, this so-called “analysis” is inadequate because it does not conform to the natural order of the “generation” of spatial ideas: It is easy to see that the geometricians wished to accomodate themselves to the generation of things and of ideas, but they did not succeed. We cannot have the use of our senses without immediately having the idea of extension with all its dimensions. The idea of the solid is therefore the first they give us. Now, take a solid and consider one extremity of it without thinking of its depth, and you will have the idea of a surface […]. If you follow this example, you will find it easy to form the ideas of point, line and surface. It is evident that it all depends on the study of experience in order to explain the generation of ideas in the same order in which they are formed. […] Essai, Part I, Sect. III, §12, 39a-b; E transl. 74–75)

In the Essai then, from the epistemological perspective of the generation of our knowledge, the basic idea is the idea of three-dimensional extension from which the notions of surface, line, and point are derived.53 It is thus the idea of point that should be derived from the idea of volume, not the other way round.54 As we will now see, in the Traité, Condillac gives up the claim according to which three-dimensional space is immediately perceived. However, Condillac still considers his research as the description of the actual genesis of ideas, and in the case of space, this actual genesis is a double one: it is the genesis of spatial ideas, but also of the senses apt to receive them. Also in the description of this double genesis, no place is made for a decomposition of space into its simplest elementary parts.

 However, Condillac has always underlined the difficulties proper to the thesis of the infinite divisibility of space (for instance, Cours d’études: Art de penser (1775) Cours d’études V. De l’Art de Penser, chap. Xii. Condillac 1947–1951. I:754). 53  The primacy of three-dimensional extension explains why Condillac is neither interested in determining the smallest part of extension perceptible by the senses, nor in suggesting that there are some simple constitutive parts of extension, similar to the sensible points or minimum, as Locke, Berkeley and especially Hume did. 54  This idea that a point should be defined in terms of volume will find a new expression with the development of point-free geometry, initiated by Whitehead. On this, see Whitehead 1919.

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1.5.2  Space in the Traité des sensations To describe this genesis in the Traité, Condillac imagines “a statue internally organized like ourselves, and animated by a mind deprived of every kind of idea” (Traité, Dessein de cet ouvrage, 222a, T transl. 170). Then, he unlocks its senses one by one, beginning with smell, and supposes that, already at this first stage, the statue is capable of receiving pleasure and pain from the experience of different objects. Condillac describes how the statue, starting from the sensations of the different smells, will progressively develop attention, memory, comparison, desire, and most of the other cognitive faculties (Traité, Part I, ch. ii-vii). Already in these first chapters, Condillac asserts his main thesis that not only our ideas, but also our faculties, have a common principle that has its origin in sensation.55 The narrative fiction of the statue is for Condillac the means to describe the first stages of an experience which has transformed itself before attaining its most developed stage, that is, the only one to which we, as adult human beings, have actual, conscious access to. In other words, the description of the process by which the inanimate statue reaches the level of our mental experience amounts to the description of the generation of all our present ideas and capacities starting from the simplest sensations. We won’t follow here the intricate developments of the statue’s mental life,56 but we will give a brief description of the general principles which inform the whole of the learning process. According to Condillac, the only internal driving force which raises the statue’s mind by degrees to all the knowledge of which it is capable is the research of pleasure and the wish to avoid pain. No other motive guides its evolution.57 Three kinds of situations are then considered by Condillac: first, the consequences of the unlocking of a sense modality (smell, then taste, sight, etc.);58 second, the consequences of the common exercise of different senses (as for instance, sight and smell, or sight and touch, together);59 third, the consequences of the movement of the statue’s limbs.60 This last operation is proper to the unlocking of the statue’s touch modality. One point which is especially important in Condillac, and well-illustrated in the Traité, is that the evolution of the various mental faculties (attention, memory, but also the various sense modality) cannot be separated from the evolution of the content of our ideas – and vice-versa. It is not possible to account for the generation of rich complex ideas without taking into consideration the evolution of the faculties that grasp them. In Condillac, the learning process produces at the same time both a genesis of new ideas and a genesis of new faculties, and the degree of articulation of the perceived ideas depends on the degree of articulation of the correspondent  See Traité, Part I, ch. vii, §1–4, 239a–b, T transl. 202–203.  See LeRoy 1937; Paganini 1992; Falkenstein, 2005. 57  See Traité, Part I, ch. ii, §4, 225a, T transl. 178. 58  See Traité, Part I, ch. i–vii, viii, x, xi; Part II chap. i–xii. 59  See Traité, Part I, ch. ix, x, xii; Part III, chap. i–ix. 60  See Traité, Part II, ch. vi–viii, xii. 55 56

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faculty. This feature is particularly visible in the analysis of the process leading to the idea of extension, to which we will now turn. Oversimplifying Condillac’s description, one can distinguish three kinds of ideas of extension: the first kind is the idea of extension received by the statue when it is opened uniquely to the sense of sight; the second involves both the tactile ideas and the bodily animation of the statue; the third kind is reached when sight, touch and bodily movement work together. Let me say a word about each of these stages. At the beginning of its sensorial life, the statue’s capacities of attention and memory are not developed at all. Therefore, when the sense of sight is unlocked, the statue is not able to perceive that different particular colours co-exist in its sensations. Only progressively, once having acquired the capacity of focalising its attention on different parts of the visual field (Traité, Part I, ch. xi, §5, 246b-247a, T transl. 215–216), will the being perceive, at first one particular colour, and then (thanks to the development of memory) to feel one colour without completely forgetting the preceding one, sensing in this way two or three co-existing colours, and therefore some kind of extension. At this stage, however, the statue’s sensations are still nothing other than its own ways of being. When the statue sees a red spot, it senses itself red and doesn’t yet attribute the redness to the external world. Thus, when the statue senses the co-existence of three colours, it senses itself as being at once two or three colours one next to the other: The idea of extension presupposes the perception of several things that, being outside each other, are contiguous and consequently each extended: for unextended things cannot be contiguous. Now we cannot deny the statue this perception, for it senses that it repeats itself, outside of itself, as often as there are colors that modify its state. Insofar as it is red, it senses that it is outside green, insofar as it is green, that it is outside red, and so forth. (Traité, Part I, ch. xi, §8, 248a, T transl. 217)

According to Condillac, the statue, at this stage of its development, may correctly be said to perceive extension – in the sense that it perceives a co-existence of a limited number of different and contiguous qualities. This idea of extension has some unusual features, however. First of all, as this first sensation of extension consists simply in the sensation which has a very limited number of parts (two or three), the extension perceived cannot be regarded as a surface or as a determined figure with size and length. Secondly, and most importantly, all the perceptions of the statue are considered as its own ways of being (Traité, Part I, ch. xi, §2, 245a-b, T transl. 214). The perception of extension here reached has the peculiar feature that the statue cannot localize itself in it: “insofar as it is red, it senses that it is outside green, insofar as it is green, that it is outside red, and so forth”. Only the sense of touch may allow the statue to pass outside itself and to perceive a more articulated extension. But this new way of perceiving is not immediately acquired. At the beginning, in fact, the statue may be able to perceive distinctly a sensation of warmth at one arm, of pressure to the other and a cold sensation to feet, and these perceptions are certainly co-existent, however since they do not give rise to contiguity nor continuity, they are not perceptions of extension even in its more elementary form (Traité, Part II, ch. iii, §1, 252b-253a, T transl. 228–229).

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The situation changes when the statue, opened to touch, becomes also capable of moving its own body. First of all, thanks to the movement of its own body, the statue receives the sensation of solidity (Traité, Part II, ch. v, §3, 256a-b, T transl. 233–234). According to Condillac, what is specific to this sensation is that it is two things that exclude each other. Therefore in these sensations, unlike what happened with the sensations of colours, sounds, etc., the statue will “pass out of itself”, will cease to sense all sensible qualities as its own ways of being and will attribute some of them to its own body and some others to distinct external bodies: Since the essence of this sensation of solidity is to represent at one and the same moment two things that exclude each other, the mind will not perceive solidity as one of those states in which it finds only itself; it will perceive it necessarily as a state in which it finds two things that are mutually exclusive and as a result it will perceive it in these two things. There you have then a sensation with which the mind proceeds from itself to outside of itself and we begin to understand how it will discover objects. (Ibidem)

Furthermore, the movement of its own limbs will allow the statue to actively look for pleasure and avoid pain, to receive a much richer amount of new sensations, progressively mastering from one side, the movements of the different parts of its body and from the other the comparisons, recognition and memory of the perceived qualities (Traité, Part II, ch. iii, §1, 252b-253a, T transl. 228–229). Indeed the statue, moving its hand without discontinuity on different parts of its body, “will unite in a single continuum parts formerly separated” and will make its own extension more and more perceivable.61 Therefore, it is the continuity pertaining to the movement of the statue’s limbs that confers continuity to the content of its tactile sensations. Later on, when the statue’s sight and touch are unlocked together, the spatial articulated structure acquired by touch may be transferred to the sensations of sight. Colours become progressively perceived as qualities of the external world. As Condillac says in a very suggestive way: 15. It is the hand that, guiding vision successively over the different parts of a shape, etches all these parts in memory; it is the hand, so to say, guides the engraving tool when the eyes begin to attribute to the exterior the light and colours that they first experienced as in themselves. They perceive these properties where touch teaches them they must be: they see as up what touch teaches them to judge as up and they see as down what touch teaches them to judge as down; in a word, they see objects in the same positions as the sense of touch represents them to be. (Traité, Part III, ch. iii, §15, 283a, T transl. 279)

Thus, the separation between the senses (which appear to be given and inscribed in the body of the statue) is in some ways permeable and, given certain conditions consisting in the co-existence of parts, the organization acquired by a sense modality may be transferred to another one. In this respect, Condillac clearly differs from Berkeley who thinks that the limits between the senses are impassable: for him,  Traité, Part II, ch v, §3, 256a, T transl. 234: “[…] it will experience a continuity of self at its fingertips, so to speak; and this same hand that has brought together the formerly separated parts into a single continuum will thereby render extension more perceptible”.

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even if visual ideas could be associated by the force of habit with tactile ideas, it remains that ideas are immediately perceivable by one sense alone. However, the emphasis on touch and movement in the Traité draws Condillac’s inspiration close to Berkeley’s. Indeed, for Condillac in the Traité, what is important in the analysis of the idea of extension is not its relation to a specific sensorial modality, but rather its dependency on the mastery and control of movement and on the subsequent richness of the given. It is precisely the mastery of movement that confers to touch its primacy in the perception of a full-fledged idea of a three-­ dimensional space. Therefore, even if space and extension may be perceived in different ways, only one, the one made at first accessible by touch and the movement of the statue’s body may be conceived as external, continuous, limited, figured, etc.62

1.5.3  Conclusion: On Analysis of Ideas In the Traité, Condillac claims that the idea of three-dimensional extension is built progressively through experience from more elementary sensations, whereas in the Essay, he maintained that the very same idea is a fundamental building block of our experience. One can hardly find a more contrasting opposition. In a certain respect however, there is a coherence in Condillac’s views: the rejection of using decomposition in some supposed simple component parts as a method for knowing space, is one thing common to both works. Already in the Essay, in fact, Condillac, while acknowledging that space is a complex idea, stresses the fact that, from an epistemological perspective – that is, from the point of view of its origin – the idea of extension behaves as a simple, indivisible one. And, similarly, in the Traité, Condillac describes at length the steps that progressively lead, through movements, to generate a sufficiently rich idea of extension. The description of this genesis has thus nothing to do with an analytical decomposition of the idea of space. This rejection of the decompositional analysis for the idea of space represents an important difference between Condillac, on the one hand, and Hume and Berkeley, on the other. Condillac in fact describes a dynamical genesis, the ways according to which some ideas and faculties transform themselves and become progressively more complex. Quite the contrary, Hume and Berkeley decompose the particular ideas of space into their components actually and effectively perceived by the subject. As we have seen before, Hume takes particular ideas of space as actually (effectively) composed of simple sensible points disposed in a certain manner, and Berkeley decomposes the particular ideas of space following two distinct methods: first in the PC, spatial ideas and figures are composed of sensible points, and secondly in the NTV spatial ideas are reduced to some simpler sensations perceived by touch, such as movement, pressure and protrusion. According to Berkeley, even if  The importance of the movement of proper body will be recognized by the idéologues and some of them will even propose to account movement among the senses which would not anymore be five, but six. For more, see Elisabeth Schwartz in this volume.

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the associations between ideas established by habit make us progressively unaware of the components and of their distinction, these distinct ideas are always present in our mind and attentive observation may reveal them.63 By contrast, Condillac’s generation process transforms the content of experience so deeply that the building elements, on which the actual perception of extension structures itself at the beginning, no longer exist at the end of the process, in the sense that they do not appear as parts of the content of the more developed idea. When the statue learns to perceive colour as a quality of some external surface, it loses the capacity of seeing colour as a quality of its own being. In Condillac, therefore, the senses appear endowed with a kind of plasticity that makes it impossible, once a new structure has been acquired, to go back to the previous stages and recover the former organization. This is why time matters for Condillac. The irreversibility of the process explains why Condillac, in an important “notice” that precedes the beginning of the Traité, does not ask his reader to observe and distinguish the parts of his perceptions, but rather to put himself in the place of the statue, in order to sense again the simplest contents and their relations to the simplified senses of this original, no longer actual, experience: Important Notice to the Reader […] I forewarn the reader that it is very important to put himself exactly in the place of the statue we are going to observe. He should begin to live when it does, have only a single sense when it has only one […]; in short, he must be only what it is. The statue will judge things as we do only when it has all the senses and all the experiences we do: […] As yet the reader does not understand what the statue is that I propose to observe, and this warning doubtless seem misplaced; but that will be one further reason for taking heed and remembering it. (Traité, Avis au lecteur 219, T transl. 234)

As noted at the beginning, the issue of the existence and definition of empiricism has been much discussed over the last years and is very complex. In this introduction, as in this volume, we placed ourselves, in a sense, further upstream than this debate: during the seventeenth and eighteenth centuries, among the authors that are traditionally considered as representative of empiricism such as Locke, Berkeley, Hume and Condillac a number of theories of space appear, all of them aiming to found the idea of space in experience (hence a common starting point consisting of the particular and finite ideas of extension) and to use some form of analysis to account for the genesis of this idea (hence some common problems). It is difficult to find similarities, for instance, between Locke who focuses on the content of ideas, on the one hand, and Condillac who focuses on the development of the faculties and senses, on the other; or between Berkeley who argues for a heterogeneity between visual and tangible space, and Hume who maintains a perfect

 At NTV 146, Berkeley writes: “The prejudice [about the visual perception of spatial ideas by sight …] sticks so fast ·in our minds· that it’s impossible without obstinate striving and mental labour to get entirely clear of it. […]”, my italics. Therefore, when the perceptual contents are considered with the required “obstinate striving and mental labour,” the visual ideas and their tactile meanings may be distinguished and considered separately.

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parallelism between sight and touch. However, closer scrutiny reveals some invariants. Sections 1.2, 1.3, 1.4 and 1.5 point at some elements that single out empiricist discussions of space: the issue concerning the nature of the elementary constituents of space, the question of the homogeneity or heterogeneity of visual and tactile spaces, the importance assigned to the movement of one’s own body. Through the recasting of the questions and the conceptual shifts, it is possible to see the emergence of a programmatic core common to the authors we discussed. In any event, as we said before, the aim of the preceding sections was first and foremost to provide an initial map of the area that the essays of the volume treat with specific purposes and with specific points of view. Indeed, during the seventeenth and eighteenth centuries, the concept of space was addressed in a wide variety of contexts and proceeded in different directions. Thus the subject allows us to treat it in very different ways. During these centuries, the reflection on space was closely related to the emergence of the new cosmology and to the transformations which it entailed on theology. The Newtonian distinction between absolute and relative space is at the core of the empiricist considerations, that often propose ways of maintaining the validity of Newtonian laws without the reification of absolute space. However, as at that time the reflection on space was not completely secularized, it often related to the Divine Being, his ubiquity, his omnipotence, and his forms of action in the world. In her essay, Margaret Atherton claims that one of the central goals of the Principles is epistemological and consist in showing the possibility of knowledge of natural phenomena, in line with Newtonian approach, without appealing to the notions of absolute space, place and motion. Luc Peterschmitt’s essay considers Berkeley’s criticism of Newton’s absolute space and its theological dimension. At the core of the reflection on space there are also entirely metaphysical discussions concerning the Aristotelian and Cartesian categories of substance and mode, categories that at this time undergo a major transformation. Martha Bolton’s article shows that Locke’s agnosticism concerning the substantial or modal nature of space in the Essay – usually interpreted as a mere rehearsal of the claim that substance is something-I-know-not-what – is rather a consequence of Locke’s doctrine concerning infinite space and its relation to God. In his article, Philippe Hamou considers whether and in what sense, according to Locke, mind has a location (is “in space”) and ideas are “in” the mind. He also examines Locke’s way of conceiving the relationship between this “inner” spatiality and the “external” one. The other papers of this volume remain within the topic of the relation between the notion of space and experience. Thus, the articles of Martine Pécharman on Hobbes, of Robert Schwartz and of mine on Berkeley, and of Elisabeth Schwartz on Condillac describe the different ways in which the notion of space may be anchored in experience. The preceding sections do not attempt to address all these issues, and even less to cover them thoroughly – the aim was simply to set the scene for the different issues developed in the essays.

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1.6  Summary of the Papers Chapter 2: Hobbes on Space as Imaginary Space Martine Pécharman Hobbes’s first elaboration of his doctrine of space is directed against the traditional discussion of spatium imaginarium which Thomas White is indebted to in his De mundo dialogi tres (1642). Breaking with the scholastic mode of conceiving spatium imaginarium that considers it as an extracosmic space, Hobbes’s Anti-­ White (1642–3) introduces a radically new notion of imaginary space, which identifies it with the very nature of any mental image. From this viewpoint, the paper outlines a difficulty in Hobbes’s criticism of White’s cosmology. In the Anti-White’s construction of the definition of space, the admission of an indefinite image of the whole world runs up against the problem that images are always particular for Hobbes, not universal. The author points out Hobbes’s attempts in De corpore (1655) to address this problem in the Anti-White’s definition. The paper emphasizes that, in connection with De corpore’s reshaping of the definition of space as imaginary space, the late scholastic dyad spatium imaginarium/spatium reale surviving in the Anti-White the redefinition of imaginary space against its traditional meaning is abandoned. Instead, the author argues, ‘real’ space is used in De corpore as a polemic tool against the identification of space with extension in White’s De mundo and Descartes’s Principia philosophiae. Accordingly, interpretations of Hobbes’s doctrine of space viewing it as the same from the Anti-White to De corpore distort Hobbes’s approach to the definition of space required as the first principle for natural philosophy. Chapter 3: Locke on Space and Substance Martha Brandt Bolton Locke’s Essay concerning Human Understanding defends the anti-Cartesian doctrine that infinite space independent of corporeal substance is real and penetrated by bodies, i.e. a body always occupies a commensurate part of space. But whereas Gassendi, Newton, and others who hold this sort of doctrine find reasons to say that space is neither a substance nor an accident, Locke entertains the question and declines to answer it on the grounds that our idea of substance is too obscure. In this connection, Locke mounts a vigorous attack on the utility of the idea of substance, urging that use of it has potentially atheistic materialistic consequences. Although scholars usually take this to be nothing more than an occasion to rehearse the contention that substance is something-I-know-not-what, this article argues that the response is directly relevant to his doctrine of space. This is supported in part by tracing the development of this doctrine through the early drafts and travel journal. They argue that space consists of distance relations that must be terminated in the boundaries of bodies. The Essay replaces this with the doctrine that assimilates infinite space with God who must then be somehow extended and penetrable. If space consists of relations terminated in substances, it plainly is not a substance, but

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if space is constituted by penetrable extension somehow pertaining to God, its substantiality is a more complicated question. Chapter 4: Spacious Mind and Spatial Spirits. Locke on Space and Thought Philippe Hamou Spatial metaphors and spatial discourse about the mind and ideas abound in Locke’s Essay. This raises two related kinds of questions: first, whether and in what sense the mind is “in space”, has a location, and perhaps an extension? And second: how this ‘spatial mind’ is also ‘spacious’, offering room for ideas? What sense of spatiality is involved when Locke says that ideas are “in the mind”, “lodged in the mind”, and how does this inner spatiality of ideas within relate to the spatiality of things without? In this chapter the author argues that Locke’s early relationist view of space, expounded in the manuscript notes of his 1676–8 journals, offers a better framework for understanding how space could be applied in a literal sense to ideas, than the more mitigated view expounded in the Essay itself. Chapter 5: Berkeley’s Theological Challenge of Absolute Space in the Principles of Human Knowledge Luc Peterschmitt This article examines the link between the refutation of absolute space and Berkeley’s apologetical aim. The author shows that Berkeley, in section 117 of the Principles of Human Knowledge, does not contend with drawing a consequence from his refutation, rather he gives a new argument. The argument runs as follows: to affirm the existence of absolute space leads to atheism, because it necessarily amounts to denying God’s freedom and thus God’s Providence. This is precisely the definition of atheism. Therefore it appears that Berkeley’s apologetics aims at proving the providence of God rather than proving his existence stricto sensu. Chapter 6: The Consequence of the Consequences of the Principles for the Theory of the Principles Margaret Atherton Berkeley’s philosophy of science is often assumed to be tangential to the theory laid out in the Principles, for which he is best known, and to be found instead only in minor works. It is undeniable however that Berkeley dedicates a large section of the Principles to a discussion of natural science or philosophy. I argue that this section is central to Berkeley’s conception of his goals in the Principles. Here, Berkeley is showing that a theory based on his own limited ontology of spirits and ideas can do a better job of providing knowledge of natural phenomena than its chief rival, which holds that natural phenomena are to be understood as flowing from inward but unknown essences. Berkeley’s project is ultimately epistemological. An account based on essences leads to skepticism, while instead we have certain knowledge of phenomena when we understand them to be deduced from laws of increasing generality. Berkeley takes his approach to be in line with that of Newton, with one exception. Newton supposes that his theory requires appeal to absolute space, place and motion. Berkeley argues that philosophers actually achieve their results by

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tacitly appealing only to space relative to some framework, and concludes that the only coherent account of space is relative, in line with the constructive account he had developed earlier in The New Theory of Vision. Chapter 7: Berkeleian Instrumentalism: From Substance to Space Robert Schwartz The author argues that much of the debate over the status of instrumentalism in Berkeley’s philosophy can be clarified if one sees him as Pragmatic instrumentalist. Pragmatic instrumentalism is a constructivist account of inquiry, quite similar to the views of the Classic American Pragmatists on the nature of scientific concepts, language, and truth. We forge concepts in our efforts to order and organize experience in ways that meet the continually changing evidence and intellectual needs. Hence, the content of our concepts evolve hand in hand with the theories in which they are embedded. Pragmatic instrumentalism is to be distinguished from the more standard anti-Realist instrumentalist position that challenges the status of theoretical terms and the positing of unobservable entities. From a Pragmatic instrumentalist perspective, it is not inconsistent for Berkeley to be willing to accept some claims about the existence of theoretical entities and deny others. For some run afoul of the Pragmatic Maxim, and others do not. This essay explores the implications of Berkeley’s pragmatic stance with regard to a number of controversial ontological claims about force, corpuscles, the ether, light, and space. The issues were the focus of attention not only in his time but continued to be matters of concern in the years that followed. In particular, his instrumentalist convictions play a major role in his argument against Newton’s absolute space in favor of a relativist space. According to Berkeley the empirical consequences of the former are no different from those of the latter. Thus, according to the Pragmatic Maxim, they are cognitively the same. Berkeley argues that a relative conception of space can handle all the empirical findings of an absolute conception. Moreover, the notion of relative space does not run into a number of conceptual problems that the idea of absolute space must confront. Chapter 8: Berkeley’s two notions of extension Laura Berchielli Berkeley’s theses on vision have been better accepted than those about the non-­ existence of matter. However, in spite of the success of his explanation of vision, his thesis on the non-existence of a visual space and the heterogeneity between ideas of sight and ideas of touch is far from having been unanimously accepted. On this specific point, many inconsistencies have been noted. Nevertheless, it is possible to reconcile these tensions by showing that, in his An Essay toward a New Theory of Vision, Berkeley describes two kinds of space that are different from one another in their relation to co-existence, succession and movement. An examination of these relations gives a clue to understanding the way in which Berkeley can at once admit and deny some sort of space for the ideas of sight.

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Chapter 9: The ideality of space in Enlightenment empiricism: the idéologues’ contribution Elizabeth Schwartz Last representatives of the French movement of “construction” of space starting from unextended sensory elements, the idéologues are witnesses of the turn of the eighteenth century and play an important part in this movement of metaphysical construction of space in the mind. Succeeding Kant, they offer a sort of obscure and not well-known alternative to the usual way the history of the evolution of the way space was conceived during the Enlightenment is told, a story whose main thread would be that this evolution culminated with Kant whose philosophy alone was capable of synthesizing the knowledge acquired by the empiricists and Leibnizian idealism. On the contrary, the idéologues tried, within what they called the “French era”, to defend the idea that there was an alternative future to that offered by nascent German idealism. The object of this article is therefore to demonstrate in what way Condillac’s philosophy can be thought of as an “empiricist” alternative to Kantianism with regards to space and in what way, after Kant and Condillac, the idea of space and movement were related. This article will more particularly focus on how the idéologues replaced the classical empiricist analysis of the idea of space by one proposing that the forming of the idea of space be based on the sensation of movement. In that, they initiated a way out of the limits set by an analysis of signs. However, their very loyalty to the idea of a genesis of a space of signs, in their immediate aftermath, was at the origin of a split between a sensory and an intellectual ideal of space, whereas the aim of their empiricist idealism was to propose their fundamental union.

1.7  Conclusion A collective volume provides some responses, but also opens up new research perspectives. This is particularly true of this collection, one of whose aims is to draw attention to the heterogeneity and tensions among empiricist theories of space – heterogeneity and tensions which have not been sufficiently taken into account in the secondary literature. By way of conclusion, we would like to extend these reflections by indicating some promising research topics that have not been (or only marginally) addressed in this volume.

1.7.1  Empiricism and the Secularization of Space Grant’s and Koyré’s now classical stories of the notion of space consider that the emergence of the concept of a homogeneous, isotropic, continuous, infinite space independent of God and his attributes is one of the results of the reflections on space

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in the eighteenth century.64 One might think that empiricist theories, by linking the notion of space with sensible ideas, provide the ideal framework for such secularization. However, the case of Locke and especially of Berkeley clearly indicate that the movement towards a secularized space is not linear and that the secularization of space is not an objective for all empiricists. What these examples show is that the “sensibilization” of space transforms, without making meaningless, the question of divine presence.65 It would be interesting to determine more precisely than has been done here the path taken by the secularization of space among empiricists, and also to study the concomitant transformations in the way of conceiving, starting from experience, of divine presence and action.66

1.7.2  The Space of Experience, Ideas and Spirit The link between the content of sensible ideas and the notion of space offers a new framework to the classical question of the location and extension of ideas. Hobbes, Berkeley and Hume do not hesitate to say that ideas have a form of extension and sometimes a localization, but Locke and Condillac are much more reluctant to tackle this subject directly. In this volume, Hamou examines Locke’s position. Broadening this survey to the ideas and perceptions of other empiricist authors seems very natural. This survey would make it possible to question in a more general way the relationship between the conception of space and the spatiality of the idea; it could also be used to study the modalities and reasons for the reluctance of certain authors to display, or to admit, the extension of ideas.67

 Koyré 1957, viii and 276; Grant 1981, 254–255; 417. See also Miller 2014.  See Bellis 2018 and Fabbri 2018. 66  As far as I know, there is no specific literature on the relationship between space and divine presence for empiricist authors. However, the question is treated in relation to Locke (Grant 1981, 238–240, Thomas 2013), and in a scattered way for Berkeley (see Slowik 2016; and the chapter of L. Peterschmitt in this volume tackles the issue). That Condillac does not mention this issue could be significant. For a general approach to the question of divine presence in space before the eighteenth century, see Funkenstein 1986; Grant 1981. On this issue see also Brooke 1991 and Gorham 2011. 67  On Locke see the Ph. Hamou’s chapter in this volume and Hamou 2018. Berkeley and Hume have an articulated position on this issue (see respectively Berkeley 1979d, 231 (Third Dialogue); and Hume, Treatise 1.4.5.); of course, their positions depend on their ways of conceiving ideas, minds and their relationship. Literature on this point is rather extensive, see for instance Garrett 2018; Pappas 1980; Frasca-Spada 1998; Falkenstein 2006. On Condillac’s position concerning the spatial features of mind and ideas there are divergent interpretations: see Ricken 1999; Coski 2003. 64 65

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1.7.3  The “Relational” Nature of Space Two polemical targets seem to bring together the empiricists, one is the Cartesian identification of matter and extension, the other is Newton’s absolute space. However, if the critical part of empiricist theories of space is clear, the positive part is not always clearly explained; it is often difficult to determine which positive and general concept of space empiricists promote. Let us take two examples. With regard to the relational theories of empiricists, one might ask, in a global way, what is the nature of the “constituting” relation of space? The place of subjective movement or of the idea of subjective movement in these relations brings up the question, which we have not addressed in this volume, of common points and differences between these types of relationalism and Leibnizian relationalism.68 Another example is the criticism of absolute space. Locke’s case is representative. How can Newtonian mechanics be “recovered” in a strictly relational framework?69 And, if we consider that it is impossible, within the framework of the empirical theories of space, to recover Newtonian mechanics, what status ought we give to the latter?

1.7.4  Space and Movement This volume has highlighted the role of subjective movement as a constitutive dimension of the idea of space. By examining the metaphysics of space, we have seen the emergence of a subject that moves and is active in space. This point deserves to be explored further through research on the history of ideas and representations. It seems, however, that we must remain cautious: while there is evidence of relationships between the metaphysical questions of space that we have addressed, optics70 and mathematics,71 the problems raised by empiricists seem too abstract to imagine that they could have a direct impact on practices such as cartography, pictorial techniques, etc.72 However, without going so far as to speak of a relation of filiation, it

 See Slowik 2016.  Most commentators maintain however that Locke, after having criticized Newton’s notion of absolute space, ended up defending a kind of ‘absolutism” (see, inter alia, Ayers 1991; Gorham and Slowik 2014; Grant 1981). However, the absolute space to which Locke refers in Essay II. xiii. 10 does not allow to identify any kind of absolute movement and thus is far from the metaphysical frame required by Newtonian physics. For a ‘non absolutist” interpretation of Locke’s position on space see Thomas 2018. For a more global reflection on the disunion between science and philosophy in the eighteenth century, see Gaukroger 2016. 70  Hamou 2004, 2018, chap. iv; and Brykman 1982. See also George 2006; Barfoot 1991. 71  Storrie 2012; Atherton 1990; Badici 2011; Cantor 1977. 72  For an overview of the relationships between the thoughts of space and diagrammatic devices from the twelfth to the seventeenth century, see Vermeir, K. and Regier, J., eds. 2016. 68 69

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seems possible to note at least some correspondences between the empiricist metaphysics of space and, for example, certain pictorial and medical practices.73

1.7.5  Space and Operations of the Understanding Among eighteenth century empiricists, a new reflection emerges on the operations of understanding and on the mechanisms for passing from the first ideas received by the senses to ideas of a more complex or general nature. The operation of abstraction is one of these operations, but it is not the only one – the use of signs is, for example, another, which in some contexts is of particular importance. As we have seen, theories of space involve, at different stages, these operations of the understanding, in particular to pass from particular ideas, limited and subjective, to the notion of an objective, unlimited, isotropic space, etc. More systematic work remains to be done on this question – especially with regard to the philosophies of Berkeley and Condillac. The operations of the understanding are also involved in the way of conceiving the objects and operations of mathematics and seem to determine the relationships between, for example, geometry and algebra.74 In this area, a systematic study of the conception of signs and their use could provide an interesting approach to questions of epistemology and the history of mathematics. In particular, if the relations between the symbolic algebra developed in the nineteenth century in England and classical empiricists are attested in the literature,75 a precise description of the articulation between mathematical developments and empiricist theories is still lacking. These research axes are of course only indications, and are of course not exhaustive. Other questions could be evoked, such as a systematic study of the links among conceptions of space, theories of substance (and mode), and criteria of individuation.76 In mentioning these research axes, we wanted to point out that the focus on the differences between empiricist conceptions of space should not obscure attention to the fact that the notion of space is found from the sixteenth to the eighteenth centuries at the crossroads of natural philosophy, physics, mathematics and theology, and that the analyses of the divergences within the empiricist family must be situated within the broader context of the fundamental questions central to these fields in the classical age. This volume aims to contribute to the better ­understanding

 For those pictorial representations that integrate gaze movements into the representation, see Alpers 1983; Asfour and Williamson 1997, 1998. As far as optics are concerned, it is primarily eye surgery, see Daviel 1995. 74  On this articulation between geometry and algebra see, on Condillac: Duchesneau 1999; on Berkeley: Sherry 1993; Jesseph 1993; on Hume: De Pierris 2012. 75  See Lambert 2013; Durand-Richard 1990. For a general discussion of the relationship between mathematics and empiricism see Charrak 2003. 76  The complex articulation between these three questions in Locke has been studied by M. Bolton and Ph. Hamou in this volume. See also: Hight 2008; Stuart 2013; Lodge and Stoneham (eds.) 2015. 73

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of the conceptual richness and multiform character of the empiricist approach to space.

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Chapter 2

Hobbes on Space as Imaginary Space Martine Pécharman

Abstract  Hobbes’s first elaboration of his doctrine of space is directed against the traditional discussion of spatium imaginarium which Thomas White is indebted to in his De mundo dialogi tres (1642). Breaking with the scholastic mode of conceiving spatium imaginarium that considers it as an extracosmic space, Hobbes’s Anti-­ White (1642–1643) introduces a radically new notion of imaginary space, which identifies it with the very nature of any mental image. From this viewpoint, the paper outlines a difficulty in Hobbes’s criticism of White’s cosmology. In the Anti-­ White’s construction of the definition of space, the admission of an indefinite image of the whole world runs up against the problem that images are always particular for Hobbes, not universal. The author points out Hobbes’s attempts in De corpore (1655) to address this problem in the Anti-White’s definition. The paper emphasizes that, in connection with De corpore’s reshaping of the definition of space as imaginary space, the late scholastic dyad spatium imaginarium/spatium reale surviving in the Anti-White the redefinition of imaginary space against its traditional meaning is abandoned. Instead, the author argues, ‘real’ space is used in De corpore as a polemic tool against the identification of space with extension in White’s De mundo and Descartes’s Principia philosophiae. Accordingly, interpretations of Hobbes’s doctrine of space viewing it as the same from the Anti-White to De corpore distort Hobbes’s approach to the definition of space required as the first principle for natural philosophy. Keywords  Image · Imaginary space · Extension

2.1  Preamble In 1642, ten years after Galileo’s Dialogo sopra i due massimi sistemi del mondo was published in Florence, the philosopher Thomas White published in Paris a treatise on cosmology, De mundo Dialogi tres, which he conceived as an attempt to maintain the Aristotelian framework within the contemporary context of natural M. Pécharman (*) Centre de recherches sur les arts et le langage, CNRS-EHESS, Paris, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 L. Berchielli (ed.), Empiricist Theories of Space, Studies in History and Philosophy of Science 54, https://doi.org/10.1007/978-3-030-57620-2_2

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philosophy. By this time, White was a member of the ‘Mersenne circle’.1 So was Thomas Hobbes, who produced in the following months, probably at Mersenne’s suggestion, an extremely detailed comment on De mundo – as Noel Malcolm put it, “a huge blow-by-blow refutation” of White’s book.2 This lengthy examination of White’s De mundo, the so-called Anti-White, borrows significant material from Hobbes’s early drafting in the 1640s of the ‘Elements of philosophy’ first section, De corpore, eventually published in 1655.3 The material incorporated helps to state that in Hobbes’s project, natural philosophy is not restricted to physics. Natural philosophy must include first philosophy too. Hobbes condemns White’s mistake concerning the status of metaphysics with respect to physics.4 White believes that metaphysics is heterogeneous to the science of nature: De mundo understands metaphysics as the knowledge of that which is “beyond nature”, trans naturam. For Hobbes, this shows that White is a bad reader of Aristotle, totally unaware of the first philosophy contained both in the books which have been entitled Physics and in those which have been entitled Metaphysics merely because they complement Physics. Aristotle, Hobbes stresses, views first philosophy, not as the science of the supersensible, but as the science of being qua being, foundational for all treatises on particular natural things. Hence, in addition to the notions pertaining to all bodies indifferently, which are defined in Aristotle’s Physics, being itself, to on, and the most common notions of all beings and essences, are defined in his Metaphysics. Now, whereas first philosophy is for Aristotle the science of the first elements needed for the knowledge of natural beings, De mundo makes it a ‘transnatural’ knowledge: White completely misses the point. Accordingly, it is not White’s claimed allegiance to Aristotle, but Hobbes’s redefinition of the lexicon of metaphysics used in De mundo, that proves fit to preserve Aristotle’s legacy. Aristotle’s program for first philosophy is perpetuated in the Anti-White through its semantic reformation. The conception of first philosophy as a necessary preliminary to physics within natural philosophy requires Hobbes to assign primary ontological categories their correct meaning. Ens and esse, the traditional Latin translations for Aristotle’s to on and to einai, ‘being’ and ‘to be’, truly mean corpus and accidens, ‘body’ and ‘accident’.5 Only the consideration of ens as body, that which occupies space, and of esse as accident, that by which our mode of conceiving of the body is determined, saves philosophia prima, first philosophy, from nonsense. A redefinition of essentia is annexed to this reshaping of the Aristotelian pair to on and to einai into the dichotomy between body (what is or exists) and accident (that by which what exists is conceived). The Anti-White’s definitions make it impossible that essentia reciprocates with substantia. An essence,

 See Southgate (1993, chs 1, 4).  Malcolm (2002. 17). References to the Latin manuscript (late 1642-early 1643) of the so-called Anti-White, abbreviated AW, are given in Hobbes 1973 3  References to De corpore, abbreviated DCo, are given in Hobbes 1999. 4  See AW, ch. 9, § 16 (Hobbes 1973, 169–170). 5  See AW, ch. 27, § 1 (Hobbes 1973, 312–314). 1 2

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for Hobbes, cannot be understood as a subsisting thing or substance, it is just the accident providing the reason why a body gets some specific name.6 Already in the Objectiones Tertiae published in 1641, Hobbes criticized Descartes’ nonsensical identification of substance and essence, when Meditatio Secunda adds to the right consequence because I am thinking, it follows that I am, the wrong equivalence of the conclusion I am to the conclusion I am a mind.7 The latter assertion is absurd, because I is a material subject or substance while mind is nothing other than incorporeal acts of thought. Thus, the material transposed from the De corpore project into the Anti-White provides the underlying first philosophy of this criticism. It appears then that the rejection of the conclusion I am a mind was not uniquely an anti-Cartesian stance. A systematic redefinition of Aristotle’s ontological vocabulary was in the background.8 In De corpore’s first philosophy, however, body is not the most fundamental of all notions defined. The replacement of Aristotle’s to on with corpus supposes that the notion of body is itself deduced from the antecedent notion of space. The primordial definition in first philosophy must be that of spatium. An incomplete draft of De corpore’s first philosophy, presumably dated 1643–4 (the so-called NLW draft), as well as two sets of notes taken from another draft by Robert Payne and Charles Cavendish, presumably in 1645–6, show that in Hobbes’s early project of natural philosophy, the dependence of the definition of body on the definition of space had been established from the outset.9 In all cases, the definition of space is introduced from the hypothesis that all sensible things are destroyed, but one man survives the destruction of the whole world outside him.10 Hobbes proposes this annihilatory hypothesis as a thought experiment to render the principles of natural philosophy conceivable. The same methodological device is kept in 1655  in De corpore’s final version. Now, interestingly, in the material employed in 1642–3 in the Anti-White to emphasize the inclusion of first philosophy within natural philosophy, the construction of the definition of space is far more complex than in the drafts of the same period and in the final version of De corpore. Remarkably too, in this complex construction, the annihilatory hypothesis does not constitute the first step, but appears only at a second stage; nor are the consequences drawn from it exactly the same as in De corpore’s early drafts and final version. Assuredly, these singular features do not affect the continuity between the Anti-White and De corpore’s early drafts or last version, concerning the first principle in Hobbes’s first philosophy, the thesis that space is “imaginary and mere phantasm”11. From the Anti-White to De  See AW, ch. 27, § 1; ch. 34, § 2 (Hobbes 1973, 314; 381–382).  See Descartes (1964a, 172–174). 8  On Hobbes’s reshaping of Aristotelian ontology, see Pécharman (1992, 1995a, b). For a comparison with Gassendi, see Paganini (2008). 9  This draft, NLW MS 5297, and these notes, Chatsworth MS A10 and its variants in Harleian MS 6083, are published in appendix to Hobbes 1973. See Malcolm (2002, chs 1, 4). 10  See Hobbes (1973, 449–450; 474). 11  See NLW MS 5297 (Hobbes 1973, 450). Cf DCo, ch. 7, § 2: “id quod appellamus Spatium, imaginarium quidem, quia merum phantasma” (Hobbes 1999, 76). 6 7

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corpore, the construction of the definition of space remains identical to the construction of the definition of imaginary space. In the Anti-White, actually, ‘imaginary space’, spatium imaginarium, constitutes the explicit definiendum; the proposition, however, which is reached as the definition of imaginary space immediately applies to space tout court12. In De corpore, the word spatium is clearly used as a mere abbreviation for the whole locution spatium imaginarium. “Space”, Hobbes claims, is a word by which “I always understand imaginary space”13. Yet, notwithstanding this uniform treatment of imaginary space as space tout court in the Anti-White and vice versa of space as imaginary space in De corpore, the construction of the definition of imaginary space in the Anti-White differs from the standard construction of the definition of space in De corpore’s first drafts and final version. The Anti-White’s mode of construction is not retained in De corpore. By analysing step by step the specific construction of the definition of imaginary space in the Anti-White, I would like to stress its ambiguities and the kind of difficulties it can imply for Hobbes’s first philosophy. In my view, the rewording of the definition of space from 1643–4 onwards avoids the flawed consequences tied to its mode of construction in the Anti-White. My point, furthermore, is that this self-­ critical move requires that we understand Hobbes’s use in the Anti-White of the late scholastic dyad of spatium imaginarium and spatium reale, ‘imaginary space’ and ‘real space’, as abandoned in De corpore.

2.2  T  he Construction of the Definition of ‘Imaginary Space’ in the Anti-White Although the relationship established by Hobbes between the two definitions of space and body is essential to denounce White’s misunderstanding of the function of first philosophy within natural philosophy, the ‘blow-to-blow refutation’ of De mundo calls for two separate approaches. Because of the polemical context, the definitions of space and body are not involved in the Anti-White in a single deduction. Whereas spatium is defined in chapter 3 when Hobbes examines White’s thesis that our world is unique, ens or corpus is defined in chapter 27 with respect to White’s argument concerning the external cause of the motion of the universe. Due to its critical link with De mundo’s demonstration against the plurality of worlds, the definition of space is aimed first of all at criticizing the interpretation of spatium imaginarium at work in White’s discussion of this cosmological issue. Indeed, to defend the Aristotelian framework against the revival of atomism, White refers to imaginary space in its standard scholastic meaning as an infinite void space extending beyond this world, where the omnipotent God could create as many worlds as

 See AW, ch. 3, § 1 (Hobbes 1973, 116–117).  DCo, ch. 8, § 5: “Spatium autem (qua voce semper intelligo imaginarium)…” (Hobbes 1999, 85 - this formula is inserted as the first member in the definition of place, locus).

12 13

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he pleases14. The very wording spatium imaginarium, White argues, betrays by itself the inanity of imaginary space. Imaginary space is nothing, now ‘nothing has no parts’. Consequently, White claims, even if only two worlds were supposed to be created in the imaginary space, it would be at once impossible to conceive their different places and to assert that the one is situated in this part of the imaginary space, the other in that other part. The one could not be held to be here and the other there: these terms, here (hic) and there (illic), would be made meaningless, instead of signifying distinct places15. There is no extracosmic space, therefore, where many worlds could have been created by God. White bases his rejection of the plurality of worlds on his rejection of such an imaginary space. Most interestingly, accordingly, the purpose in the Anti-White is to replace the notion of imaginary space considered in De mundo with a redefinition of imaginary space which can be proposed as the definition of space tout court.

2.2.1  Visual Images The definition of spatium imaginarium introduced in chapter 3 of the Anti-White results from a gradual construction. Two major steps can be distinguished. As a first step, Hobbes analyses the status of images in the phenomenon of vision. In The Elements of Law composed in 1640, the same analysis included a detailed description of the mechanistic model explaining the production of visual images16. The whole causal explication is not repeated in the Anti-White; it is enough to state that the image or phantasm of an external object is the effect of the action of this object on the organ of sight. What is crucial, on the contrary, is to rerun the explication of the difference between the place of a visible object and the place of its image, used in The Elements of Law to demonstrate that sensible qualities are inherent, not in the external objects, but in the perceiving subject. The Anti-White emphasizes that, regardless of the phenomenon of vision considered (direct vision, reflection, refraction), the objects perceived never are where they appear to be: the image of an object is not where this object is. This thesis statement is stronger than in The Elements of Law. In 1640, in order to make it certain that no image is in the object, Hobbes merely cites the experience of objects seen by reflection in water or in a mirror and the experience in direct vision of double vision of the same object17. But in the Anti-­ White, refraction is added to reflection to prove, from the divergent straight lines on which the image and the object are situated in both cases, that the location of the image is not in the object perceived but in the perceiving subject. Moreover, the  Concerning the scholastic meaning of spatium imaginarium, associating imagination and extracosmic space, see Grant (1981, chs 6, 7). For possible sources of Hobbes’s doctrine of space in late scholastic philosophy, see Leijenhorst (1996) or Leijenhorst (2002, ch. 3, 101–123). 15  See White (1642, 26). 16  See Hobbes (1889, ch. 2). 17  The Elements of Law, ch. 2, § 5 (Hobbes 1889, 4). 14

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Anti-White allows the contention that it is not only some direct vision, but every direct vision, which makes it manifest that the place of the image is not the same as the place of its object. In The Elements of Law, the experience of double vision is needed to assert that the image is not something real in the external object, but something ‘phantastical’ in the perceiving subject – in other words, that an image is simply an image. The two images of the same object in double vision cannot then be both inherent in this object, Hobbes claims, because this would mean that the same object is in two places at the same time, which is impossible. But, Hobbes continues, it would be wrong to conclude that, since one of these two images cannot be inherent in the object, then the other can. The right conclusion reads: “the one of them is no more inherent than the other, and consequently neither of them both are in the object”.18 The Anti-White follows another line of reasoning. What is stated now is that, even though in direct vision the image of the sun appears in the sky, whereas in reflected vision it appears beneath water, this does not make the phenomenon of direct vision different from the phenomenon of reflected vision. The image of the sun in direct vision is no more inherent in the real sun than the image of the sun in reflected vision is. Direct vision of the sun occurs along a straight line on which the sun’s place is at the extremity opposite the eye; but this does not imply that the place of the real sun is the same in direct vision as the place of its image. The distance of the sun from the eye is such, that necessarily, Hobbes says, the place of the real sun is further from the eye than the place where it appears, the place of its image. In the Anti-White, the way is therefore open to the assertion that not only a special case of direct vision  - double vision -, but generally any case of direct vision, helps to reject the reality of images, namely, the identification of images with their objects. Indeed, the Anti-White’s argument based on the vision of far distant objects might be extended to all objects of direct vision, insofar as direct vision involves the object’s distance from the eye, whatever this distance is. Any case of vision, thus, either direct or reflected or refracted, leads to the same conclusion: the place where an object appears to us is not the place where the object is. From this, the Anti-White deduces that what is true about the whole image, is necessarily true about its component parts. The conception we must have of space as imaginary space is introduced, thus, as resulting from the demonstration that the place of an image is other than the place of the thing of which it is the image. Hobbes’s argument runs as follows. Figure, which is, with colour, a component part of an image, cannot be in the same place as the thing of which it is the figure. Now, “a figure is a finite space”.19 Therefore, the “apparent space” of an object, that is to say, the definite space under which an object appears to us, is not inherent in this object itself, but is “purely imaginary”, spatium mere imaginarium.20 As a component part of image, space cannot be an accident of something outside of the perceiving subject. Space is in the image we have of an external thing, not in the external

 Ibid.  AW, ch. 3, § 1 (Hobbes 1973, 116). 20  Ibid. 18 19

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thing itself: space is imaginary. To confirm the irrefutability of this conclusion, Hobbes relies again on the example of the sun: “how could a circle as small and close as the apparent circle of the sun be the inherent and adequate quantity of an object as remote and big as the body of the sun?”.21 The finite space constituting the figure of a body cannot be identical to the dimensions of this body.

2.2.2  Two Hyperboles ‘Imaginary space’, thus, is demonstrated to be simply the name for space as an essential component of image. The scholastic conception of imaginary space as the imagination of an extracosmic space is wrong, which makes White’s reasoning about the unicity of the world defective.22 We must say ‘imaginary space’ only to designate space as the very nature of image, not to signify our imagination of a kind of space. Every image is some space: such is the true meaning of imaginary space. The first step in the Anti-White’s construction of the definition of space is accomplished with the right localisation of space - in the perceiving subject, not in external things. The second step, thus, must attain the definition of space corresponding to its inherence in all images of bodies. The transition from the first step to the second is provided by the consideration of image when image is no longer an immediate image - an image of sensation -, but, if I may say so, an afterimage, the image retained in the mind after the original image has ceased. The distinction just made by Hobbes between two kinds of accidents, on the one hand the apparent circle of the sun, which is the figure or finite space inherent in the image of the sun, and on the other hand the quantity or dimensions inherent in the body of the sun, helps to emphasize that images persist in the absence of their objects. When objects vanish from our sight and are no longer perceptible, their dimensions disappear with them, but “their images, that is to say, the figures or spaces by which they were apparent, remain in the mind”.23 The presence of images in the mind does not require that their objects are co-present: images in the mind are not all of them images produced in sensation. In Hobbes’s m ­ echanistic model, the contemporaneity of objects perceived with the perceiving subject does not exhaust the causal explication of images.24 Images are not removed together with the objects which are the agents of their production. Accordingly, the dissociation in sense perception between the properties inherent in the external things and the spaces under which these things are perceived by the mind becomes primordial

 Ibid.  See AW, ch. 3, § 4 (Hobbes 1973, 119). When he summarizes White’s argumentation, Hobbes replaces the locution spatium imaginarium with the phrase spatium quod imaginamur esse extra mundum. 23  AW, ch. 3, § 1 (Hobbes 1973, 116). 24  See AW, ch. 30, § 4 (Hobbes 1973, 350). Cf. The Elements of Law, ch. 3, § 1 (Hobbes 1889, 8). 21 22

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to explain all mental phenomena deriving from sense perception, that can all be summed up under the heading of imagination. This consideration of images of imagination in addition to images of sensation allows the introduction of the annihilatory hypothesis, the supposition that “the whole world, one man being excepted, is annihilated”.25 Only through the consequence annexed to the supposition that the survivor still is an imagining subject, can the definition of imaginary space, that is to say the definition of space, be achieved. Now, strikingly, the consequence derived in the Anti-White from the annihilatory hypothesis gets an unexpected content. The methodological prerequisite or premise for introducing the annihilatory hypothesis consists in the permanence in mind of images of individual things after these things are removed. The imaginary spaces through which external bodies are the objects of sense perception remain in the mind when these objects are absent. From such a premise, we would expect the annihilatory hypothesis to aim at stressing that, even if we envisage that all present external bodies are removed, the mind of the supposed survivor will retain all the imaginary spaces through which it has perceived bodies. In other words, individual images of individual things would be expected as that which is preserved in the mind. But the conclusion deduced in the Anti-White is not this, so that the consequence of the annihilatory hypothesis seems to be disconnected from its very prerequisite. In the refutation of De mundo, the annihilatory hypothesis is used to claim that the supposed only survivor will have “the image of the world seen once”, that is to say, Hobbes specifies, “the thought of a space extending from himself in all directions as far as he will please”.26 A double hyperbole, thus, is involved in the Anti-White’s annihilatory hypothesis. This very hypothesis constitutes by itself a first hyperbole. By supposing their destruction, it transfers to all sensible objects currently present in the external world what is normally the characteristic feature of absent objects, the incapacity to cause sense perception. But moreover, this hyperbolic supposition that all things exterior to the mind are suppressed is redoubled with another hyperbolic assertion. Namely that what is still inherent in the mind after the destruction of the exterior world is the image of the whole world, understood as an indefinite multidirectional space extending from the imagining subject as from a fixed point. Rather than finite spaces of multifarious things, an indefinite space is said to remain in the mind. In Hobbes’s refutation of White, it is this hyperbolic meaning imparted to the image of the world which proves to be the centerpiece for completing the construction of the definition of imaginary space. This deduction, however, is not without its difficulties. Certainly, the ‘image of the world’ once perceived does not mean the analogue on another and much wider scale of the figure retained in the mind after an individual body is no longer perceived by sense. Figure is understood as a finite space, whereas the image of the world is said to consist of an indefinite space. The core difficulty, thus, results from the ambiguity underlying the notion of ‘image of

25 26

 AW, ch. 3, § 1 (Hobbes 1973, 117).  Ibid.

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the world’: how could an image in the mind be indefinite? How could a non-finite space constitute the nature of an image? The image of the world asserted as the decisive means to deduce the definition of imaginary space might seem to introduce the threat of a universal, against Hobbes’s thesis that only a name - not a thing, nor an idea or image - can be a universal.27 This, though, is only because Hobbes does not make it clear in the Anti-White’s annihilatory hypothesis that the image of the world is no other than many images of external things. Before introducing his definition of space in chapter 3, Hobbes has stated in chapter 2 that world is understood as “a body extending in all directions” and that this is an equivalent wording for “the definition of world” as “the aggregate of all the bodies which are existing”.28 The latter definition recurs other times in the Anti-White, notably in chapter 27 after defining ens or corpus: “the world is the aggregate of all bodies”, “I take universe […] as the aggregate of all bodies”.29 Thus, corresponding to the aggregative nature of the world, the so-called ‘image’ retained in the mind after the world is annihilated might be said to consist of a mental addition of space to space: a computation of spaces, rather than strictly speaking an image, would be meant by the ‘image of the world’. In the polemical context of the annihilatory hypothesis in the Anti-White, the scholastic imaginary space, a void space imagined as indefinitely extending beyond this world, is substituted with the ad libitum increasing of space by the imagining subject, that is to say, the mind’s ability to compound finite spaces once singular bodies are annihilated. Later in the Anti-White, Hobbes states again that the signification of space is understood from the images kept in the mind once bodies are no longer existing. The annihilatory hypothesis is not repeated then: instead, from the thesis that images are spaces, Hobbes immediately infers that space is potentially infinite, because other spaces can be added to some space in the mind as often as we will.30 In this case, space is viewed as the constant element in all images of bodies, without any reference to the whole exterior world being useful to understand its signification; it cannot be mistaken for a general image in the mind. By contrast, the Anti-White’s annihilatory hypothesis is not unequivocal, since the ‘image of the world’, when it is said to be the equivalent of an indefinite space, is not said to be no other than the multiplicity of images-spaces representing annihilated individual bodies.

27  For the demonstration of this thesis (which makes Hobbes’s nominalism quite radical), see AW, ch. 2, § 6 (Hobbes 1973, 112–113). 28  AW, ch. 2, § 2, § 3 (Hobbes 1973, 110, 111). 29  AW, ch. 27, § 5, § 6 (Hobbes 1973, 317). See also AW, ch. 40, § 1 (Hobbes 1973, 434). Leviathan takes on in 1651 the same canonical definition: “the Universe, being the Aggregate of all Bodies, there is no reall part thereof that is not also Body; nor any thing properly a Body, that is not also part of (that Aggregate of all Bodies) the Universe” (Hobbes 2012, vol. 3, ch. 34, 610). Cf DCo, ch. 26, § 1(Hobbes 1999, 281). 30  See AW, ch. 28, § 1 (Hobbes 1973, 331). Cf DCo, ch. 7, § 12 (Hobbes 1999, 80).

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2.2.3  Two Reduplication Strata In all events, the problematic consequence asserted in the Anti-White as the result of the annihilatory hypothesis leads to the statement with which the construction of the definition of spatium imaginarium is brought to its conclusion: “Therefore, imaginary space is nothing other than the image, or phantasm, of a body”.31 Hobbes at once specifies the absolute meaning of this final statement. Imaginary space, he adds, is the image of “a body simply”.32 Thus, from the assertion that the image of the world consists of an indefinite space, the Anti-White deduces, as its direct and necessary conclusion, that “space is the image of a body, insofar as it is a body”.33 A new discontinuity, however, is involved in this deduction. The gap in the Anti-­ White’s construction of the definition of space is not merely between the premise of the annihilatory hypothesis and its consequence (the ‘image of the world’), but also between this consequence and the conclusion drawn from it. Hobbes does not justify, but just asserts, that space, insofar as it can be extended ad libitum by the mind, must be considered as the image of every body insofar as every body is a body. The indefinite space equivalent to the image of the world becomes the permanent undifferentiated structure in all differentiated images of determined bodies, insofar as determined bodies are primarily bodies.34 Assuredly, the previous ambiguity does not remain, since space is defined as that which structures every image and applies to all images taken distributively of all bodies. But the elimination of the equivocal meaning of the indefinite space image of the world is at the cost of continuity in the deduction of the final definition of space. The hiatus, on the contrary, is avoided in the NLW draft of De corpore’s first philosophy. In the NLW manuscript, the first sentence reads: “The mind of man is a mirror capable of receiving the representation and image of all the world”.35 Now, a few lines further on, the annihilatory hypothesis makes it clear that “the representation and image of all the world” is the same as “the ideas or images of all the things […] seen”. 36 Already in The Elements of Law Hobbes had highlighted in the annihilatory hypothesis the inseparability of the image of the world with the images of things in the world: “if a man could be alive, and the rest of the world annihilated, he should nevertheless retain the image thereof, and of all those things which he had before seen and perceived in it”.37 In contrast, the Anti-White leaves open to doubt the status of imaginary space; this doubt about space as a general image is removed only after the definition of spatium imaginarium has been deduced. Only then does the Anti-White make it 31  AW, ch. 3, § 1: “Spatium igitur imaginarium nihil aliud est quam imago, sive phantasma corporis” (Hobbes 1973, 117). 32  Ibid.: “Corporis dico simpliciter”. 33  Ibid.: “dicemus spatium esse imaginem corporis, quatenus corporis”. 34  See also AW, ch. 27, § 1: “concepta omnis corporis imago est spatium” (Hobbes 1973, 312). 35  Hobbes 1973, 449. 36  Ibid. 37  The Elements of Law, ch. 1, § 8 (Hobbes 1889, 2). Cf DCo, ch. 7, § 1 (Hobbes 1999, 75).

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obvious that space is not a universal in the mind, when Hobbes stresses the difference between space tout court and space with the addition of some characteristic. The finite space “purely imaginary” which at first was stated to be the same as figure is now part of a series of spaces with characteristics that differentiate them as images of a body such or such from the image of a body as merely a body. In the first step of the Anti-White’s construction of the definition of space, spatium finitum was a component in every image, its figure-component; but when the construction is completed, spatium finitum is just an item within a list of spaces distinguished from the image of a body insofar as it is a body, and it becomes dissociated from figure. Spatium finitum only means then a certain delimitation of the imagined quantity of a body, without this representation being associated to a precise figure. Like spatium album, a white space, and spatium quadratum, a square space, spatium finitum, a finite space, adds a determined feature to the simple image of a body. The imaginary space is no longer, together with the colour-component, the figure-component in the images of bodies: spatium imaginarium is now the whole image of a body as a body, an image to which different determinations, either qualitative (colour) or quantitative (delimitation, figure) are added. The reduplicative assertion “space is the image of a body, insofar as it is a body”, which develops the definition of imaginary space as “nothing other than the image, or phantasm, of a body”, is followed in the Anti-­ White with an enumeration of other reduplicative statements: “a white space is the image of a white body, insofar as it is white”; “ a finite space is the image of a finite body, insofar as it is finite”; “a square space is the image of a square body, insofar as it is square”. When the reduplication marked with the Latin sign quatenus (“insofar as it is”) falls on some other mode of conceiving a body than its being simply a body, the image of a body is more than an image, it is in addition this particular image. The reduplication “insofar as it is a body” constitutes a basis for a second reduplication. The reduplication “insofar as it is white”, for instance, differentiates a particular image both from imaginary space and from spaces or images involving another kind of determination than colour. Of course, the image of a body insofar as it is a body is not itself indeterminate. Also the imaginary space representing a body qua body is a determined image, but its determination is then only the representation of the merely numerical difference between this body and other bodies – as it were, the representation of the degree zero of individuality.38 We may say that the image of a body simpliciter is space simpliciter, space insofar as it is space, merely the representation in the mind of the most original individuation of a body. Arguably, space that is only space - not a coloured space, nor a finite space or a figured space – constitutes the absolute image in every image, that which composes every image qua image. Space, thus, is defined as the image which is the principle immanent in all images taken severally: the prior and most basic image without which the particular image of a body, the image of a body as such a body, would not be an image. But this definition is attained through a mediation (indefinite space as the undifferentiated image

38

 On degrees of individuality in Hobbes’s philosophia prima, see Pécharman (1995b).

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of the world) which does not seem to be appropriate to its deduction. This mediation, indeed, runs the risk of being understood, against Hobbes’s project, as a general image of all bodies, that is to say, as a universal in mente. Moreover, the threat is reiterated in the Anti-White after the definition of imaginary space is completed. Hobbes underlines then the dependency of the existence of space, not on the existence of body, but on the existence of imagination. In the same way, he claims, as the removal of a certain body from some given space does not imply the disappearance of this space - it remains the same space, whether it is refilled with another body or it is left empty – so, “if the world disappears, provided that imagination does not disappear at the same time, unmoved space will nonetheless exist”.39 This analogy between the permanence of the same space successively filled with different bodies and the continued existence of space, although the world ceases to exist, supposes Hobbes’s reworking of Aristotle’s antimetastasis argument for the independent existence of place, topos. For Aristotle in his Physics, the phenomenon of “displacement” of contents from a particular place proves that this place is distinct from each and all of the material substances which occupy it in turn.40 But, whereas Aristotle concludes from the experience of antimetastasis that place is “something beside bodies” (ti para ta sômata), another thing independent of things coming into it and going out of it,41 Hobbes’s analogical reasoning is not aimed at proving that space is a reality. Hobbes’s target, when reworking the antimetastasis argument, is to corroborate the strictly mental or imaginary nature of space. However, his analogical reasoning still raises doubt as to whether the unmoved space remaining after the destruction of the world is the general image of all bodies, or an image indefinitely repeated in spaces which represent successively different bodies. This additional proof of the imaginary nature of space once the construction of the definition of space is completed, raises again the spectre of a conceptual universal. As it were, this supplementary reasoning takes a step backwards, it obscures again the definition of imaginary space as the image of a body qua body with the ambiguity linked to the image of the world.

 AW, chapter 3, § 1 (Hobbes 1973, 117). I correct the Jacquot-Jones edition, which reads: “deficiente mundo, modo non una deficiat, existet tamen immotum spatium”. The Latin manuscript actually reads: “deficiente mundo, modo non una deficiat imaginatio, existet tamen immotum spatium” (Bibliothèque Nationale, Paris, MS 6566 A, f. 15r). Both the English translation “if the world were to vanish, then unmoved space, provided that it did not disappear at the same time, would still exist” (Hobbes 1976, 41) and the Italian translation “quando venga meno il mondo, purchè non scompaia tutto insieme, sussisterà tuttavia lo spazio immoto” (Hobbes 2010, 150) misunderstand the argument. 40  See for this proof Aristotle, Physics, Δ, 1, 208b 1–8. 41  Aristotle, Physics, Δ, 1, 208b 28. 39

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2.3  From the Anti-White to De corpore: A Change in Perspective 2.3.1  The Dual Nature of Images Both in De corpore and in the Anti-White, the reason why the annihilatory hypothesis constitutes the best way to define space lies in the nature of images. But the Anti-White’s demonstration begins with the consideration that images are effects produced on sense organs by the action of external bodies, whereas De corpore goes beyond this. In contrast to The Elements of Law, which describes in its totality the causation of a visual image,42 the Anti-White’s oversimplifies the causal process in sense perception. To rebut the scholastic conception of imaginary space implied in De mundo’s rejection of the plurality of worlds, Hobbes deems it sufficient to state that images of vision are the effects in the mind of motions from external agents.43 Now, it seems to me that this restriction makes the Anti-White’s construction of the definition of space more vulnerable to an interpretation of imaginary space as a conceptual universal. Indeed, taken in its totality as it is in The Elements of Law, the process causing a visual image is not simple, but double. It consists not only of a motion from the external agent to the patient, but also of a counter-motion from the patient to outside. Hobbes’s schema for explaining sense perception is not linear, it includes a reaction or ‘rebound’ from inside to outside. As a result, images produced in the mind cannot be reduced in Hobbes’s mechanistic model to mere cerebral impressions - that is to say, they are not “images of material things depicted in the corporeal fantasy” (Hobbes’s definition of ideas according to Descartes44). Instead, images consist of motions from within the patient’s body which appear to this patient as being without: images in sense perception are ‘apparitions’ out of the perceiving subject. Hence there is a significant difference between the two constructions of the definition of space, in the Anti-White and in De corpore. In De corpore, however, the whole process of the causation of images may be omitted in the Philosophia prima;45 it is enough to build the definition of space as imaginary space on the last stage of this causal process. What matters is the dual nature of images implied in it: internal accidents but appearing as if they were external and ­independent from the imagining subject.46 Images get then “a double name”: they are named both ‘internal accidents of the mind’ and ‘appearances of external

 See The Elements of Law, ch. 2, § 7–8 (Hobbes 1889, 5–6).  See, for example, AW, ch. 3, § 1: “sun by acting upon the eye makes it see a bright circle” (Hobbes 1973, 116). Against the belief that this “bright circle” is the sun in the sky, Hobbes demonstrates the non inherence of images in external bodies. 44  Descartes (1964a, 181). 45  See DCo, ch. 25, § 2–3 (Hobbes 1999, 268–270). Cf AW, ch. 30, § 3 (Hobbes 1973, 350). 46  See DCo, ch. 7, § 1 (Hobbes 1999, 75). Cf NLW MS 5297 (Hobbes 1973, 449). 42 43

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things’.47 This, not the first ab extra stage in the causal process, must be the starting point. The definition of space in De corpore supposes, thus, that an image always appears to the perceiving subject as if it were an external reality: together with images of bodies when bodies are removed, the mind also retains their fictitious externalization. The fundamental duality in De corpore’s argumentation is not the Anti-White’s one, between the place of the image and the place of the external object, but the duality which characterizes images themselves, the duality of their inherence in the mind and their apparition outside of the mind. Because of its internal-­external duality, in other words because of its double-sided nature, every image can be the object of a double consideration. There are two ways of abstracting from an image one of its faces. Any image can be considered either as an internal accident of the mind, without any regard to its mode of appearing to the mind, or vice versa as something which appears to be external to the mind, without any regard to its being in the mind. The latter consideration, or latter way in which the two sides of an image are separable, provides the basis for the demonstration leading in De corpore to the definition of space as imaginary space. Correlatively, this demonstration no longer needs an indefinite space-image of the world as a mediation for conceiving space as the image of a body simply as a body. In my opinion, the ambiguities and difficulties linked to the Anti-White’s argumentative device are prevented when the consequences to be drawn from the annihilatory hypothesis are developed from the central point of view of existence. Both the actual existence of bodies outside of the mind before the supposed annihilation and the fictitious existence of images appearing outside of the mind are involved in De corpore’s rewording of the annihilatory hypothesis. The proportion between the two features of things annihilated, to have been objects of perception, and to have existed in the external world, is modified from the Anti-White to De corpore. In De corpore, the annihilatory hypothesis intends to limit the mind to imagination understood as the power to recover images of things previously existing, rather than simply previously perceived. The prior existence of things annihilated, not their prior perception by sense (the Anti-White’s main point of view), comes to the fore.48 This change in perspective, from that which was an object of perception before the supposed destruction of all external things to the same insofar as it was existing, is essential for De corpore’s definition of space. The single survivor of the universal annihilation does not keep only images of things previously perceived. He also keeps the power of abstracting the consideration of these images as external apparitions from any other consideration. The annihilatory hypothesis makes it possible that any image retained in the mind of a thing previously existing is considered in regard to its pure appearing to the mind, its appearing simply as external, regardless 47  DCo, ch. 7, § 1 (Hobbes 1999, 76). Cf NLW MS 5297 (Hobbes 1973, 450) and Cavendish’s notes, which are more concise (Hobbes 1973, 474 [1]). 48  See DCo, ch. 7, § 2, ch. 8, § 1 (Hobbes 1999, 76, 82). Cf NLW MS 5297 (Hobbes 1973, 450, 452). Also see Cavendish’s notes (Hobbes 1973, 476 [1]) for a passage corresponding word for word to DCo, ch. 8, § 1.

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of the particular content of this apparition. The hyperbolic destruction of all things external to a single survivor leaves the way open for this abstraction. The annihilatory hypothesis has become the means to reduce any image in the mind to its former relationship, not to the specific nature of the external object which it represented in sense perception, but merely to this external object as external, that is to say as existing outside of the mind. The mode of apprehension of an image by the mind cannot be separated from a postulation of external existence. By appearing to the mind as if it were external to the mind - as if it were itself existing outside - an image represents its object to the mind primordially as an existing thing, not as this particular thing. The feigned destruction of the world, thus, makes the imagining subject able to experience with any image the most radical nature of all images, whatever their specific contents. ‘Space’, ‘spatium’, can be defined accordingly in relation to just one image in the mind of the supposed survivor, provided that the object of this image is considered strictly as to its former existence, that is to say, its former externality to the mind. As of the 1643–4 draft of De corpore, the definition of space deduced from the annihilatory hypothesis reads: “Space is a phantasm of a thing existing (quatenus existing) i.e. no other accident thereof considered besides that it appeared without or out of the imaginant”.49 Space is the image ‘simply’ of an existing thing qua existing.50 The definition of space entirely based on the most fundamental consideration  - the consideration of existence  - allowed by any image remaining in the mind when all external things are feigned to be annihilated is the definition of space as imaginary space. Indeed, in the 1643–4 draft, the passage introducing the definition of space in Hobbes’s first philosophy reads: “If we remember or have a phantasm of any thing which did exist before the supposed sublation of external things and would not consider what kind of thing it was but merely that it existed or was without the mind we have that we call space: imaginary and mere phantasm”.51 The final version of De corpore reads the same.52 Interestingly, however, an excursus is inserted in the final version of De corpore between the passage introducing the definition of space and this definition itself. The excursus bears both upon the equivalence of the proposed definition of imaginary space to the commonly accepted definition of space and upon some wrong conclusions derived in natural philosophy when space is by contrast ill-defined and fails to suit its ordinary sense. On the basis of the annihilatory hypothesis, De corpore underlines that the survivor’s mind recovers in itself, as a phantasm, that is to say as imaginary space, space as it is usually understood: ‘that which can be occupied’.53 It is generally agreed, Hobbes claims, that bodies do not carry their  Hobbes 1973, 450. See Payne’s and Cavendish’s notes (Hobbes 1973, 474 [2]) and the final version in DCo, ch. 7, § 2 (Hobbes 1999, 76–77): in Cavendish’s notes and the final version, the tense of the verb appear is changed from past to present. 50  See Hobbes 1973, 474 [2]. 51  Hobbes 1973, 450. 52  See DCo, ch. 7, § 2 (Hobbes 1999, 76). 53  Ibid. See, reciprocally, the commonly accepted definition of body as ‘that which occupies a space’ in AW, ch. 27, § 1 (Hobbes 1973, 312); see also Leviathan, ch. 34: “The Word Body, in the 49

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places with them, but that sometimes some body, sometimes some other, is contained in one and the same place. This phenomenon (Aristotle’s antimetastasis, again) would not be possible if a space accompanied forever a body which would be in it at some time.54 This proves that space has not the same nature as the body it contains, which is perfectly consonant with Hobbes’s notion of space as an image or phantasm. Conversely, as De corpore’s first philosophy later makes it obvious, the equivalence of the definition of imaginary space to the avowed definition of space implies that, for Hobbes, a body does not ‘occupy’ an extra-mental space, but some imaginary space. The occupation of a space by an existing thing must be held this thing’s being “coincident and coextended” with this space, that is to say, with an image in the mind.55 The ‘place’, locus, of a body, is in turn defined as that imaginary space which is coincident with this body.56 This doctrine was among Hobbes’s contemporaries a source of puzzle. A letter from François Peleau by the end of 1656 expresses some bafflement after reading De corpore: “Vous dites. dans vre Metaphisique, ou philosophie premiere, que le Lieu, est phantasma corporis existentis, quatenus existentis, mais, Monsieur, vous m’avoueréz, que tout corps, est in Loco, […] et qu’il n’est pas, in phantasmate; doncques le lieu, non est phantasma. &c.”.57 Even Charles Cavendish, when Hobbes showed him a draft of the first chapters of his Philosophia prima, misunderstood Hobbes’s position. A letter from Cavendish to Joachim Jungius, dated 11 May 1645, reports fairly faithfully the different definitions required in Hobbes’s philosophy for defining motion: not only the definition of the place of some body as “a space with is coincident with this body”, but also the definition of space as imaginary space, inferred from the supposed annihilation of the world.58 Cavendish highlights the essential function of the nature of images in this deduction of the definition of space. Because images necessarily appear as external to the mind, they remain in the mind as the images of things which were really external to the mind before their supposed annihilation. Those images, Cavendish stresses, are as many ‘spaces’ for Hobbes, who understands ‘space’ merely as an ‘imaginary space’, not as an accident of

most generall acceptation, signifieth that which filleth, or occupyeth some certain room, or imagined place” (Hobbes 2012, 610). 54  Later in his Philosophia prima (DCo, ch. 8, § 5), Hobbes uses another argument to prove that place is immovable - a confirmation of his definition of place as a phantasm: if a place were carried away when a body moves from some place to another, then this would require ad infinitum a place of a place, now this is impossible (see Hobbes 1999, 85; also Hobbes 1973, 454). Cf Aristotle, Physics, Δ, 1, 209a 23–26, for Zeno’s relating the same absurdity to the assertion that place exists: if place exists it must have a place to exist in, and so on ad infinitum. 55  See DCo, ch. 8, § 1 (Hobbes 1999, 82 - already in the 1643–4 draft and in Cavendish’s notes: see Hobbes 1973, 452 and 476 [1]). 56  Place can be defined only after body is defined, and body itself is defined on the basis of the definition of space. See DCo, ch. 8, § 5 (Hobbes 1999, 85). Cf. Hobbes 1973, 453 and 477 [5]. 57  See Hobbes (1994, 381): Letter 103, [30 November/]10 December 1656, François Peleau to Hobbes. 58  See Schuhmann (1998, 84).

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bodies: “space is the phantasm of a body simply”,59 regardless of the diverse qualities of this body. So far, Cavendish’s description is accurate enough. But Cavendish’s uneasiness with the corollary of Hobbes’s definition of space as imaginary space, the redefinition of the occupation of some place by a body, becomes at once manifest. When he reports Hobbes’s definition of body, indeed, Cavendish writes: “if there is something in the external space which is not dependent on our imagination, calls it Body […]”.60 The imaginary space fails to be that to which the occupation of some place by a body must be referred; the purely mental space, which is for Hobbes coincident with a body, becomes under Cavendish’s pen (lapsus calami?) an “external space”. It definitely seems to be harsh for Hobbes’s contemporary readers, even among his close friends or admirers, to agree with the thesis that a body occupying a place is not situated in an extra-mental space but subjected to an imaginary place.

2.3.2  The Blurring of Spatium Reale De corpore’s approach to the definition of space eliminates the threat hanging over the Anti-White’s construction, the threat of a universal which would be other than a general name. In De corpore, only the representation of existence is required for the definition of space, now any particular image provides this fundamental representation. Space is defined as an image for an existing thing considered merely as existing: it cannot be mistaken for a universal image. In my view, however, the difference between De corpore and the Anti-White on the topic of space goes beyond the elimination in De corpore of the very possibility of misunderstanding space as a universal. It seems to me that Hobbes’s emphasis on the synonymy of spatium and spatium imaginarium - when he says: “Space (by which word, I always understand imaginary space)” 61- points to more than the exigence to consider the nature of image in order to define space. It also points to Hobbes’s questioning of the scholastic dyad of spatium imaginarium and spatium reale. Interestingly, this declaration about the constancy of Hobbes’s ‘imaginary’ meaning for the word spatium comes into De corpore’s definition of place as some space coinciding with the magnitude of some body. Now, the argumentative context of the definition of place in De corpore is particularly important. Hobbes had previously defined the magnitude of a body as

 The definitions of space and place quoted by Cavendish in his Letter to Jungius (“spatium est corporis simpliciter phantasma”; “locus cujus libet corporis est spatium, quod cum illo corpore coincidit”) are not the definitions verbatim of his notes on an early draft of De corpore (“spatium est phantasma rei existentis simpliciter, quatenus existentis”; “locus est corporis cujus cumque spatium imaginarium, quod cum ipsa corporis magnitudine coincidit”: Hobbes 1973, 474 [2]; 477 [5]). 60  See Schuhmann (1998, 85 - my emphasis). 61  DCo, ch. 8, § 5 (Hobbes 1999, 85). See NLW MS 5297: “Space (which I always understand imaginary)” (Hobbes 1973, 453). 59

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consisting of its extension. ‘Magnitude’, he then adds, is “that which some call real space”, “id quod aliqui vocant spatium reale”.62 Before insisting that in his Philosophia prima, ‘space’ is always understood as ‘imaginary space’, thus, Hobbes introduced the notion of ‘real space’. Does this mean that Hobbes agrees in De corpore with the scholastic dyad? What strikes me, rather, is that ‘real space’ has been relegated to the equivalent, for some anonymous authors, of that which Hobbes calls ‘magnitude’ (“magnitudo”), whereas De corpore claims for the univocity of the term ‘space’, which only means ‘imaginary space’. When he remarks that his notion of ‘magnitudo’ and some authors’ notion of ‘spatium reale’ have the same meaning - both signify the extension of a body - Hobbes manifestly does not intend to replace the name ‘magnitudo’ with the locution ‘spatium reale’. Instead, he highlights that this locution, spatium reale, is not his, that it is not the expression he uses for signifying the extension of body, even though it is allowed this signification in some philosophers. The incidental reference to those anonymous thinkers who call magnitude ‘spatium reale’ reflects no doctrinal agreement. To my mind, the reason why it is made is that Hobbes intends to stress the difference between magnitude (or extension) and space, defined at the beginning of the Philosophia prima as a mere phantasm: “this magnitude does not depend on our thought, as imaginary space does”, Hobbes specifies after defining magnitude as the extension of body.63 The purpose is to underline that, in contrast with space, magnitude (or extension) is an extramental accident, inherent in an external body. For Hobbes, this opposition between space and magnitude or extension must work as the principle of the definition of place, locus, in first philosophy: the mention of spatium reale is accordingly to be reassessed with regard to the definition of place as an imaginary space. Now, from this viewpoint, it is only negatively, that real space is granted some consideration in De corpore: the aim is not to agree with the scholastic dyad of spatium imaginarium and spatium reale, but to denounce false definitions of place which understand locus as a spatium reale, that is to say, which mistake extension for space. De corpore develops no strategy to make the notion of spatium reale the necessary complement to the notion of spatium imaginarium. The summaries of chapters 7 and 8 in the Philosophia prima announce, the one the definition of space (“Quid sit spatium”), the other the definition of magnitude (“Magnitudo quid”).64 Now, Hobbes does not relate in the same way and on equal terms the two members of the traditional pair spatium imaginarium/spatium reale to his definitions of space and of magnitude. Actually, spatium imaginarium is demonstrated to be the necessary meaning for space, the meaning imposed by the nature of the images without which we would have no knowledge of external bodies. Tradition has nothing to do with this definition of space as imaginary space. Only spatium reale is referred to its  DCo, ch. 8, § 4 (Hobbes 1999, 84). Cf. NLW MS 5297: “The extension of a body is the same with the magnitude or that which some call real space” (Hobbes 1973, 453). The published version of De corpore retains the formulation of NLW MS 5297, which prohibits the double usage of the term ‘space’. See, in contrast, the notes by Payne and by Cavendish (Hobbes 1973, 477 [4]). 63  DCo, ch. 8, § 4 (Hobbes 1999, 84). 64  See DCo, ch. 7, § 2, ch. 8, § 4 (Hobbes 1999, 75, 82). 62

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official meaning in some authors. But then, ‘real space’ is not claimed to be also Hobbes’s name for magnitude or extension  - as if the use of the word space for another space than imaginary space would bring the risk of a misinterpretation of place, which would be fatal for natural philosophy. The scholastic dyad, thus, is significantly altered and disordered in De corpore. Imaginary space has the chief doctrinal function in the Philosophia prima, but this function is due to Hobbes’s argument concerning images, not to some authoritative source. As to real space, it has no doctrinal function: Hobbes is not eager to adopt the identification of the extension of a body to a real space of this body; his aim, instead, is to use the notion of spatium reale for a critical purpose in his analysis of place.65 Hobbes’s position was quite different in the Anti-White. In this work, although the definition of spatium imaginarium is understood as the definition of space simply, a second sense is admitted for spatium, complementary to the definition of space as the phantasm of a body insofar as it is a body. The imagination on which the phantasm of body qua body, space, is dependent, is itself ultimately dependent on the action of an external agent, some body or matter. Thus, after the hypothesis of the annihilation of bodies is used to define space, the reverse fiction of the non-­ existence of any imagining subject is introduced in the Anti-White. This is to show that the existence of bodies, by contrast with the existence of spatium imaginarium, has no relation to the existence of imagination. In order to define space as imaginary space, Hobbes claimed that bodies, when they vanish out of our sight, carry away with them their dimensions; he claims next that we cannot judge that some body exists without deeming at the same time that this body is provided with dimensions, that is to say, with “its own spaces”.66 From these two premises: 1. bodies exist independently of imagination, 2. bodies are provided with spaces, their dimensions, the Anti-White concludes: “this space - which can be called real - inherent in a body as an accident in its subject, certainly would exist even though nothing would exist which could imagine it”.67 So, corresponding to the definition of imaginary space, a definition of real space, spatium reale, must be provided: “I define therefore real space as corporeity itself, that is to say, simply the essence itself of a body qua body”.68 Space is not inherent in objects perceived but is purely imaginary; the essence, however, of a body insofar as it is a body (namely, the essence of that which is represented by imaginary space) can be called a space too, provided that its opposition to imaginary space is specified: a real space. In the context of Anti-White’s chapter 3, neither magnitude nor extension is claimed to be the essence of a body qua body: only the name spatium reale seems to be appropriate then to signify the accident which defines a body absolutely.  For the disparity between spatium and spatium reale in Hobbes’s final doctrine, see DCo, ch. 8, § 9 (Hobbes 1999, 87). Strikingly, from the three occurrences of spatium reale in the Philosophia prima of De corpore (ch. 8, § 4, § 5, § 9), the two latter get a purely negative or critical function: see Hobbes (1999, 84, 85, 87). 66  AW, ch. 3, § 2 (Hobbes 1973, 117). 67  Ibid. 68  Ibid. 65

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Interestingly, in other passages dealing in the Anti-White with the essence or nature of body, spatium reale is no longer mentioned: Hobbes, instead, uses the name corporeitas, or the names extensio and magnitudo.69 Obviously, it is only when his argument is devoted to the definition of imaginary space against its wrong scholastic sense, that Hobbes considers it useful in the Anti-White to juxtapose the notion of spatium reale to the notion of spatium imaginarium as its correlate, and to highlight how this late scholastic pair can still hold when the target is to eliminate the traditional understanding of imaginary space as an extracosmic space.70 In passages that do not have the same polemical context there is no need to replace ‘corporeity’ and ‘extension’ or ‘magnitude’ with ‘real space’. All these terms, however, receive the same meaning. The definition of spatium reale is deduced in the Anti-White from a body’s being possessed with dimensions; likewise, to be endowed with dimensions is the property defining corporeity and magnitude or extension.71 The possession of dimensions is held to be the same as the occupation of a place by a body. “A body”, chapter 27 reads, “is that which is endowed with dimensions, that is to say, that which occupies an imaginary space”; again, a few lines further down: “the essence of body, or corporeity, […] consists in that it is endowed with dimensions, or, which is the same, in that it is in a place”.72 In contrast, from the very first drafts, what defines extension or magnitude in De corpore is the exteriority of the parts of a body to each other: extension, as the essence of a body qua body, has become that accident in a body which constitutes the reason why its parts are perceived in different places, one here, another there.73 The reason for the imposition of the name ‘body’ on something is the same as the reason for the perception of this thing’s partes extra partes: “when we see something or conceive in our mind something visible, that thing appears, or is conceived, not in one point, but as having parts remote from one another, that is, as extended through some space; therefore, since we have resolved  For corporeitas see AW, ch. 27, § 1, § 8; ch. 34, § 2 (Hobbes 1973, 312, 319, 381). For extensio and magnitudo, see AW, ch. 7, § 6 (Hobbes 1973, 149). 70   For late scholastic uses (Suarez, Fonseca, the Conimbricenses) of the dyad spatium imaginarium/spatium reale in defense of the opinion that God is omnipresent in an extracosmic infinite space, see Grant (1981, 153–163). Schuhmann (1992) has suggested that Hobbes’s doctrine of space shares important features with late scholastic commentaries on Aristotle. Leijenhorst (1996, 374–380) has demonstrated that in some sense of his doctrine of spatium imaginarium, Hobbes is close to Suarez, and in another sense closer to Toletus. However, Schuhmann and Leijenhorst do not differentiate Hobbes’s position in De corpore from his position in the AntiWhite. I argue, instead, that the two positions are not identical, and that the analogy between Hobbes’s doctrine of space and the late scholastic dyad spatium imaginarium/spatium reale does not suit Hobbes’s mode of argumentation in De corpore. 71  See AW, ch. 7, § 6; ch. 27, § 8 (Hobbes 1973, 149, 319). Cf AW, ch. 5, § 2: “extension or quantity”, together with figure and colour, is a part of the image of a body (Hobbes 1973, 129). In the Anti-White, extension, as well as space, is considered twice, in the mind and in the body conceived by the mind. 72  AW, ch. 27, § 1, § 8 (Hobbes 1973, 312, 319). 73  See DCo, ch. 8, § 2 (Hobbes 1999, 83). Cf NLW MS 5297: “whence it is that of a body one part appears here and another there? it is answered…by reason of the extension” (Hobbes 1973, 452) and Cavendish’s notes (Hobbes 1973, 476 [2]). 69

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to call body a thing so conceived, the cause of its name is that this thing is extended, that is to say, extension or corporeity”.74 To my eyes, this confirms that, for his De corpore project, Hobbes has reconsidered the possibility of associating his notion of extension with the notion of real space. The property on which the Anti-White has based the synonymy between real space and extension or magnitude is no longer put to the fore in De corpore.75 The blurring of spatium reale in De corpore constitutes a significant change in regard to the Anti-White’s constructive or positive use of this notion. In the refutation of De mundo, the definition of real space immediately follows the definition of imaginary space, and the definition of place is derived from the correlation between the two kinds of spatium, space-accident of the mind and space-accident in an external body: when the real space of some body coincides with some part of the imaginary space, Hobbes states, the latter is called the ‘place’ of this body76. On the contrary, in the Philosophia prima of De corpore, real space is introduced only indirectly, by reference to some other thinkers who say ‘spatium reale’ instead of ‘magnitudo’. This oblique way is not casual. Hobbes stresses that the notion of real space is no longer required to signify the accident which is the cause in an external body of the phantasm of this body qua body. To hold that extension or magnitude, the counterpart in an external thing of space in the mind, is another space, does not fit Hobbes’s doctrine. It is about magnitude, not about real space, that De corpore asserts its independency on our thought, and conversely its causal function on our knowledge.77 Magnitude, rather than real space, is said to constitute, unlike imaginary space, an accident of a body existing out of the mind.78 As a whole, the distinction between magnitude (or extension) and imaginary space supplants the distinction between real space and imaginary space. Whereas the definition of place in the Anti-White requires the latter dyad, in the De corpore’s project of natural philosophy, obviously, it is of fundamental concern to Hobbes to keep the definition of place away from the notion of spatium reale. The only notion of space allowed when defining locus in De corpore is that of imaginary space: real space is shown then to work only in wrong definitions of place thought out by philosophers who fail to acknowledge the essential dichotomy of space and extension.

 DCo, ch. 3, § 3 (Hobbes 1999, 33). Cf Payne’s notes (Hobbes 1973, 466).  Surprisingly, when Schuhmann (1992, 71) writes: “L’espace réel est […] l’essence du corps”, his reference is to DCo, ch. 8, § 23, which reads: “extension is said to be the essence of a body” (see Hobbes 1999, 92). Schuhmann feels authorized to substitute systematically in Hobbes’s first philosophy spatium reale for extension and to read De corpore according to the doctrine of space in the Anti-White. To my eyes, Hobbes’s use of the notion of spatium reale in chapter 8 of De corpore is no longer the positive use found in chapter 3 of the Anti-White. 76  See AW, ch. 3, § 3 (Hobbes 1973, 118). 77  See DCo, ch. 8, § 4 (Hobbes 1999, 84). NLW MS 5297 is comparable with the published version: see Hobbes (1973, 453). 78  Ibid.

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2.3.3  Spatium Reale as a Polemic Tool In De corpore, thus, real space is not defined in its own right, but only indirectly. Furthermore, as I have just said, when Hobbes’s Philosophia prima deals more specifically with real space, it is not positively, but negatively, for the sake of criticism. Beyond the simple mention that ‘spatium reale’ may be used by some writers as a name for magnitude, the two other occurrences of this scholastic expression are linked to a critical function. The definition of place is followed in chapter 8 of De corpore with a series of propositions constituting particular variations of the “phantastical” nature of place. Not only a body, but also the place occupied by a body, is not to be mistaken with the extension of this body: “place differs from the magnitude of the things placed”.79 The difference between place, as an internal accident of the mind, and extension, an accident inherent in body, is as essential as the difference between body, the extended substance, and its extension. The diverse aspects of the difference between place and extension, thus, deserve enumeration to Hobbes’s eyes. When a body is moved, the Philosophia prima outlines, it keeps the same magnitude, whereas it does not keep the same place; also at several times, a body keeps the same magnitude, whereas it does not keep the same place. A place is nothing out of the mind, Hobbes adds, whereas magnitude is nothing in the mind; lastly, place is “a feigned extension”, not “a true extension”, as magnitude is.80 In De corpore, the assertion that magnitude is the cause of our thought of a body qua body (the cause, thus, of imaginary space) necessarily implies the refusal to consider place as an entity out of the mind. A per absurdum demonstration of the immobility of place completes this analysis of place as a phantasm, a kind of accident other than the magnitude of the body occupying it. That which moves, Hobbes says, moves from place to place; thus, if a place is moved, its motion implies that a place is transferred from one place to another; a place for a place would be therefore required, and again a place for the place in which a place is, and so on ad infinitum, now this is impossible.81 The supposition that place is movable, in other words the supposition that a place is an accident inherent in a body, which a body carries away with itself when it moves, opens an indefinite regression. This absurd consequence confirms the purely imaginary nature of place. Significantly, in the final version of De corpore, by contrast with the 1643–4 NLW draft, which had already developed a similar demonstration, the thesis of the immobility of place is not immediately followed with the criticism of the definition

 DCo, ch. 8, § 5 (Hobbes 1999, 85). Cf NLW MS 5297; Payne’s and Cavendish’s notes (Hobbes 1973, 453, 477). 80  Ibid. The enumeration reproduced in Payne’s notes is not as worked out as in Cavendish’s notes or in NLW MS 5297: see Hobbes (1973, 453–454, 477). 81  Ibid. Cf NLW MS 5297 (Hobbes 1973, 454). This per absurdum demonstration is not developed in Payne’s and Cavendish’s notes. 79

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of place as “the superficies of the ambient”.82 This criticism directed against the Aristotelian notion of place shifted in 1655 after another criticism, directed against two modern demonstrations of the immobility of place. The authors of these wrong philosophical doctrines of place remain anonymous, but the descriptions provided by Hobbes reveal their identity: Descartes on the one hand, White on the other hand. Both, Hobbes contends, ground the demonstration that place is immovable on the thesis that place is the same as spatium reale. Now, any proof of the immobility of place based on the premise of the identity of place with real space necessarily rounds against its foundation. Therefore, when demonstrating that place cannot be moved, even a doctrine allowing no difference between the nature of place and real space is doomed to acknowledge that place is a phantasm: Descartes and White, in other words, unwillingly make place to be an accident of the mind, an imaginary space. Actually, in the demonstrations turned by Hobbes to the advantage of his own doctrine of place, neither Descartes nor White expressly defends the thesis that the nature of place is the same as spatium reale; but, in the argumentative context of De corpore, the notion of real space takes on an essential critical function. Instead of presenting their common premise as stating the identity of place with extension, De corpore ascribes to Descartes and to White the use of the notion of real space: although the notion of spatium reale cannot be found as such in the two demonstrations condemned, for Hobbes it answers to the indistinction in these reasonings between place, or space, and extension. Real space, thus, is denounced as misused as a synonym for place in Descartes’ and White’s demonstrations of the immobility of place. The reason why the diptych of imaginary space and magnitude or extension is substituted in De corpore for the diptych of imaginary space and real space is therefore made clear: real space has become a label for the misunderstanding of place by some modern philosophers. The preceding mention that some authors apply to magnitude the name ‘spatium reale’ seems to have been intended to make the name ‘spatium reale’ work as a polemic weapon. Hobbes’s purpose in De corpore is to proscribe the usurpation by extension (which he designates then as ‘real space’) of that which should be attributed uniquely to space understood as the image of an existing thing qua existing: the definition of the nature of place. The passage in Part II of Descartes’s Principia philosophiae, article 10, which can be recognized from Hobbes’s description in De corpore deals with the definition of ‘space or internal place’, spatium sive locus internus.83 According to Descartes, “space or internal place does not in reality differ from the corporeal substance contained in it”: the difference is only in our mode of conception. The same tridimensional extension that constitutes space, he asserts, constitutes body, but we consider that in body extension is singular and changes whenever the body changes, whereas in space we attribute to extension a unity only generic. Accordingly, we do not think that the extension of space is changed when the body filling space  DCo, ch. 8, § 5 (Hobbes 1999, 85). Cf NLW MS 5297 (Hobbes 1973, 454). No corresponding passage in Payne’s and Cavendish’s notes. 83  See Descartes (1964b, 45). For Hobbes’s reception of Descartes’s Principia philosophiae according to the Cavendish-Pell correspondence, see Brandt (1928, 179). 82

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is changed; we think, instead, that it remains one and the same.84 By contrast with individual extension, viewed as inseparable from body, generic extension is considered as separate: it is in this regard, that place is immobile. For Hobbes, this reasoning assuming that space is extended and its extension the same as the extension of body mistakes place with ‘real space’. Now, such a notion of place cannot escape an immediate self-confutation. The author, Hobbes says, who claims that place is held to be immobile because what is considered in this case is ‘space in general’, spatium in genere, the same container for many bodies successively, contradicts his fundamental thesis that the nature of place is the same as the nature of body. In the demonstration that the immobility of place can suit the identity of space with the corporeal substance it contains, place-extension is allowed by Descartes a kind of unity - generic unity – which it ought not to be granted. Because “nothing is generic or universal except names”, Hobbes objects to the demonstration in the Principia, the space which is said to be considered generically, in genere, is actually nothing but the phantasm of a body.85 Descartes’s attempt to prove the immobility of place by means of an abstraction, the consideration of space apart from the body with which it is according to the Principia really the same, results for Hobbes in the necessary understanding of place as imaginary. The second demonstration of the immobility of place criticized by Hobbes for its being derived from a conception of place as “real space” comes from White’s De mundo. After refuting the plurality of worlds because the distinction of here and there in the extracosmic space would be meaningless, since this imaginary space is ‘nothing’, White refutes the suggestion that their diverse ‘ubicationes’ might explain the plurality of worlds, ‘ubicatio’ being understood as “a certain being inseparable from the subject” and the reason therefore why a body is constituted here or there.86 Against this suggestion, White defends the universal understanding of place in all our locative expressions as meaning “something ambient”, namely the same understanding, he says, as Aristotle’s notion of “a certain immobile vessel”.87 A further difficulty, however, is examined afterwards in De mundo, precisely concerning the immobility of place: how can the doctrine rejecting the notion of imaginary space (namely, White’s doctrine) demonstrate the immobility of place, since for the defenders of imaginary space, nothing can remain immobile, except imaginary space? White’s reply to this difficulty defends the compatibility of the Aristotelian notion of place with the immobility of place. Aristotle’s definition of place as an immobile surface must not be refused, White says, by arguing that it is impossible to find in things themselves, which are mobile, some surface possessed with immobility. This impossibility does not allow us to contend that place is ill-defined in Aristotle: instead, we must pay attention to our intellect’s capacity to join from

 Principia philosophiae, II, art. 10. About Descartes’s doctrine of space/place in articles 10–12, see Garber (1992, 134–136; also 149–150 for a comparison with Toletus). 85  DCo, c. 8, § 5: Hobbes (1999, 85). 86  For this ‘ubicatio’ argument, see White (1642, 27). 87  White (1642, 28). 84

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outside the notion of immobility to surface, which by its own nature is not immobile. Even the flowing surface of a river can be immobile, White claims: although the uninterrupted succession of water means that a river is always changing, our intellect can relate its surface to something immobile (a bridge, a house, for instance), so that the surface in itself mobile gains immobility, not really, but in our conception.88 In the Anti-White, Hobbes condemned this explication as inconsistent: to avoid self-contradiction, White should have considered that the surface of flowing water is not an accident inherent in water, but a surface in the mind, an imaginary surface. Now, the imaginary surface of flowing water is the image of water insofar as water is a body, not insofar as water is water; so, the immobility of surface can be asserted, since this image can represent any body with the same magnitude and figure. Thus, for the Anti-White, when the immobility of place is explained in De mundo from the intellectual link established between a mobile surface and something immobile, actually White unintentionally recognizes the imaginary status of the immobile surface. When a body moves, Hobbes affirms in the Anti-White, its real surface can be retained only by the links of imagination. So, White’s argument in De mundo involves its self-refutation, since it is finally reduced to the very notion of place it was aimed at refuting: place is an imaginary space.89 In De corpore, when Hobbes attacks anonymously the philosopher who says that “real space is made immobile by the intellect”, he just summarizes the criticism developed in the Anti-White: to contend, like White, that the surface of flowing water is made an immobile place by the intellect amounts to declaring in an intricate way that it is made a “phantastical place”, an imaginary place.90 The reference to spatium reale is thus intended in De corpore to show that, if natural philosophy understands place as a real space, then natural philosophy cannot escape a fundamental internal contradiction in the demonstration of the immobility of place. Moreover, the two philosophers who are said to prove against their will that the nature of place is necessarily imaginary are tackled at the beginning of Philosophia prima in the excursus inserted within the opening definition of space. Indeed, as I said earlier, when this excursus stresses that Hobbes’s notion of space as a mere phantasm fits the commonly accepted definition of space as that which can be occupied by a body, the target is to highlight that some philosophers fail to grasp the true notion of space. Two anonymous philosophers, easily identified as being Descartes and White, are condemned then for their wrong definition of space as the same as “the extension of bodies themselves”.91 From this wrong conception of space, Hobbes insists, the one deduces the thesis that the world is infinite, the other the thesis that the creation of more than one world is impossible even to God;

 See White (1642, 32–33).  See AW, ch. 4, § 2 (Hobbes 1973, 126–127). 90  DCo, ch. 8, § 5 (Hobbes 1999, 85). 91  DCo, ch. 7, § 2 (Hobbes 1999, 77). 88 89

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inevitably, both demonstrations are flawed from the outset.92 Thus, the same modern authors who are said afterwards to contradict themselves in their demonstration of the immobility of place, represent at once in Hobbes’s Philosophia prima a counter-­ model for the fundamental definition of space as the phantasm of an existing thing insofar as it is existing. Both Descartes and White have misunderstood the first principle of natural philosophy. Manifestly, from the viewpoint of Hobbes’s project in the Philosophia prima of De corpore, the mere attribution initially (in chapter 7) of a wrong definition of space to Descartes and White does not constitute a sufficient refutation of their physical doctrines. The same criticism has to recur. It even recurs twice in the following chapter of De corpore, and in both cases, the notion of spatium reale is used negatively, as summing up the erroneous thesis that the nature of space or place is the same as the nature of extension. Descartes and White are guilty of an eviction of imaginary space by real space; they are not satisfied to maintain real space within the limits of an alternative name for magnitude or extension, they attribute to real space the function which must be attributed to imaginary space in definitions which are primordial for natural philosophy. Thus, in chapter 8 of De corpore, after being condemned concerning the demonstration of the immobility of place, Descartes and White are again implicitly refuted concerning the definition of contiguous bodies. The right definition of contiguity for Hobbes reads: “bodies between which there is no space are contiguous”.93 Hobbes specifies that ‘space’ in his definition cannot be other than imaginary space: “an idea or phantasm of a body”.94 So, it is clear for him that when no other body is interposing between two bodies, that is to say, “no magnitude, or, as they call it, no real space”, these two bodies are not ipso facto contiguous.95 The attempt to define contiguity without paying attention to the possibility that another body interposes between two bodies - in other words, without considering that a space which may be occupied by another body intervenes between them – results into an erroneous definition. In Hobbes’s view, only philosophers making a show of metaphysical subtlety are prone to miss something so conspicuous. He does not specify who are the philosophers he condemns then for their foolish notion of contiguity. No description of the blamed doctrines is given in this case. It is easy, however, to find in the Principia philosophiae on the one hand, in De mundo on the other hand, theses corresponding to the false statement denounced in De corpore, that two bodies necessarily are touching each other if no other body interposes between them (a statement which, Hobbes claims, even departs from common sense). According to Part II of Principia philosophiae, article 18, when nothing is placed between two bodies, it is necessary that they touch each other.96 For Descartes,

92  For the demonstrations to which Hobbes alludes in this passage, see Principia philosophiae, II, art. 21 (Descartes 1964b, 52); De mundo, Dialogus I, Nodus III (White 1642, 26). 93  See DCo, ch. 8, § 9 (Hobbes 1999, 87). 94  Ibid. 95  Ibid. 96  See Descartes (1964b, 50).

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it would be a contradiction to assert both that there is a distance between two bodies, and that this distance is nothing: “every distance is a mode of extension, and therefore no distance can be without an extended substance”.97 Likewise, according to De mundo’s argumentation against the plurality of worlds, any distance between two bodies supposes “the interposition of a real space, spatium reale”: “two quantities with a third intervening quantity are therefore separate, whereas the same quantities without the third intervening are therefore conjoined”.98 Instead of conceiving that two things are distant when it is possible that some being interposes between them, White contends that those things are distant, between which no being is now interposing. In the Anti-White, after the dyadic definitions of spatium imaginarium (the image simply of body qua body) and spatium reale (the essence simply of body qua body), plus the correlate definition of place as a part of imaginary space with which the real space of a body coincides, Hobbes has immediately emphasized that the definition of contiguous bodies follows easily. Bodies called contiguous are “those bodies between which there is no imaginary space, that is to say, between which no body may be”.99 Contiguity, Hobbes adds, requires more than the actual absence of any body between two bodies: what is required, is that no body may interpose. This definition is used in the Anti-White against De mundo’s thesis about the ‘conjunction’ of ‘quantities’: for Hobbes, it is wrongly asserted by White that two bodies are contiguous when there is no intervening body, since there is still the possibility that a body interposes between them. Yet, although the refutation of White on the topic of space and place is based in 1642–3 on a constant recalling of the purely imaginary nature of space, Hobbes at this time does not highlight in White’s erroneous demonstrations a perverted use of spatium reale instead of the right use of spatium imaginarium. ‘Real space’ is not then called up as a critical weapon to denounce White’s misunderstanding of space. In the Anti-White, real space is still a notion defined by Hobbes as complementary to the notion of imaginary space: the notion of the accident inherent in a body which is the cause of the image - space - representing this body insofar as it is a body. Remarkably, thus, some critiques already developed in the Anti-White without being then accompanied with the accusation that real space usurps in De mundo the function of imaginary space, recur in De corpore to show on the contrary how some modern doctrines of natural philosophy misuse the notion of real space. The duet Descartes-White (if I may speak so) has become the main target for Hobbes’s criticism of ill-founded natural philosophy, and real space is now considered in order to denounce a fundamental error common to Descartes and to White: both mistake the nature of extension for the nature of space. Real space is no longer considered as the correlate in things of imaginary space in the mind, but as the symbol of the  Ibid. For that reason, “what would happen if God did remove from some vessel all the body contained in it and did not permit another body to occupy the place of the body removed”, is for Descartes that “the sides of the vessel would be therefore contiguous to each other”. 98  See White (1642, 29). Cf AW, ch. 3, § 7 (Hobbes 1973, 121): Hobbes criticizes the sliding from contiguity to conjunction in White’s argumentation. 99  AW, ch. 3, § 3 (Hobbes 1973, 118). 97

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ill-­foundation of natural philosophy. The misunderstanding of space attributed in De corpore to Descartes’s Principia philosophiae and to White’s De mundo explains, in my opinion, the blurring of real space in Hobbes’s final doctrine. In 1655, Hobbes takes into account the impact of Descartes’s Principia philosophiae on natural philosophy. The convergent theses of White and Descartes concerning the extended nature of space causes the renunciation of the use of the dyad spatium imaginarium/spatium reale, which was held in 1642–3 to be convenient for the refutation of the theses on space and place in De mundo. The critiques addressed to De mundo’s doctrine within the compass of Hobbes’s distinction of two spaces, imaginary and real, are reconsidered for the De corpore project, which has to compete with the Principia’s doctrine. The refutation of White, thus, is modified when White is criticized in Descartes’s company. In Descartes’s Principia, the thesis of the identity of space with body is asserted as an essential principle for the new physics. Therefore, Hobbes’s criticism of the confusion between imaginary space and extension must be made quite unambiguously, which requires that Hobbes’s former admission of a double notion of space be abandoned. The attack on Descartes and White conjointly in De corpore relinquishes the Anti-White’s scholastic dyad. For it had given too much rope to an application of the notion of real space liable to overstep its limits to the prejudice of the notion of imaginary space. Real space is viewed then as a falsification of the notion of space, not as another space.

2.4  Conclusion The absence in De corpore of a description of spatium reale complementary to the description of spatium imaginarium urges a careful reading of Hobbes’s declaration in this work that magnitude is called by some authors ‘spatium reale’. It seems rash, upon the basis only of this laconic mention, in chapter 8 of Hobbes’s Philosophia prima, of the semantic equivalence in some authors between real space and magnitude, to conclude that Hobbes recognizes there his indebtedness to scholastic philosophy. In his article “Le vocabulaire de l’espace” published in the early 1990s, Karl Schuhmann comments as follows on the De corpore’s statement, “Extensio corporis idem est quod magnitudo ejus, sive id quod aliqui vocant spatium reale” (“the extension of a body is the same as its magnitude, or that which some authors call real space”): Cette phrase est la seule que je connaisse où Hobbes fait un aveu public d’avoir emprunté cette notion (ainsi que celle de l’espace imaginaire qui lui correspond) à la tradition (scolastique). Cf. Suarez, Disp. Meta., disp. 51: ‘reale spatium non est res distincta a corpore’100.

Cees Leijenhorst adopts the same reading of Hobbes’s statement in his article “Jesuit Concepts of Spatium Imaginarium and Thomas Hobbes’s Doctrine of Space”, published a few years later: 100

 See Schuhmann (1992, 71, n. 41).

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Hobbes says that he follows ‘some people’ who call this magnitude which inheres in bodies ‘real space’ (spatium reale)101.

To my eyes, the De corpore’s statement is over-evaluated in this interpretation. For Schuhmann and Leijenhorst, Hobbes’s agreement with the scholastic dichotomy spatium imaginarium/spatium reale is constant from the Anti-White to De corpore. I doubt, however, that their reading of this sentence in De corpore as the public and explicit acknowledgment of Hobbes’s debt to Suarez would have been as positive if the Jesuit dyad had not been employed in the Anti-White. Would the distinction of imaginary space from real space be attributed to the Philosophia prima of De corpore if this duality were not known to be the object of a specific demonstration in the Anti-White?102 Without the Anti-White, would not the dissymmetry in De corpore between the detailed construction of the definition of space as imaginary space and the mere reference to ‘real space’ as a synonym of ‘magnitude’ in some philosophers be perceived as a sign that Hobbes’s concern in this passage is other than a debt to the scholastic tradition? The criticism of a perverted use of the notion of ‘real space’, when the equivalence of real space with extension is understood as the equivalence of space tout court with extension, has become primordial. So, to my eyes, there is neither an explicit nor even an implicit allegiance to Suarez in the De corpore’s statement. Instead, I read this statement as marking that Hobbes is uninterested in the renewal of the scholastic diptych. The constructive use of the notion of spatium reale is abandoned: it is now extension or magnitude, not another ‘space’, that works positively as the correlate in things of imaginary space in the mind (that is to say, of space simply). Hobbes’s Philosophia prima only deals with the notion of real space to denounce its misuses in contemporary natural philosophy. De corpore does not repeat the Anti-White on the topic of space, the relationship between the two developments is not one of continuity. The elaboration by Hobbes of his doctrine of space was not completed with the Anti-White’s refutation of the wrong scholastic conception of spatium imaginarium as an extra-cosmic space. Hobbes still has to oppose a wrong conception of spatium reale as space tout court. In many respects, De corpore subverts the argumentative scheme of the Anti-White, in which the duality of imaginary space and real space constitutes the very frame of the doctrine of space. The Anti-White’s construction of the definition of imaginary space is modified in De corpore so that the threat of a definition of space as a universal image is swept away. In addition, De corpore eliminates another ambiguity, tied to the duality of spaces, imaginary and real. To make it sure that space is recognized as the purely imaginary first principle of natural philosophy, De corpore divests real space of a positive or doctrinal role. Thus, from the Anti-White to De corpore, the construction of the definition of space is really achieved, for Hobbes, when contemporary misuses of the notion of real space are denounced as a destruction of the

 See Leijenhorst (1996, 378).  The attribution to De corpore of the scholastic distinction between real space and imaginary space is first found in Grant (1981, ch. 8). My question applies to his reading too: see Grant (1981, 226 and 401, n. 255).

101 102

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notion of imaginary space. Instead of remaining the correlate of imaginary space in natural philosophy, real space has become its challenger in modern physics: Hobbes’s doctrine of space had to oppose the usurpation by real space of the function of imaginary space in the principles of natural philosophy.

References Aristotle. 1936. Physics, ed. W. D. Ross. Oxford: The Clarendon Press. Brandt, Frithiof. 1928. Thomas Hobbes’ Mechanical Conception of Nature. Copenhagen: Levin & Munksgaard. Descartes, René. 1964a. Œuvres, ed. Adam-Tannery, vol. VII, Meditationes de prima philosophia. Paris: Vrin. ———. 1964b. Œuvres, ed. Adam-Tannery, vol. VIII-1, Principia philosophiae. Paris: Vrin. Garber, Daniel. 1992. Descartes’ Metaphysical Physics. Chicago: The University of Chicago Press. Grant, Edward. 1981. Much Ado about Nothing. Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. Cambridge: Cambridge University Press. Hobbes, Thomas. 1889. The Elements of Law Natural and Politic. London: Simpkin, Marshall, and Co. ———. 1973. Critique du De mundo de Thomas White, ed. J. Jacquot and H.W. Jones. Paris: Vrin. ———. 1976. Thomas White’s De Mundo examined, transl. H.  W. Jones. London: Bradford University Press. ———. 1994. The Correspondence, ed. N. Malcolm. Oxford: Clarendon Press. ———. 1999. De Corpore. Elementorum philosophiae Sectio prima, ed. K. Schumann. Paris: Vrin. ———. 2010. Moto, luogo e tempo, transl. G. Paganini. Torino: UTET. ———. 2012. Leviathan. The English and Latin Texts, ed. N. Malcolm. Oxford: Clarendon Press. Leijenhorst, Cees. 1996. Jesuit concepts of spatium imaginarium and Thomas Hobbes’s doctrine of space. Early Science and Medicine 1 (3): 355–380. ———. 2002. The Mechanisation of Aristotelianism. The Late Aristotelian Setting of Thomas Hobbes’ Natural Philosophy. Leiden/Boston/Köln: Brill. Malcolm, Noel. 2002. Aspects of Hobbes. Oxford: Clarendon Press. Paganini, Gianni. 2008. Le néant et le vide. Les parcours croisés de Gassendi et Hobbes. In Gassendi et la modernité, ed. S. Taussig, 177–214. Turnhout: Brepols. Pécharman, Martine. 1992. Le vocabulaire de l’être dans la philosophie première: ens, esse, essentia. In Hobbes et son vocabulaire. Études de lexicographie philosophique, ed. Y.C.  Zarka, 31–59. Paris: Vrin. ———. 1995a. La logique de Hobbes et la ‘tradition aristotélicienne. Hobbes Studies VIII: 105–124. ———. 1995b. Hobbes et la question du principe d’individuation. In L’individuo nel pensiero moderno. Secoli XVI-XVIII, ed. G.M. Cazzaniga and Y.C. Zarka, 203–222. Pisa: Edizioni ETS. Schuhmann, Karl. 1992. Le vocabulaire de l’espace. In Hobbes et son vocabulaire. Études de lexicographie philosophique, ed. Y.C. Zarka, 61–82. Paris: Vrin. ———. 1998. Hobbes. Une chronique. Paris: Vrin. Southgate, Beverley C. 1993. “Covetous of Truth”. The Life and Work of Thomas White, 1593–1676. Dordrecht/Boston: Kluwer Academic Publishers. White, Thomas. 1642. De mundo Dialogi tres. Paris: Dionysius Moreau.

Chapter 3

Locke on Space and Substance Martha Brandt Bolton

Abstract Locke’s Essay concerning Human Understanding defends the anti-­ Cartesian doctrine that infinite space independent of corporeal substance is real and penetrated by bodies, i.e. a body always occupies a commensurate part of space. But whereas Gassendi, Newton, and others who hold this sort of doctrine find reasons to say that space is neither a substance nor an accident, Locke entertains the question and declines to answer it on the grounds that our idea of substance is too obscure. In this connection, Locke mounts a vigorous attack on the utility of the idea of substance, urging that use of it has potentially atheistic materialistic consequences. Although scholars usually take this to be nothing more than an occasion to rehearse the contention that substance is something-I-know-not-what, this article argues that the response is directly relevant to his doctrine of space. This is supported in part by tracing the development of this doctrine through the early drafts and travel journals. They argue that space consists of distance relations that must be terminated in the boundaries of bodies. The Essay replaces this with the doctrine that assimilates infinite space with God who must then be somehow extended and penetrable. If space consists of relations terminated in substances, it plainly is not a substance, but if space is constituted by penetrable extension somehow pertaining to God, its substantially is a more complicated question. Keywords  Locke · Substance · Space

It is difficult to sort out the empiricist, skeptical, physical, metaphysical, theological, and scriptural considerations that affect the discussion of space in Locke’s Essay concerning Human Understanding, but several things are clear. For one, it advocates the anti-Cartesian doctrine that spatial extension without body, or matter, is not only possible, but real; space is not to be identified with the essential attribute of corporeal substance. For another, every body occupies a portion of space that is distinct from, equal to, and coincident with its solid extended parts. For a third,

M. B. Bolton (*) Department of Philosophy, Rutgers University, New Brunswick, NJ, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 L. Berchielli (ed.), Empiricist Theories of Space, Studies in History and Philosophy of Science 54, https://doi.org/10.1007/978-3-030-57620-2_3

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beyond the bounds of the created world, there is infinite space empty of finite beings and somehow associated with the omnipresence of God. Finally, the Essay poses a question often asked by certain philosophers, whether infinite empty space is substance or accident, and firmly declines to answer. This combination of views may be unique to Locke. Several prominent thinkers of his time hold similar views about the existence of infinite empty space but attach some importance to denying that space is either a substance or an accident. Pierre Gassendi, Henry More, and Isaac Newton all deny that infinite space is a categorical being although they justify it in different ways. But Locke refuses to address the question on grounds that our idea of substance is inadequate. Our deep ignorance of the nature of substance and the inherence relation is a theme running throughout the Essay. Yet the discussion in the chapter on simple modes of space, Essay 2.13, elicits Locke’s most concerted attack on the utility of the notion of substance. This may give the impression that his views on substance have little relevance to his thinking on the specific topic of space, that he just takes the opportunity to underscore his general wariness of putting theoretical weight on the substance-accident metaphysics.1 Instead, I will urge that Locke’s views on space raise a particular question squarely in bounds of his carefully circumscribed skepticism about the nature of substance. To put this in a preliminary way, late seventeenth century thinkers who deny that spatial extension pertains to corporeal things alone generally maintain that space is common to all substances and accidents. That is, if a substance or an accident exists, it has, or must have, a location in space. Locke is no exception. Regarding substance, Locke subscribes to a general thesis to which virtually all other substance theorists agree, that no quality, or combination of qualities, can exist without a substance, a self-subsistent being in which they subsist. Unlike others, however, he holds that nothing about the nature of a substance can be inferred from the qualities found to depend on it. According to Locke, we have reason to think a quality cannot exist without a self-supporting substance, but we have no way of knowing its nature. We know what it does, but not how it does it (Essay 2.23.1–2).2 This merely functional notion gives scope to the question whether substance may account for the spatiality of everything that exists, or so I will argue.3 The general picture is consistent with either of two mutually incompatible views: (i) that substances incorporate space which is thus imparted to the accidents that depend on substance and (ii) spatial location is an extrinsic condition on the existence of substances which are constituted independently of space. To answer the question whether or not space is a substance, Locke would need a more determinate notion of the constitution of a 1  This might be inferred from M.R.  Ayers, Locke, II: Ontology, 447–50; also Samuel Rickless, Locke, (Chichester, West Sussex, UK: Wiley-Blackwell, 2014). 2  Quotations and citations of the Essay are based on John Locke, Essay concerning Human Understanding, ed. P. H. Nidditch (Oxford: Clarendon Press, 1975). 3  ‘Accidents’ refers to nine of the ten categories of things said to be in Aristotelian-scholastic metaphysics. Locke’s ontology posits substances with various qualities (or powers), modes, and relations (see Essay 2.12; 2.27.2). Qualities, powers, modes, and relations can be regarded as accidents because they depend for their existence on one or more substances (see Essay 2.13–28).

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substance than his account of the experiential origin of the idea countenances. If this is roughly right, ignorance about substance is not an occasion, but a theoretically motivated reason for him to remain silent on the category question. To make a case for this, I will first review the development of Locke’s thinking about space from the early drafts written in 1671 through the journals he kept while traveling in France (1677–1679). These entries aim at constructing ideas of space and its modes based on the simple ideas we can acquire from experience but different in key respects from Gassendi’s theory of space. The second part of the paper considers the doctrines on space propounded in the Essay. It retains some of the earlier views but jettisons others; the most notable change is recognition of the existence of infinite space independent of finite things that occupy parts of space. The aim of this section is to identify, and motivate, changes in the way space is conceived. The third and final part of this paper turns to the tirade against the idea of substance in the chapter on the simple modes of space (Essay 2.13.16–20). I argue that it has special pertinence to the newly formed theory of space and helps to explain why both Gassendi and Newton, who are also concept empiricists and skeptics about the essences of substances, take stronger metaphysical stands.

3.1  Space in the Early Drafts and Journal Entries Already in Draft A (1671), there is a challenge to Descartes’ contention that space empty of body implies a contradiction. The context is a discussion of how ideas are given names which are used to state necessary truths. According to the draft, Descartes gives the name ‘idea of body’ to the idea he names ‘idea of extension’. It follows that everything that has extension is a body; the impossibility of a vacuum is then a tautology. Someone else may use ‘idea of body’ to stand for an idea that consists of extension and impenetrability, or resistibility, together in the same thing, and by taking ‘idea of space’ to stand for the idea of extension, prove that space without body is possible just as certainly as Descartes proves the opposite. The point is that the assignment of names and formation of propositions about names proves nothing about what there is. Experience is needed for that.4 Draft B (1671) overtly attacks those who ‘have made the whole essence of body to consist in extension’. This opinion is traced to imagination, and hence to experience. It suggests that some people find their minds so flooded with the sensory idea of extension, which attends ideas of all visible and tactual things, that they think they can’t imagine a sensible quality without extension. Odors and tastes notwithstanding, they come to believe that extension is the essence of body. Whereas in fact, according to the draft, extension is nothing but a quality discoverable by our senses which provides no information about the essences of things.  John Locke, Drafts for the Essay concerning Human Understanding and Other Philosophical Writings, 3 vols, Peter Nidditch and G.A.J.  Rogers, ds (Oxford: Clarendon Press, 1990), v. 1: Drafts A and B, 44–47.

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In the course of explaining the genesis of human ideas from sense and reflection, the draft explicates ideas of the modes of time, duration, place, and extension under the rubric ‘ideas of relations’. Temporal ideas receive much more attention than ideas of space but they are assumed to be analogous in important respects. According to Draft B, time is the ‘assigning of length or distance of duration betwixt any two assigned instants in which something(s) did or might exist’ (Nidditch & Rogers 224) and extension is ‘assigning the distance of any two points by some common knowne measure as inch(es), feet, [etc.]’ (Nidditch & Rogers 225).5 The question how it is possible to establish repeatable physical standards by which to measure duration, on one hand, and space, on the other, is discussed at length. Such standards are needed to explicate compound ideas of finite and infinite time and space because, as Locke puts it, the infinity of anything is the infinity of number. That is, infinity belongs only to things that have parts of the same kind which can be counted by a standard unit of magnitude, repeated, and added.6 Locke applies the notion of a unit of length to regions beyond the boundaries of the supposedly finite material world. Abstracting a measured mile from all bodies: ‘[W]e can in our thoughts apply … this measure of a mile to any extension beyond the utmost bodys, & by [it]… measure extensions in our thoughts where there is noe body.’ (Nidditch and Rogers, 244). It is not entirely clear how to understand this. It might seem to imply that empty space contains parts at a distance ready to be measured. If so, Locke thought better of it later when making a journal entry (A&G 95, quoted below). It might perhaps imply that we can literally mark miles of empty space without laying a measure of a mile alongside them. With more charity, we can take the quotation to expresses a subjunctive conditional—if a person where somehow to glide out into empty space, the person could mark a part that is a mile long. The idea of the place of a body is explicated as a three-termed distance relation. Place is ‘is noe thing but extension with relation to some other bodys or imaginary points that are at a certain determinate distance from it’ (Nidditch & Rogers, 259). A thing is in the same place provided these distance relations remain the same, so if a thing moves relative to the designated reference points, its place goes along with it. Its place is nothing other than the thing considered in relation to certain other things. The journals Locke kept while traveling in France (1677–79) contain several entries on extension, distance, and empty space among other topics.7 In comparison

5  The journals define the idea of extension in a way different from the Drafts and different from the Essay. 6  ‘Ideas of duration & Space doe include in them an aggregation of parts the one conceived coexistent, the other in succession, & both measureable or recond by number, & noe other Ideas but these doe originally include parts in them… & so Ideas of them [those that do not consist of parts] have noe tendency to infinity or are boundlesse for infinite can properly belong to noething but what consists of parts.’ (Draft B, Nidditch & Rogers, 250). 7  Five such entries are published in An Early Draft of Locke’s Essay together with excerpts from his journals, R. I. Aaron and J. Gibb, eds, (Oxford: Clarendon Press, 1936) (hereafter ‘A&G’). The journals have not yet been edited and published.

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with the early drafts, they seem to show more knowledge of non-Cartesian theories of space in that they argue for views opposed to them. It is likely that Locke’s thoughts are affected by conversations with François Bernier whom he befriended during his stay in Montpelier.8 Bernier, who promoted Pierre Gassendi’s philosophy, had just published a French language abridgement of his major work Syntagma.9 A few years later, Bernier would publish a short treatise summarizing Gassendi’s views on space and expressing a number of doubts about them.10 Both books are in the library Locke left at his death. Although there is, to my knowledge, no record of the subjects the companions spoke about, it can hardly be doubted that the pros and cons of Gassendi’s doctrine came up. The first entry on space (27 March 1676) concerns the notion of imaginary space which was devised by medieval scholastics and used by Hobbes and Gassendi to frame their theories of matter and material things. In brief, imaginary space was said to be what a person can imagine would remain if all created things other than her soul were annihilated.11 Supposedly, one could imagine a mere extension where the material world had been and where it is possible that a different world might be created by God. The journal entry argues against the reality of imaginary space: ‘Space or extension separated in our thoughts from matter or body seemes to have noe more reall existence then number has (sine re numerata) without any thing to be numbered.’ (A&G 77). Number is an affection of all real existences and extension is an affection proper to bodies. Each can be conceived in abstraction and enlarged in thought by addition without end. The entry notes that additivity is proper to quantities. But there is no need to posit two quantities, one abstract and the other pertaining to things. If the things comprised by the world were annihilated, space would be just nothing. Even so, an item dated 20 June 1676 (A&G 78–80) defends the possibility of bounded empty space between two or more bodies. Cartesians as well as scholasticAristotelians mount two arguments that it is not possible. According to Descartes’ Principles: if God were to remove the air and all other bodies from a closed vessel, its sides would meet because ‘where there is nothing between two bodies they must necessarily touch one another’. That is, ‘as I have often said, nothingness cannot possess any extension.’ (Principles 2.18–19; CSM 1.230–1). The second argument 8  Bernier was a physician and traveler who wrote books on the classification of human beings by race and an account of his travels in India, composed an abridgement of Gassendi’s Syntagma in French and publishing some doubts about a part of it. 9  François Bernier, Abrégé de la philosophie de Gassendi, 8 vols., 2nd edition, (Lyons: Chez Annison, Posuel et Rigaud: 1684; modern edition edited by Sylvia Murr (Evreux. Les Presses de l’imprimerie Hérissey, 1992)). The first edition was published in two parts (1674 and 1675). Locke’s library contains the second  1678 edition. It also contains a copy of the first edition of Bernier’s Doutes. See The Library of John Locke, eds. John Harrison and Peter Laslett, Oxford Bibliographical Studies, 1971. n.s v. 13. 10  Doutes de Mr. Bernier sur quelques-uns des principaux châpitres de son Abrégé de la philosophie de Gassendi (Paris: Estienne Michallet, 1682). On the relations between Gassendi and Bernier, see Sylvia Murr, ‘Bernier et le gassendisme’, Corpus, 20–21 (1992), 115–136. 11  See e.g. Edwin Grant, Much Ado About Nothing (Cambridge: CUP, 1981).

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is that space empty of body would seem to be an indestructible being independent of God. The journal entry effectively argues as follows.12 (1) Extension, i.e. partes extra partes, is proper to bodies because bodies alone have parts which are divisible, or mutually separable. (2) Distance is the relation arising when there are two noncontiguous bodies. It is real, not imaginary; it can be measured by a body and assigned a magnitude, such as three feet in length. (3) Distance is distinct from extension. This is because extension consists of parts that can be separated from each other, but although distance can be measured by partes extra partes the measured parts are inseparable. This is the primary argument against the Cartesian identification of spatial extension and corporeal substance abroad in the journal entries that have been published. As Locke points out, it answers the first objection by showing that space empty of body is something, namely, a relation among beings which has a determinate magnitude. It disarms the second argument because, if God creates two bodies which don’t touch each other, he thereby creates a determinate distance between them. According to Bernier’s abridgement, Gassendi’s anti-Cartesian theory ascribes three properties to spatial extension which distinguish it from corporeal extension. 1. Spatial extension existed before God created the world and will remain when God destroys it. 2. Space is immobile, whereas bodies change locations in space. 3. Spatial dimensions are ‘incorporeal’, i.e. they do not resist penetration by corporeal dimensions; so every part of a body occupies a part of space which is equal to it. Gassendi goes on to say there is no need to have scruples about the implication that space is uncreated and independent of God, because he explicitly states that he means by ‘space’ what is popularly called ‘imaginary space,’ which many theologians allow to exist beyond the world. It is imagined to have dimensions in the style of sensible bodies but it would exist whether or not anyone thought of it. ‘They do not believe it an inconvenience to say that these spaces are uncreated and independent; because they are nothing positive, that is, they are neither substance nor accident; these two terms comprising everything that God produces.’ (Abrégé, 21). By contrast, Locke’s response to the Cartesian objections is more parsimonious: it is not committed to the existence of space independent of the existence of bodies or the distinction between positive beings and other things that exist or the duality of space on one hand, and things that occupy space, on the other. As for the last point, a later journal entry rules it out: For when we speake of space (as ordinarily we doe) as the abstract distance between two bodys it seems to me to be a pure relation, and we call it distance but when we consider it as the distance or space between the extremitys of a continued body we call it extension and this is lookd on to be a posessive inhaerent property of the body because it keeps constantly with it always the same and every particle has its share of it … But when we speake of Space in generall abstract and separate from all consideration of any body at all or any other being it seems not then to be any reall thing but the consideration of a bare possibility of body to exist. (20 Jan. 1678; A&G 99–100).

12

 A&G, 78–80.

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Space empty of body is constituted by distance relations between discontinuous bodies, and the distance between extremities of a continuous body is extension constituted by impenetrable parts and proper to bodies. Space in abstraction from all bodies, in the manner of Gassendi, can be regarded only as bare potentiality. A subsequent journal entry dated 16 September 1677 sounds a note of tension by contending that we naturally and correctly conceive that space continues without end beyond the bounds of the created world; nothing can arrest this mental progression, and yet in actuality it is nothing. It is nothing ‘but the consideration of a bare possibility of body to exist there’ (A&G 100). ‘[D]istance I suppose to be the relation of two bodys or other beings neare or remote to one an other … For where there are noe beings at all we might truly say there were noe distance.’ (A&G 95). We are apt to imagine that there already is a place in empty space where, say, a globe of a foot diameter could exist; but this is an error. There is nothing on the other side of the bounds of the created world, no differentiation or division of parts. This same entry undertakes to explain how we conceive a vacuum, e.g. two bodies which are a yard apart exist in vacuo if they are related by a distance filled with nothing. The empty region is nothing but a capacity, but fully determinate and actual. In particular, one could put between them a yard-long body that touches a boundary of each without removing anything. By contrast, according to this entry, there are no given points in infinite empty space between which we can conceive that a measure might be placed. Locke is wholly persuaded that human beings can conceive empty space outside the limits of the finite universe in spite of its being nothing. The entry questions whether it is possible to conceive nothing, but Locke is undeterred: ‘[I]f there be a necessity to suppose a being there it must be god whose being we thus make, i.e. suppose extended but not impenetrable but be it one or other extension seemes to me mentally separable from body, and distance noe thing but the relation of space resulting from the existence of two positive beings or … two parts of the same thing.’ (A&G 96). We have the abstract idea of endless space without body, but what there is beyond the limits of the finite universe is not an abstraction. Locke is adamant that there is no space unless it comprises distance relations terminated in beings. So either we conceive infinite empty space as nothing or we conceive that God is present in it. In that case, God must be taken to be extended and penetrable so that there are distance relations between two parts of the same thing, namely, God. Bernier’s French abridgment of Syntagma cites the authority of Augustine in support of the presence of the All-mighty in the reaches beyond the limits of the material world. But Locke’s suggestion that God has penetrable parts, which found the distances comprised by space, may allude to the more fully articulated doctrine of Henry More.13 The journal seems to treat this alternative as a last resort; it is not mentioned elsewhere in the published material from the journals.  According to More’s Enchiridion (1656), space is a spiritual (immaterial), infinite organ through which God operates, a main exemplar of the ‘spirit of nature’ in many ways like God, but distinct from him. According to More, everything there is exists in space and spiritual as well as material substances are extended. Locke’s library includes copies of several earlier works of More, but not

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A later item defends the view that empty space is properly conceived as nothing: ‘[W]hen we speake of Space in general abstract and separate from all consideration of any body at all or any other being it seems not then to be any reall thing but the consideration of a bare possibility of body to exist.’ (20 January 1678, A&G 102). To the objection that space, unlike nothing, is capable of being greater or less, the entry replies that space beyond the finite universe is not capable of greater and less because there is nothing in it that terminates distances: ‘it is evident that there is always required some real existence to be the other term of the relation’ (AG 102). So although we may think that a distance of a foot beyond the most remote created thing is smaller than a yard, and it is true that a foot is smaller than a yard, ‘space antecedent to all determinate being is not capable of existing.’ (A&G 102). The main positions urged in these early writings can be summarized as follows. 1. The Cartesian doctrine that space empty of body is impossible is false. This is proved on the basis of the distinction between the relation of distance which holds between the endpoints of two discontinuous bodies, on one hand, and the extension of a continuous body which consists of solid parts, on the other. Distances have parts with properties opposite those of the extension of a body—penetrable, inseparable, and unmovable parts as opposed to impenetrable, separable, moveable parts. So it is possible that two bodies are separated by a distance in which no body exists, contra the doctrine of Descartes. 2. Space (and duration) are composed of relations, distances between distinct things or between parts of the same thing. Vacuum, or an empty bounded part of space (i.e. a thing consisting of parts) is possible and positive in character because it is terminated in the extremities of bodies and has a measurable length. 3. It is impossible that space exist if there are no bodies at all. 4. Although we cannot set bounds to the empty space beyond the limits of the created world, we cannot conceive it as anything real but only as the possibility of the existence of bodies. We cannot conceive it to have parts or structure of any sort. 5. If it is not possible to conceive a mere uncharacterized potentiality, then we may conceive that God pervades infinite space and has penetrable parts that terminate the distances of which empty space consists according to the journal entries.

3.2  Space in the Essay The Essay retains several of these doctrines with only minor revisions, but departs markedly from the early work by maintaining that space independent of body exists and bodies occupy parts of space. Item 3 from the early writings is openly denied. In connection with this, there is a significant shift in terminology. Whereas ‘extension’ refers to a quality proper to bodies in the journals, in the Essay, ‘extension’ signifies ‘the space that lies between the extremities of those solid coherent parts [of

Enchiridion which contains his theory of space. See John Henry, “Henry More”, Stanford Encyclopedia of Philosophy (on-line source).

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bodies] and is possessed by them.’ (2.13.1). Thus extension has parts that are penetrable, inseparable and unmovable, which can be occupied by bodies whose parts are impenetrable (2.13.11–14). In short: ‘Bodies do each singly possess its proper portion of [space] according to the extent of its solid Parts; and thereby excludes all other Bodies from having any share in that particular portion of Space, whilst it remains there.’ (2.15.11). Regarding terminology, eventually Locke feels the need of words that clearly mark the difference between distance, or space (penetrable extension) and impenetrable extension, a quality proper to bodies, and introduces the word ‘expansion’ for space, leaving ‘extension’ for the bodily quality (see Essay 2.15.1). In view of the shift in vocabulary just mentioned, the contrast between things composed of penetrable parts and those composed of impenetrable parts, which is the basis of Locke’s argument that empty space is possible, is reformulated. But the form of the argument remains the same. See Essay 2.13.11–16. The Essay retains the theory that space is constituted by distance relations (item 4). According to the later work, ‘This space considered barely in length between two Beings, without considering any thing else between them, is called Distance’. (Essay 2.13.3). Distance is also considered in three dimensions and then called ‘capacity’ (Essay 2.13.3). Distance is, then, a measurable quantity of three-­dimensional extension that lies between two or more bodies or other beings. So just as the journal entries demand that the distance relations that constitute space be terminated in actual relata, the infinite penetrable space posited in the Essay must consist of distance relations founded on their respective terminations. This follows from the essentially compositional structure of space and duration:14 ‘Yet none of the distinct Ideas we have of either [space or duration] is without all manner of composition, it is the very nature of both of them to consist of Parts; the mind is not able to frame an Idea of any space without Parts.’ (Essay 2.15.9; also 2.15. 1). The Essay adduces three considerations that favor the view that the existence of space is not dependent on the existence of bodies. The first, and most important, argues that motion would be impossible if there were no empty spaces between bodies, assumed to be composed of rigid naturally inseparable particles (Essay 2.13.22–23). The second argues from limitations on God’s power implied by the claim that space empty of creatures is impossible (Essay 2.13.21–21(bis)). The third is more a response to an objection to this position, the pointed question whether space is a substance or an accident (Essay 2.13.16–20). Because the first two arguments are peripheral to the topic of this paper, they will not be mentioned here again. Locke’s treatment of the question of category is considered in the next section. To finish comparing earlier and later doctrines on space, the view that infinite empty space beyond the finite world must be conceded but can be conceived to be

14

 As we saw, it was articulated in Draft B.

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nothing isn’t repeated in the Essay. But the infinite reaches of bodiless space are somehow incorporated in the boundless presence of God: But whether any one will take Space to be only a relation resulting from the Existence of other Beings at a distance; or whether they will think the Word of the most King Solomon, The Heaven, and the Heaven of Heavens, cannot contain Thee; or those more emphatical ones of the inspired Philosopher St. Paul, In Him we live, move, and have our Being, are to be understood in a literal sense, I leave everyone to consider. (Essay 2.13.26; also 2.15.2)

The second view is endorsed on the authority of scripture although further inducements to credit the literal interpretation are mentioned (Essay 15.2–4).15 In Locke’s own words, infinite space is ‘possessed by GOD’s infinite Omnipresence’ (Essay 2.17.20); again, ‘Duration and Expansion comprehend all finite Beings, and in their full Extent, belong only to the Deity’ (Essay 2.15.8). The passage opposes a view of space on which it consists of nothing but relations among beings other than space with the view that divine omnipresence should be taken as spatial presence. But the Essay is committed to the view that spatial extension comprises parts whose endpoints terminate the infinitely many distance relations that constitute space. The implication is that these points are in space itself, that is, they are present in the penetrable extension of the divine immensity. It is difficult to see just how Locke wants to understand how infinite extension pertains to God—whether as an affection, an attribute, or the constituting property of omnipresence which is one of the attributes of God. This theory is put to work in Essay 2.27, the chapter on identity that was added to the second edition of the work. It advocates a general principle of individuation on which no two things of the same kind can exist in the same place at the same time (Essay 2.27.1). The kinds of things subject to this principle are substances, modes, and relations. In this connection, we have ideas of exactly three kinds of substance: God, finite intelligences, and bodies. God is ‘eternal, unalterable, and every where’ and his identity is never in doubt. ‘[T]hough these three sorts of Substances… do not exclude one another out of the same place; yet we cannot conceive but that they must necessarily each of them exclude any one of the same kind out of the same place’ (Essay 2.27.2). So a finite spirit, a body, and the omnipresence of God are mutually penetrable, but bodies and finite spirits are each impenetrable by substances of their respective kinds.

 In view of the interest in Biblical hermeneutics shared by Locke and Newton, it is interesting to consider the account of Newton’s interpretation of the words of King Solomon (I Kings 8:27) in the original Hebrew, quoted in J. E, McGuire, ‘Predicates of Bare Existence: Newton on God’s Space and Time’, in Philip Bricker and R.I.G.  Hughes, eds, Philosophical Perspectives on Newtonian Science, (Cambridge, MA: MIT Press, 1990), 91–108. But it is unlikely that Newton influenced the theory of space in the Essay. Locke and Newton met probably for the first time in 1689, the year publication of the Essay began. They soon grew to be trusted friends who spoke and corresponded on a number of controversial subjects, especially the interpretation of certain sensitive passages of scripture.

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3.3  R  esponse to Question Whether Space is Substance or Accident After arguing that the simple idea of space is sufficiently different from the idea of body to establish that space without body is possible, Locke turns to objections raised by those who advocate the identity of space and body. The objection of most interest to us is this: ‘If it be demanded (as usually it is) whether this Space void of Body, be Substance or accident, I shall readily answer, I know not; nor shall be ashamed to own my Ignorance, till they that ask, show me a clear distinct Idea of Substance.’ (Essay 2.13.17). The challenge is benign for Cartesians who identify space with corporeal substance and deny that immaterial substances are spatial, but it has bite for those philosophers who maintain that all things that exist have a position in space and time as Locke does. They can hardly say that all substances are located in a substance, or all accidents (and substances) have location in a certain accident, so they are under pressure to admit that space and time belong to neither category. In the following passage, Gassendi begins by stating that spatiality is a condition on the existence of all substances and accidents and ends by proving the existence of space which can be neither substance nor accident: ‘[T]here is no substance and no accident for which it is not appropriate to say that it exists somewhere, or in some place, and exists sometime, or at some moment, and in such a way that even if the substance or the accident would perish, the place would continue, nonetheless, to abide and the time would continue to flow.’16 Substances must ocuppy a part of space; space need not exist in substance; so space is not a substance. Walter Charleton, a sometime follower of Gassendi, argues that because place and time are ‘more general’ than substance and accident, they cannot be reduced to substance and accident. That is, space, time, substances, and accidents exist, but the latter two have an existence that depends in some way on that of the former one; so there is more to the existence of space and time than that of categorical beings. Isaac Newton derives this result differently in an early unfinished essay De gravitatione (1666–79): ‘Space is an affection of being in so far as it is being. No being exists, or can exist, which is not related to space in some way.’ Later in the same essay: [E]xtension has a mode of existing proper to itself that pertains neither to substance nor to accidents. It is not substance both because it does not subsist absolutely per se, but is, as it were, an emanative effect of God and an affection of all being, and because it does not underlie [substat] proper affections of the kind that denominate substance, namely, actions, such as thought in the mind, and motions in body.17

 Gassendi, Syntagma, Selected Works of Pierre Gassendi, tr. Craig Brush (Texts in Early Modern Philosophy), p. 384. 17  Isaac Newton, De gravitatione, translated and quoted in J. E. McGuire, ‘Existence, Actuality and Necessity: Newton on Space and Time’, Annals of Science, 35 (1978), 466, 471–2. 16

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On this account, space (extension) is an affection of being as such, pertaining to God, substances, and those affections that are proper to substances, namely actions. Space is not a substance because being passive, it does not underlie actions. Moreover, space is an affection of all beings, and substance is not. It follows that extension (space) is neither a substance nor an affection that exists in substance; it is said to be an affection of a more general kind—an emanative effect of God.18 Locke also favors the view that everything that exists is related to every other in space and time:19 ‘Where and when are Questions belonging to all finite Existences’ (Essay 2.15.5); ‘For to say that the World is somewhere, means no more, than that it does exist’ (Essay 2.13.10). He is inclined to think that all things that exist are spatially extended: ‘tis near as hard to conceive any Existence, or to have an Idea of any real Being, with a perfect Negation of all manner of Expansion, as it is to have the Idea of any real Existence, with a perfect Negation of all manner of Duration.’ (Essay 2.15.11). Moreover, his theory of individuation plainly exposes him to the same pressure as Gassendi and Newton to answer ‘neither’ to the question of category. Still, his notion of substance is more skeptical than that of the thinkers just mentioned. The argument of Gassendi on this question states that substances and accidents have properties that space does not have. According to Abrégé 21 (quoted above, p. 7) and Charleton’s Physiologia (quoted above p. 13), substances and accidents are positive beings, whereas space is ‘imaginary’, in the sense that we imagine its dimensions on analogy with those we perceive by our senses in bodies. Here the term ‘positive’ seems to stand for a thing that possess a property by contrast with a thing deprived of that property. The point is that imaginary space lacks, but is imagined to have, corporeality and its modes. Newton’s reasoning might seem attractive to Locke. De gravitatione mentions ‘a certain unintelligible reality that they call substance’ in which all the qualities of body ‘are said to inhere’.20 Yet he infers that the nature of substance is active, rather than passive. He has at least three reasons to be sure that space is not part of the constitution of substance: space is passive, an affection of being as such, and would remain if God annihilated all substance. By contrast, Locke’s idea of substance is too thin to license assigning different properties, or different functions, to substance and space. We know what substance does, but not the means or manner in which it does it. It is conceivable that space is somehow comprised in its constitution; the idea of substance offers no basis on which to deny this or affirm it. In fact, Locke knew of a theory of what bodies are on which they are partly constituted by space. Essay 4.10.18 opposes the argument that matter is eternal because  Zvi Beiner, ‘De Gravitatione Reconsidered’, Journal of the History of Philosophy, 55 (2017), 583–608 argues that this a priori argument is not the basis of the account of the relation between space and God in the Principia. 19  This is stated already in Draft B: ‘Supposing any thing to exist we cannot conceive it but to be in some place, i.e. at a certain distance from some other things that doe exist.’ (Nidditch & Rogers, 260) 20  McGuire, ‘Existence, Actuality and Necessity, etc.’, 472. 18

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it could not come to exist out of nothing; Locke argues, in part, that this is no more difficult for God than creation of immaterial substances ex nihilo. A passage added in the second edition of the Essay mentions an account of how God could easily create matter, drops the remark that it is radically opposed to established notions and ways of speaking, and says no more about it. Pierre Coste, who translated the Essay into French, traced the remark to a conversation between Locke and Newton. Newton is reported as saying that: One could … in some fashion form an idea of the creation of matter by supposing that God could through his power prevent everything from entering a certain portion of pure space, space being by its nature penetrable, eternal, necessary, infinite; for thereafter that portion of space would possess impenetrability, which is one of the essential qualities of matter. And as pure space is absolutely uniform, we have only to suppose God to have communicated this kind of impenetrability to another similar portion of space, and that would give us some sort of idea of the mobility of matter, another quality which is also utterly essential to it.21

Although this deserves discussion, the gist is plain enough. The suggestion is that bodies are created by God’s preventing certain limited parts of space from penetrating other parts by force of his will, and doing so in different parts of space at different times. Coste complained in effect that God’s preventing a part of space from being penetrated neither alters the penetrability of space nor creates the impenetrability essential to a body.22 Yet the interesting implication of the scenario is that the existence of mutually resisting forces exerted in limited parts of space which change in regular ways is adequate to explain the known behavior of bodies. If so far as we know, it is possible that bodies are constituted by a distribution of forces over space, then so far as Locke can claim to know, space might be comprised in the substance in which solidity, extension, mobility, and so on subsist. Locke defends his omission to answer the question on the ground that the idea of substance we have is nearly useless for theoretical purposes. The argument consists of a series of questions: when the word ‘substance’ is applied to God, finite spirits, and bodies, does it have the same sense? does it stand for the same idea? if so, does its application to the three beings in question imply that they have the ‘common nature of substance’? If so, does it not follow that ‘God, finite spirits, and Body, agreeing in the common nature of Substance, differ not any otherwise than in a bare modification of that Substance; as a Tree and a Pebble, being in the same sense Body, and agreeing in the common nature of Body, differ only in a bare modification of that common matter; which will be a very hard Doctrine’ (Essay 2.13.18)— materialistic, monistic, arguably atheistic. If philosophers think that ‘substance’

 Jonathan Bennett and Peter Remnant, ‘How Matter Might Easily be Made’, www.earlymoderntexts.com/assets/jfb/howmat.pdf, p. 4. Coste included this report in a note to Essay 4.10, 18 in the second edition of his translation of the Essay. Philipp Hamou, who edited the modern edition of this translation, is one of several scholars who note that Newton worked this theory of creation out in De gravitatione. 22  See Bennett and Remnant, ‘How Matter Might at First Be Made’, 7. 21

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signifies three distinct ideas, they should say what they are in an effort to avoid such unwelcome conclusions. In fact, Locke contends, ‘substance’ as ordinarily used, signifies no clear and distinct idea at all. He tells the story of the Indian philosopher who was reduced to saying the world ultimately rests on an unknown something to make the point that European philosophers are no more informative when they say substance is ‘the support of Accidents.’ ‘Of Substance,’ Locke concludes, ‘we have no Idea of what it is, but only a confused obscure one of what it does’ (Essay 2.13.19). This is not the argument to be found in Essay 2.23.2 where the Indian philosopher is also invoked. The present argument takes the idea of substance to be that of the nature of a substance. In connection with substances, qualities, and powers, Locke seldom uses the word ‘nature’; when he does, it is used along with ‘cause,’ ‘constitution,’ and ‘manner of operation’ to specify things we do not know: ‘[we] have no Knowledge [of things] beyond [the few qualities we discover by sense and reflection], much less of the internal Constitution, and the Nature of things’ (Essay 313: 34–35); ‘If we would inquire further into the Nature, Cause, and Manner, we perceive not the Nature of Extension, clearer than we do of Thinking’ (Essay 312: 24–26).23 In the present argument, the question whether ‘substance’ stands for an idea of the ‘common nature of substance’ makes the point that the idea of substance we have, according to Locke, provides no information at all about the nature of substance.24 To assume otherwise in the face of this emptiness, risks licensing the unwelcome conclusion that assimilates the nature of God and that of bodies. This is the crux on which the issue depends. The claim that spatial position is a condition for existence extrinsic to the nature of a substance is the basis on which Gassendi and Newton purport to show that space is neither substance nor accident. The legitimate idea of substance recognized by Locke cannot decide whether space is internal to the nature of substance, on the one hand, or extrinsic to independently constituted substances, on the other. In conclusion, Locke’s skepticism about the nature of substance is the basis of his skepticism about the substantiality of space. Newton’s speculation about the creation of bodies provides a model on which to conceive that space is an element of corporeal substance although Locke takes no advantage of it in the Essay. He  ‘Our [idea] of extension, (which is nothing but the cohesion of solid parts,) [is no] clearer, or more distinct, when we would enquire into the Nature, Cause, or Manner of it, than the Idea of Thinking’ (Essay 311: 10–12). ‘But when the Mind would look beyond those original Ideas [of extension in body and communication of motion by thought in Minds] and penetrate into their Causes, and manner of production, it discovers nothing but its own short-sightedness.’ (Essay 312: 15–26). 24  M. R. Ayers, Locke, II: Ontology, 48, takes the argument to show that the idea of substance we have is ‘obscure’ in Locke’s non-Cartesian sense, i.e. it is associated with several words which we take to be names of different sorts of things among which the idea cannot discriminate. This argument is abroad in Essay 2.13.18, but I would urge that there is a more explicit argument focused on the inability of the idea of substance we have to provide any information about the nature(s) of substances. This is the more particular reason the idea of substance stands in the way of a reasonable answer to the question about the status of space. 23

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relies on the thinness of our idea of substance to rebuff the Cartesians’ attempt to embarrass their opponents, but he never takes seriously the possibility that space might be part of the constitution of corporeal substances. This is because the idea of a body, according to Locke, contains not just the idea of substance but also the idea of the quality, having impenetrable extension. Having opted for the view that infinite space beyond the created world is to be conceived as the omnipresence of God, Locke takes for granted that the penetrable extension that belongs to bodies occupies a part of the penetrable extension that somehow pertains to God.

Chapter 4

Spacious Minds and Spatial Spirits: John Locke on Space and Thought Philippe Hamou

Abstract  Spatial metaphors and spatial discourse about the mind and ideas abound in Locke’s Essay. This raises two related kinds of questions: first, whether and in what sense the mind is “in space”, has a location, and perhaps an extension? And second: how this ‘spatial mind’ is also ‘spacious’, offering room for ideas? What sense of spatiality is involved when Locke says that ideas are “in the mind”, “lodged in the mind”, and how does this inner spatiality of ideas within, relates to the spatiality of things without? In this chap. I argue that Locke’s early relationist view of space, expounded in the manuscript notes of his 1676-8 journals, offers a better framework for understanding how space could be applied in a literal sense to ideas, than the more mitigated view set forth in the Essay itself. Keywords  Space · Spatial relations · Mind · Place · Extension

There are two related kinds of questions that I wish to address in this chapter. The first concerns John Locke’s conception of ‘finite spirits’1 and their relation to space. What exactly does Locke mean when he affirms that the question ‘where’ applies to all finite beings?2 Are spirits, like bodies, somewhere in space? Do they have a ‘place’, in the technical sense of the term? Do they change places, move from one place to another? And do they have, besides a place, an extension? Do they 1  In Locke’s usage, spirits (without qualification) usually refers to finite thinking substances – like human souls, or angels (whether these are considered as united to bodies, or as “pure spirits”). God is sometimes refered to as ‘the Infinite Spirit’. See for example An Essay concerning Human Understanding, P. Nidditch (ed.), Oxford, Oxford University Press 1975, book 2. Chap. 23. §19 (henceforth Essay, followed by the triplet book, chapter, paragraph) The issue of God’s relation to space raises specific problems, which are not the main focus of this paper but about which I shall say a few words in the last part of this paper. 2  See Essay 2.15.8: ‘Where and when are questions belonging to all finite existences’.

P. Hamou (*) Université Paris Nanterre, Institut de Recherches Philosophiques, Paris, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 L. Berchielli (ed.), Empiricist Theories of Space, Studies in History and Philosophy of Science 54, https://doi.org/10.1007/978-3-030-57620-2_4

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substantially occupy some portion of space, coextensive for example with the brain, or with a part of it? Shall we rather confine them to single unextended points? Or shall we understand their presence in space in some other, non-extensional, ways? The second related kind of question is about minds and ideas. Both terms are extensively used in the Essay, and both are left almost undefined. Or rather it may be said that one is defined in terms of the other, and reciprocally. Ideas are precisely what the mind is about when it thinks; whatever their nature, they are just what the mind finds in itself.3 In return the mind can be defined, minimally, as some sort of container for the ideas: whatever its true nature or constitution is, it is where ideas are, and are dealt with – the enclosing circle of our ideas. This co-defining relationship is generally expressed in a local way: ‘ideas are in the mind’, ‘ideas are lodg’d in the mind’, the mind is ‘stored’ or ‘furnished’ with ideas, ideas are ‘conveyed’ or introduced into the mind, they represent things ‘without the mind’. Locke also talks of ‘capacious’ minds or understandings, ‘large’ memories, etc.4 These are metaphors involving spatial relations and spatial properties such as inclusion, interiority and exteriority, size, motion, etc. Of course, spatial metaphors for describing the mind are rather common, and many of them are just ordinary language metaphors. However, they recur significantly in Locke. Usually, Locke is keen on avoiding or criticizing any metaphorical language where one cannot clearly assign the various senses in which the same word is used. For example, Locke famously asks the philosophers who ‘lay so much stress on the sounds of these two syllables, Substance, to consider whether applying it, as they do to the Infinite Incomprehensible God, to finite Spirit and to Body, it be in the same sense’ (2.13.18). It seems that one is also entitled to ask Locke if there is a special sense of spatiality that applies specifically to ideas in the minds, and, in case there is, how this inner spatiality relates to the spatiality of things without. I have said that the two kinds of questions are related, but this obviously requires some justification. It is well known that Locke draws a strict dividing line between two possible kinds of knowledge defining two different sorts of sciences, two distinct provinces in the intellectual world. There is, on the one hand, the knowledge of things as they are in their proper being; and there is, on the other hand, the knowledge of ideas and words, that is of those signs through which the understanding 3  Essay, 1.1.8: “I must here in the entrance beg pardon of my reader for the frequent use of the word idea, which he will find in the following treatise. It being that term which, I think, serves best to stand for whatsoever is the object of the understanding when a man thinks, I have used it to express whatever is meant by phantasm, notion, species, or whatever it is which the mind can be employed about in thinking; and I could not avoid frequently using it. I presume it will be easily granted me, that there are such ideas in men’s minds: every one is conscious of them in himself; and men’s words and actions will satisfy him that they are in others.” 4  The spatial relations are especially compelling in this passage: ‘Nor let anyone think these too narrow bounds for the capacious mind of man to expatiate in, which takes its flight further than the stars, and cannot be confined by the limits of the world; that extends its thoughts often even beyond the utmost expansion of Matter, and makes excursions into that incomprehensible Inane.’ (Essay 2.7.10). cf. also 3.3.2: ‘every bird and beast men saw; every tree and plant that affected the senses, could not find a place in the most capacious understanding’.

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comes to know and contemplate the things outside, and which it uses to make his thoughts known to others. Questions about the spatial existence of spirits clearly pertain to the first sort of science, they belong to physics in the somewhat ‘enlarged sense of the word’, as Locke says in the last chapter of the Essay (4.21.2): spirits are together with bodies, the sorts of things that make up the furniture of the world. The mental space of ideas, on the other hand, seems to belong to the other kind of science that Locke calls logic or semiotic. This science is not grounded in the ‘physical consideration’ of things, but, it is, so to speak, a phenomenological one: it considers objects as they appear to us, or as they are in ideas – or again as they are ‘in the mind’. The disjunction between the two kinds of considerations, and the decision not to ‘meddle with the physical consideration of the mind’ (1.1.2), are very important methodological features of the Essay, and this is why one should not too hastily conflate questions pertaining to one type of science, with questions pertaining to the other. However, it must be said in the first place that the Essay is not entirely devoid of ‘physical considerations.’ Locke sometimes acknowledges that he needs to depart from his methodological restraint, in order to render his own descriptive results more intelligible (the use of the corpuscular hypothesis in the discussion of qualities in 2.8.5 is one salient example). Sometimes the ontological, physical or metaphysical counterparts of Locke’s ideas, are expressed in a more conjectural way, and with some reluctance. But still these excursions, especially the ones concerning the nature and state of souls and spirits, are quite numerous in the text of the Essay, and it is certainly an interesting and rewarding task to gather them together in order to reconstruct the somewhat elusive metaphysical subtext of the Essay. But, and this is my second point, there is also a special reason why the connection between the two sorts of questions is especially important and must be considered: in some very crude sense, the distinction between the two sciences mentioned in Essay 4. 21 is a spatial one. Physics deals with the things without us; logic with whatever is within the mind. This is crude of course, because one could say that these terms are only metaphors. But again we should ask why the spatial metaphor makes sense here, or whether it is a metaphor at all. Here is what I take to be a very significant example in Locke of a non-metaphorical use of the preposition “in”/or “within”. Spirits, intelligent beings, like angels, are generally considered as beings without us; however, there is one exception, a spirit or thinking thing that is not outside but, as Locke repeatedly says, that is ‘within us’.6 The envelope of our own bodies is clearly here the spatial boundary that gives sense to the local preposition “in”. In our own body there is a thinking thing ‘that we consider as ourselves’, and 5  See Essay, 2.8.22: ‘I have in what just goes before been engaged in Physical Enquiries a little further than perhaps I intended. But, it being necessary to make the Nature of Sensation a little understood; and to make the difference between the qualities in bodies, and the ideas produced by them in the Mind, to be distinctly conceived, without which it were impossible to discourse intelligibly of them.’ 6  Cf. Essay 2.27.27: ‘that thinking thing, that is in us, and which we look on as our selves,’ or 4.4.19: ‘that thinking thing within you’.

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there are also thinking things outside, in other human or perhaps non-human bodies, or even, as some think, separated from body, floating somewhere at large. So my general question is: when Locke says that ideas are representations in the mind of things without, shall we say that he points here to an actual spatial boundary to be traced between reality and ideas?

4.1  Spatial Spirits We start with the physical or metaphysical question, concerning spirits or thinking substances. Before raising the specific issue of their spatiality, it might be useful to premise some considerations about what it means for Locke in general to be somewhere or to be in a place. Locke technically defines place as ‘the relation of Distance betwixt any thing, and any two or more Points, which are considered as keeping the same distance one with another, and so considered as at rest’ (2.13.7). It is clear from this definition that there is a conventional element in place allocation. It is a matter of convention and usage which points are considered as at rest. It may be a constellation in the sky, or it may be the four angles of a chess board. So the particular place assigned to a thing depends on the frame of reference that has been picked out. It is to be noted that motion in the Essay is strictly defined in terms of places. It is the process through which something changes place, and so it is strictly relative to the chosen frame of reference. The chess men move in one frame of reference and they do not move in another. This is pure Galilean relativity, and Locke seems content with it, never suggesting that an “absolute” motion is required to understand the relative ones. However, although it is a matter of convention which place a being occupies, having a place or being somewhere does not depend on any convention. It is on the contrary a necessary feature of any existing thing: ‘Where and when are questions belonging to all finite Existences.’ (2.15.8) Place is the answer given to the question where, so I take this assertion to mean that all finite existences (including spirits) have a place, can be said to be “somewhere”. Locality should be considered a universal feature of all finite beings existing in this world. We need a right understanding of this principle to see how it could be applied to spirits. First of all, locality is not universal in the sense of a common essential property that would be shared equally by thinking and non-thinking beings. Place is purely relational, and so it is nothing in the things themselves. Its universality originates in the fact that nothing can come into existence, without entering ipso facto into spatial relations with other things that were already there, and so allowing to be referred to, or designated in relation to them, such as ‘to their left’ or ‘to their right’, ‘above’ or ‘below’… It is worth noting that location is a universal affection of all finite existences, if and only if these existences are considered as beginning in a world or a universe that was already ‘there’, capable of providing potential frames of reference for them. If the universe were annihilated and if there were only one single thing left in the world, it would be impossible to say that this thing is

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“somewhere”. For the same reason, as Locke acknowledges, the universe itself, taken as a whole, has no proper place: For to say that the World is somewhere, means no more, than that it does exist; this though a Phrase, borrowed from Place, signifying only its Existence, not Location; and when one can find out, and frame in his Mind, clearly and distinctly, the Place of the Universe, he will be able to tell us whether it moves or stands still in the undistinguishable Inane of infinite Space. (Essay 2.13.10)

This text is important for two reasons. For one thing it shows that there is an ambiguity in the phrase ‘being somewhere’, meaning either existence or location. In the strict sense, ‘being somewhere’ means to coexist with other existing and perceptible beings. But there is also a loose sense of the term according to which being somewhere means simply ‘to exist’, with or without coexistent beings. The second important thing in this text concerns motion. As far as we human beings can judge, something that exists utterly unrelated, such as the universe in the undistinguishable inane of infinite space, cannot be said to move or be at rest. Without external arbitrary points of reference, motion and rest are indistinguishable in the bodies as such. Conversely, wherever something appears to us as endowed with mobility, we are entitled to say that this thing is spatially related to the physical world, it has a place in it. We are now in a better position to answer the initial question: in what sense shall we say that spirits exist somewhere? My contention is that the where of spirit must not be understood simply in the general sense of existence, but in the precise and determined sense of locality: for Locke, spirits belong to the sensible universe of bodies, they are related to bodies through spatial relations. The main reason adduced for that is precisely mobility: even though we do not “see” spirits in the world, we know with certainty that mobility pertains to our idea of spirit. The central textual evidence is found in 2.23.18, where Locke considers successively the ideas that belong specifically to bodies (namely, cohesion of solid parts, and power to communicate motion by impulse), the ideas that belong specifically to spirits (thinking and will), and finally the ideas that are common to both, where he lists existence, duration and mobility. There are a couple of other texts in the Essay where Locke offers a somewhat similar partition, but usually the general ideas that are said to belong to both bodies and minds are listed as ‘number, existence, and duration’.7 In the passage we are considering Locke departs from this list and, forgetting number, considers ‘mobility’, as one of the three general common ideas. I do not think that Locke is inconsistent. In II, 23 Locke looks for the ideas we have of bodies and souls as substances, whereas elsewhere he considers the various sources of our ideas, and this explains the discrepancy. Mobility, however applicable to spirits as well as bodies, is nevertheless an idea that is only perceived in bodies. It is 7  See Essay 2.21.75: ‘Extension, Solidity, Mobility, or the power of being moved; which by our senses we receive from body. Perceptivity, or the power of perception, or thinking; Motivity, or the power of moving: which by reflection we receive from our minds. (…) To which if we add Existence, Duration, Number, which belong both to the one and the other, we have, perhaps, all the original ideas on which the rest depend.’

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an idea of sensation, and spirits do not offer themselves directly to external senses as mobile things. So it is not through direct perception, but by way of inference that mobility is said in this chapter to apply to spirits or thinking things as well as to bodies. Locke presents such inference in the following way (Essay 2.23.19): having no other idea of motion, but change of distance with other beings that are considered as at rest; and finding that spirits, as well as bodies, cannot operate but where they are; and that spirits do operate at several times in several places, I cannot but attribute change of place to all finite spirits: (for of the Infinite Spirit I speak not here). For my soul, being a real being as well as my body, is certainly as capable of changing distance with any other body, or being, as body itself; and so is capable of motion. And if a mathematician can consider a certain distance, or a change of that distance between two points, one may certainly conceive a distance, and a change of distance, between two spirits; and so conceive their motion, their approach or removal, one from another.

The thrust of the argument is that spirits change place because they can operate in several successive times in several successive places. The assumption on which such an argument is built is what we may call a presentist principle, a principle which, as Thomas Lennon has shown, dominates seventeenth-century conceptions of causality.8 There is no action at a distance: a cause must be physically present to its effect, intimately united to the place where it exerts its effects. This should be true for bodies (where the principle allows ruling out any action that is not mechanical, reducible to impulse), but Locke, together with many authors of his time (including Malebranche and Cureau de la Chambre), extends the validity of the principle to spirits: spirits, as well as bodies, cannot operate but where they are. So if spirits can act in different places at different times, the presentist principle imposes the conclusion that they actually are in those different places at different times. Locke adds to this a puzzling side argument, taken from mathematics: if the mathematician can consider a change of distance between two points, motion and place of spirits should be even more conceivable. The argument is a bit strange because it comes after the contention that it is precisely on account of their reality as beings, that spirits possess locality and motion. But mathematical points are not real beings. So it seems that the passage offers a rather unconvincing a fortiori argument. But it is possible that Locke has something else in mind: he may want to discard the possible objection that spirits could not have any place or motion, because of their supposed immateriality, the fact that they are neither solid nor extended. Mathematical points are unextended and unsolid as well, but these negative properties do not preclude the attribution of place and motion to them. I shall have more to say later about the question of the extension of spirits, but I want now to return to the main argument on place and motion that we find in chap. 23. How do we know that finite spirits do actually act in successive places? If we think about angels, this is only a matter of conjecture and perhaps biblical testimony. But besides angels, our own soul gives us a sensible example of the operation of spirits or thinking things: that is, we find, not through conjecture but by direct

 Cf. T. Lennon, The Battle of the Gods and Giants, 1993, p. 251-273.

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perception, that there is something in us that thinks from inside the body; moves the body and is moved by it. Every one finds in himself that his soul can think, will, and operate on his body in the place where that is, but cannot operate on a body, or in a place, an hundred miles distant from it. Nobody can imagine that his soul can think or move a body at Oxford whilst it is at London; and cannot but know that being united to his body it constantly changes place all the whole journey between Oxford and London; as the coach or horse does that carries him, and I think may be said to be truly all that while in motion: or if that will not be allowed to afford us a clear idea enough of its motion, its being separated from the body in death, I think, will; for to consider it as going out of the body, or leaving it, and yet to have no idea of its motion, seems to me impossible. (Essay, 2.23.20)

When Locke says that everyone “finds [this] in himself”, I take it to mean: it is something that one cannot fail to conclude to on the basis of introspective data. Here is a tentative list of such introspective data: 1/ our thought, at least when it is directed towards what we perceive (as it is most of the time), is locally constrained. That is, the content of our perceptive field, and consequently the content of our thoughts, change constantly when we (our body) change place. 2/ In visual perception (without the help of a mirror), we do not have a full view of our own body, the mental image we get makes clear that we perceive from the inside of the bodily envelope, that the seat of visual sensation is located within the body. 3/ Our thought is able to move our body directly or whatever is in immediate contact with it; but unable to move anything that is separated from it by some ‘space’. From such considerations and others of the same sort, one may conclude that the soul is indeed located inside the body, which is the seat of its operations, and also that it follows it in all its movements. Its place is “inside” the body, in the literal sense, and its relative movement should be appreciated accordingly. In relation to the bodily envelope, the soul is, as far as we know, at rest;9 and in relation to other bodies that one may consider as at rest in the outside world, the soul shares every motion of its own body. We already hinted at the fact that Locke very often presents his own version of the cogito in that local way: he is not saying I think, but rather there is something within me that thinks, there is a thinking thing in me.10 I take these striking turns of language to be connected with how Locke understands the identity of the self. It is important to say a few words on this difficult topic, because it helps understand in which sense for something to exist is always to exist locally, in spatial connection with bodies. One finds in Locke a spatio-temporal definition of identity, which holds for all kinds of beings. Two temporal occurrences of a finite being are said to be occurrences of the same identical being when they both belong to the same continuous and incommunicable spatial trajectory, which can be traced backward to the first beginning of the said being.11 This definition in my view is a very general one, 9  At least until death, when the soul is, supposedly, ‘leaving’ the body. See the slightly sarcastic ending of the preceding quote in 2.23.20. 10  See supra note 6. 11  See 2.27.2-3.

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and the idea that identity through time requires a continuous spatio-temporal trajectory holds as well for what I call myself, the person I am. However, as is well known, what makes a person the same person in different times is ‘consciousness’ alone (2.27.9), and, as the same consciousness (the same train of conscious thoughts12) can conceivably be annexed to various successive corporeal or spiritual substances, persistence in time of the same self is not necessarily related to the persistence in time of the same body or persistence in time of the same spirit. However this does not mean that Locke holds that I am not identical with my soul and body at each time I consider them to be mine. Locke’s point,13 quite the contrary, is rather to say that I am precisely whatever, at this present time, my consciousness appropriates to myself: that is my present body in so far as I am aware of it, my present thoughts, including my memories, my feelings. So it makes sense to say that my body is, at the time I consider it as mine, part of myself, and this explains why Locke does not say, as Descartes would, that I am the thinking principle inside my body, but rather says that I am the body within which a thinking principle (which is also ‘me’) resides. All along my temporal existence, all the parts that constitute my present body are perpetually renewed and changed, but this does not mean that one single train of conscious thoughts, cannot be successively instantiated in a fleeting succession of animated bodies. In any case, to follow the self in its existential history is to follow the local and continuous trajectory of something that is, at each time of its existence, bodily instantiated, and so necessarily, locally situated. To sum up, Locke is clearly attached to a literal understanding of the locality of the finite spirits and of the mental events (the conscious thoughts) inherent to them. Spirits and their thoughts exist in space and time. Whether they are or not intimately united to one special body through causal relations, they are at least connected to the universe of bodies through spatial relations, and their identity through time should be defined as one continuous spatial trajectory inside this universe. This literal understanding is of course, and Locke is perfectly aware of that, a rather unorthodox conception of what the tradition used to call the “ubietas” of spirits. Leibniz in the Nouveaux Essais gives us a useful reminder of the three scholastic senses of “ubiety or ways of being somewhere”:14 THÉOPHILE. The Scholastics have three sorts of ubiety, or ways of being somewhere. The first is called circumscriptive. It is attributed to bodies in space which are in it point for point, so that measuring them depends upon being able to specify points in the located thing corresponding to points in space. The second is the definitive. In this case, one can ‘define’ i.e. determine – that the located thing lies within a given space without being able to specify exact points or places which it occupies exclusively. That is how some people have thought that the soul is in the body, because they have not thought it possible to specify an exact  More on this way of construing the identity of a person through the same ‘continued consciousness’ in my ‘Mémoire et Conscience continuée, une lecture de Locke sur l’identité personnelle’ (2014). 13  This is made quite clear in Essay 2.27.10: ‘Thus the Limbs of his Body is to every one a part of himself. (…) Thus we see the Substance, whereof personal self consisted at one time, may be varied at another, without the change of personal Identity.’ 14  Leibniz, Nouveaux Essais sur l’entendement humain, 2.27, English transl. p. 221. 12

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point such that the soul or something pertaining to it is there and at no other point. Many competent people still take that view. (It is true that M. Descartes sought to impose narrower limits on the soul by locating it specially in the pineal gland; but since he did not venture to say that it is restricted to some one point in that gland, he achieved nothing, and it would have made no difference if he had given the soul the run of its whole bodily prison.) What should be said about angels is, I believe, about the same as what is said about souls. The great Thomas Aquinas believed that an angel can be in a place only through its operations [upon what is there], which on my theory is not immediate and are just a matter of the pre-established harmony. The third kind of ubiety is the repletive. God is said to have it, because he fills the entire universe in a more perfect way than minds fill bodies, for he operates immediately on all created things, continually producing them, whereas finite minds cannot immediately influence or operate upon them. I am not convinced that this scholastic doctrine deserves the mockery which you seem to be trying to bring down on it. However, one can always attribute a sort of motion to the soul, if only by reference to the body with which it is united or by reference to the sort of perceptions it has.

As Leibniz suggests, the orthodox conception of the ubiety of spirits can be traced back to Aquinas. In his conception, to be in a place is equivocal and does not mean the same for corporeal beings and for incorporeal ones, such as spirits. To be in a place for an angel means to be there through its action, but not to be there ‘substantially’, through the contact of some ‘dimensive’ quantity, an angel having no quantity of that sort. The soul itself, however substantially united to the living body, should not be considered as spatially included in it: it is a container (the very form of the body) rather than a content15. Descartes, as one can see in his letters to Henry More16, shares this conception to a certain extent, but he applies what Aquinas says of angels to the human soul itself. Its presence and union to the body, however narrow and intimate, is not local presence, but a metaphorical way to express an intimate relation of power. In 2.23.21 Locke declares this “equivocity” of ubietas properly unintelligible: If it be said by any one that it cannot change place, because it hath none, for the spirits are not in loco, but ubi; I suppose that way of talking will not now be of much weight to many, in an age that is not much disposed to admire, or suffer themselves to be deceived by such unintelligible ways of speaking. But if any one thinks there is any sense in that distinction, and that it is applicable to our present purpose, I desire him to put it into intelligible English;  Cf. Summa Theologica, Part. 1, Questio 52, art1: ‘I answer that, It is befitting an angel to be in a place; yet an angel and a body are said to be in a place in quite a different sense. A body is said to be in a place in such a way that it is applied to such place according to the contact of dimensive quantity; but there is no such quantity in the angels, for theirs is a virtual one. Consequently an angel is said to be in a corporeal place by application of the angelic power in any manner whatever to any place. Accordingly there is no need for saying that an angel can be deemed commensurate with a place, or that he occupies a space in the continuous; for this is proper to a located body which is endowed with dimensive quantity. In similar fashion it is not necessary on this account for the angel to be contained by a place; because an incorporeal substance virtually contains the thing with which it comes into contact, an d is not contained by it: for the soul is in the body as containing it, not as contained by it. In the same way an angel is said to be in a place which is corporeal, not as the thing contained, but as somehow containing it.’ 16  “… the mind cannot be extended at one time or shrunk at another time according to place in the way of a substance, but only in regard to power, which it can apply to greater or smaller bodies.” April 151,649 (AT, 5, 347/ CSM III 375). 15

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and then from thence draw a reason to show that immaterial spirits are not capable of motion. Indeed motion cannot be attributed to God; not because he is an immaterial, but because he is an infinite spirit.

Although he dismisses here the scholastic concept of ubietas with mere sarcasm, Locke has a solid ground for rejection: such concept is simply incompatible with the already stated principle of the necessary co-presence of cause and effect. If spirit really operates on matter, as Aquinas and Descartes (but not Leibniz) allow, then spirit must be present to matter in a literal sense. Malebranche shared with Locke, against the Thomistic tradition of ubietas, the same requisite of causal co-presence. To be acted upon and to act require being united to its object. But Malebranche considers that soul and body, having no proportion one to the other, the one being simple and unextended and the other composed and extended, cannot really interact. So, in Malebranche, it is the presentist postulation that imposes the seemingly aberrant doctrine of vision in God: bodies are not seen in the physical space where they are, neither are they seen in the cerebral space where their images are conveyed, but they are seen through their ideas in the spiritual space of intelligible extension, to which the human souls are united17. One strange sequel of this doctrine is the definition of God as a second sort of space: God is the place of the souls, just as space is the place of bodies. Locke, in his Examination of Malebranche does not spare his irony:18 But when this simile is applied to God and spirits, it makes this saying, that “God is the place of spirits,” either to be merely metaphorical, and so signifies literally nothing, or else being literal, makes us conceive that spirits move up and down, and have their distances and intervals in God, as bodies have in space. When I am told in which of these senses he is to be understood, I shall be able to see how far it helps us to understand the nature of ideas.

This rather incongruous representation of swimming spirits in Godly space is of course a tacit denunciation of that equivocation of words of which Malebranche is no less guilty than his scholastic predecessors. There is only one sense in which something can be said to be in a place, and there is only one sense in which space can be said to be the place of things. On Locke’s view, Malebranche’s absurdities are the effect of not acknowledging that the union of body and soul, however incomprehensible, is factually undeniable, and so must be the true locus of their interaction: … what it is for two souls or spirits to be intimately united; for intimate union being an idea taken from bodies when the parts of one get within the surface of the other, and touch their

 See for example, Malebranche La Recherche de la Vérité, III, 2, 1, English translation, p. 217: ‘I think everyone agrees that we do not perceive objects external to us by themselves. We see the sun, the stars, and an infinity of objects external to us; and it is not likely that the soul should leave the body to stroll about the heavens, as it were, in order to behold all these objects. Thus, it does not see them by themselves, and our mind’s immediate object when it sees the sun, for example, is not the sun, but something that is intimately joined to our soul, and this is what I call an idea. Thus, by the word idea, I mean here nothing other than the immediate object, or the object closest to the mind, when it perceives something, i. e., that which affects and modifies the mind with the perception it has of an object.’ 18  Examination of Malebranche (1706), §25. 17

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inward parts; what is the idea of intimate union, I must have, between two beings that have neither of them any extension or surface? … The reason that he gives why “material things cannot be united to our souls after a manner” that is necessary to the soul’s perceiving them, is this, viz. That, “material things being extended, and the soul not, there is no proportion between them.” This, if it shows any thing, shows only that a soul and a body cannot be united, because one has surface to be united by, and the other none. But it shows not why soul, united to a body as ours is, cannot, by that body, have the idea of a triangle excited in it, as well as by being united to God, (between whom and the soul there is as little proportion, as between any creature immaterial or material, and the soul,) see in God the idea of a triangle that is in him, since we cannot conceive a triangle, whether seen in matter, or in God, to be without extension.

An important question is still in order: if spirits do have a place in space, shall we say that they have ipso facto an extension? Or shall we concentrate them and their causal powers in simple “mathematical points” as the comparison of 2.23.19 seems to suggest? The Essay is officially agnostic on this question but Locke admits nevertheless that it seems almost impossible to conceive the existence of any real being without extension:19 2.15.11: “Whether angels and spirits have any analogy to this, in respect to expansion, is beyond my comprehension : and perhaps for us, who have understandings and comprehensions suited to our own preservation, and the ends of our own being, but not to the reality and extent of all other beings, it is near as hard to conceive any existence, or to have an idea of any real being, with a perfect negation of all manner of expansion, as it is to have the idea of any real existence with a perfect negation of all manner of duration. And therefore, what spirits have to do with space, or how they communicate in it, we know not

Of course, as Locke often says, inconceivability is not a right measure of what can or cannot be. And it should be noted that even in the famous conjecture of thinking matter, Locke does not draw his argument for the possibility of an extended and solid thing endowed with thought  from considerations taken from existence  and extension, but rather from the consideration of God’s incomprehensible power, and the fact that our understanding is not a good measure of what God can or cannot do. In any case, one should note that the question of the extension of spirits is distinct from the question of whether the soul is material, because for Locke the main feature of materiality is solidity rather than extension. So, even when Locke describes spirits as ‘immaterial beings’ (in agreement with the ordinary metaphysical opinions of his time) such phrasing does not preclude the possibility that spirits were unsolid extended beings. It seems clear from the preceding quote that, although agnosticism is required at the level of knowledge and certainty, Locke is nevertheless inclined to judge it  It’s obvious that Locke had serious thoughts on the questions, as can be seen in several manuscript notes, where he tries to weight the probability of the human soul being immaterial or material. See Locke’s writing on religion, p. 31 sq. (MS Adv theol. 94). ‘We can conceive noe movable substance without extension, for what is not extended is no where. i e is not JL From this & the opposite we must conclude there is something in the nature of Spirits or thinking beings which we cannot conceive JL.’ Again, in MS c. 28 fol. 115r: ‘Anima. A thing that hath noe extension we cannot conceive to exist or have any being. And an extended solid being we cannot conceive to have life i.e. motivitie and perception. And yet we know and must grant there are thinking beings.’

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probable that spirits, just like any other real existences, are extended beings. One ground for judging this probable is the very fact of causal interaction between minds and bodies. If the soul is able to act on bodies and be acted on by them, it seems, according to the ‘presentist’ postulation, that it has to be at their contact, or even permeates them, be coextensive to some special space of the brain where this causal interaction takes place. In my view however, Locke’s inclination towards the idea of an extended mind was not only motivated by such causal considerations. It may have had also a more direct justification, drawn from the reflective investigation on our ideas: whatever the ideas are, it seems indeed that we literally need space to lodge them in our minds. This leads to my second part.

4.2  Spacious Minds This part, I should say from the start, is more speculative. It raises issues about which textual evidence is harder to obtain, or deal with. As I stated in the introduction there are numerous spatial metaphors that Locke makes use of when he considers the relation of the minds to their ideas. My question is how literally such metaphors are to be understood? Reflection is not sensation. Through sensation we see bodies in the external, physical space, but what does it mean to say that through reflection we see ideas in an internal mental space? This is a legitimate question to ask of Locke, because as we just saw in his response to Malebranche, or to the scholastic conceptions of ubietas, Locke considers that the use of spatial metaphors should be regulated in the strictest way. To start answering the question, we need to consider why for Locke ideas should in the first place be said to be in the mind. The spatial vocabulary in connection to ideas and minds recurs significantly in the ten or twelve first chapters of book II, where Locke is concerned with proving that the true and unique origin of our ideas is sensory experience. Simple ideas are not created by the mind, nor found originally in it as ‘native uniform impressions’. They are received through the inlets of the senses. They have been ‘conveyed’ into the mind, projected into the ‘camera obscura’ of our Understandings (2.11.17). Whatever is in our thoughts, whatever the mind is about when it thinks, has first come into it from outside. Even the ideas of our own faculties that we get from reflection could not have been obtained, if some impression of the sense was not firstly conveyed into our heads, stirring our mental operations and making them known to us. So one can say that Locke’s insistence on the interiority of ideas is firstly connected with his empiricism, the doctrine that simple ideas, the material of all our ideas and knowledge, were not originally into our minds, but have been introduced there. Let us consider three basic tenets on Locke’s ideas: the minimal definition of ideas says that it is ‘that term which … serves best to stand for whatsoever is the object of the understanding when a man thinks, … or whatever it is which the mind can be employed about in thinking’ (1.1.8). The second important thesis about ideas is, as we just saw, the intromissive thesis: ideas are no innate material, they came

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into our minds through the canal of the senses. And the third one is the thesis that ideas are essentially conscious items. From these three features, one may gather the following picture of Lockean ideas20: ideas, or at least sensory ideas, which are the material out of which all other ideas are made, are effects produced in us by the affections of the external objects on our senses; these effects are not precisely these affections or bodily modifications, but rather these affections in so far as they are the object of an act of awareness, or in so far as we are conscious of them. So when Locke says that ideas are in the mind, whereas the thing they represent are not, it seems clear to me that he means quite literally that there is something inside our brain, some event or bodily modification of which we are aware. It is a minimal ontological commitment, but one Locke cannot dispense with, even though he says that for the sake of his enquiry on knowledge, he does not need to know what sort of internal and material event it is of which we are conscious. We may consider that this ontological commitment is another important consequence of the presentist principle already mentioned: consciousness, this power of thinking substances, mysterious as it is, does not apply magically at a distance, in a place where the thinking substance is not present. We are not directly conscious of trees or fields in the outside world, but we are conscious of something, whatever it is, that happens in our brain when we see the trees or smell the fields. This may be called indirect realism or representationalism. And I take it (pace Yolton21) that Locke had no qualms in accepting it. Locke was not original in considering that we see all things not directly in the world, not anymore in God, but in the inner material surfaces of our brain. It was in fact a common conception among his British contemporaries. Newton is clearly committed to it in his Cambridge notebooks,22 and Robert Hooke offers also a striking example. In a Hypothesis framed for explaining memory and thought – published in the Philosophical transactions, in the 1680, and reprinted in Hooke’s posthumous Lectures of light – he goes quite a long way towards what we may call the spatialization of the mental. The organ of memory, Hooke describes as some sort

 See on these issues my recent book, Dans la chambre obscure de l’esprit (2018).  John Yolton (in various publications including his Perceptual Acquaintance from Descartes to Reid, 1984) insisted that Locke was, against appearance of the contrary, a defender of direct realism. In his view Lockean ideas are not mental items, existing somewhere in the mind, but either the very act of perception, or, on the objective side, the external things themselves as they appear, or look to us. For criticisms of Yolton’s construal of Lockean ideas, see M. Ayers, Locke, Ontology and Epistemology, Routledge, 1990; P. Dlugos “Yolton and Rorty on the Veil of Ideas in Locke”, 1996; G. Yaffe, “Locke on ideas of substance and the veil of perception” (2004). 22  See Newton (c. 1665), Certain Philosophical Questions, p. 450-2. Newton is quite explicit there: what we see is what is ‘delineated in the brain.’ He goes so far as explaining why these objects then are not judged to be in the brain: ‘Resp: Because the image of the braine is not painted there, nor is the Braine perceived by the soule it not being in motion, & probably the soule perceives noe bodys but by the helpe of their motion. But were the Braine perceived together with those images in it wee should thinke wee saw a body like the braine encompasing & comprehending our selves the starrs & all other visible objects. &c.’ On Newton’s seemingly ‘naïve’ representationalism, see my ‘Vision, color and method in Newton’s Opticks’, 2014. 20 21

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of “repository”, in the center of which the soul operates and “senses” its ideas, just as the sun in the “great world” acts and is acted upon, through its rays of light. Ideas are construed as tiny material objects that the soul lodges in this repository in successive orbs. In order to give place to new ideas these orbs are expanding  with time and removed further and further from the center, towards the periphery of the repository. In this way, the soul is able to sense not only the idea it focuses on, but also the various spatial relations that it holds with other ideas, and also its distance from the center of the repository, evaluating by this means how ancient the idea is23. In a fascinating page, Hooke tries to calculate the number of ideas that may enter a man’s mind in the course of an ordinary life, some hundreds of millions in his reckoning, and he explains that we should not fear that the brain were too narrow for lodging so many distinct ideas – alleging the recent discovery of microscopic animalcules, that shows almost the same number of perfectly formed creatures, in a much shorter space. I do not say that Locke would have subscribed fully to such a model of the mind, but I guess that it is exactly the kind of ‘curious’ and ‘entertaining’ (1.1.2) considerations that he would have agreed to consider as possible physical explanations of the mental phenomena that he, for his part, was describing, through the plain historical method. Besides representationalism, a second order of considerations concerns what I would call the spatial structure of the Lockean perceptual consciousness. It is tempting to consider consciousness as a simple, undivided act. But for Locke what happens in our minds when, for example, we see, is not simple and undivided. What we see is from the start spatially displayed in our consciousness, which is able to capture simultaneously a plurality of coexisting elements, just as the sensory impression itself to which our act of consciousness is correlated, is displayed on a certain surface, for example of the brain, or the eye. Thus, Ideas received from visual sensation are like ‘plain(s) variously colored’ (2.9.8); ‘Pictures of things’ or ‘mental Draughts’ (2.29.8). The faculty of discerning ideas, or distinguishing them one from the other, without which our mind ‘would be capable of very little Knowledge’ (2.11.1) requires the mental ability to set into one picture several representations

 “‘… But supposing he could by recollecting remember 100 millions, and consequently must have as many distinct ideas, I see no reason why all these may not actually be contained within the sphere of the activity of the soul acting in the center. For if we consider in how small a bulk of body there may be as many distinct living Creatures as here are supposed ideas, and every of these Creatures perfectly formed …, we shall no need to fear any impossibility to find out room in the brain where this sphere may be placed… But to return to the Description of this Organ. I do suppose that what we call attention is nothing else but the action of the Soul in forming certain ideas, which for the present I will call little images, which bear the stamp, seal or mould according to which the soul formed it in the Center of the Repository. So that the greater the number of ideas are that have succeeded anyone formation, the greater is the space of time of which we have sense: and the ideas become further and further removed from the center and more and more new form’d ideas interpose themselves between the center and the said ideas placed in orbs at a greater distance, by the intrusion of fresh ideas between the center and them”’ (Lectures of Light, in Posthumous Works, p. 143-4).

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one beside the other and capture them in one view. Similarly, intuitive knowledge require that several  ideas are brought together, juxtaposed and compared in one single act of perception (4.2.2). Perhaps the most explicit text on this spatial structure of Lockean ideas is a passage in the Examination of Malebranche where Locke examines and criticizes an argument that Malebranche has brought against the scholastic theory of species. Malebranche says that it is impossible that vision could take place in us in virtue of an intromission of the similitude of external things into our eyes, because it would amount to the impossible task of packing the whole visible hemisphere into one single point, the point towards which converge the rays transmitting the species into the eye. Locke, who defends against Malebranche a kind of modern version of species intromission (updated with corpuscular physics and modern optics) where species are replaced by physical pictures painted in the sense organs or in the brain), denounces this argument, saying that, as Malebranche in fact very well knows, vision does not take place in one single point but on the illuminated area of the retina whose little surface is room enough for hosting the distinct image of a whole visible hemisphere24. As to what is said, that from one point we can see a great number of objects, that is no objection against the species, or visible appearances of bodies, being brought into the eye by the rays of light; for the bottom of the eye or retina, which, in regard of these rays, is the place of vision, is far from being a point. Nor is it true, that though the eye be in any one place; yet that the sight is performed in one point, i. e. that the rays that bring those visible species do all meet at a point; for they cause their distinct sensations by striking on distinct parts of the retina, as is plain in optics: and the figure they paint there must be of some considerable bigness, since it takes up on the retina an area whose diameter is at least thirty seconds of a circle, whereof the circumference is in the retina, and the centre somewhere in the crystalline; as a little skill in optics will manifest to any one that considers, that few eyes can perceive an object less than thirty minutes of a circle, whereof the eye is the center.

Then Locke mentions the famous experiment of Mariotte25, disclosing the existence of a blind spot in the middle of the retina, at the root of the optical nerve: And he that will but reflect on that seeming odd experiment of seeing only the two outward ones of three bits of paper stuck up against a wall, at about half a foot, or a foot one from another, without seeing the middle one at all, whilst his eye remains fixed in the same posture, must confess that vision is not made in a point, when it is plain, that looking with one eye there is always one part between the extremes of the area that we see, which is not seen at the same time that we perceive the extremes of it.

What we have here is a very interesting philosophical use of an experimental data: Locke is not interested in the anatomical interpretation of the experiment. Rather, what he finds here is direct proof that visual awareness of space is not constructed out of successive punctiform visual impressions, but is from the start spatialized, coextensive with a corporeal space (at least a bidimensional space) which

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 An examination of Malebranche § 9.  See Mariotte, Nouvelle découverte touchant la vue, 1668.

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communicates to our mental awareness its spatial structures, even including its holes or blind spots. The main and difficult question is still ahead: how literally spatial is the mental space of ideas? I think that one of the main obstacles that hinder the application of spatiality to mental representations or mental events such as ideas, is the fact that we tend to have a Cartesian-like idea of space, as some substantial stretch of transparency that fills the gaps between opaque bodies. We tend to see space as a physical thing rather than a pure relation of coexistence, and this is why the application of our idea of space to mental objects or mental operations seems so crudely materialistic, and its ascription to Locke perhaps quite implausible. In what follows, I would like to argue that a pure relationist view of space is much more hospitable to spacious minds and spatial ideas, and that this relationist view was indeed held by Locke, and in the most straightforward way, as in the manuscript’s notes of his 1676-8 Journals, before being somewhat blurred or play-downed in the chapters of the Essay devoted to our ideas of space (2.13 and 2.15), where Locke seems to allow for a more realist position. According to the notes of the Journals, there is a precise and distinct notion of space, and it is the notion that we have when we consider the distance between two existing things, or between parts of the same thing. This is the relational space that we measure and into which we assign places. But there is also a confused and vague notion of space, when we try to capture the being of what is just in between the relata, or when we try to represent to ourselves what would be left if all things actually ‘in space’ were annihilated. Space understood in this abstract and general manner is properly nothing: the pure darkness of nothingness – Space or extension (…) are only affections of real existences (…) if the world were annihilated one had no more reason to think space anything, then the darkeness that will certainly be in it”.26

This general notion of space is, as Descartes would say, a materially false idea, an idea that represents what is not as being something. What is actually imagined in ‘space’ understood that way is not some substantial extension, or body, nor even a being suo modo, but nothing but the bare possibility of existence or, as Locke says, the mere ‘existibility of body.’ Space is just noething, and signifies noe more but a bare possibility that a body may exist where now there is none.27 Space in its confusd and genrall sense signifies noething but the existibility of body, when we have a more distinct and precise notion of it and make it the same with distance it is noe thing but the relation of two reall beings and supposes them actually to exist.28

 Journal Ms. 1676, in Aaron and Gibb ed., An Early draft of Locke’s Essay, together with extracts from his Journals, p. 77. 27  Ibid. p. 96 28  Ibid. p. 105 26

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So, according to Locke’s strict relationist view in these notes, without bodies, or real beings, space is nothing. It has no parts, no bulk, no measure. We tend to believe that pure space has indeed such properties, quite independently of bodies, but in fact this is only an effect of imagination: these properties are surreptitiously imported from the image that we have of bodily extension, an image that only sensation can give, and that we unconsciously superimpose over our idea of space. Although Descartes himself would have agreed that space without body is a pure abstraction29, the view that space in itself, space without bodies, has no properties at all is strongly anti-­ Cartesian.30 For Descartes, what Locke will call ‘pure space’ (space without bodies) does not really exist because extension is the very essence of material beings: so, whatever is extended, is ipso facto material. Space cannot be without body. Locke’s point is very different. He holds that spatiality belongs to bodies just as “paternity”31 belongs to men. It’s a feature that may be shared universally by all bodies whatsoever, but it is no intrinsic property, it marks only the aptitude of certain kind of beings to enter a certain kind of relation that is proper to them. As we said, the relationist view seems, in the Essay, somewhat down-played. It still surfaces in the treatment of place (where Locke re-uses a number of arguments from the Journals); but as for space itself, Locke seems less prone to consider it as ‘just nothing’. It is worth remarking that Locke’s main target in the chap. 2.13 is still precisely the Cartesian-like idea of space, the conceit that space and body are one and the same thing. The chapter as a whole however is a bit perplexing because Locke seems to follow two distinct and partially incompatible strategies in his attack on Descartes. On the one hand, he still has in mind his former treatment of space as a pure relation, which offers a straightforward argument against the Cartesian substantiation of all extensions; but on the other hand he insists that we do have an idea of space or extension distinct from our idea of body, and that this idea has a real content. It may look like Locke is now allowing that pure space, space existing without matter, is something real  – although perhaps something that is neither substance nor accident. The hesitation between the two views of space is explicit in this passage from 2.13.26: But whether any one will take space to be only a relation resulting from the existence of other beings at a distance ; or whether they will think the words of the most knowing King Solomon, « The heaven, and the heaven of heavens, cannot contain thee » ; or those more emphatical ones of the inspired philosopher St. Paul, « In him we live, move, and have our being, » are to be understood in a literal sense, I leave every one to consider.

It should be noted that the line of argument according to which ‘space’ could exist without matter because we do have distinct ideas of space and matter, is still very general. It could accommodate the Gassendist view of pure space as a being suo  See Principia Philosophiae II, 10 sq. [CSM, I, 227].  The view that space is something that falls under the description of mathematics, and consequently has properties, is instrumental in the Cartesian demonstration that space or extension is a real being. As Descartes says, ‘it is important to consider that nonbeing can have no true attribute’, Descartes, Letter (for Arnauld) July 291,648 [CSM, III, 348]. See also Principia Philosophiae, II, 16. 31  Cf. Journal Ms. Relation 1678, Early Draft, p. 99-103. 29 30

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modo, uncreated, distinct from bodies and distinct from God. It could also fit the views of Henry More, according to whom pure space is the very immensity of God Himself, that is an attribute of the divine immaterial substance. Locke however never committed himself to such explicit formulations. As we just saw, he seemed content to quote St. Paul, or Solomon, leaving his reader to decide how literally he should take their words (2.13.26), and whether it is not probable that God’s infinite Being ‘fills Immensity’ just as well as it ‘fills Eternity’ (2.15.3). These latter formulations may suggest, in a Gassendist guise, that pure space is, rather than God’s Immensity itself, an uncreated receptacle for his omnipresence. But one may also think that the formula indicates only that Locke does not want to commit himself to the idea that space is an attribute of God’s essence. An alternative view may be that space, infinite pure space, is related to and contingent on God’s existence, resulting from the simple fact that He is here, there and everywhere. God would ‘fill immensity’ not as the content of an infinite container, but rather because one cannot posit or imagine a place where God is not.32 This last interpretation could help to dispel, or attenuate the contradiction between the two views of space. If relational space is conceived as relative and consequential to the existence of beings, pure infinite space may also be conceived as consequential to the existence of one infinite and eternal being. Infinite space would be an affection or resulting effect of God’s existence. His identity in space and time, the fact that He is present simultaneously in every place, and successively in every time would be, if one may say so, the prime relation, out of which the possibility of existence (or ‘existibility’) of everything else would result. This, of course, is quite speculative, and Locke, who is content in displaying his many arguments against Descartes’s identification of space and body, does not seem to have been interested in giving a clear account of the metaphysical frame that would make these arguments mutually consistent. In any case, and whatever Locke’s final thoughts on the topic of space are, my contention is that the relationist/nihilist view of pure space was best fitted to account for the spatiality of ideas, or to understand in which specific sense the mind is literally spatial. Two beings of the same kind, says Locke in his chapter on identity, cannot exist in the same place at the same time (2.27.3). The ‘existibility’ of bodies offers the mental counterpart of this principle when applied to spaces where no bodies are to be seen. Where a body is, no other body can exist, but conversely where no body is, that is between two existing bodies, there is some mental room for ‘existible’ bodies. This mental room is the very material with which we fill our idea of space.

32  See 2.15.2: ‘And he, I think, very much magnifies to himself the capacity of his own understanding, who persuades himself that he can extend his thoughts further than God exists, or imagine any expansion where He is not.’ The view that space is an affection (or ‘consequence’) of existence, and infinite space the affection of the first infinite existing being, was basically Newton’s view of the matter. See his De Gravitatione and the manuscripts quoted in J.  E. McGuire “Newton on Place, Time, and God: An Unpublished Source”, 1978. See also J.  E. McGuire “Existence, Actuality, and Necessity: Newton on Space and Time”, 1978.

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Let us consider things from another perspective. There is an interesting phenomenological counterpart to the analysis of space as pure ‘nothingness’. When we see or rather conceive a void space between two bodies, what is usually seen is some background body that fills the visual gap – of course perspective clues usually indicate that this body is not really filling the gap, but is somehow behind the empty space that we see (or rather, that we infer from what we see). Now if we look at two stars in the night sky, what we have in between is not any more a substantial background but a stretch of darkness. In both cases the events on our retina are analogous: we do not perceive bodies or space, we perceive different degrees of light and colors coexisting in such a way that we can make (or compute) the difference between foreground and background, body and space, being and nothingness. These retinal events, whatever their cause, positive or privative, are all translated into ideas that are all equally positive. It is this mental patchwork of ideas that make up the mental drafts or pictures of which we are aware in perceiving. As Locke says in the very important opening of chap. 8 (a chapter whose aim is precisely to explain the differences between ideas and things outside), privative cause may produce positive ideas, and that is why ‘one may truly be said to see darkness’ (2.8.7). This also explains why spatial void is actually seen, and conceived with a positive idea of space, even though it is actually nothing. So, if we follow this line of thought, it seems – and it is a striking reversal – that we do not have really to consider the space of ideas as something that would be only ‘metaphorically’ spatial; it might very well be that exactly the contrary is the case: the external space, the way external things appear to be extended in space would be indeed a ‘metaphorical space’, or, so to speak, a mere projection of the way ideas are dispatched and related inside our minds. Ascribing to Locke such an ‘idealist’ position concerning space and extension is tempting, especially because it would help to connect and make coherent the various layers of spatial talk that we find in the Essay. However, and for several reasons, it cannot be considered as an official doctrine of the Essay. For one thing, it belongs to the kind of metaphysical speculations that Locke was not really desirous to enter into. Second, it may appear to conflict with the more ordinary Lockean stance, according to which extension, the space within bodies, is a real (or primary) quality of them. It may be interesting to remark on this point that Locke, in his most considerate statements, tends to define extension as a certain kind of relation of cohesion between solid parts33 rather than as an intrinsic property of matter. Of course, internal spatial relations belong primarily to body, because the very concept of body includes the idea of ‘partes extra partes’, composition of material parts, but it seems clear to me that solidity has, in Locke’s description of the essence of matter, a privilege of intrinsicality. Solidity, together with the power of communicating motion are indeed the only properties of matter 33  See 2.23.17: ‘the primary ideas we have peculiar to body, as contradistinguished to spirit, are the cohesion of solid, and consequently separable, parts, and a power of communicating motion by impulse. These, I think, are the original ideas proper and peculiar to body; for figure is but the consequence of finite extension.’

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as such, the only ones that one can attribute to matter without considering the fact that actual material bodies possess parts34. Finally, as we saw, the doctrine that physical space is a projection of the mental space of ideas is related to a strict relationist view of space and place, of the kind Locke was clearly defending in the Journals, but from which, perhaps because of his new acquaintance with Newton’s work, he seemed at the time of the publication of the Essay somewhat to retreat.

References Aquinas. 1920. Summa theologiae, The Summa Theologiæ of St. Thomas Aquinas, Second and revised edition, Dominican translation, Online Edition 2017 by Kevin Knight. Ayers, M. 1991. Locke: Epistemology & Ontology, 2 vol. London: Routledge. Descartes, R. 1964-1974. Œuvres, 11 vol., edited by C. Adam et P. Tannery, revised by P. Costabel et B. Rochot, reprint Vrin, 1996. Paris: Vrin-CNRS [AT], partial English translation, in The Philosophical Writings of Descartes, 3 vols., transl. J. Cottingham, R. Stoothoff, D. Murdoch, A. Kenny, Cambridge: Cambridge University Press, 1991 [CSM]. Dlugos, P. 1996. Yolton and Rorty on the Veil of Ideas in Locke. History of Philosophy Quarterly 13: 317–329. Hamou, Ph. 2014a. Mémoire et ‘Conscience continuée’. Une lecture de Locke sur l’identité personnelle, Philosophical Enquiries, Revue des philosophies anglophones 3: 1-33 . ———. 2014b. Vision, color and method in Newton’s Opticks. In Newton and Empiricism, ed. Z. Biener and E. Schliesser. Oxford: Oxford University Press. ———. 2018. Dans la chambre obscure de l’esprit. Locke et l’invention du mind. Paris: Ithaque. Hooke, R. 1705. The Posthumous Works of Robert Hooke, edited by R. Waller. Reprint Frank Cass and Company, 1971. London: Royal Society. Leibniz, G.  W. 1996. Nouveaux Essais sur l’entendement humain, English translation by P. Remnant & J. Bennett, in New Essays on Human Understanding. Cambridge: Cambridge University Press. Lennon, T. 1993. The Battle of the Gods and Giants, the Legacies of Descartes and Gassendi, 1655-1715. Princeton: Princeton University Press. Locke, J. 1706. An Examination of P. Malebranche’s Opinion of Seeing all Things in God. In The Posthumous Works of John Locke, ed. P. King and A. Collins. London: A. & J. Churchill. ———. 1936. An Early Draft of Locke’s Essay Together with Excerpts from His Journals, ed. R.I. Aaron and J. Gibb. Oxford: Clarendon Press. ———. 1975. An Essay concerning Human Understanding, ed. P.  Nidditch. Oxford: Oxford University Press. ———. 2002. Writing on Religion, ed. V. Nuovo. Oxford: Oxford University Press. Malebranche, N. 1674. La Recherche de la vérité, English translation by P. J. Olscamp & T. Lennon. 1997. The Search after truth. Cambridge: Cambridge University Press. Mariotte, E. 1668. Nouvelle découverte touchant la vue. In Œuvres de Mariotte, vol. II, 1717. La Haye: Pierre Vander. McGuire, J.E. 1978a. Existence, Actuality, and Necessity: Newton on Space and Time. Annals of Science: 463–508.

 Locke recognizes however that solidity ‘cannot exist without extension and figure’ (3.10.15), but I take this to mean that occupation of place and time are existential conditions of material beings, rather than to mean, in a Cartesian way, that solidity is derived from extension.

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———. 1978b. Newton on Place, Time, and God: An Unpublished Source. British Journal for the History of Science 11: 114–129. Newton, I. 1990. Certain Philosophical Questions. Newton’s Trinity Notebook, edited by M. Tamny and T. McGuire. Cambridge: Cambridge University Press. Yaffe, G. 2004. Locke on ideas of substance and the veil of perception. Pacific Philosophical Quaterly 85: 255–272. Yolton, J. 1984. Perceptual Acquaintance from Descartes to Reid. Oxford: Blackwell.

Chapter 5

Berkeley’s Theological Challenge of Absolute Space in the Principles of Human Knowledge Luc Peterschmitt

Abstract  In this article, I intend to examine the link between the refutation of absolute space and Berkeley’s apologetical aim. Section 117 of the Principles of Human Knowledge is crucial. I show that, in this section, Berkeley does not contend with drawing a consequence from his refutation. He gives a new argument, which runs as follows: to affirm the existence of absolute space leads to atheism, because it necessarily amounts to denying God’s freedom and thus God’s Providence. This is precisely the definition of atheism. A consequence of my reading of section 117 of the Principles is that Berkeley’s apologetics aims at proving the providence of God rather than proving his existence stricto sensu. Keywords  Absolute space · Divine providence · Atheism

Generally, commentators pay little attention to section 117 of Berkeley’s Principles of Human Knowledge. However, as A. Koyré noticed, this section gives a key to understanding Berkeley’s criticism of Newtonian absolute space (Koyré 1957, chap. X). Indeed, section 117 begins as follows: What is here laid down, seems to put an end to all those disputes and difficulties, which have sprung up amongst the learned concerning the nature of pure space. But the chief advantage arising from it, is, that we are freed from that dangerous dilemma, to which several who have employed their thoughts on this subject, imagine themselves reduced, to wit, of thinking either that real space is God, or else that there is something beside God which is eternal, uncreated, infinite, indivisible, immutable. Both which may justly be thought pernicious and absurd notions. (PHK § 117)

If such a declaration is to be taken seriously, it would be misleading to read the whole passage only as a part of natural philosophy or of Berkeley’s theory of perception. I want to stress the importance of this section. Even if, as Withrow noticed, L. Peterschmitt (*) STL UMR 8163 – CNRS, Université de Lille – Sciences Humaines et Sociales (SHS), Villeneuve d’Ascq Cedex, France © Springer Nature Switzerland AG 2020 L. Berchielli (ed.), Empiricist Theories of Space, Studies in History and Philosophy of Science 54, https://doi.org/10.1007/978-3-030-57620-2_5

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“although Berkeley claimed that the chief merit of his rejection of Newtonian space was theological, the principal arguments which he formulated in support of his idea were not” (Withrow 1953, 107),1 this passage is not only a corollary of Berkeley’s main criticism of absolute space. Firstly, the whole passage bearing on the criticism of Newtonian absolutes is preceded by a section in which Berkeley underlines that it is more important to consider God and one’s moral duty than try to explain each phenomenon in nature: As in reading other books, a wise man will choose to fix his thoughts on the sense and apply it to use, rather than lay them out in grammatical remarks on the language; so in perusing the volume of Nature, it seems beneath the dignity of the mind to affect an exactness in reducing each particular phenomenon to general rules, or shewing how it follows from them. We should propose to our selves nobler views, such as to recreate and exalt the mind, with a prospect of the beauty, order, extent, and variety of natural things: hence, by proper inferences, to enlarge our notions of the grandeur, wisdom, and beneficence of the CREATOR: and lastly, to make the several parts of the Creation, so far as in us lies, subservient to the ends they were designed for, GOD's glory, and the sustentation and comfort of our selves and fellow-creatures. (PHK § 109)

This section ends the first part of the reflection on natural philosophy. Then, it makes sense to consider that section 117 gives the very sense of Berkeley’s criticism, far from being only a consequence – Berkeley refutes Newton’s absolute in order to free us from skepticism and atheism. Secondly, a close reading of the section shows that Berkeley does not only draw a consequence. He gives a new argument against absolute space. This is what I intend to comment on in this paper, in order to show that Berkeley’s constructivist theory of space has some theological or, more properly speaking, some apologetical motives which should not be neglected. According to section 117, the confutation of the existence of absolute space frees us from a dangerous dilemma. The “danger” is the key of the theological argument. Here it lies. The existence of absolute space implies a false choice between two equally “pernicious and absurd notions”. The argument is twofold. At a first level, saying that a notion is “absurd” amounts to criticize it from a theoretical point of view. Given that the notion of a real space existing without us is meaningless, it is impossible to attribute space to God. The preceding sections have shown that absolute space is either inconceivable or useless. Then, the question is to examine why attributing space to God would be absurd as well. On the other hand, saying that a notion is “pernicious” amounts to call its legitimacy in question on a practical level: in Berkeley’s thought, this means that it leads to atheism and irreligion. Thus, the dilemma is dangerous, because it implies choosing between skepticism (one says that something exists, which is inconceivable) or atheism (or, which is maybe even worse, both). Berkeley’s last remark stresses the fact that considering that there is an absolute space forces one to adopt a doctrine “unworthy … of the Divine Nature” – either because one divinizes space (by making space an attribute of God) or sustains “that the incommunicable attributes of God agree to it” (PHK § 117). The argument seems to be this. In both cases, according to Berkeley, one is led to affirm that space  Withrow does not mention anymore this theological aspect of Berkeley’s criticism in his discussion. Note that Koyré does not comment on Berkeley’s theological argument more than Withrow.

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is divine; this should mean that one does not really consider God as a god. Indeed, one can wonder whether the notion of a “spatialized” God really makes sense; this would mean an extended God. But according to Berkeley, there are only two kinds of things: spirit and bodies,2 the latter only being extended. An extended God is thus an extended spirit, which is a plain contradiction. On the other hand, if the incommunicable attributes of God can be also properties of space, it means that they are not incommunicable and by consequence that there are two Gods, which is also impossible. Such contradictions make of such a doctrine a road to atheism, because it leads to substitute God with something that cannot be God. If my reading of the dilemma is correct, then Berkeley gives a properly theological argument in this section. Moreover this argument is a new one in the Principles of Human Knowledge. Berkeley does not only draw an interesting consequence from his refutation. However, this argument supposes a certain way to consider God. Indeed, it is not enough to say that the doctrine is “pernicious” only because it is “absurd”: Berkeley does argue explicitly in that way: he declares immediately that this doctrine is “unworthy … of the Divine Nature”, which means that it fails to take into account an essential feature of God’s nature. In the Principles of Human Knowledge, Berkeley does not explain what he means by this “unworthiness”. A look at the Notebooks helps to establish his meaning. Of course, it is not easy to determine precisely when Berkeley began to examine the problem of the relation between God and space or extension. The problem of space is recurrent in the Notebooks: it is a crucial question of the New Theory of Vision, and it is a crucial stake for the constitution of immaterialism. The Notebooks show how Berkeley built his position. Once he noticed the problem of the relation of space and God, Berkeley seems self-confident: whatever space is or may be, it cannot be an attribute of God. And he comes back to such remarks from time to time. Thus, it seems that he quickly found a solution; but the question is nevertheless urgent. This is shown by the way in which the notes that mention the question are scattered all over the Notebooks. The “first”3 certain occurrence is to be found in 2  See for example PHK § 89: “‘Thing’ or ‘Being’ is the most general name of all; it comprehends under it two kinds of entirely distinct and heterogeneous, and which have nothing in common, but the name, to wit, spirits and ideas.” In the De Motu, Berkeley is even clearer: “There are two supreme classes of things, body and soul. We know with the help of senses something that is extended, mobile, shaped and endowed with other qualities that strike the senses; however, we know by a certain internal consciousness something that is sentient, perceiving and intelligent. Besides, we see that these things are obviously different from each other, and that they are very heterogeneous” (DM § 21). 3  By “first” appearance, I do not mean anything chronological – about the difficulties of giving a chronological order for writing the Notebooks, see Belfrage 1985; in a reply to another paper by B. Belfrage, R. McKim has underlined the difficulties that an attempt to put the entries in a chronological order necessarily meets (McKim 1985). Thus, I will keep Luce’s order as the conventional order. One “earlier” entry may raise the question. In entry 90, Berkeley writes: “In my doctrine all absurditys from infinite space &c cease”. In his explanation, Luce refers to the problem of the relation between God and space (among other questions)  – see Berkeley, Notebooks, 151. Indeed, Berkeley uses the term “absurd”. However this is not convincing: Berkeley underlines also other

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entry 290; then the question is mentioned again in entries 298, 310, 391, 695 and 825. These entries help to retrace how the problem arose in Berkeley’s thought. It will help us to see precisely what he had in mind when he wrote section 117 of the Principles of Human Knowledge, beyond the evident reference to Henry More, Samuel Clarke and Joseph Raphson.4 The first entry is the following: 290 M The great danger of making extension exist without the mind. in yt if it does it must be acknowleg’d infinite immutable eternal &c. wch will be to make either God extended (wch I think dangerous) or an eternal, immutable, infinite, increate being beside God.

Berkeley does not explain what the danger he mentions is. But it seems to be even more dangerous to say that God is extended. The entry 298 makes this danger precise: 298 M Locke, More, Raphson etc seem to make God extended. 'tis nevertheless of great use to religion to take away extension out of our idea of God & put a power in its place. it seems dangerous to suppose extension wch is manifestly inert in God.

Such a conception of God is obviously a danger for religion. This may explain why Berkeley does not comment on the second term of the dilemma in entry 290: it does not affect religion directly. The problem is that an extended God is a passive God. Berkeley seems unable to consider that extension may be active or that there could be another kind of extension than bodily extension.5 Before examining why introducing passivity in our conception of God is dangerous from a religious point of view, it is necessary to insist on the fact that Berkeley has mainly, if not only, religious concern in mind. In entry 391, he writes: 391 M The Philosophers lose their Matter, The Mathematicians loose their insensible sensations, the Profane their extended Deity Pray wt do the Rest of Mankind lose, as for bodies &c we have them still. N.B. the future Philosoph: & Mathem: get vastly by ye bargain.

The doctrine of an extended God is impious. And this is Hobbes’ and Spinoza’s doctrine (and maybe Locke’s one too6): absurdities that affect the Newton conception of space before entry 90 – see especially entries 18, 33, 55, 96 etc., which show some of Berkeley’s difficulties to conceive an absolute space or an extension which would not depend on the mind, without even mentioning the problem of God’s relation to space. 4  At the time of the first edition of the Principles of Human Knowledge, Berkeley might have imagined what could be Newton’s position concerning that question; but Newton published (a part of) his thought only in the second edition of the Principia mathematica, three years after the publication of Berkeley’s Principles. If one takes into account the second edition of the Principles of Human Knowledge, then Newton should evidently be added to Berkeley’s target. However, it may be significant that Berkeley does not give any names. Did he want to avoid to name Newton? 5  For example, More states it quite clearly: “Since I have so clearly proved space or internal place to be really distinct from matter, I conclude it, therefore, to be a certain incorporeal substance, or spirit.” (More 1679, 167); following More, J. Raphson will sustain a comparable position in his De spatio reali. 6  Berkeley’s hesitation about Locke is justified: Locke does not affirm clearly that God is extended, but it remains possible. For example, he declares: “The boundless invariable oceans of duration

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825 G Hobbs & Spinosa make God Extended. Locke also seems to do the same.

Berkeley obviously condemns Hobbes and Spinoza. In the preceding entry, he describes Hobbes’ and Spinoza’s philosophies as “Enemy of Religion” (825).7 It is highly significant that when he deals with enemies of religion, Berkeley thinks about their conception of an extended God. If one admits continuity between these notes and section 117 of the Principles of Human Knowledge, it appears that, when Berkeley says that a doctrine is “unworthy … of the Divine Nature”, it signifies that it is impious. Thus a key for a proper understanding of Berkeley’s argument in section 117 is to examine the relation between “atheism” and “irreligion”. But before examining this relation, we have to face two possible objections. The continuity that our reading assumes may be challenged. In the last entries that we have read, Berkeley deals with extension and not space. In Berkeley’s view they might be different: the extension of a body is a tactile perception (thus it exists) whereas there is nothing as an external space (space is a mere nothing: the word refers at best to the absence of obstacles that could hinder movements of our limbs8). However, in the Notebooks, there is no real difference, as entry 695 shows: 695 M Mem: candidly to take Notice that Locke holds some dangerous opinions. such as the Infinity & eternity of space. The Possibility of Matter’s Thinking.

Just as his adversaries did, Berkeley does not distinguish in these notes space and extension.9 Moreover, this entry shows that considering that God is extended is a consequence of the affirmation of the existence of an infinite and eternal space. Secondly, identifying More, Locke, Raphson on the one hand and Hobbes and Spinoza on the other may appear disputable. If Berkeley is completely wrong, then and expansion, which comprehend in them all finite beings and in their full extent belong only to the Deity. And therefore we are not to wonder that we comprehend them not, and do so find our thoughts at a loss, when we would consider them either abstractly in themselves, or as any way attributed to the first incomprehensible Being” (Locke 1975, 2.15.8). 7  Note that this last entry is marked by a “M”; entry 825 is marked by a “G”. According to Berkeley’s own indications (M stands for “Matter” and G for “God”) these two marks link the conception of an extended God with materialism. 8  See especially De Motu, § 55: “We are sometimes deceived by the fact that when we imagine the removal of all other bodies, yet we suppose our own body to remain. On this supposition we imagine the movement of our limbs fully free on every side; but motion without space cannot be conceived. None the less if we consider the matter again we shall find, 1st, relative space conceived defined by the parts of our body; 2nd, a fully free power of moving our limbs obstructed by no obstacle; and besides these two things nothing. It is false to believe that some third thing really exists, viz. immense space which confers on us the free power of moving our body; for this purpose the absence of other bodies is sufficient. And we must admit that this absence or privation of bodies is nothing positive”. Even if Berkeley writes this tract about ten years after he wrote the Principles of Human Knowledge, there are no inconsistencies between them (given Berkeley’s immaterialism, it is possible to argue that the bodies do not exist at a distance at all) – he attached a footnote to section 55 of De Motu in which he sends back to the Principles of Human Knowledge. 9  For example, Raphson defines space as follows: “I call space the most inner extension (whatever it is), first by nature” (Raphson 1702, 72 - my translation).

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his reading makes little sense. However, it is possible to explain why Berkeley identifies these authors. The mere resemblance is enough, even if it is superficial – and all these authors explicitly say that God is extended. Of course, they do not mean exactly the same thing: God is a material being for Hobbes, which is not the case for Raphson, who writes that extension as attributed to God is “spiritual” (Raphson 1702, 82). But not only one may wonder what a spiritual extension is (clearly in Berkeley’s view it is a plain contradiction), but one may ask if such distinctions are not too subtle when the stake is religion. So even if Raphson’s position is philosophically justified, it would be dangerous if the common man cannot understand it. Once again, a perfume of spinozism is enough to declare a doctrine dangerous from a practical point of view. The stake of the criticism of absolute space is quite clear. It is now necessary to stress how important this confutation is in Berkeley’s thought since he aims to build an apologetics. The way in which Berkeley presents his aims shows how to understand his apologetical goal. In the Preface of the Principles of Human Knowledge, Berkeley writes: What I here make public has, after a long and scrupulous inquiry, seem’d to me evidently true, and not unuseful to be known, particularly to those who are tainted with scepticism, or want a demonstration of the existence and immateriality of GOD, or the natural immortality of the soul. (PHK, Preface, 23)

But it is not clear whether Berkeley gives a proof of the existence of God or not – at least, if there is such a proof in the Principles, Berkeley does not present it as a separate proof nor as a crucial step in the demonstration of immaterialism. The very last section of the Principles shows a shift as to this question: For after all, what deserves the first place in our studies, is the consideration of GOD, and our duty; which to promote, as it was the main drift and design of my labours, so shall I esteem them altogether useless and ineffectual, if by what I have said I cannot inspire my readers with a pious sense of the presence of God: and having shewn the falseness or vanity of those barren speculations, which make the chief employment of learned men, the better dispose them to reverence and embrace the salutary truths of the GOSPEL, which to know and to practise is the highest perfection of human nature. (PHK § 156)

The goal is not anymore to prove the existence of God. Of course, to inspire the feeling of the presence of God, such a proof could seem a good strategy. But it is not necessarily the best one. Indeed, the feeling that Berkeley wants to inspire is a “pious” one. At least, giving a mere proof of the existence of God is not enough for that purpose. And it might be unessential. Indeed, in the preface of the Three Dialogues between Hylas and Philonous confirms this shift. Berkeley explains that, in the Principles, his aim was to avoid some embarrassments and he continues: In order, therefore, to divert the busy mind of man from vain researches, it seemed necessary to inquire into the source of its perplexities; and, if possible, to lay down such principles, as, by an easy solution of them, together with their own native evidence, may, at once, recommend themselves for genuine to the mind, and rescue it from those endless pursuits it is engaged in. Which, with a plain demonstration of the immediate Providence of an all-­ seeing God, and the natural immortality of the soul, should seem the readiest preparation, as well as the strongest motive, to the study and practice of virtue.

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This design I proposed, in the First Part of a Treatise concerning the Principles of Human Knowledge, published in the year 1710. (DHP, Preface, 166–167)

The mention of the proof of the existence of God has disappeared. Berkeley seems to acknowledge that he did not give such a proof, his concern being only to show the Providence of God. In such a context, the fact that Berkeley writes that he demonstrates in the Principles the immateriality of God might be important: this refers discretely to the question of the relations between God and space.10 Thus, we can consider that the properly theological problem is the following: to affirm the existence of an absolute space would amount to deny the existence of divine Providence. Affirming the existence of absolute space leads to atheism. This is not the case because it leads to denying the existence of God, but only because the existence of an absolute space is not compatible with God’s Providence. This loose sense of atheism was common at the beginning of the eighteenth century. For example, Samuel Clarke defines atheism as follows: I confess it appears to me […] that the essence of atheism lies in making God either an unintelligent being [such as is the material world] or at least a necessary agent [such as Spinoza makes his one substance to be] void of all freedom, wisdom, power and goodness; and that other metaphysical dispute are only about the accessories (Clarke 1706 (1964), Preface).11

But to say that there is an absolute space entails the negation of God’s Providence. Suppose that space is distinguished from God; if space is infinite then it must be eternal and necessary. For example, Clarke writes: The idea of infinity as well as of eternity is so closely connected with that of self-existence that because it is impossible but something must be infinite independently and of itself (for else it would be impossible there should be any infinite at all unless an effect could be perfecter than its cause), therefore it must of necessity be self-existent. (Clarke 1705, 86–87)

Thus, God is not free since he must create space, in one sense or another. The only solution is to say that space is an attribute of God (this is Clarke’s conclusion). But this leads to a materialist conception of God comparable to the doctrine of Spinoza, who denies as well that God is free. But the only way to give sense to God’s Providence is to assume that he is free. If God acts necessarily, then it does not make any sense to say that he is good or benevolent. The necessary existence of absolute space threatens religion because it leads to deny the divine Providence. This is a valuable argument against the existence of absolute space in Berkeley’s philosophy. However, it might introduce a tension in

 The first entries devoted to this question are marked with a “M”, which signifies that Berkeley’s concern was the theory of matter when he wrote them. 11  This definition explains why Berkeley considers that Spinoza and Hobbes are atheists even if he perfectly knows that they gave demonstration of the existence of God. It would make no sense to say that God is extended without supposing that God exists. Berkeley had obviously read Spinoza’s demonstration of the existence of God – see Notebooks 825, 87, 845. But these proofs do not demonstrate a firm belief in a Christian and Providential God. 10

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Berkeley’s thought. In this last part of my paper, I would like to show that section 117 has important consequences for the task of philosophy and apologetics: it might hinder Berkeley from giving a certain kind of proof of the existence of God. He can prove only the moral attributes, such as intelligence and freedom, that is to say the attributes which constitute the immediate and particular Providence of God. Thus, section 117 of the Principles of Human Knowledge is implicitly a criticism of a certain kind of philosophical and highly theoretical theology, which might be inefficient if the goal of philosophy is to promote religion. The difficulty is well illustrated by the beginning of the Fourth Dialogue of the Alciphron. In this passage, Alciphron refuses a certain kind of proof of the existence of God: First, then, let me tell you I am not to be persuaded by metaphysical arguments: such, for instance, as are drawn from the idea of an all-perfect being, or the absurdity of an infinite progression of causes. This sort of arguments I have always found dry and jejune: and, as they are not suited to my way of thinking, they may perhaps puzzle, but never will convince me. (Alc. IV, 2, 143)

These proofs are too metaphysical for Alciphron and thus unconvincing. Interestingly enough, Euphranor does not discuss this point and proposes an entirely new proof. It is not the place to comment on this proof here. It should only be noted that Euphranor also seems to consider that the metaphysical proofs are not really convincing (Peterschmitt 2011). Moreover, in Berkeley’s view, such proofs may be impossible. On the one hand, he cannot give an a priori demonstration of the existence of God comparable to Descartes’ one. Such a proof evidently supposes that existence is a property of the thing considered; this does not make sense, given Berkeley’s definition of existence (to exist is to perceive or to be perceived). This might be unimportant, since there is another kind of proof, which seems possible in an empiricist context: the a posteriori proof. However, such proofs do not give a real solution. This is the sense of Descartes’ discussion of the proof of God’s existence. Descartes noticed that using the impossibility of an infinite regression does not prove anything: the impossibility for us to conceive such a regression does not mean that it is impossible in reality (Descartes, AT IX-a, 85, Scribano 1994). But, and this is even worse, Descartes shows that the traditional a posteriori proofs say nothing about the cause of which they prove the existence. That is why he gives a conclusive version of such a proof by using the notion of a positive causa sui. But such a proof is completely metaphysical. Descartes construes the causa sui as a formal cause: God exists because he is omnipotent and can give himself all the properties, including existence.12 Thus the a posteriori proof is strictly equivalent to the a priori demonstration.

 In the Quatrièmes Réponses, Descartes affirms that a negative understanding of the notion of causa sui must be rejected, because, he says, “if this understanding of the word by itself [that is to say not by anything else] was accepted, we could not prove the existence of God by the effects, as it has been well proved by the author of the First Objections; that is why it must not be accepted” (AT, IX, 185 – my translation).

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This difficulty is not only a problem in Descartes’ philosophy. It seems to be acknowledged by philosophers after him. This is especially the case of Clarke. Clarke does not admit Descartes’ demonstration, because he considers that we do not have a clear idea of God: we cannot know God’s nature. But he is in great troubles when he has to prove the essential attributes of God, that is to say when he has to show that the cause of which he has proven a posteriori the existence is God (an infinite, eternal, omnipotent etc. cause).13 The solution used by Clarke consists in resting on space and time in order to consider necessary existence under the form of eternity and infinity: Infinite space is nothing else but an abstract idea of immensity or infinity; even as infinite duration is of eternity: And it would be not much less proper to say that eternity is the essence of the supreme cause, than to say immensity is so. Indeed they seem both to be but attributes of an essence incomprehensible to us. (Clarke 1705, 79)

Clarke’s argument runs as follows: since the idea of space and time cannot be removed, space and time should be the attribute of a necessary being. But space is infinite; so is the substance of which it is an attribute. Clarke’s rational theology supposes the existence of a real space. Berkeley’s rebuttal of absolute space might be a problem for rational theology. At least, it forbids one way to escape the problem raised by Descartes. And Berkeley does not propose another possibility. However, the difficulty would be insuperable if Berkeley’s aim was completely comparable to Clarke’s.14 Let us turn back once again to the distinction between a priori and a posteriori arguments. According to Clarke, they do not have the same purpose. The a priori arguments allow to demonstrate the necessary existence of God and to deduce his natural attributes: uniqueness, omnipotence etc. – all attributes which the a posteriori argument is unable to establish. But the a posteriori arguments allow proving the moral attributes: wisdom, goodness, benevolence, justice, intelligence etc.: Now that the self-existent being is not such a blind and unintelligent necessity, but in the most proper sense n understanding and really active being, cannot indeed be demonstrated strictly and properly a priori; because we know not wherein intelligence consists nor can see the immediate and necessary connection of it with self-existence, as we can that of eternity, infinity, unity etc. But a posteriori, almost everything in the world demonstrates to us this great truth and affords undeniable arguments to prove that the world, and all things therein are the effect of an intelligent and knowing cause. (Clarke 1705, 102)

But the main discussion between theologians and atheists bears on the question of the moral attributes. The latter could admit the existence of an eternal being, existing by himself etc. This being could be, for example, matter. Berkeley will

 It is impossible to prove these attributes a posteriori: since the world is not infinite in time, the cause required to create it may be finite; it is just needed that it is more powerful or contains more reality than the world. Similarly, it has not to be eternal and so on. 14  Berkeley did not fully answer this difficulty. Even with the new proof that he gives in the fourth dialogue of Alciphron, he is unable to give a clear comprehension of God’s infinity (Peterschmitt 2011). Thus, he cannot prove that the author of the language of nature is really God (that is an infinite etc. being). The problem is that Berkeley cannot give a positive account of infinity, nor use a substitute as did Clarke. 13

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clearly recall this in the Alciphron. Alciphron avows that he has been convinced by Euphranor’s proof of the existence of God. But he fears not being an atheist. Lysiclès is able to reassure him: You must know then that at bottom the being of God is a point in itself of small consequence, and a man may make this concession without yielding much. The great point is what sense the word God is to be taken in. The very Epicureans allowed the being of gods; but then they were indolent gods, unconcerned with human affairs. Hobbes allowed a corporeal God; and Spinosa held the universe to be God. And yet nobody doubts they were staunch free-thinkers. I could wish indeed the word God were quite omitted, because in most minds it is coupled with a sort of superstitious awe, the very root of all religion. I shall not, nevertheless, be much disturbed, though the name be retained, and the being of God allowed in any sense but in that of a Mind, which knows all things, and beholds human actions, like some judge or magistrate, with infinite observation and intelligence. The belief of a God in this sense fills a man's mind with scruples, lays him under constraints, and embitters his very being: but in another sense it may be attended with no great ill consequence. This I know was the opinion of our great Diagoras, who told me he would never have been at the pains to find out a demonstration that there was no God, if the received notion of God had been the same with that of some Fathers and Schoolmen. (Alc. IV, 16, 163)15

The stake of an apologetics is not to demonstrate the existence of God, but to show that the first cause is intelligent, wise and free, that is to say, to demonstrate the moral attributes of God which define his Providence. This is clearly Berkeley’s aim in the Principles of Human Knowledge. I have already quoted the last section of the Principles. Let me add that, if one counts the occurrences of the divine attributes, the moral ones are clearly more numerous, which show enough that Berkeley’s concern is to prove the existence of divine Providence. If Berkeley makes this distinction perfectly clear in the Alciphron, it is quite clear that he also perfectly knew what he had to prove as soon as 1710 – in spite of his declarations in the Preface of the Principles of Human Knowledge.16 The way in which he describes his adversaries does not leave any room for ambiguity: From what hath been said it will be manifest to any considering person, that it is merely for want of attention and comprehensiveness of mind, that there are any favourers of atheism or the Manichean heresy to be found. Little and unreflecting souls may indeed burlesque the works of Providence, the beauty and order whereof they have not capacity, or will not be at the pains to comprehend. But those who are masters of any justness and extent of thought, and are withal used to reflect, can never sufficiently admire the divine traces of wisdom and goodness that shine throughout the economy of Nature. But what truth is there which shineth so strongly on the mind, that by an aversion of thought, a wilful shutting of the eyes, we may not escape seeing it? Is it therefore to be wondered at, if the generality of men, who are ever intent on business or pleasure, and little used to fix or open the eye of their mind,

 Note the mention of Hobbes’ “corporeal God”, which clearly recalls the notion of an extended God. It confirms our interpretation: an extended God is a corporeal God, which makes no sense according to Berkeley’s ontology. 16  Perhaps this kind of declaration was less ambiguous at that time: everybody could understand that if a philosopher claims to prove the existence of God, he means a Providential God. Berkeley could have written his preface loosely. However, there are still some ambiguities, since he modified his presentation in the Preface of the Dialogues three years later. 15

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should not have all that conviction and evidence of the being of God, which might be expected in reasonable creatures? (PHK § 154)

Berkeley’s concern in the Principles is not to demonstrate the existence of God strictly speaking. Berkeley wants to make evident the existence of God: theoretically, everybody should see it, but men are blinded by prejudices. To this aim, it is enough to show that the world is the effect of a Providential cause. Berkeley’s concern is not to demonstrate the necessary existence, but the evidence of the existence of God: Hence it is evident, that GOD is known as certainly and immediately as any other mind or spirit whatsoever, distinct from our selves. We may even assert, that the existence of GOD is far more evidently perceived than the existence of men; because the effects of Nature are infinitely more numerous and considerable, than those ascribed to humane agents. (PHK § 147)

This section concludes the only “proof” of the existence of God that might be found in the Principles of Human Knowledge (Brykman 1984, I, 394). If section 146 were a proof, it would be paradoxical. Indeed, Berkeley establishes first that “There is therefore some other spirit that causes them, since it is repugnant that they should subsist by themselves” (PHK § 146).17 He describes this cause in two ways: on the one hand, it rests on the beauty, variety etc. of the world; on the other hand by “[attending] to the meaning and import of the attributes, one, eternal, infinitely wise, good, and perfect, we shall clearly perceive that they belong to the aforesaid spirit, who works all in all, and by whom all things consist” (PHK § 146). Such an attention is supposed to allow to see evidently that these attributes belong to this spirit. Let us admit that all the preceding sections have demonstrated that the spirit is wise, good and perfect; this is obviously not the case as to unity, which is mentioned for the very first time in the Principles of Human Knowledge in this passage (even in section 117, Berkeley does not mention unity). Berkeley constantly presupposes the essential attributes of God. Perhaps it is possible to perceive that they agree to the cause of our sensations. But this is not a demonstration. We know God only as a spirit, by analogy with us: this is our notion of God. But we do not know God as an infinite, absolutely one etc. being. We may even add that, if the difference between us and God is only a difference in degree (which is absolutely required if an analogy between us and God is to be drawn), then it is quite difficult and even impossible to see how it is possible to say that God is infinite. This is the meaning of Thomas Aquinas when he writes: Now, in considering the divine substance, we should especially make use of the method of remotion. For, by its immensity, the divine substance surpasses every form that our intellect

17  In section 146, Berkeley refers to section 29: “But whatever power I may have over my own thoughts, I find the ideas actually perceived by sense have not a like dependence on my will. When in broad day-light I open my eyes, it is not in my power to choose whether I shall see or no, or to determine what particular objects shall present themselves to my view; and so likewise as to the hearing and other senses, the ideas imprinted on them are not creatures of my will. There is therefore some other will or spirit that produces them”. It is quite clear that the proof is not complete: “some other” spirit does not necessarily mean God. And it is certainly possible to show that this spirit must certainly be more powerful that any finite spirit; but it does not follow that it is infinite.

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reaches. Thus we are unable to apprehend it by knowing what it is. Yet we are able to have some knowledge of it by knowing what it is not. (Aquinas 1955–1957, I, XIV, 2)

God’s immensity, according to Aquinas, hinders us from knowing him directly. There is no proportion between God and his creatures. Thus, if God is infinite, then we cannot know him; conversely, if we can know him, one should conclude that God is not infinite. However, Berkeley does not really seek to demonstrate the essential attributes of God. But proving that the world is the effect of Providence does not exactly amount to giving a proof of an almighty God’s existence. Once again, this was not the main point. And one may consider that to acknowledge the existence of a divine Providence requires acknowledging first the existence of God. Indeed, if one denies the Providence, then one may deny the existence of God: if not Providential, God is nothing other than an abstract entity, which may be said unknown and unknowable, before it is reputed useless. Thus, if the stake is to restore a true religious belief, one has to prove first the existence of Providence. That this Providence is the true God should follow naturally. As a conclusion, I want to stress the importance of Berkeley’s argument against absolute space in section 117 of the Principles of Human Knowledge. It is part of a coherent philosophical strategy which aims at refuting atheism, construed as the denying of God’s Providence. In his last work, he once again expresses his position: Concerning absolute space, that phantom of the mechanic and geometrical philosophers, it may suffice to observe that it is neither perceived by any sense nor proved by any reason, and was accordingly treated by the greatest of the ancients as a thing merely visionary. From the notion of absolute space springs that of absolute motion; and in these are ultimately founded the notion of external existence, independence, necessity and fate – Which Fate, the idol of many modern, was by old philosophers differently understood and in such a sense as not to destroy the autexousion of God or man. (Siris, § 271)

In this passage, Berkeley provides once again his arguments; it appears clearly that the apologetical one (the existence of external space as construed by the moderns contradicts God’s freedom) is not a consequence of the first argument (nothing can prove the existence of an external absolute space). But this consistency of Berkeley’s thought concerning space and theology is only the consequence of a problem that Berkeley met. The question of space largely exceeds natural philosophy: it concerns theology directly (Grant 1981). That is why it is necessary to take seriously what Berkeley says about the “chief advantage” of his refutation of Newtonian absolute space.18

References Aquinas, T. 1955–57. Contra Gentiles. Transl. A. Pegis, J.F. Anderson, V.J. Bourke and C. O’Neil. New York: Hanover House.

 I thank S. Daniel who has read and corrected earlier drafts of this paper. All defects that remain are mine.

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Belfrage, B. 1985. The Order and Dating of Berkeley’s Notebooks. Revue Internationale de Philosophie 39: 196–214. Berkeley, G. 1948–1957. Principles of Human Knowledge, § 117. In The Works of George Berkeley, Bishop of Cloyne, ed. A.A. Luce and T.E. Jessop, 9 vol. London/Edinburgh: Nelson, vol. 2 [PHK]. ———. 1948–1957. Three Dialogues Between Hylas and Philonous. In The Works of George Berkeley, Bishop of Cloyne, ed. A.A. Luce and T.E. Jessop, 9 vol. London/Edinburgh: Nelson, vol. 2 [DHP]. ———. 1948–1957. Alciphron. In The Works of George Berkeley, Bishop of Cloyne, ed. A.A. Luce and T.E. Jessop, 9 vol. London/Edinburgh: Nelson, vol. 3 [Alc.]. ———. 1948–1957. Siris. In The Works of George Berkeley, Bishop of Cloyne, ed. A.A. Luce and T.E. Jessop, 9 vol. London/Edinburgh: Nelson, vol. 5. ———. 2009. De Motu, Eng. Transl. in Berkeley. Philosophical Writings, ed. D.M.  Clarke. Cambridge: Cambridge University Press, [DM]. ———. Philosophical Commentaries, Transcribed from the Manuscript and Edited with an Introduction and Index by G.H.  Thomas, Explanatory Notes by A.A.  Luce, Mount Union College (Ohio) [Notebooks]. Brykman, G. 1984. Berkeley, Philosophie et Apologétique, 2 vols. Paris: Vrin. Clarke, S. 1705. A Demonstration of the Being and the Attributes of God More Particularly in answer to Mr. Hobbs, Spinoza and their followers. Wherein de Notion of Liberty is Stated, and the Possibility and Certainty of it Proved, In opposition to Necessity and Fate, London, 1705, reprint Stuttgart-Bad Cannstatt: Friedrich Fromann Verlag (Günther Holzboog), 1964. ———. 1706. A Discourse concerning the Unchangeable Obligations of Natural Religion and the Truth and Certainty of the Christian Revelation, London, 1706 reprint Stuttgart-Bad Cannstatt: Friedrich Fromann Verlag (Günther Holzboog), 1964. Descartes, R. 1996. Œuvres, ed. Adam and Tannery, 12 vol. Paris: Cerf, 1897–1909, 2 ed. reviewed, 11 vol. Paris: Vrin/CNRS, 1969–1974, reed. Paris: Vrin, 1996 [AT followed by vol. and page]. Grant, E. 1981. Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution. Cambridge: Cambridge University Press. Koyré, A. 1957. From the Closed World to the Infinite Universe. Baltimore: Johns Hopkins Press. Locke, J. 1975. An Essay Concerning Human Understanding, ed. Peter H.  Nidditch. Oxford University Press: The Clarendon Edition of the Works of John Locke. McKim, R. 1985. The Entries in Berkeley’s Notebooks: A Reply to Bertil Belfrage. Hermathena, “George Berkeley: Essays and Replies”, 193, pp 156–161. More, T. 1679. Enchiridion Metaphysicum. In Opera Omnia. London. Peterschmitt, L. 2011. Quelle preuve de l’existence de quel Dieu? A propos de la ‘démonstration de l’existence de Dieu’ dans Alciphron IV. Science et esprit 63/2: 193–204. Raphson, J. 1702. De spatio reali. London. Scribano, E. 1994. L’Esistenza di Dio. Roma-Bari: Gius. Laterza & Figli Spa. Withrow, G.J. 1953 Berkeley’s Critique of the Newtonian Analysis of Motion. Hermathena, n° 82.

Chapter 6

The Consequences of the Consequences of the Principles for the Theory of the Principles Margaret Atherton

Abstract  Berkeley’s philosophy of science is often assumed to be tangential to the theory laid out in the Principles, for which he is best known, and to be found instead only in minor works. It is undeniable however that Berkeley dedicates a large section of the Principles to a discussion of natural science or philosophy. I argue that this section is central to Berkeley’s conception of his goals in the Principles. Here, Berkeley is showing that a theory based on his own limited ontology of spirits and ideas can do a better job of providing knowledge of natural phenomena than its chief rival, that holds that natural phenomena are to be understood as flowing from inward, but unknown essences. Berkeley’s project is ultimately epistemological. An account based on essences leads to skepticism, while instead we have certain knowledge of phenomena when we understand them to be deduced from laws of increasing generality. Berkeley takes his approach to be in line with that of Newton, with one exception. Newton supposes that his theory requires appeal to absolute space, place and motion. Berkeley argues that philosophers actually achieve their results by tacitly appealing only to space relative to some framework, and concludes that the only coherent account of space is relative, in line with the constructive account he had developed earlier in The New Theory of Vision. Keywords  Knowledge · Natural phenomena · Newton

Towards the end of the Principles, Berkeley dedicates some pages to a discussion of natural philosophy, the term prevailing at that time for what we now might call natural science.1 In this passage, he makes some remarks of a general nature about the proper way to construe statements in natural philosophy, and some others more

 To be precise, the discussion occurs in sections 101–117.

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M. Atherton (*) Department of Philosophy, University of Wisconsin-Milwaukee, Milwaukee, WI, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 L. Berchielli (ed.), Empiricist Theories of Space, Studies in History and Philosophy of Science 54, https://doi.org/10.1007/978-3-030-57620-2_6

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specifically raising difficulties with Newton’s distinctions between absolute and relative space, time and motion. Berkeley returned to the topic discussed in these pages some eleven years later when he published his De Motu, but he made no significant use of this material in his Three Dialogues between Hylas and Philonous, his re-presentation of his ideas he wrote immediately after the disappointing reception of the Principles. Perhaps for this reason, Berkeley’s views on natural science in the Principles are not always included in general expositions of this theory, but rather are relegated to specialist work on “Berkeley’s philosophy of science.”2 There are several reasons, however, that suggest that looking at the material on natural science as it is embedded in the theory laid out in the Principles might prove fruitful. For one thing, there is a very early entry in Notebook B, PC 30, which reads: “Qu: how to reconcile Newtons 2 sorts of motion with my doctrine.” The presence of this entry makes it likely that the material on natural philosophy was on Berkeley’s mind from the time he first started planning out his early work. Moreover, the discussion of natural philosophy forms an undoubted link between the explicitly immaterialist Principles and his subsequent work, De Motu, which does not mention Berkeley’s strictures against matter. A better understanding of the role Berkeley’s remarks about natural science play in the overall structure of the Principles might help to illuminate the murky relationship between Berkeley’s early and his later works. Perhaps the most important consideration, however, is that the very language in which Berkeley introduces his final section of the Principles, in which the discussion of natural philosophy occurs, suggests that Berkeley himself intended a close connection between the initial account of his theory and the consequences laid out at the end. In PHK 85, where Berkeley introduces his final section on the consequences of his theory, he tells us that he is going to “take a view of our tenets in their consequences.” Berkeley, that is, intends his discussion of the consequences of his theory explicitly to shed light on or enrich our understanding of the tenets or principles of his theory. We can expect, therefore, that an examination of what Berkeley sees as the consequences of his theory will help to highlight what Berkeley takes to be central and of chief importance to his central theory. The issue, then, that I am going to be addressing in the bulk of this paper is: What light did Berkeley expect his discussion of natural science to shed on his overall theory? From which of his earlier principles do his consequences follow? I shall also have some general remarks to make at the end of the paper about the relationship that can be revealed between the Principles and De Motu, but these will be largely of a promissory nature. As we embark upon an examination of Berkeley’s excursion into the consequences of his theory, a relevant question to ask is, consequences with respect to what? While at least initially, in PHK 86, Berkeley speaks as though he is willing to entertain any consequences, a closer inspection of the succeeding paragraphs suggests a narrower focus. In PHK 87, having reminded us that, according to his principles, human knowledge is of two sorts of entities, ideas or unthinking things

 A particularly notable exception is Dominique Berlioz’s Berkeley (Vrin 2000).

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and spirits, Berkeley undertakes an examination of the consequences of his views first with respect to ideas (before of course concluding the book with a discussion of spirits), and it is within this broader category of ideas that the material on natural philosophy appears. From the way in which Berkeley first initiates the discussion, saying, “as to ideas or unthinking things, our knowledge of these hath been very much obscured and confounded,” it seems that Berkeley is chiefly interested in exploring the consequences of his views for the success of our knowledge, first, of ideas and then, subsequently, of spirits. That is, up until now, Berkeley has been concentrating on matters of ontology—he has been looking at how we are to understand the existence and nature of ideas and spirits. He is now going to draw out the consequences of what he has learned for an assessment of the nature of our human knowledge, allowing him to raise at this point what was to become the framing issue of Three Dialogues: who is the greater skeptic, a proponent of Berkeley’s views or one who is convinced of the existence of a mind-independent reality. Berkeley pursues this question of the relationship of our understanding of the nature of ideas for the success of our knowledge in several sections, PHK 86–100, before turning to the matter of natural philosophy. Although this discussion here is general, Berkeley does on several occasions single out the specific concepts of importance for natural science, as extension and motion, and it seems reasonable that he regards the more general discussion as, in part, a preamble to the account of natural philosophy. Berkeley indicates two areas in which confusions about the nature of ideas can have adverse consequences for knowledge. The first has to do with what he calls “the twofold existence of objects of sense.” We think, that is, that reality is located in a mind-independent external existence and that real knowledge consists in the conformity of our ideas with such entities. This misapprehension creates problems for our attempts to gain knowledge, leading as it does pretty directly to skepticism. If real knowledge is thought to be knowledge that conforms to mind-independent real things, then we will never be in a position to judge that ideas that are perceived conform to things that are not perceived. Not only will we be unable to know whether this confirmation relation obtains, but we will also never be able to know anything about the nature of things unperceived. On this view, Berkeley writes, “[w]e see only the appearances and not the real qualities of things. What may be the extension, figure or motion of any thing really or absolutely, or in itself, it is impossible for us to know, but only the proportion or relation they bear to our senses.” (PHK 87) And since our ideas of extension, figure and motion as we register them by our senses are constantly changing, none of these ideas can be judged to conform to an absolute or unchanging reality. The way out of this skeptical morass of course is to recognize that there is no twofold existence of unthinking things, since “the very being of an unthinking being consists in being perceived,” (PHK 88) that an unthinking being or idea can only be like another idea, and that therefore the only support for unthinking things is spiritual substance. Now we are back on firm ground, epistemologically speaking, because no one can deny the reality of an idea as it is actually being perceived. Understanding the nature of ideas puts our knowledge back firmly in touch with real things.

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The second mistake we are apt to make with respect to ideas is to suppose that it is possible to subject our ideas to a meaningful process of abstraction. We think that we are capable of framing new ideas by abstracting away all the circumstances in which ideas are perceived by us. But, Berkeley thinks, our attempts to make use of the ideas we suppose ourselves to be able to frame creates confusion rather than knowledge. The problem, as Berkeley diagnoses it, is that we think we are working with ideas that are in actual fact incomprehensible. It is not possible to extract from sensible ideas as we perceive them the circumstances of their being perceived so as to arrive at an idea of extension existing unperceived, nor can we peel off an idea of extension from the other sensible qualities, like color, with which it is perceived, so as to get an idea of extension in the absence of color. In these kinds of cases, the threat to our knowledge stems from difficulties that arise when we suppose ourselves to have conceived the inconceivable. Quite literally, our attempt to know fails because we don’t know what we are talking about. In sum, Berkeley sees that we can trace complications for human knowledge from two confusions about the nature of ideas, that sensible objects have a mind-­ independent as well as a mind-dependent existence, and that we are able to conceive the nature of these mind-independent objects through a process of abstraction. The first confusion leads to skepticism and the second to inconsistencies and puzzles arising from attempts to conceive the inconceivable. So these are the issues to which Berkeley has directed our attention before raising the matter of natural science. If we ask, at this stage, what are the important tenets from which these consequences for human knowledge follow, it seems pretty clear that they are, first, the anti-­ abstractionism that is laid out in the Introduction to the Principles, and second, the set of principles that emerge in the earliest sections of that work, that is, the idealist claims that the esse of unthinking things is percipi, and that an idea can only be like another idea, and the immaterialist claim that the only substance is spirit. As we move on, then, to look at the discussion of natural science, the question I want to address is: Do these matters, all deriving from the very early stages of Berkeley’s theory, remain the central issue from which Berkeley will deduce his consequences for our knowledge of natural science? Is the case of natural science an example of the disabilities with respect to ideas that our knowledge can fall into or does the discussion of natural science illustrate further tenets of Berkeley’s theory? Berkeley’s discussion of natural philosophy begins with an extension of the skeptical issues he has just raised. Those who, he says, mistrust the senses because they do not reveal the real nature of things end up maintaining that “the real essence, the internal qualities, and constitution of even the meanest object, is hid from our view; something there is in every drop of water, every grain of sand, which is beyond the human understanding to fathom or comprehend.” (PHK 101) The skepticism induced by the belief in the twofold existence of sensible objects, together with the conviction that reality is to be located in the mind-independent leads inexorably to the view that the attempts by natural philosophers to uncover the nature of the mind-­ independent are doomed to failure. Berkeley, that is, initially endorses the negative conclusion that an attempt to conceptualize human knowledge that does not recognize the esse is percipi principle will lead to skepticism. But, having made this

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point, Berkeley begins to drive in a different direction. He begins in the next few sections to develop a positive account of natural science. What is, I think, particularly intriguing, is that he also begins in these sections to reference other material from earlier parts of the Principles besides the central tenets of the earlier portions of his argument that are important to the section on ideas just discussed. In PHK 102, Berkeley introduces a different reason for our professions of ignorance about the nature of things besides the skepticism of the senses he has previously discussed. We take objects, he says, to have an “inward essence” which we suppose to be the source of their observable properties, and this inward essence has been assumed to itself possess mechanical properties, such as figure and motion. But we are led in the wrong direction in this investigation because we have failed to recognize that such mechanical properties, being inert, can’t be causes. At this point in his argument, Berkeley introduces a positive claim about the nature of causation: only spirits can be causes. For this claim, he references a later section from the initial argument, 1–33, Sect. 25. PHK 25 occupies an interesting location in the argument of 1–33. In the preceding section, Berkeley concludes his argument against the view that ideas can represent a mind-independent reality, summing up what he is maintaining is the conclusive result of the Master Argument, that it is not possible even to conceive the mind-independent existence of sensible objects. PHK 25 starts a new thought, that since ideas have no activity discernible in them, it is not possible that ideas can be the cause of anything. This section then introduces a new positive line of thought identifying the true nature of causality and reality, completing the argument of 1–33. So it is at least plausible at this point that Berkeley will seek to ground some positive consequences for knowledge of natural science on the principles, or tenets, that emerge at the end of 1–33. In the passage on natural science, once having, through the appeal to PHK 25, rejected attempts to understand the causation of observable qualities through such properties as shape and motion, Berkeley turns to the concept that has recently achieved importance through Newton’s work, that of attraction (and which has also of course been found problematic by those committed to explanations in terms of the impulsion of shaped, moving bodies.) Berkeley is dismissive of attempts to use attraction as itself an explanatory concept, since, as he points out, to say that a falling body is attracted to the earth or that particles of steel are attracted to each other does no more than name the effect needing explanation and says nothing about the means by which such an effect is produced. This is not to say, however, that the concept of attraction is without value, for what it does do is to allow us to recognize similarities between familiar events, like falling bodies, and others that are more puzzling, so that we can identify a number of otherwise disparate events as being of the same sort. The concept of attraction therefore tells us nothing about the mechanisms underlying what we label attraction, but it does allow us to treat different events as falling under the same general law. In this example, Berkeley performs a pivot from identifying scientific explanations in terms of causal mechanisms, inward essences, to one of subsuming events under laws. Berkeley enlarges on this observation in a central passage, PHK 105, which I want to quote in its entirety.

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If therefore we consider the difference there is betwixt natural philosophers and other men, with regard to their knowledge of the phenomena, we shall find it consists, not in an exacter knowledge of the efficient cause that produces them, for that can be no other than the will of a spirit, but only in a greater largeness of comprehension, whereby analogies, harmonies, and agreements are discovered in the works of Nature, and the particular effects explained, that is, reduced to general rules, see Sect. 62, which rules grounded on the analogy, and uniformness observed in the production of natural effects, are most agreeable, and sought after by the mind; for that they extend our prospect beyond what is present, and near to us, and enable us to make very probable conjectures, touching things that may have happened at very great distances of time and place, as well as to predict things to come; which sort of endeavour towards omniscience, is much affected to by the mind.

Berkeley makes several important points in this paragraph. The first, picking up on the lesson of PHK 25, is that knowledge of natural science is not knowledge of causes, because the subject of natural science is not the sort of thing that can be a cause. The second is that knowledge of natural science does consist in reducing a wide range of natural phenomena to general laws. In justifying this claim in PHK 105, Berkeley makes reference to a previous section, PHK 62, which appears in the middle portion of the Principles, in which Berkeley considers and replies to various objections. PHK 62 occurs in a reply to an objection that asks why bodies contain minute parts, since God could have achieved the same observable effects without recourse to this tiny machinery. This is the last of a series of objections concerning aspects of natural philosophy. PHK 62, in turn, refers back to PHK 31, which is part of the final section of Berkeley’s original statement of his argument. What I propose to do is to start by looking at the principles laid down in PHK 31, and then to see how they might be seen as being extended or enriched in PHK 62 and PHK 105. PHK 31 follows upon and enlarges the conclusions of PHK 30, a paragraph distinguishing ideas of sense from ideas of the imagination, that is, the ideas of sense, unlike the ideas of the imagination, that Berkeley will shortly declare to be real things. Berkeley, like many others, holds that sensory ideas are stronger and more lively than those of the imagination, but the characteristic he stresses is that they have a “steadiness, order and coherence,” that they occur, not at random, but in regular patterns. These regular patterns are what we call the Laws of Nature. In PHK 31, Berkeley enlarges on the advantages to us of being able to learn through experience these Laws of Nature. He writes: This gives us a sort of foresight, which enables us to regulate our actions for the benefit of life. And without this we should be eternally at a loss: we could not know how to act anything that might procure us the least pleasure, or remove the least pain of sense. That food nourishes, sleep refreshes, and fire warms us; that to sow in the seed-time is the way to reap in the harvest, and, in general, that to obtain such or such ends, such or such means are conducive, all this we know, not by discovering any necessary connexion between our ideas, but only by the observation of the settled Laws of Nature, without which we should be all in uncertainty and confusion, and a grown man no more know how to manage himself in the affairs of life, than an infant just born.

Berkeley is here in this passage adding something to the initial idealism encapsulated in the esse is percipi principle, which tells us that ideas immediately perceived exist when and as we see them or feel them. Berkeley’s point in PHK 31 goes

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beyond this claim to establish that ideas of sense, frequently referred to by him as fleeting and changing, have nevertheless a stability about them. This stability, however, is not grounded in some mind-independent basis, but instead in the regular patterns in which we experience these ideas. What Berkeley is stressing here in this passage, moreover, is not just that the same groups of ideas occur time and time again, but that we experience these regular groups as predictive. Because our ideas are experienced as lawful, our present ideas allow us to anticipate those ideas with which they are regularly connected. These anticipations are driven, Berkeley suggests, by what he elsewhere describes as “the never enough admired laws of pain and pleasure.” (PHK 146) From the shifting array of ideas of sense before us, we look for patterns that will allow us to achieve future pleasure and avoid future pain. Berkeley has added to the original suggestion that what is, or what is real is what is actually perceived, a further suggestion that what is real is what is experienced as predictive, that is, can be experienced as a sign of further experiences that will follow. Real things are those that reliably confirm their predictions. In this passage, what the orderliness and coherence of our ideas of sense, their occurrence according to the Laws of Nature, allows us to explain is our ordinary experience. We are flooded with sensible ideas and we struggle to make sense of them when we recognize them as members of familiar patterns. When we get to the discussion of the Laws of Nature in PHK 62, however, the context has changed somewhat. At this point Berkeley is facing an obvious objection: If the regularities among my ideas have been provided for me by a benevolent Maker so that I will be able to know that fire warms me or that a seed in the ground in Spring will be wheat by harvest time, why is it that these results seem to require so much in the way of complicated inner workings? Surely God could have achieved his purpose of giving me foresight without all this fussy clockwork, which, since most of us are completely ignorant of this inner machinery, must be irrelevant for the predictions we need? In his answer to this question, Berkeley enlarges on the use of the Laws of Nature beyond that of allowing us to deal with Nature’s day-to-day doings. PHK 62 reads: But to come nearer the difficulty, it must be observed, that though the fabrication of all those parts and organs be not absolutely necessary to the producing any effect, yet it is necessary to the producing of things in a constant, regular way, according to the Laws of Nature. There are certain general laws that run through the whole chain of natural effects: these are learned by the observation and study of Nature, and are by men applied as well to the framing artificial things for the use and ornament of life, as to the explaining the various phenomena: which explication consists only in shewing the conformity any particular phenomenon hath to the general Laws of Nature, or, which is the same thing, in discovering the uniformity there is in the production of natural effects; as will be evident to whoever shall attend to the several instances, wherein philosophers pretend to account for appearances. That there is a great and conspicuous use in these regular constant methods of working observed by the Supreme Agent, hath been shewn in Sect. 31. And it is no less visible, that a particular size, figure, motion and disposition of parts are necessary, though not absolutely to the producing any effect, yet to the producing it according to the standing mechanical Laws of Nature. Thus, for instance, it cannot be denied that God, or the intelligence which sustains and rules the ordinary course of things might, if he were minded to produce a miracle, cause all the motions on the dial-plate of a watch, though nobody had ever made

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the movements, and put them in it: but yet if he will act agreeably to the rules of mechanism, by him for wise ends established and maintained in the Creation, it is necessary that those actions of the watchmaker, whereby he makes the movements and rightly adjusts them, precede the production of the aforesaid motions; as also that any disorder in them be attended with the perception of some corresponding disorder in the movements, which being once corrected all is right again.

From this passage we learn that it is not just the case that there are regular patterns among our ideas that allow us to make use of inductive generalizations, to recognize the apple pattern or the cherry pattern so as to behave with respect to appropriate predictions. Instead, what this passage stresses is that there are in nature general laws, laws that hold of all natural effects. That there are these discoverable general laws is useful for us for two reasons. In this passage, Berkeley introduces the idea that we explain phenomena by recognizing that they fall under general laws. That is, just as we make sense of or explain to ourselves a set of ideas by recognizing that they fall into the apple pattern, so we can also anticipate that the apple will fall down from the tree by recognizing that general laws applying to all heavy bodies will obtain in this case. And, having grasped these general laws, we can use them, not just for explanation, but to make for ourselves objects that are useful or add to the “ornaments”, the pleasures of life. What Berkeley is adding to our understanding of the Laws of Nature is that they do more than provide an orderliness and regularity to our daily life, but through their increasing generality, make the natural world explicable to and manipulable by us.3 This passage in PHK 62 provides the link that allows Berkeley to explain how the knowledge of natural scientists resembles and differs from the knowledge possessed by ordinary people. In the daily course of events, we all have knowledge of real things surrounding us by our ability to make predictions grounded on the resemblance patterns established by the Laws of Nature. PHK 62 extends this way of knowing beyond that grounded in the immediately observable, by calling attention to the possibilities of extending knowledge of reality by means of general laws based on uniform features of our experience. In this way we able to come to understand otherwise puzzling phenomena and to introduce into our explanations entities that are, from our perspective, only in principle perceivable. In PHK 105, Berkeley exploits this new account of explanatory knowledge to identify the special knowledge of the natural scientist, who doesn’t have knowledge of different kinds of entities than those we learn about by means of our senses, nor of different kinds of connections among entities. Natural scientists don’t come by their knowledge by special means. The connections among ideas they rely on are arbitrary, just like any of the ideas we come to expect to go together and to follow one upon another. But natural scientists do possess a “greater largeness of comprehension,” by means of

3  Lisa Downing, in her “Berkeley’s Philosophy of Science” in The Cambridge Companion to Berkeley, edited by Kenneth Winkler, Cambridge, 2005, although she discusses PHK 62 extensively, nevertheless holds that it is not until De Motu that Berkeley places great emphasis on the generality of scientific laws. Nevertheless, I find this point important to the discussion of this passage.

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which they are able to draw out hitherto unnoticed similarities among ideas, thereby producing an account of laws of greater generality and uniformity. Berkeley has introduced here a normative conclusion: a natural scientist has better knowledge of reality to the extent that phenomena are subsumed under wider, universal, although not necessary, laws. In stressing that the model of knowledge that he favors does not insist on necessary connections between the elements in the laws of nature, Berkeley returns to the issue of the concept of attraction with which his discussion began. Part of the difficulties that have arisen with respect to attraction is that it has been assumed that if attraction is governed by law, then it must be essential to all bodies. This assumption, in turn, is problematic because there seem to be many counter-­ examples, such as the fixed stars or the elasticity of the air, which are not subject to attraction. But this confusion arises because, first, the cause of attraction is assumed to rest in the nature of bodies, instead of in a spirit, and second, that the general laws provided for our use by this spirit are not required for that purpose to be exceptionless. Berkeley concludes, while warning about the dangers of overgeneralization, to which he thinks those enamored of necessary connections are prone, with language expressive of his typical approach: “Those men who frame general rules from the phenomena, and afterwards derive the phenomena from these rules, seem to consider signs rather than causes.” (PHK 108) Natural scientists, just like anybody else, in their dealings with nature are learning to understand a language, by coming to identify signs with the meanings associated with them. In his discussion of natural science so far, Berkeley has shown that, with respect to an important Newtonian concept of attraction, if we understand scientific knowledge according to his preferred linguistic model, there is no need to fall into skepticism. Newton’s own practice stresses laws, not essences, and so is entirely in accordance with the model of scientific knowledge Berkeley recommends. He concludes this examination with an aspect of Newton’s thought that he finds less congenial. Newton, Berkeley reports, while admitting that space, place, and motion can be measured and defined only relative to our senses, nevertheless insisted on the need to assert the existence of absolute or mind-independent space, place, and motion. As far as Newton is concerned, relative space, place, and motion will always be ambiguous, because the same body will be identified as at rest or in motion depending on how its place is defined. So we need a notion of absolute space in order to provide a true place and a true motion. Berkeley’s prime concern is to show that we can disambiguate while retaining a relative conception of space. It is clear, however, that Newton’s is exactly the sort of approach that for Berkeley leads to skepticism and in the final paragraph of this discussion, PHK 116, he lays out his reasons for rejecting the notion of absolute space. He has both negative and positive reasons. The negative reason rests on Berkeley’s anti-abstractionism. The idea of pure space without bodies could only be framed if we could abstract it from our sensible experiences of bodies. But, as Berkeley has amply demonstrated, we cannot. Next, Berkeley gives a positive account of idea of what we call pure space. It derives, he says, from our experience of the motion of our bodies until we meet with resistance, which resistance we call “body.” Berkeley tellingly ends this section with a reference to something he has written earlier, but in this case, it is the New

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Theory of Vision. “Some may perhaps think,” he writes, “the sense of seeing doth furnish them with the idea of pure space; but it is plain from what we have elsewhere shewn, that the ideas of space and distance are not obtained by that sense. See the Essay concerning Vision.” (PHK 116) The account that Berkeley has just given here in PHK 116 of our idea of space is that same as that of the New Theory, in terms of the kinematic sensations of movement of our bodies and the tangible feeling of resistance. And it is in the New Theory that Berkeley first makes us of his language model, writing, “Upon the whole, I think, we may fairly conclude that the proper objects of vision constitute an universal language of the Author of Nature, whereby we are instructed how to regulate our actions in order to attain those things that are necessary to the preservation and well-being of our bodies, as also to avoid whatever may be hurtful and destructive of them.” (NTV 147) The similarity of this language and that of PHK 31 is illustrative of the close relation between these two works. Berkeley has here at the end of his discussion of natural science supported his approach with reference to his earlier positive tenets about the nature of knowledge. In putting forward his constructive account of space perception, that is, space relative to our senses, Berkeley stresses that what visible signs stand for is equally ideational, that is, they signify tangible ideas or meanings. This is of course the central claim of the New Theory. So Berkeley’s project more generally is to present an account of the laws of nature, even laws of broad generality, that are expressible in terms of ideas that suggest one another. We can see Berkeley exploiting this picture when he begins in PHK 113 to work out a way of introducing an asymmetry into the laws of motion between the body moved and the body moving by introducing the concept of force as a “felt sense of motion.” While his understanding of force had become much more sophisticated by the time he wrote De Motu, Berkeley nevertheless continued to require a sense of force in terms of what we feel in our own bodies. In De Motu he references our felt experience with heavy bodies: “While we support heavy bodies, we feel in ourselves effort, fatigue and discomfort.” (DM, 4) Even though we are led to falsely attribute force to the bodies themselves, the actual sense of the term is provided by and made true by actual or imagined sensations in ourselves.4 While it is of course the case that in De Motu, Berkeley developed an account that included “metaphysical hypotheses” or calculating devices, he nevertheless insisted upon a way of rendering such laws true, about real things, in terms of ideas signified. Among the principles or tenets from which the consequences for knowledge of natural science can be derived are certainly to be included the important tenets of idealism and immaterialism. But I am proposing here that Berkeley traced the importance consequences underlying his positive account of what is to be contained in an explanation of natural processes back specifically to lie in his theory of signs are laid out in the final stages of PHK 1–33. The important issue that Berkeley 4  For a development of this account see Lawrence A.  Mirarchi’s “Dynamical Implications of Berkeley’s Doctrine of Heterogeneity: A Note on the Language Model of Nature” in Berkeley: Critical and Interpretive Essays, edited by Colin Turbayne, University of Minnesota Press, 1982.

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underlines at the end of this argument is his new understanding of what it is to be a real thing, an understanding that does not depend upon a mind-independent existence of a thing for it to be real. Berkeley sums up this new picture of reality in PHK 36: If any man thinks this detracts from the existence or reality of things, he is very far from understanding what hath been premised in the plainest terms I could think of. Take here an abstract of what hath been said. There are spiritual substances, mind or human souls, which will or excite ideas in themselves at pleasure: but these are faint, weak, and unsteady in respect of others they perceive by sense, which being impressed upon them according to certain rules or laws of Nature, speak themselves the effects of a mind more powerful than human spirits. These latter are said to have more reality in them than the former: by which is meant that they are more affecting, orderly, and distinct, and that they are not fictions of the mind perceiving them. And in this sense, the sun I see by day is the real sun, and that which I imagine by night is the idea of the former. In the sense given of reality, it is evident that every vegetable, star, mineral, and in general each part of the mundane system, is as much a real being by our principles as by any other. Whether others mean anything by the term reality different from what I do, I entreat them to look into their own thoughts and see.

In the discussion of natural science, Berkeley is showing that we can avoid skeptical conclusions and establish a viable account of scientific knowledge by relying on the account of reality reflected in this passage and embedded in the doctrine of signs. And, if it turns out that the account of motion put forward in De Motu, embodies this same version of reality and the doctrine of signs by means of which we know real things, then De Motu might not be as divorced from the metaphysics of the Principles as is sometimes alleged.

References Berkeley, G. 1948–1957. The Works of George Berkeley Bishop of Cloyne, ed. A.  A. Luce and T. E. Jessop, Nelden, 9 vols. London: Thomas Nelson and Sons. [abridged Works]. ———. 1948a. Philosophical Commentaries. In Works, 1: 9–104. [abridged PC]. ———. 1948b. An Essay toward a New Theory of Vision. In Works, 1: 171–239. [abridged NTV and New Theory]. ———. 1949a. Treatise Concerning the Principles of Human Knowledge. In Works, 2: 41–113. [abridged PHK and Principles]. ———. 1949b. Three Dialogues between Hylas and Philonous. In Works, 2: 163–263. ———. 1949c. De Motu. In Works, 4: 11–52. Berlioz, D. 2000. Berkeley. Paris: Vrin. Downing, L. 2005. Berkeley’s Philosophy of Science. In The Cambridge Companion to Berkeley, ed. K. Winkler, 230–265. Cambridge: Cambridge University Press. Mirarchi, L.A. 1982. Dynamical Implications of Berkeley’s Doctrine of Heterogeneity: A Note on the Language Model of Nature. In Berkeley: Critical and Interpretive Essays, ed. C. Turbayne. University of Minnesota Press.

Chapter 7

Berkeleian Instrumentalism: From Substance to Space Robert Schwartz

Abstract  The author argues that much of the debate over the status of instrumentalism in Berkeley’s philosophy can be clarified if one sees him as Pragmatic instrumentalist. Pragmatic instrumentalism is a constructivist account of inquiry, quite similar the views of the classic American Pragmatists on the nature of scientific concepts, language, and truth. We forge concepts in our efforts to order and organize experience in ways that meet the continually changing evidence and intellectual needs. Hence, the content of our concepts evolve hand in hand with the theories in which they are embedded. Pragmatic instrumentalism is to be distinguished from the more standard anti-Realist instrumentalist position that challenges the status of theoretical terms and the positing of unobservable entities. From a Pragmatic instrumentalist perspective, it is not inconsistent for Berkeley to be willing to accept some claims about the existence of theoretical entities and deny others. For some run afoul of the Pragmatic Maxim, and others do not. This essay explores the implications of Berkeley’s pragmatic stance with regard to a number of controversial ontological claims about force, corpuscles, the ether, light, and space. The issues were the focus of attention not only in his time but continued to be matters of concern in the years that followed. In particular, his instrumentalist convictions play a major role in his argument against Newton’s absolute space in favor of a relativist space. According to Berkeley the empirical consequences of the former are no different from those of the latter. Thus, according to the Pragmatic Maxim, they are cognitively the same. Berkeley argues that a relative conception of space can handle all the empirical findings of an absolute conception. Moreover, the notion of relative space does not run into a number of conceptual problems that the idea of absolute space must confront. Keywords  Pragmatism · Instrumentalism · Space

R. Schwartz (*) Department of Philosophy, University of Wisconsin-Milwaukee, Milwaukee, WI, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 L. Berchielli (ed.), Empiricist Theories of Space, Studies in History and Philosophy of Science 54, https://doi.org/10.1007/978-3-030-57620-2_7

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There is by now a sizable literature arguing that Berkeley is an instrumentalist. In turn, there has been much controversy whether his instrumentalism conflicts with a number of his expressed views about science and scientific concepts. Some argue Berkeley is simply inconsistent. Some argue that Berkeley has reason to be an instrumentalist on several issues and not on others. There are also some who find neither of these answers satisfactory. On their accounts, the claim that Berkeley is an instrumentalist itself is unjustified. Hence, there is no need to square his scientific writings with instrumentalism.1 In this paper, I will argue that Berkeley is an instrumentalist, but not your garden-­ variety instrumentalist. He is a pragmatic instrumentalist. His position has much in common with that of the classic American Pragmatists, who saw Berkeley’s instrumentalist account of inquiry, language, truth, and his use of something akin to the Pragmatic Maxim as quite similar to their own positions on these matters.2 Thus, Peirce says, “It was he [Berkeley] more than any other single philosopher who should be regarded as the author of that method of modern ‘pragmatism’.” Elsewhere Peirce comments that “Among all the doctrines of metaphysics, there is none that seems to me to be more obviously favoured of metaphysics by this rule of methodeutic than what may be called conditional idealism, which is Berkeleyanism with some corrections.” In addition, he says, Berkeley, not Kant, “first produced an Erkenntnis-theorie, or ‘principles of human knowledge’, which was for the most part correct in its positive assertions”.3 Although pragmatic instrumentalism agrees with other forms of instrumentalism in holding that the basis for accepting theories lies in their epistemic utility, it differs from them in ways that significantly affect its account of inquiry and ontic commitment. Pragmatic instrumentalism is a Constructivist thesis. All concepts and theories should be understood as instruments constructed for coping cognitively and physically with the environment. We forge them in our efforts to order and organize 1  Throughout this paper I compare Berkeley’s views to those found in late 19th and 20th century science and philosophy. I am well aware that there are significant differences between how these issues were understood and debated in Berkeley’s time and thereafter. On the other hand, I do believe that later theorists faced problems comparable to those Berkeley encountered and attempted to answer. My explication of Berkeley’s ideas in these more modern terms is meant to help explicate and clarify his position. I do not claim Berkeley was working on the very same problems, or against the same background and knowledge as those who subsequently explored the issues. Moreover, the focus of this paper is on the methodological stance Berkeley adopts in arguing for his claims; a stance that I will argue, as did the classic American Pragmatists, was akin to and foreshadowed their own pragmatic instrumentalist account of inquiry. For a variety of views on this topic, see Popper (1953), Moked (1988) Winkler (1989) Jesseph (1993), Downing (1995, 2005), Peterschmitt (2008), Hight (2010), and Pearce (2013). 2  According to the Maxim, if the empirical consequences of adopting two beliefs are the same, they amount to the same thing cognitively. Unlike the Logical Positivists, the maxim is not meant to distinguish meaningful from meaningless discourse, nor is it a reductionist or a verificationist doctrine. Rather it is a criterion for distinguishing real controversies from those that are verbal and non-substantive. 3  For both citations and discussion of these quotes, as well as Pierce’s criticism of Berkeley’s nominalism and anti-Realism about possibilities, see Friedman (1997).

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experience to meet our intellectual and practical needs. Concepts and theories do not reflect or attempt to capture natural kinds and essences, for there are none. Thus, it is a mistake to assume that science, or knowledge more generally conceived, aims to correspond to reality, or carve the world at its inquiry-independent ontological joints. Perhaps the most significant difference between pragmatic instrumentalism, and other forms of instrumentalism, is that it neither makes nor relies on any invidious distinction between observable and non-observable entities, or between theoretical and non-theoretical terms. Pragmatic instrumentalism is instrumentalist in its treatment of “red”, “radish”, and “radium”. All must earn their keep in helping to order and organize experience. Pragmatic instrumentalism is not an anti-Realist doctrine per se. It does not claim that theoretical terms do not refer, or that statements in which they occur are not truth evaluable. Some non-theoretical terms as well as some theoretical terms may be usefully employed; others may not. Positing some unobservable entities is warranted, positing others is not. But the same holds for observable entities. Cats are countenanced; centaurs are not accepted. Another related difference is that many instrumentalists reject “inference to the best explanation” arguments as providing warrant for belief. The goal of science, they say, is to be observationally adequate. To meet this criterion, it is not necessary to infer or posit theoretical entities that go beyond what direct experience can reveal.4 By contrast, pragmatic instrumentalists do not reject “inference to the best explanation” arguments. When properly employed they have no objection in principle to using them to support positing both observable and unobservable entities.5 Now I believe that when read along these pragmatic lines, many of the supposed inconsistencies and problems critics have found in Berkeley’s instrumentalist approach to knowledge and ontology can be clarified, if not dismissed. In particular, I hope to show that there is no deep puzzle why Berkeley: a. rejected substance, b. denied causal forces, c. had qualms about dynamics, d. accepted corpuscles, e. had mixed things to say about the aether, and f. denied the existence of absolute space. Although I have sympathies with Berkeley’s positions, I will not here examine or defend his individual claims and arguments. My main goal is to explain how Berkeley’s pragmatic instrumentalist ideas fit together with his overall picture of inquiry. In Berkeley’s Philosophy of Mathematics, Jesseph characterizes Berkeley’s instrumentalism as “the doctrine that a theory can be accepted and applied for reasons of utility, even if the claims made in the theory or its application are not accepted as literally true”. Other commentators have adopted Jesseph’s or comparable definitions. I think this characterization of instrumentalism does not adequately capture Berkeley’s position. In explaining Berkeley’s position, it is also most important to keep in mind that Berkeley’s account of truth does not jibe with  See, for example, Van Fraassen’s (1980) extensive instrumentalist arguments against its use.  For further explication and defence of this analysis of the Pragmatists’ positions on these matters, see Schwartz (2012). In many current discussions of pragmatism, the position is often and mistakenly treated as anti-Realist instrumentalism. 4 5

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prevailing intuitions about the concept then and now. Berkeley does not deny that in everyday talk truth can be thought of as agreement with Reality. But like the Pragmatists, he does not want to take the slogan at face value. For Berkeley and the Pragmatists, the notions, “correspondence” and “reality,” are obscure. When used philosophically they distort the nature of knowledge and the processes by which it is acquired.6 In Principles7 Berkeley says, “Nothing seems of more importance, towards erecting a firm system of sound and real knowledge … than to lay the beginning in a distinct explication of what is meant by thing, reality, existence.” [PHK 89] A coherent account of truth cannot be given without a proper understanding of these notions. What then is Berkeley’s gloss on the everyday claim that the truth of an idea lies in its “correspondence to Reality”? Consider Berkeley’s explanation of what it is for perception to be veridical. In section 61 of the NTV, he asks with respect to the size of a tower, “which of all these [visual] extensions [that change with movement] is that stated, determinate one that is agreed for the common measure of other magnitudes?” And he answers, “No reason can be assigned why we should pitch on one more than another”. No appearance of the tower can be singled out as the one that corresponds to its physical magnitude. Rather, visual perception of the magnitude of the tower is veridical, when it serves as a sign for the tangibly experienced tower, as well as accurately predicts subsequent visual ideas we may experience when encountering it. Similarly, for Berkeley the bent appearance of an oar in water is not in itself non-­ veridical. In Three Dialogues (3D, D3, 238) he says, “Thus in the case of the oar, what he [a perceiver] immediately perceives by sight is certainly crooked. … But if he thence conclude, that upon taking the oar out of water he shall perceive the same crookedness; or that it would affect his touch, as crooked things are wont to do: in that he is mistaken.” Veridicality lies in whether the person knows the correct correlations between a given visual experience and other experiences of touch and

6  According to the Pragmatists, it is not possible to understand the role truth plays in inquiry independent of the consequences that follow from evaluating a claim as true. Truth, nevertheless, is objective. Individual preferences and goals are not given epistemic weight. To understand and accept the Pragmatists’ account of truth, however, does require buying into their instrumentalist account of meaning and reference, an account that differs from classic realist analyses of both semantic notions. For Pragmatists, neither meaning nor reference is fixed or determinate; both evolve over time in response to inquiry. 7  All works by Berkeley are cited in the text from the nine- volume A. A. Luce and T. E. Jessop edition (Berkeley 1948–1957), where they appear as follows (abbreviated titles used in the text are given in parentheses): An Essay towards a New Theory of Vision [NTV] and Philosophical Commentaries [PC] in vol. 1; A Treatise Concerning the Principles of Human Knowledge [PHK] Three Dialogues between Hylas and Philonous [TD] and Siris in vol. 2; Alciphron [Alc] in vol. 3. References in the text are by work title and Berkeley’s section number for all works except TD (where references are by title, part number, and page number) and Alc (where references are by title, dialogue number, and Berkeley’s section number).

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vision. On this account, if the appearance of a straight oar out of water leads us to expect the oar will look straight when submerged it too will be non-veridical.8 For Berkeley, though, knowledge is not a matter of sense, “[A]lthough the mind may use both sense and fancy, as a means to arrive at knowledge, yet sense or soul so far as sensitive, knoweth nothing”. [Siris 305] As he remarks in Three Dialogues, in both ordinary perception and when looking through a microscope, the “aim is only to know what ideas are connected together; and the more a man knows of the connexions of ideas the more he is said to know the nature of things”. [3D, D3, 245] In Siris [253] he says, “We know a thing when we understand it; and we understand it when we can interpret or tell what it signifies.” And in even more epistemic terms, Berkeley argues in Alciphron, “Though it is evident that, as knowledge is the perception of connexion or disagreement of ideas, he who doth not distinctly perceive the ideas marked by the terms, so as to form a mental proposition answering to the verbal, cannot possibly have knowledge”. [D 7, 3] [Emphasis added.] Most often, Berkeley talks about perceptual veridicality in terms of connections between the visual and the tangible. These linkages are developed on the basis of experience. “The ideas of sight and touch” he says “make two species, entirely distinct and heterogeneous.” [PHK 44] There is no a priori or necessary connection between the two realms. In several places, though, he makes clear that correlations with all the other sense modalities can also enter the picture. Perceptual knowledge requires detecting useful regularities among ideas, not in discovering correspondences of ideas to prefigured joints or kinds lying “out there”, ready-made in Reality. Substituting “correlation” for “correspondence”, though, is only half of the story. What remains to be done is provide a philosophically acceptable explication of Reality. Now according to Berkeley, “[A]n idea can be like nothing but an idea.” [PHK 8] We cannot compare an idea with the inarticulate world as it is independent of our understanding.9 The most we can do is determine how well hypotheses stack up against the evidence. But evidence can only be the world as conceptualized. Statements or ideas confirm hypotheses, not sensations or the world itself. For example, neither a green emerald, nor simply seeing one, confirms the hypothesis: “All emeralds are green”. Rather it is the conceptualization/perception of something as an emerald and as green that does. If not known as such, our encountering a green emerald does not support the hypothesis. What counts as an emerald, or any other real thing, is to be perceivable by the understanding as a such and such. For Berkeley, we have no coherent notion of the world’s ontology as simply experienced, independent of some characterization by mind. In the Notebooks, Berkeley puts his claim this way. “Knowledge or certainty or perception of agreement of Ideas as to Identity & diversity & real existence Vanisheth of relation becometh meerly Nominal of Coexistence remaineth.”  See my (2018) and Austin 1962. See also my pragmatic account of perceptual veridicality (2017).  For a modern statement of this thesis, one shared by many contemporary philosophers, see Davidson’s (1983) claim that “Nothing can count as a reason for holding a belief than another belief.” 8 9

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[emphasis added, PC, 739] Later, in Principles, Berkeley explains that men who may have the same phenomenal experiences may “perhaps when they came to the use of speech … call it the same thing; others … might choose the denomination of different things.” Berkeley goes on further down in the paragraph to say to Hylas, “you superadded to your idea of the house the simple abstracted idea of identity, whereas I did not; I would tell you I know not what you mean by that abstracted idea of identity … Are you not yet satisfied, men may dispute about identity and diversity, without any real difference in their thoughts and opinions, abstracted from names?” [PHK 247-48] What counts as being the same/identical thing or the same kind of thing is mind-dependent, it depends on how we name or group what we experience.10 The mere claim that the external world, Reality, or something, exists is useless, for it is content-less. It tells us nothing we want to know, namely, what sorts of things exist. Ontological commitment to an object or objects of kind K only makes sense with respect to criteria that individuate what are and are not K’s. The identity and diversity of things is carved out of experience by the names we construct and use to group them. Identity conditions or criteria of individuation are not found in the world but are imposed on experience by the use of ideas or words. There is no telling what there is without them. An ontology is not the world simpliciter. Reality just is. And it does not come divided up or otherwise articulated into real things or kinds that our theories merely attempt to mirror or correspond. Ontology aims to tell us what there is. This depends on and is reflective of the useful conceptual devises we construct to organize and individuate objects. Thus, Berkeley maintains “It is very obvious … to know whether it is possible for us to understand what is meant by the absolute existence of sensible objects in themselves, or without the mind. To me it is evident those words mark out either a direct contradiction, or else nothing at all.” [PHK 24] “I say, moreover, that in the naked conception of things divested of words, there will not be found any notion of what you call the actuality of absolute existence.” (emphasis added) [D3, 251–2] An ontology of “absolute existents” is no ontology, for it does not individuate or provide a basis for determining what there is and what things should be treated the same. “[A]s to ‘absolute existence’ was there ever known a more jejune notion than that?” [D3, 251] There is no mention in the Bible “of this naked conception of things … what you call the actuality of absolute existence”. [D3, 253]. Berkeley’s discussion of number serves to make the same point in a slightly different way. Imagine trying to justify any statement about the number of the actual things/absolute existents in Reality, as it is simply given. We would not know where to begin. Counting requires a specification of units or principles of  See James (1978), Lecture V, where he argues that all concepts found in science or common sense are human constructions, including our ideas of “thing,” “object,” “cause,” “possible,” “the same” or “the same again”. This constructivist thesis about the nature and origin of our concepts is what James means when he says in various places that “the human serpent is over everything”. The point is also reflected in Quine’s frequently made claim, fifty or so years later, that “there is no entity without identity”.

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individuation  – concepts that indicate where one object leaves off and another begins. As Berkeley says, “… number is nothing fixed and settled … It is entirely the creature of mind, considering either the idea by itself or any combination of ideas it gives one name, and so makes it pass for a unit. According as the mind variously combines its ideas, the unit varies; and as a unit, so the number, which is only a collection of units, also varies. … Now this naming and combining of ideas is perfectly arbitrary, and done by the mind in such sort as experience shows it to be most convenient – without which our ideas had never been collected into such sundry distinct combinations as they now are.” [NTV 109].11 For Berkeley, too, controversies over whether Reality is “the world as described theoretically” or “the world as characterized in terms of middle sized physical objects” are not substantive. Not because there is no difference between the two descriptions. They have different meanings and content. The accounts not only are distinct they may be in tension. Nevertheless, they both can be true. For once Berkeley gives up privileging the tangible, as the real, as he does in Principles, he has no reason to identify the real with either the visible or the tangible (or for that matter the tasted, smell, and heard). A lemon, is a thing that smells W, looks X, feels Y, tastes Z, and in a specific case, will take five paces to reach. Of course, a lemon examined under a microscope does not appear visually as it does to unaided vision. Although the sensations (objects of perception, the immediately seen) in both cases belong to the same modality, the appearances are different. According to Berkeley, there is no reason to identify a lemon exclusively with either the macro or micro description. The first characterization is most useful as a guide to action, the second as an instrument of intellectual cognition. We gain knowledge of lemons, when we correlate the macro and micro visual versions, just as we acquire knowledge of lemons when we correlate visual and tangible experiences. We do not acquire further knowledge by positing an underlying substance. “Strictly speaking, Hylas, we do not see the same object [of perception, i.e. sensation] that we feel; neither is the same object perceived by the microscope, which was by the naked eye. But in case every variation was thought sufficient to constitute a new kind or individual, the endless number or confusion of names would render language impracticable. Therefore … men combine together several ideas, apprehended by diverse senses or by the same sense at different times, or in different circumstances … all which they refer to one name, and consider as one thing.” [D3, 245]. Questions about whether the Real was to be identified with macro or micro version descriptions, or with some underlying ineffable, inaccessible substance were a central concern of late nineteenth-century scientists such as Ostwald, Duhem,  Similarly, he says in PHK 12, “That number is entirely the creature of the mind … will be evident to whoever considers, that the same thing bears a different denomination of number, as the mind views it with different respects. … Number is so visibly relative, and dependent on men’s understanding, that it is strange to think how any one should give it an absolute existence without the mind.” We cannot count absolute existents, assign a number to the totality of absolute existents, or count anything else without determining the unit of measure to be used for individuating them.

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Mach, and Poincare.12 It surfaced again in the early twentieth century with the much discussed “two-table” problem raised by the physicist Eddington. (1929, ix–x) His puzzle did not hinge on the doubts about the existence of atoms or other theoretical entities, or on positing some ineffable underlying substance, as it did with some anti-realist instrumentalists. The issue in question was a metaphysical one as to what tables “really” are. Should tables be identified with the observable solid table we ordinarily speak of, or are tables “essentially” swarms of atoms with more empty space than occupied, and so not really solid. Theorists had to choose since a table cannot be both solid and not solid at the same time.13 Berkeley discusses the problem explicitly in New Theory of Vision. “A microscope brings us, as it were into a new world: It presents us with a new scene of visible objects.” [85] Old correlations between sight and touch will not hold for “what seems smooth and round to the touch may to sight, if viewed through a microscope seem quite otherwise”. [105] We gain new knowledge of the same object when we learn what to expect visually and tangibly under different viewing conditions. Both descriptions are correct, just they as are when we correlate the alternative appearances of a tower with expected visual and tangible experiences. Berkeley’s solution to the two-table puzzle was the same as pragmatic instrumentalist responses to Eddington. The Pragmatists argued it is pointless to make invidious distinctions between the micro and macro versions of the world. For everyday purposes, everyday macro descriptions are the best to employ. For more theoretical purposes, micro accounts have more utility. Both are useful cognitive instruments, and both are true. One description is no better a reflection of the real table than the other. Berkeley nowhere doubts that we perceive real, existent, things. Thus, when Alciphron asks, “Do we see anything at all, or is it altogether fancy and illusion? … Do we not, strictly speaking perceive by sight such things as trees, houses, men, rivers and the like?” [AL, 4, 10] Euphanor responds, “We do indeed perceive or apprehend those things by sight.” [AL, D4, 10] We can be said to perceive the same things (individual lemons) by the different modalities, although the objects of sense, the distinctive experiences of each sensory realm, differ. “And as several of these are observed to accompany each other, they come to be called by one name, and so to be reputed to be one thing.” [PHK 1] We are directly in touch with a real lemon, when we have experiences that we find useful to group together under the name or label, ‘lemon,’ and treat as one thing. According to Berkeley and the Pragmatists, concepts cannot be defined or reduced to observational ideas. Phenomenal reduction or elimination is not possible because the number and types of correlations that fasten themselves to a concept are neither fixed nor determinate, and in principle, none are essential.14 In light of new experiences, new correlations come and old ones may go. A child uses the word

 See, Liston (2017).  Versions of this puzzle are now the focus of much attention in meta-metaphysics. 14  And as will be discussed below, it is legitimate to posit non-observables when they are properly related to experience. 12 13

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“lemon” as a hook on which to hang her knowledge of lemons, i.e. her knowledge of the correlations between the ways lemons look, feel, and smell. But it may, for example, be only at a later time that correlations with taste are added to her mix. At a still later date, new correlations may be added as a result of examining lemons under a microscope or with some other device. What counts for a theory to correspond to Reality is not fixed, it evolves in the course of inquiry. No one correlation or single group of correlations captures the essential to-be-­ ness of a lemon, for there is none. “Words are of arbitrary imposition and … men are used to apply the word same where no distinction or variety is perceived… But whether philosophers shall think to call a thing the same or no, I conceive of small importance.” [Three D, D3, 247] We employ the same word to experiences that go together and are useful to keep track of. The concept or term “lemon” is such a word. It is a cognitive instrument on which it is useful to pin our evolving knowledge of lemons. When we speak of lemons as part of the world’s ontology, what we are referring to are entities so labelled. Naming is essentially a mind-dependent enterprise. It is something we do. We construct categories and name them, because we think they will be useful in thought and action. We would be literally lost without them. The correlations we name do not correspond to the world as it is given or comes to us ready-made. Named entities are out there, in tangible space, but what they are, their individuation, are cognitively carved out of experience, and the carving does not follow pre-existing or necessary contours. Therefore, Berkeley maintains that he does not deny the existence of those things we all agree exist. In Principles, he maintains, “In the sense here given of reality, it is evident that every vegetable, star, mineral, and in general each part of the mundane system, is as much a real being by our principle as by any other. Whether others mean anything by the term reality different from what I do, I entreat them to look into their own thoughts and see.” [PHK 36] Berkeley’s claim is that determining the nature of the what it is that exists is mind-dependent. This, though, does not mean that everything is in the mind in some problematic sense. Nor does it mean we can think worldly things into existence. “All that exist,” he says “exist only in the mind, that is, they are purely notional … [B]y the principles premised, we are not deprived one thing in Nature … There is a rerum natura and the distinction between realities and chimeras retains its full force”. [PHK 34]. He goes on in PHK 35 to say, “I do not argue against the existence of any one thing that we can apprehend, either by sense or reflexion. That the things I see with mine eyes and feel with my hands do exist, really exist, I make not the least question.” Moreover, “[T]he things perceived by sense may be termed external, with regard to their origin, in that they are not generated from within”. [PHK 90] Berkeley pithily summarizes his ontological position thus: “I am not for changing things into ideas but rather ideas into things”. [3D 3, 244] Our ideas or conceptualizations do not make Reality. Rather they make it possible to have a substantive ontology; an ontology not only of what is, but when things do not pan out, what is not. For all intents and purposes an ontology of everything, Reality, the world, Being, or absolute existents, is empty. They do not tell us specifically what there is, nor for that matter, what is not.

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For Berkeley, then, truth, as the vulgar say, may be thought of as correspondence to Reality, as long as the relationship is understood as he explicates it. Correspondence must be analyzed in terms of correlation, not mirroring. What is correlated are ideas with other ideas, not ideas with the “really” Real, the mind-independent ontology of the world as it is given or simply presented. Further, the correlations are not necessary connections, but empirically determined. There is no problem saying, as the vulgar do, that the goal of inquiry is truth, and knowledge is what is gained when truth is acquired. No problem, that is, if we recognize that veridicality is a matter of the correlation of ideas, and knowledge is gained when empirical inquiry brings these correlations to light. The more we know the better we understand and know what things, exist, and are real. Does this mean that Berkeley is an anti-Realist? Viewed from a pragmatic instrumentalist perspective the question is ill put. It is clear that Berkeley holds we are not “in touch” with the inherent ontology of a ready-made world. There are no absolute existents. The idea makes no sense. We are, nevertheless, “in touch” with reality in the only good sense that can be made of the notion. Our concepts and theories enable us to navigate our cognitive and behavioural environment successfully. Our predictions of what experiences to expect are correct. Berkeley’s position is not subjectivist, and he does not deny the existence of any objects sound inquiry needs to posit. Acceptable theories are constrained by experience; wishing does not make it so. Failure to predict accurately what experience teaches is grounds for dismissal. But there is no blanket rejection of the theoretical or unobservable. If a willingness to posit such objects makes one a Realist, Berkeley fits the bill. On the other hand, if being a Realist requires holding that inquiry is the pursuit of truth, and truth lies in finding ideas that correspond in the vulgar or classical semantic sense of correspondence, he is not a Realist. The very idea of the world as it “really” is metaphysically is a chimera. Like the Pragmatists, Berkeley believes in fact that his position is more realistic than the standard Realist picture of the nature of scientific inquiry, semantics, and truth. I turn now to examining how Berkeley’s views on truth, knowledge and inquiry fit in with and can explain the positions he takes on substance, force, dynamics, corpuscles, the aether, and space. Berkeley not only allows positing theoretical entities, he is willing to accept entities that can be perceived only in the imagination. He says, “And here it may not be amiss to observe that figures and motions which cannot be actually felt by us, but only imagined, may nevertheless be esteemed tangible ideas, forasmuch as they are of the same kind with objects of touch, and as the imagination drew them from that sense.” [TVV 51] Berkeley allows that we can be justified positing things we cannot see immediately. His pragmatic instrumentalism is neither reductive nor eliminative. Direct observation is one route to take, but it is not the only one. Inference to the best explanation is another. Thus, Berkeley comments, “That from a cause, effect, operation, sign, or other circumstance, there may reasonably be inferred the existence of a thing not immediately perceived and that is absurd for any man to argue against the existence of that thing, I freely own.” [3 D, D 2, 223] Of course, positing

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observable entities as well as those too small to be perceived is never free from empirical constraints. There must be adequate evidence along with argument that meets scientific standards of justification. Admittedly, positing unobservable entities is much more risky than positing things that are directly perceivable. Methods like inference to the best explanation must be employed with great care and constraint. Being the best among otherwise unacceptable explanations does not justify believing it.15 What then are Berkeley’s reasons for challenging some of scientific posits and not others? The story is somewhat different in each case. Berkeley has a number of reasons for rejecting substance. By definition, substance is taken to be something having no empirically accessible properties of its own. Thus, it cannot be directly perceived. What’s more, there are no experienced regularities that would justify inferring its existence. Instrumentally speaking, hypotheses that appeal to substance have no more empirical content than those that avoid the idea. Positing substance provides no predictions beyond those that can be gained without it, and has no additional consequences for thought and action. Hence, reifying material substance has no advantages, while it does obfuscate and hinders inquiry in science and philosophy. Perhaps even more significantly it leads to scepticism. Simply positing material substance is not to take an informative or useful stance about what things exist. It plays no role in individuating or setting identity conditions for ontological commitment. In Three Dialogues Berkeley writes, “Moses tells us of a Creation. A Creation of what? of unknown quiddities, of occasions or substratums? No certainly.” … “as to “absolute existence” was there ever known a more jejune notion than that?” [D3, 251] Material substance, is such a jejune absolute existence. “Matter, or material substance, are terms introduced by philosophers … but are never used by common people. … so long as the names of particular things are retained the word matter should never be missed in common talk. And in philosophical discourses it seems the best way to leave it out.” [D3, 261] Neither the vulgar nor scientists have need for notions like material substance. Positing corporeal substance in science makes for problems or non-sense. And in denying “that which philosophers call matter or corporeal substance… there is no damage done to the rest of mankind, who, I dare say will never miss it.” [PHK 35].16 For Berkeley, the situation is somewhat different with force. The warrant for positing force was a bone of contention in Berkeley’s time and for many years to follow. And Berkeley’s reasons for rejecting the reification of force are quite similar

 See also, Siris 228, where Berkeley cautions that one is not justified in general to infer from conclusions to premises. Without significant constraints, the method is not logically justified or otherwise warranted. 16  Compare with Austin in Sense and Sensibilia (7–8), “… ‘material thing’ … as here put forward [by philosophers] … [is not] what the ordinary man would say, but as designating in a general way the class of things of which the ordinary man … says that he perceives particular instances. The expression ‘material thing’ is simply … a foil…; it is not here given and is never given, any other role to play, and apart from this consideration it would surely never have occurred to anybody to try to represent as some single kind of things…” 15

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to those made at much later dates. Berkeley argues that for scientific investigation and practice an “account must be given of the composition and resolution of any direct force into any oblique ones by means of the diagonal and parallelogram. They serve the purpose of mechanical science and reckoning; but to be of service to reckoning and mathematical demonstration is one thing, to set forth the nature of things is another.” [DM, 18] Force is a measure of the effects of motion on bodies. We compute this measure on the basis of principles of motion associated with what would later be termed a “vector analysis” of parallelograms. In scientific practice, force is employed as a device to simplify computation and to provide an economical statement of regularities. There is, therefore, no need to treat the term ‘force’ as purporting to denote anything, especially not an active power in matter. Berkeley goes on to argue that hypostasizing force does not even make sense in the theories that employ it. In De Motu, he points out “Newton recognizes that fact when he says that the force of inertia is the same as impetus. But body inert and at rest, does nothing; therefore, body moved does nothing.” [DM, 26] According to Berkeley, the two ways of putting the claim amount to the same thing, and in that sense the debate is empirically idle.17 Berkeley is opposed to positing forces more generally, in that he rejects the idea that any corporeal thing can have causal or agential powers. And he challenges a range of scientific theories that he takes to do so. This is particularly evident in his criticism of realist positions with regard to dynamics. Berkeley does not object to Newtonian dynamics on the grounds that it posits unobservable entities and processes. He thinks problems only arise, when force is thought of as a corporal entity having a causal power. This is a serious mistake. However, when the laws are understood as kinematic principles that merely describe the phenomena of motion, all is fine. Our everyday idea of force is not meaningless or without content. We can acquire it from experience of our own movement and resistance. Still we cannot conceive of causal forces existing in physical objects. This does not disbar use of the term ‘force’ in science. Formulas such as F = MA are clear, and they capture real relationships or regularities that describe what happens when masses are accelerated. Berkeley, though, appreciates the pull of hypostatization. He says in Siris (250): “[I]f we consider the proclivity of mankind to realize their notions, will it seem strange that mechanic philosophers and geometricians should, like other men, be mislead by prejudice, and take mathematical hypotheses for real things existing in bodies.” Or as he says in De Motu (6): “Again force, gravity, and terms of that sort are more often used in the concrete (and rightly so) so as to connote the body in motion, the effect of resisting, etc. But when they are used by philosophers to signify certain nature carved out and abstracted from all these things … they breed errors and confusion.” Ideas of force, gravity, and the like play a useful role in science. They make for a more economical statement of empirical laws, and allow

 The Pragmatists argued similarly on the basis of the Pragmatic Maxim. Berkeley’s attempt to demonstrate that force should not be reified with causal powers is also much like that given many years later by Peirce (1987) in “How to Make Our Ideas Clear”.

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calculations to go more smoothly. Nevertheless, there is no need to reify and give them causal powers. This only leads to “errors and confusion”. For Berkeley, there remains then an importance difference between force and substance. We do not have a clear idea of substance even in everyday contexts, and it has neither a useful role to play in simplifying theory, nor does it provide any scientific insight. It is not an explanatory or predicatively valuable cognitive instrument. By contrast, using the term ‘force’ enables accurate computation and the statement of empirical regularities we wish to know. Berkeley suggests calling hypotheses that make use of concepts that in context do not purport to denote “mathematical hypotheses”. They are, however, truth apt. ‘F = M × A’ is true; ‘F = M × 3A’ is false. Such statements have instrumental use, yet not all the terms employed are meant to name entities, force being a prime example. Although there is this difference between ordinary empirical hypotheses and mathematical hypotheses, both are to be justified instrumentally. To the extent each captures real empirical correlations, they are both true. There is no reason to claim that mathematical hypotheses are not “fully” true or only “as if” true. Controversies over the status of corpuscles was much in the air when Berkeley was writing, and comparable debates over the status of atoms continued into the early twentieth century. Many of the same issues and arguments pro and con positing such entities are found in the scientific literature of both periods. The reason for rejecting corpuscles and atoms was not simply the difficulties posed by their happening to be unobservable. Corpuscular and atomic theories had problems. It was thought that some of their hypotheses were logically inconsistent, some conflicted with the empirical data or other accepted hypotheses, and some seemed untestable in principle.18 In spite of these difficulties, both theories had predictive merit, and most scientists did not want to abandon their use. One option was to treat the terms ‘corpuscle’ and ‘atom’ as Berkeley treats ‘force’ – useful concepts that do not purport to refer. Others thought that the problems just mentioned could be worked out, and they had no reluctance treating them as “real” bodies. Over the years, a variety of more nuanced positions were taken. For example, William James thought there were sound reasons both for and against reifying atoms. The best policy was to work with the concept and let the corporality issue go wherever empirical research led. This was not a job for philosophy to tackle. James indicates, though, he thought the atomists would win out.19 In De Motu Berkeley rejects force but countenances corpuscles. This has led to debates concerning Berkeley’s seemingly different treatment of the two. Is he an instrumentalist, or isn’t he? Or is he simply inconsistent – an instrumentalist in the case of force and a realist in the case of corpuscles? On the assumption that Berkeley  It is interesting here to consider James’ treatment of Ostwald’s influential and much debated attempt to replace atomist dynamic theories with Ostwald’s own kinematic theory of “energetics”. See James (1907) Lecture V, p. 93. 19  For most scientists debate over the reality of atoms was pretty much settled in the early twentieth century with Einstein’s and Perrin’s work on Brownian motion. 18

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is a pragmatic instrumentalist, the answer is neither. The idea of a corpuscle does make empirical sense and the theories that posit corpuscles had proven their worth. Inference from “cause, effect, operation, sign, or other circumstances” could support reifying corpuscles that were too small to see. The term, ‘force’, also had utility for inquiry. The problem for Berkeley was that he thought it was not possible to conceive of the idea of forces existing in matter, and treating forces as causes or powers only led to error in physics and philosophy. Berkeley’s account of the aether is less clear than his treatment of substance, force, and corpuscles. Berkeley often seems firm in his belief in the existence of the aether. He also suggests the aether may be thought of as a form of light or fire. The aether, though, cannot be felt or seen in the way ordinary fire and light can be perceived. It was invisible and perhaps could only be “seen” by the imagination. But for Berkeley, this was not reason enough to reject it. If positing a corpuscular aether along these lines had a scientific payoff, if the theories that appealed to it worked, by all means countenance its existence. At the same time, Berkeley did have qualms with positing aether as a medium, as a carrier of light and fire. He says in Siris: “To explain the vibrations of light by those of a more subtle medium seems an uncouth explanation.” [Siris 225] “It doth not seem necessary, from the phenomena, to suppose any medium more active and subtle than light or fire. … Light or fire seems the same with aether”. [226] The main problem Berkeley confronts in positing aether is that like light and fire, it seems to attribute inherent active powers to matter, and Berkeley is insistent throughout his work that material things cannot be causes. Only spirits can cause or initiate movement. The bulk of Siris, then, is taken up with his attempt to explain away the supposedly active properties attributed to aether, light, and fire. Berkeley had no need to confront this issue in the case of force, since on his construal, force is not corporeal. I think Berkeley’s treatment of space and his insistence that space is relative, is of a piece with the pragmatic instrumentalist stance I attribute to him. We do have an understandable idea of space. We acquire it from our experience of extension as it is tangibly experienced. Visual experience also has extension, but it does not provide the kind of experience that is constitutive of our idea of (physical) space. Visual and tactual extension are heterogeneous; the two extensions are incommensurable. Visual extension cannot be measured in tangible units; nor can tangible extension be measured in visible units. It makes no sense to do so. The space that physics and geometry study is tangible space, and underlying this concept is the idea of motion, as experienced tangibly. Thus, Berkeley argues in the NTV (153–55) that a spirit lacking a tangible experience of movement could have no idea of space and geometry.20 In general, Berkeley held that Newton’s physics was the best science around. He also has no qualms with most of what Newton said about the physics of space. He did object, however, to Newton’s claim that space is absolute, and he had several

 See Schwartz (2019) for my most recent attempt to clarify Berkeley’s position on the heterogeneity of visual and tangible extension.

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reasons for doing so. To begin on a conceptual note, Berkeley thought that there were obstacles to having a clear idea of absolute space. I pointed out earlier that Berkeley allows that we can have legitimate theoretical ideas based on analogies and imagination, for example, of force and things too small to see. He argues, though, that people believe as well that they can conceive of absolute space, because they think they can imagine space with nothing in it. This, Berkeley argues, is an illusion. The space they imagine is not empty. What they actually imagine is a space with them in it, and they picture being able to move around in it. The space they thus conceive is one understood in terms of tangible motion, and the motion they imagine only makes sense in relativist terms. Berkeley’s reasons for rejecting the claim that space is absolute, however, are not simply that there were problems explaining our ability to have a clear idea of it. Newton’s hypothesis had content, and Berkeley was aware of the sort of evidence that might count in favor or against it. So, he turns to considerations that lie more squarely within the realm of physics. Berkeley’s main objection to Newton is that it is impossible to measure space in absolutist terms. The only units that could be employed to measure space are relativistic. Berkeley notes, moreover, that Newton actually agrees that all measurements of space must be relative. On that score, then, there is no difference between the two hypotheses. Positing absolute space had no additional instrumental purpose, and in empirical terms the dispute was idle. As I interpret Berkeley’s account of truth, the statement “Space is relative” is literally true. On the other hand, if the statement, “Space is absolute”, is taken to have consequences incompatible with relativist space, it is literally false. There is no need to treat either claim as metaphors. Newton argued, however, there were facts about circular motion that could only be explained if space were absolute. Newton presents his case in terms of his famous “bucket experiment”. Water in a spinning bucket rises, although the rotating water is stationary with respect to the rotating bucket, but he claimed there is no relative motion. Newton concluded that there was no way to explain the phenomenon without the supposition of absolute space. Berkeley’s response to this challenge was to argue that Newton’s explanation was not the only available account of the phenomenon. Berkeley did not cite additional direct empirical evidence to defend his position. Nor did he argue that Newton’s solution should not be accepted, because it rested on an inference to the best explanation argument. Instead, Berkeley suggested that another explanation of the phenomenon was available, and that it was consonant with space being relative. According to Berkeley the perceived movement of the water could be explained in terms of the presence of an increase in tangential impetus in the absence of equal increases of circular impetus. In addition, Berkeley argued there actually is relative motion when measured with respect to the fixed stars. Hence, Berkeley maintains that his theory can capture all the relevant empirical facts. His analysis not only could explain the phenomena; it was a better explanation than Newton’s. Thus, there was no need to appeal to absolute space.21

21

 For a nice set of readings and discussion of the issues see Huggett (1999).

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Berkeley does not comment in any detail on the relationship between absolute space and what he takes to be Newton’s conception of the aether as medium. He says, “It is the opinion of Sir Isaac Newton that somewhat unknown remains in vacuo, when the air is exhausted. This unknown medium he calls aether.” [Siris 223] According to Berkeley, Newton’s aether, so understood, is all-pervasive. “In a word, all the phenomena and properties of bodies attributed to attraction, upon later thoughts seem ascribed to this aether, together with the various attractions themselves.” [Siris 224] But if the aether were an all-pervasive medium, it could provide a framework against which to treat motion and spatial relations as absolute. This would undercut Berkeley’s claim that it was not possible to measure or empirically distinguish absolute from relative motion. Berkeley, we have noted above, denied there was a need to posit an aether medium. It was possible to account for all the properties of light, fire, bodies, and attractions without it. If, as Berkeley urged, the aether is best understood along the lines of invisible light and fire, there was no problem for his relativist account of space since the aether was not functioning as a medium.22 Berkeley’s account of space drew considerable attention at the time, and it continues to do so today. This is not surprising, for many think his arguments were not only on target, but that his analysis of the issues is the one that eventually triumphed. Space we have learned is relative.23 Nonetheless, even those who praise Berkeley for his insights, tend to find fault with what they assume to be his philosophy of science. They take him to be a Positivist. Accordingly, they argue that they cannot accept Berkeley’s antirealist instrumentalism because it rejects theoretical entities, and wrongly treats theoretical terms as having dubious epistemic status. The problem with such criticism is that Berkeley was not committed to instrumentalism in the unacceptable form attributed to him by many of those who praised him for his analysis of spatial relations. His Pragmatic Instrumentalism is not an anti-­ Realist thesis. When all these facts are taken into account, a fuller picture of truth and its place in inquiry comes into view. Berkeley can agree with the vulgar that truth is correspondence with reality, as long as the notion “corresponds to reality” is properly understood in pragmatic instrumentalist terms. Moreover, there is no reason why hypotheses couched in theoretical terms cannot be “literally” true. Whether or not one wishes to label some or all of these hypotheses ‘mathematical’, the truth is they are testable and truth evaluable. Thus, Berkeley says, “the mechanician makes use of certain abstract and general terms … which are of first utility for

 Questions about an aether medium, however, remained the focus of attention into the twentieth century, and played a prominent role in debates about absolute space. 23  Popper (1953), Myhill (1957), and others have argued that Berkeley should be seen as a precursor to Mach, and Einstein claimed that Mach’s work was a seminal influence on his development of the theory of relativity. It is not possible for me here to examine the claim that Berkeley really is a precursor of Mach. Nor do I wish to discuss the ins and outs of Mach’s own version of instrumentalism. Mach, in fact, explicitly tries to distance himself from what he takes to be Berkeley’s philosophy. 22

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theories and formulation even if in truth of things and in bodies actually existing they would be looked for in vain.” [DM 39] They would be looked for in vain, because not every term found in meaningful, true statements needs to purport to denote. “[S]igns may be significant, though they should not suggest ideas represented by them, provided they serve to regulate and influence our wills, passions or conduct … consequently the mind of man may assent to propositions concerning such terms.” [AL, D7, 8].24 Reluctance of critics to allow that Berkeley’s mathematical hypotheses are truth evaluable, stems largely from a misguided adherence to the idea of truth as correspondence. It depends on faulty assumption about how language works, and it distorts the nature of actual inquiry. To appreciate Berkeley’s analysis, it is helpful to consider the following examples. The statements, “Argentina is south of the Equator,” and “The average family’s income rose in the period 1948 – 1998,” may be labelled ‘mathematical hypotheses,’ but this does nothing to detract from their use to guide thought and regulate conduct. The “facts” they state serve to organize experience, are justified on the basis of empirical evidence, and are true. Of course, no one thinks this means he or she can bump into the Equator or meet a family with 2 ½ children. To search for either would be fruitless. Nevertheless, for the pragmatic instrumentalist, these statements are pragmatically true, and pragmatic truth is the only notion of truth that is useful and needed in a realistic account of inquiry.

References Austin, J. 1962. Sense and Sensibilia. New York: Oxford University Press. Berkeley, G. 1948–1957. In The Works of George Berkeley Bishop of Cloyne, ed. A.A.  Luce, T.E. Jessop, and Nelden, vol. 9. London: Thomas Nelson and Sons. Davidson, D. 1983. A Coherence Theory of Truth and Knowledge. In Kant oder Hegel, ed. D. Henrich, 423–438. Stuttgart: Klett-Cotta. Downing, L. 1995. Siris and the Scope of Berkeley’s Instrumentalism. British Journal for the History of Philosophy 3 (2): 279–300. ———. 2005. Berkeley’s Natural Philosophy and the Philosophy of Science. In The Cambridge Companion to Berkeley, ed. K. Winkler, 230–265. Cambridge: Cambridge University Press. Eddington, A. 1929. The Nature of the Physical World. New York: The Macmillan. Friedman, L. 1997. Peirce’s Reality and Berkeley’s Blunders. Journal of the History of Ideas 35 (2): 253–268. Hight, M. 2010. Berkeley’s Metaphysical Instrumentalism. In George Berkeley: Religion and Science in the Age of the Enlightenment, ed. S. Parigi, 15–29. Dordrecht: Springer. Hugett, N. 1999. Space from Zeno to Einstein. Cambridge: MIT Press. James, W. 1978. Pragmatism. In Pragmatism and the Meaning of Truth. Cambridge: Harvard University Press. Jesseph, D. 1993. Berkeley’s Philosophy of Mathematics. Chicago: University of Chicago Press. Liston, M. 2017. Duhem: Images of Science Historical Continuity, and the First Crisis in Physics. Transversal: International Journal for the Historiography of Science 2: 72–84.  For more on this point, see Winkler, 2005 and a response by Prichard (2012). See also, Pearce (2017)

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Moked, G. 1988. Particles and Ideas. Oxford: Oxford University Press. Myhill, John. 1957. Berkeley’s “De Motu” – An Anticipation of Mach. In University of California Publications in Philosophy, 29. Berkeley and Los Angeles: University of California Press. Pearce, K. 2013. (unpublished manuscript) Berkeley’s Meta-Ontology: Bodies, Forces, and the Semantics of ‘Exists’. ———. 2017. Language and the Structure of Berkeley’s World. Oxford: Oxford University Press. Peirce, C. 1987. How to Make Our Ideas Clear. In Popular Science Monthly. Reprinted in Pragmatism: The Classic Writings, ed. H.S. Thayer, 79–100. Cambridge: Hackett Publishing. Peterschmitt, L. 2008. Can Berkeley be an Instrumentalist? Berkeley Studies 19: 19–31. Popper, K. 1953. Note on Berkeley as a Precursor of Mach. British Journal for the Philosophy of Science 4: 26–36. Pritchard, T. 2012. Meaning, Significance, and Suggestion: Berkeley on General Words. History of Philosophy Quarterly 29: 301–317. Schwartz, R. 2012. Rethinking Pragmatism. New York: Blackwell-Wiley Publishers. ———. 2017. Perceptual Veridicality. Philosophical Topics, special issue New Directions in the Philosophy of Perception 44(2): 380–403. ———. 2018. Berkeley and Austin on the Argument from Illusion. In Interpreting Austin: Critical Essays, ed. S. Tésohatzidis. Cambridge: Cambridge University Press. ———. 2019. Berkeley’s Account of Extension and its Place in Vision Science. In Perception and the History of Science, ed. B. Glenny and J. Silvia. New York: Routledge. Van Fraassen, B. 1980. The Scientific Image. Oxford: Oxford University Press. Winkler, K. 1989. Berkeley: An Interpretation. Oxford: Oxford University Press. ———. 2005. Berkeley and the Doctrine of Signs. In The Cambridge Companion to Berkeley, ed. K. Winkler, 125–165. Cambridge: Cambridge University Press.

Chapter 8

Berkeley’s Two Notions of Extension Laura Berchielli

Abstract  Berkeley’s theses on vision have been better accepted than those about the non-existence of matter. However, in spite of the success of his explanation of vision, his thesis on the non-existence of a visual space and the heterogeneity between ideas of sight and ideas of touch is far from having been unanimously accepted. On this specific point, many inconsistencies have been noted. Nevertheless, it is possible to reconcile these tensions by showing that, in his An Essay toward a New Theory of Vision, Berkeley describes two kinds of space that are different from one another in their relation to co-existence, succession and movement. An examination of these relations gives a clue to understanding the way in which Berkeley can at once admit and deny some sort of space for the ideas of sight. Keywords  Berkeley · Heterogeneity · Space

The main thesis of Berkeley’s An Essay toward a New Theory of Vision is that vision is a language – and, more particularly, is a divine language through which God communicates with men. The signs of this language are visual ideas of light and colours, their meanings being ideas of the tangible properties of objects. Berkeley bases his thesis on the observation of the contents of experience – observation of the actual visible and tangible contents present to the mind in different visual situations, observation of the differences between these contents, and observation of the way these contents are correlated. The claim that vision is a language is then established a posteriori, as the only way to simultaneously account for the differences between visual and tangible ideas, and for the kind of connection linking these two types of ideas. It is in the process of proving the thesis that vision is a language that, in NTV, Berkeley develops his analyses of the idea of extension I will focus on in this paper.1 1  All references to Berkeley are from Berkeley 1979. The following abbreviations are employed: “PC” for Philosophical Commentaries (Berkeley 1979a) followed by entry number; “NTV” for An Essay toward a New Theory of Vision (Berkeley 1979b) followed by section number.

L. Berchielli (*) Université Clermont Auvergne, Clermont-Ferrand, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 L. Berchielli (ed.), Empiricist Theories of Space, Studies in History and Philosophy of Science 54, https://doi.org/10.1007/978-3-030-57620-2_8

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More precisely, in developing his argument, Berkeley is led to address two (connected) problems. The first is whether and how it is possible, given the content of our visual ideas, to see the distance, size, figure and situation of objects. The second is whether there are ideas equally perceivable by sight and by touch (NTV 1).2 The description of the spatial content of visible and tangible ideas have first and foremost an instrument role in NTV. At no point in this work does Berkeley present a theory of space, nor treat the idea of space in itself. Rather, he uses the analyses of extension, including those related to the content of our visual ideas and those dealing with the heterogeneity of visual and tangible ideas, to support his conception of vision as a language. Can we extract a unified conception of space and its determinations from these scattered developments that deal with space in a radically different context?3 The answer is not obvious. Two features, at least, make it difficult to attribute to Berkeley a well-articulated conception of space. The first is that the immediate content of visible ideas – which are the basis of Berkeley’s claims about spatiality – do not seem to be observable in the ordinary way, as the other objects of consciousness are. Indeed, some of Berkeley’s descriptions of the immediate content of visual ideas do not correspond to our first intuitions of them (in particular because of the difficulty of separating the visual content from what comes from the association with tangible ideas). The second is that in different places in NTV, Berkeley makes apparently inconsistent claims. These inconsistencies emerge within some points of central importance to Berkeley’s explanation of vision, points that cannot be set aside without undermining the whole of his theory or at least some important parts of it. To cite an example, by the end of the NTV, Berkeley maintains that sight can perceive neither two- nor three-dimensional figures, while in earlier places in NTV, he regularly refers to the ideas of figures perceived by sight, and even more particularly to visible circles and visible squares. One can then wonder how a supposed theory of space, based on ideas and their contents, may leave indeterminate such a nodal point as the possibility or impossibility for visual ideas to have a figural content, and whether this figural content (if there is one) is two-­ dimensional or three-dimensional. The aim of this paper is to extract from the different passages in NTV the main features that Berkeley assigns to spatial ideas. Through the description of these features, I would like to show, first, that Berkeley develops a unified and coherent way of conceiving of extension and its determinations and, second, that Berkeley’s view offers us the means for resolving the apparent contradictions internal to NTV. Section 8.1 introduces the structure of NTV and the model of mediate visual perception. Section 8.2 summarizes Berkeley’s arguments for the theory of the mediate visual perception of distance, size and situation. Section 8.3 focuses on Berkeley’s account of the content of visible and tangible spatial ideas and on the 2  In this paper I will focus on Berkeley’s description of the content of ideas (whether visible or tangible). The fact that Berkeley treats the objects of touch as “external” (NTV 64, 99, 117) and as existing “outside the mind” (NTV 111) in NTV has no consequences on these descriptions and on my proposal. 3  Distance, size, figure and situation are what I call spatial “determinations”.

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proof of the heterogeneity between visible and tangible ideas. In Sect. 8.4, I discuss the critical passages of NTV that appear to introduce important inconsistencies within NTV. Finally, in Sect. 8.5, I suggest that these tensions can be resolved by recovering, within NTV, the description of two different heterogeneous ways of having extension, proper to visible and tangible spatial ideas respectively. Section 8.6 supports this reading, making reference to some particular features of extension described in Philosophical Commentaries and in The Analyst.

8.1  Preliminary Remarks Before moving on to Berkeley’s analyses of spatial ideas of sight and touch, it is important to set out the structural organization of NTV. Berkeley sets out the structure and aims of NTV in the very first section where he announces four parts: the first three deal with the visual perception of, respectively, distance, magnitude, and situation, and the fourth deals with the question of the existence of ideas equally perceivable by sight and by touch. Hereafter, I will refer to these thematically distinct parts of NTV as Part 1 (sections 2–51, on distance), Part 2 (sections 52–91, on magnitude), Part 3 (sections 92–120, on situation), and Part 4 (sections 121–159, on the heterogeneity between visible and tangible ideas). In the first three parts, where he tackles separately the more specific subjects of visual perception of distance, size, figure and situation, Berkeley develops his new explanation of vision based on the model of mediate perception and on the clear distinction between tangible and visible ideas. Part 4 moves from the level of the difference between particular ideas, which is proper to the first three parts, to the level of the difference between species of ideas. It aims to show that ideas of sight and ideas of touch, considered as two species, are different, i.e. that there is no one single idea or kind of idea equally perceivable by sight and by touch (heterogeneity thesis).4 For a rapid description of this model, I will sketch out Berkeley’s explanation of the visual mediate perception of the idea of distance – but let me make clear that the same kind of explanation can also be applied to the visual perception of magnitude and situation. Berkeley’s starting point is that sight cannot immediately perceive the 4  On this difference, see NTV 121 quoted below, Section 8.2. In NTV, Berkeley does not deal with the topic of general ideas that will become the main topic of the Introduction of the Treatise Concerning the Principles of Human Knowledge (Berkeley 1979c) published in 1710, only one year after the publication of NTV. However, inter alia, the estimated date of composition of the so-called Manuscript Introduction being summer 1708 (see Belfrage 1987), as well as what Berkeley writes in NTV 124–125 (on the possibility of universal propositions without abstract ideas) plausibly indicate that Berkeley, at the time he was writing NTV, already had a grasp on at least the outline of his theory of generalization and had the means to deal with the distinction between particular and general or specific ideas. On this point, especially in relation with the question of the universality of geometry, see Storrie 2012, 260–263.

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distance at which the objects are located, because distance, as he says, being a line directed to the eye, invariably projects itself in a single point and therefore leaves no traces of its length on the retina (NTV 2 and 46). However, sight may perceive distance in an indirect, mediate way when the ideas it actually (i.e. directly or immediately) perceives, such as light and colours – by virtue of an association progressively established by habit – function as a sign for the idea of distance actually perceived only by the sense of touch. According to this model, once the association between ideas of sight and ideas of touch has been established, the idea of touch, which usually accompanies the idea of sight, will spontaneously present itself to the understanding when the visible idea is perceived, and it is in this sense “mediately” perceived (mediate visual perception thesis). To illustrate this model, Berkeley refers to the relation between the word and the meaning: when hearing a word in a known language, the understanding conceives the idea corresponding to its meaning (NTV 50–51). In a similar way sight perceives directly (or immediately) the ideas of light and colours, whose different features and configurations work as signs for the ideas not only of distance, but also of the magnitude and the situation of objects that are actually perceived only by the sense of touch. For Berkeley, two features make the relation of sign to meaning attractive in order to represent the structure of the relation between visible and tangible ideas. The first is that it does not imply a relation of resemblance (as signs do not usually resemble their meanings). The second is that the association between signs and their meaning is established by habit and learned through experience. There is thus no necessary connection between the two. These two features allow Berkeley to distance himself from two alternative explanations of vision. The first assumes that vision works by constructing representations that are related to the object they represent as a geometric projection is related to the projected figure. The second explanation of vision presupposes a resemblance between the content of visual sensation and the perceived object: according to this model, the content of sensation represents an external object because it resembles it. The assessment of the mediate visual perception of distance, size, and situation is not identical to the claim that vision is a language. This thesis is only a necessary, but not a sufficient, condition for its establishment. According to Berkeley most sets of signs do not constitute a language.5 Another important step in the establishment of the claim that vision is a language is the affirmation of the heterogeneity thesis, namely the assertion that there is no one single idea or kind of idea equally perceivable by sight and touch. In order to give a system of signs the status of language, other features must be added such as richness, articulation or compositionality;

5  Berkeley 1979d, Alciphron IV. 12: “That there are signs is certain, as also that language and all other signs agree in the general nature of sign, or so far forth as signs. But it is as certain that all signs are not language [...] It is the articulation, combination, variety, copiousness, extensive and general use and easy application of signs (all which are commonly found in vision) that constitute the true nature of language. Other senses may indeed furnish signs; and yet those signs have no more right than inarticulate sounds to be thought a language.”

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however, because we do not need to deal with these additional features, I will focus here only on the theses of mediate visual perception and heterogeneity.6 In this paper, I take the expression, “idea immediately perceived by sight,” as referring to the ideas whose content corresponds only to ideas directly perceived by sight (such as light and colours), excluding anything deriving from or dependent upon some conscious cognitive process of inference, calculation or association. Furthermore, I consider that according to Berkeley, all the ideas immediately perceived by sight may be the object, at least under some particular conditions of observation, of a conscious, actual experience, and this remains true even for an adult human being that has learned to mediately see the objects at a distance. Therefore, when Berkeley says that distance is not immediately perceived by sight, I take it as admitting the possibility of having a conscious, purely visual experience of light and colours that do not appear at a distance, or, in other words, of having a conscious visual experience of light and colours in which distance is lacking.7 More generally, I take all Berkeley’s claims concerning the content of immediate visual perception as claims that always correspond to some possible actual content of visual experience.

8.2  P  arts 1–3 of NTV – The Numerical Difference Between Visible and Tangible Particular Ideas The structure of Berkeley’s explanation of vision in the Parts 1–3 (respectively on distance, magnitude, and situation) is relatively straightforward. Berkeley maintains that the attentive observation of the contents of ideas present to the understanding, when we believe to see the distance, size and situation of objects, makes three things manifest: first, that the visible ideas present to the understanding when we believe to see the distance, size, and situation of objects are different from the ideas of 6  Berkeley makes explicit the necessary and sufficient conditions for a system of signs to be a language in the fourth dialogue of the Alciphron (Berkeley 1979d) and in Theory of Vision Vindicated and Explained (Berkeley 1979e). For a thorough discussion of these conditions see Pearce 2017, 173–188. For a discussion of issues related specifically to the role of the heterogeneity thesis for the affirmation of vision as a language see Atherton 2008 and 1990, 175, and Wilson 1999. 7  See for instance, NTV 41: “[...] The objects intromitted by sight would seem to him (as in truth they are) no other than a new set of thoughts or sensations, each whereof is as near to him as the perception of pain and pleasure [...],” my italics; NTV 45: “I say, neither distance, nor things placed at a distance are themselves, or their Ideas, truly perceived by sight. This I am persuaded of, as to what concerns my self: and I believe whoever will look narrowly into his own thoughts [...] will agree with me [...]”; NTV 130: “[...] shall calmly attend to his own clear and distinct ideas [...]”; NTV 157: “... this plainness of the picture, is not perceived immediately by vision: For it appeareth to the eye various and multiform.” See also NTV 51. For an account sympathetic to mine of the meaning and status of Berkeley’s NTV 2, see Schwartz 2006a, 13–18. Atherton considers Berkeley’s claim that distance is not immediately perceivable by sight as a claim that is not derived from the contents of experience, but rather from the prior identification of the information that can be represented by the working of the visual system, see Atherton 1990, 69.

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distance, size, and situation actually perceived by touch; second, that variations of the visible ideas associated with them do not correspond to the variations of the tangible ideas of distance, size, and situation following a mathematical function or a necessary rule, and third, that visible and tangible ideas are rather connected by an arbitrary relation grounded in habit similar to the relation connecting a sign to its meaning. The way in which Berkeley develops these points varies according to the feature under consideration. The arguments are straightforward in the case of distance and magnitude, but more intricate in the case of situation. Because of its greater complexity, and because I will be led to employ the results of the description of the “situational” content of visual ideas below in Sect. 8.4, I will devote more time to the case of situation.

8.2.1  Distance As we have seen before, Berkeley claims that distance cannot be perceived by sight and that when we believe to see the distance at which the objects are, the visible ideas present to the understanding are different from the tangible content actually corresponding to distance. The observation of the visible contents actually present in these cases shows that the degrees of confusion of the different distributions of colours of the visual field, properly perceived by sight, serve as signs for the idea of distance actually perceived only by touch.8 By virtue of these signs, sight may be said to “mediately” perceive the distance at which the objects are located.

8.2.2  Magnitude Similarly, in Part 2, on the visual perception of magnitude, Berkeley shows, first, that visible and tangible sizes are different since tangible magnitude is stable and unchangeable, while the visible size varies continuously following the variations of distance and position of the observer (NTV 55); and, second, that visible and tangible ideas are not linked by any kind of necessary connection, since a small visible size may correspond to a large tangible one, and vice-versa (NTV 58, 62–64). The well-known discussion of the case of the eye-microscope is supposed to show

8  NTV 21: “[...] And this being found constantly to be so, there ariseth in the mind an habitual connexion between the several degrees of confusion and distance; the greater confusion still implying the lesser distance, and the lesser confusion, the greater distance of the object.” See also NTV 38. In Part 1, Berkeley indicates also two other ideas that suggest distance to the mind. These ideas are respectively the turn of the eye (NTV 16) and the straining of the eye (NTV 27). However, since these ideas are perceived by touch, in what follow, Berkeley does not refer to them to explain the visual mediate perception of distance.

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precisely this mutual independence (NTV 85–86). Finally, Berkeley shows that, in the case of distance, and also in the case of magnitude, there are visible contents, such as visible magnitude, the confusion or distinctness of the parts of the visual field, as well as their vividness or faintness, that become signs of the stable tangible size (NTV 55–56, 65). At the end of Part 2, Berkeley adds that, since figure is nothing other than the limits of magnitude, exactly the same kind of difference between visible and tangible contents discovered for magnitude has to be admitted for ideas of figures (insofar as they are conceived as the limits of the particular magnitudes; NTV 105). When figure is understood in this way, the visual idea of figure varies in accordance with the modifications of distance and the subsequent modification of magnitude. By contrast, tangible figures are stable. It is because the ideas of figure are taken as the particular content perceived at a given instant (corresponding to the limits of a particular magnitude) that there is no place here for any consideration concerning the internal properties, invariable despite differences of magnitude, as for instance the number of sides and angles. Therefore, as figure is dealt with here as the limit of particular magnitudes, a small figure cannot be the same as a large one. Berkeley will not deal with the internal properties of figures, invariable despite differences of magnitude, until Part 4, where the topic will no longer be the identity or difference of particular ideas, but rather the identity or difference of species of ideas. Indeed, it is in Part 4, discussing geometrical figures, that he will deal with such properties as the number of sides and angles and ideas of figures such as squares and circles.9

8.2.3  Situation Part 3 tackles the question of the visual perception of the “situation” of objects, i.e. of such spatial determinations as being up, down, on the right or on the left. For the future establishment of the heterogeneity thesis, the subject appears to be a thorny one, since it seems that situational organization cannot be given in two different manners. And if sight and touch can both perceive situation, then situation has to be an idea equally accessible by sight and by touch. In order to avoid this inference (i.e. from the perception of situation by sight to the negation of the heterogeneity thesis), Berkeley proves here that there is no genuine visual idea of situation, and that the visual perception of situation is mediated. Despite its greater complexity, his argument resembles in structure the one employed 9  M. Wilson thinks that Berkeley, in his discussion of magnitude, does not restrict himself to considerations concerning particular ideas and that he “generally assume[s] the difference or nonresemblance as well as the numerical distinctness of ideas of sight and touch. (Cf. ## 79; 94–95).”, Wilson 1999, 266. See also ibid. 265. I believe, on the contrary, that although the heterogeneity thesis may be seen as a consequence of what has been proven in the first three parts, the heterogeneity thesis is neither assumed nor proven before Part 4.

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to prove the indirect perception of distance by sight. As in the case of distance, Berkeley’s argument has two steps. The first is negative, showing that sight has no immediate access to situation; the second is positive, and explains how it happens that we believe to see the situation of objects. Both contribute to the establishment of the thesis that visible and tangible ideas do not share the same situational organization. Both result from a careful distinction between the ideas perceived by sight and by touch (NTV 91). With regard to the first step, assessing the inaccessibility of situation by sight, Berkeley argues that “up” and “down” are determinations intrinsically linked either to the perception of the movement of his own body naturally attracted by the Earth, or to the perception of the effort necessary to move the body in the opposite direction; and therefore, since sight has no access to these perceptions, Berkeley suggests that “up” and “down” are not possible contents of sight: 93. It is certain, that a man actually blind, […] wou’d by the sense of feeling attain to have ideas of upper and lower. By the motion of his hand he might discern the situation of any tangible object placed within his reach. That part on which he felt himself supported, or towards which he perceiv’d his body to gravitate, he wou’d term lower, and the contrary to this upper. And accordingly denominate whatsoever objects he touch’d.10

The perception of situation supposes the perception of movement (and some natural directions), therefore since sight has no access to movement in some natural directions, sight cannot perceive situation. But then, how it is that we see or we believe to see things up or down, to the right or to the left of the visual field? Also, in this case, Berkeley explains that it is because different visible contents function as sign for the tangible ideas of situation. From section 97 to section 99, he particularizes the process that associates visible ideas lacking situational organization to the tangible directions of up, down, left and right. The key of the connection between the contents of visible ideas and the tangible situational order is the way distinctness of parts of the visual contents vary according to the movement of the head or of the eye: 97. Afterwards, when upon turning his head or eyes up and down to the right and left he shall observe the visible objects to change, and shall also attain to know that they are called by the same names, and connected with the objects perceived by touch; then indeed he will come to speak of them and their situation, in the same terms that he has been used to apply to tangible things; and those that he perceives by turning up his eyes he will call upper, and those that by turning down his eyes he will call lower. 98. […] And without this motion of the eye, this turning it up and down in order to discern different objects, doubtless erect, inverse, and other the like terms relating to the position of tangible objects, would never have been transferred, or in any degree apprehended to belong to the ideas of sight: The meer act of seeing including nothing in it to that purpose; […]

The process of connection between the visible ideas and the tangible determinations of up, down, right and left is a complex one. It presupposes that the subject has learned, first, that the contents of visual ideas vary in a regular way according to the 10

 See also NTV 94.

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movement of the head, as when some part of the visual field becomes more distinct when the head is moved up, or down, on the right or on the left, and, second, that the contents whose distinctness co-varies with the movement of the head have been associated to some tangible object called by the same name (“shall also attain to know, that they are call’d by the same names, and connected with the objects perceiv’d by touch”). Therefore, it is only once that the visible objects become associated with tangible ones and that their distinctness is observed to co-vary with bodily movements, that visible objects acquire (in the sense that they are associated with) the tangible ideas of up, down, right and left. Note however that there is a difference between the visual mediate perception of situation and the visual mediate perception of distance. In the case of distance, in fact, the visual signs for the tangible ideas of distance are ideas – as the vividness or faintness of colours and light – that are immediately perceived by sight, whereas, in the case of the mediate visual perception of situation the so-called visual signs are a complex structure where the visible content is associated with a complex of tangible and visible ideas. In the case of situation, a given visual idea may become the sign for a tangible situation only insofar as its visual variations have been associated with the variation of some tangible objects. Therefore, since the visible signs for situation are not purely visible ideas, but rather a sequence of visible ideas linked to ordered bodily movements, I propose that these ideas signs should be more properly called “visible-coordinated” or “visible-mixed,” instead of “purely visible” ones.11 Note, however, that the model of mediate perception, according to which visible signs are associated with tangible ideas, applies to the visible-coordinated ideas just as well as it applies to the purely visible ones. That means that visible-coordinated ideas are signs whose tangible meaning need to be learnt. I will return to the topic of the nature and structure of the visual sign for situation later, in Sect. 8.4. Furthermore, Berkeley maintains that, since tangible ideas cannot be in the same “place” as visible ones, the parts ordered according to the directions of up, down, etc. have to belong to the same sensorial space. In other words, the visual and tangible spatial orders are, in a sense, hermetic one to the other, and the situation of an object is given uniquely in relation to the situation of the objects perceived by the same sense. Therefore, according to Berkeley, the supposed problem of the inversion of the retinal image is merely nonsensical since it supposes a comparison between the orders of a tangible object (the retinal image) and of a visible one (the perceived visual field), which is actually impossible (NTV 115).

 This echoes another important phenomenon of mixing visible and tangible ideas that Berkeley describes in NTV 145 (in Part 4): “145. Add to this, that whenever we make a nice survey of any object, successively directing the optic axis to each point thereof, there are certain lines and figures described by the motion of the head or eye, which being in truth perceived by feeling, do nevertheless so mix themselves, as it were, with the ideas of sight, that we can scarce think but they appertain to that sense. [...]” On this process of association and transfer of situation and other spatial features from tangible ideas to visible one, see Atherton 2008. In Sect. 8.4, I will make a few comments on this article.

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In summary, in Parts 1–3 of NTV, Berkeley shows that sight does not perceive immediately the distance, size or situation of objects, although it perceives them mediately, since it perceives different combinations of light and colours that function as signs of the tangible ideas of distance, size, and situation. More specifically, he maintains that there are no visible ideas for the distance and situation of objects, and that visible and tangible magnitude are different. For all these kinds of contents, visible ideas are signs for the tangible content, which is not immediately perceivable by sight. I will move now to Part 4 of NTV, where Berkeley attempts to prove more generally that there is no a single idea or kind of idea equally perceivable by sight and by touch.

8.3  The Proof of the Heterogeneity Thesis in Part 4 In section 121, Berkeley clearly states the nature of the difference between the topic of Parts 1–3 and that of Part 4: […] From what we have at large set forth and demonstrated in the foregoing parts of this treatise, it is plain there is no one self same numerical extension perceived both by sight and touch; but that the particular figures and extensions perceived by sight, […], are nevertheless different, and have an existence distinct and separate from them: So that the question is not now concerning the same numerical ideas, but whether there be any one and the same sort or species of ideas equally perceivable to both senses; or, in other words, whether extension, figure, and motion perceived by sight are not specifically distinct from extension, figure and motion perceived by touch.

However, in the details, the difference in nature between the propositions in Parts 1–3 and those of Part 4 is not always easy to grasp. One reason for this difficulty is that in the proof presented in Part 4, Berkeley often employs some of the conclusions obtained in Parts 1–3. This use is legitimate and entails neither that the proof is invalid, nor that Berkeley repeats in Part 4 what was already presented earlier.12 More specifically, in Part 4, Berkeley tries to show that there is no idea of extension, figure and movement equally perceivable by sight and by touch.13 To prove this thesis, he shows that visible and tangible ideas are structurally different. He proceeds by describing in detail the contents of these spatial ideas as they are perceived

 Atherton claims that the relationship between discussions of heterogeneity of Parts 1–3 and that of Part 4 are “at least initially, a little unclear” (Atherton 1990, 173). She also claims that the arguments for the heterogeneity thesis of Part 4 are extremely terse (ibid., 173) and that “the reason of their terseness, however, is that Berkeley [...], regards his point as having already been established in earlier sections [i.e. Parts 1–3]” (ibid., 183). See also ibid. 172–174, 183–184, 202, and Wilson 1999, 266, quoted note 9 supra. 13  In Part 4, figure is considered as a specie of ideas rather than (as was the case in Part 2) as the limits of a particular magnitude. For a discussion of figure as a specie of idea, see below part c. of this section. 12

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by touch, each time highlighting some components of the notion that make it structurally inaccessible to sight.14 Berkeley presents separate arguments for the heterogeneity of the visible and tangible ideas of extension, figure and movement, all of them uncovering interesting aspects of his general conception of visible and tangible spatiality. In what follows, for each examined feature, I will first report the arguments in view of the heterogeneity thesis, and then I will take them as a source of a first, partial account of the spatial contents of visible and tangible ideas and their structural difference.

8.3.1  Extension To prove the heterogeneity of visible and tangible ideas of extension, Berkeley gives two distinct arguments. Both contain relevant information concerning the essential features of visible and tangible extension. The first argument (NTV 129–130) is that the only ideas perceivable by sight are light and colours and, since these ideas are not perceived by touch, there are no ideas equally perceivable by sight and touch. In NTV 130, Berkeley explains this very short argument maintaining that, even if many people think that, besides light and colour, sight perceives also extension and figure, it must be clear that visible extension (and figure) are not visible ideas perceivable separately and independently from light and colours. The explanation becomes more perspicuous when it is read together with NTV 135 (that I will discuss more in detail below), where Berkeley explains that ideas of tangible figures are not perceivable by sight because they are composed of ideas, which are each of them not perceivable by sight. Therefore, we can infer that what Berkeley is actually saying at NTV 130 is that, since visible extension is not analysable in anything else than light and colours, and lights and colours are not perceivable by touch, necessarily visible extension cannot be perceived by touch. The second argument (NTV 131) is an application of the claim that it is impossible to add visible and tangible extension (or figure) – an impossibility that is presented here as a mark of heterogeneity. According to Berkeley, as we do not add lines to surfaces nor surfaces to volumes in geometry because they are quantities of a different kind, we cannot add tangible lines with visible lines because tangible ideas and visible ideas are heterogeneous. Concerning the features of tangible and visible extension, these arguments give us interesting information. First of all, it appears that visible extension is not analysable into anything other than light and colours. Secondly, it appears that tangible (and visible) extension are additive quantities, and that the possibility of

 As this part concern visible and tangible ideas in general and not the actual connections between particular visible ideas and particular tangible ones, the arguments focus on the structure or the component parts of the ideas and generally set aside all questions relative to the connection between particular occurrences of visible ideas and the tangible ideas of which they are signs.

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accomplishing some operations as adding or uniting two given entities is a mark of their “homogeneity,” or of their being of the same kind.

8.3.2  Movement Concerning movement, Berkeley claims that there is no common idea of movement equally perceived by sight and by touch, since, as he has shown in the part on situation, the idea of movement is connected to the ideas of direction and the ideas of direction correspond to the ideas of being supported or of being attracted – ideas that can be perceived only by touch.15

8.3.3  Figure To prove the difference between visible and tangible ideas of figure, Berkeley uses the case of the blind man made to see. In order to show that he cannot discern nor recognize the previously known ideas of figure, he details the content of the tangible ideas corresponding to words such as “cube” or “sphere”. Berkeley writes: 135. […] Cube, sphere, table are words he has known applied to things perceivable by touch, but to things perfectly intangible he never knew them applied. Those words, in their wonted application, always marked out to his mind bodies, or solid things which were perceived by the resistance they gave: But there is no solidity, no resistance or protrusion perceived by sight. […]

Following this description, tangible ideas of figure are complex ideas composed of some more elementary ideas such as solidity, resistance and protrusion. The immediate consequence of this description is that sight, which has no access to any of these component ideas (i.e. solidity, resistance, and protrusion), cannot perceive the ideas of figure as perceived by touch. Other interesting differences concerning the idea of a figure perceived by sight and perceived by touch emerge when Berkeley considers the case of a mind able to see but missing the sense of touch (an “unbodied spirit”, as he calls it).16 Two different but not independent questions are asked. The first is whether such a spirit may understand the principles of Euclidean geometry, and the second is whether he may at least have the ideas of planar or solid figures as they are given in geometry. For both questions, Berkeley’s answer is negative. First, the disembodied spirit would not be able to know even the first elements of Euclidean geometry because it could neither understand the manner of construction of geometrical figures nor the use of

 NTV 137 (employing a conclusion of the part about situation, NTV 95).  NTV 153. For a rich discussion of the case of the unbodied spirit and its meaning in relation to Berkeley’s conception of geometry and geometrical figures, see S. Storrie 2012.

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the straightedge and compass, nor, lacking the idea of distance, could it exactly know their equality or difference. Second, such a spirit would not be able to perceive ideas of solid or planar figures because what it would see, would be different combinations of lights and colours that, being not at a distance, could not be on a planar or solid figure. The reason for that is that the “smoothness and uniformity” proper to plan (which are the ideas perceived by touch, the ones denoted by the expression of “plainness of the picture”) are actually absent from the content of visible ideas, that are instead “various and multiform”.17 Therefore, visible ideas in themselves are neither ideas of planar nor solid figures. Indeed, visible combinations of colours are not figures at all – or, at least, not in the same sense that tangible figures are. There is another contrast between visible and tangible ideas of figure: in section 156, Berkeley describes the visible combinations of colours as being fleeting and unstable and therefore incapable of being used according to the operations of geometry.18 By contrast, tangible figures appear to be stable. Indeed, visible and tangible figures are perceived in a different manner. Berkeley presents the co-existence of distinct parts as a feature that visible and tangible extension share, but, in the case of sight, these distinct parts are said to be perceived in a single instant or “at once”, whereas tangible figures are identified with the figures successively described by the (tangible) movement of some parts of the body, and perceived precisely through this movement.19 Therefore, the perception of figures by touch is the perception of distinct parts that co-exist successively, so to speak, since they are not all given at the same time, but are apprehended through the unity and continuity of the movement that follows their contours.20

 NTV 157–158: “157. [...] But, with a little attention we shall find the plains here mentioned, as the immediate objects of sight are not visible but tangible plains. For when we say that pictures are plains, we mean thereby that they appear to the touch smooth and uniform. But then this smoothness and uniformity, or, in other words, this plainness of the picture, is not perceived immediately by vision: For it appeareth to the eye various and multiform. 158. From all which we may conclude that plains are no more the immediate object of sight than solids. [...] But though they [the immediate objects of sight] are called by the same names with the things marked by them [tangible plains and solids], they are nevertheless of a nature intirely different, as hath been demonstrated.” 18  NTV 156: “All that is properly perceived by the visive faculty, amounts to no more than colours with their variations, and different proportions of light and shade: But, the perpetual mutability, and fleetingness of those immediate objects of sight render them incapable of being managed after the manner of geometrical figures; nor is it in any degree useful that they should. It is true there are divers of them perceived at once; and more of some and less of others: But accurately to compute their magnitude and assign precise determinate proportions between things so variable and inconstant, if we suppose it possible to be done, must yet be a very trifling and insignificant labour.” We can find a synthesis of the contents of vision in section 44 of The Theory of Vision Vindicated and Explained (Berkeley 1979e): “The proper, immediate object of vision is light, in all its modes and variations, various colours in kind, in degree, in quantity; some lively, others faint; more of some and less of others; various in their order and situation. [...]” 19  NTV 145, quoted above note 11. The same description of visual perception as given in a single instant may be found in several sections, see also NTV 83, 105, 110, 124, 156. 20  A similar description of tangible extension is in Falkenstein 1994, 78. 17

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It seems possible to link the difference concerning the contents of visible and tangible figures not only to the absence/presence of the idea of a distance, but more importantly, to the difference in the ways in which they are perceived. Indeed, we can suppose that it is because tangible figures are perceived through a successive, ordered movement that these figures are stable, measurable and can be managed according to the requirements of geometry. Similarly, it is because distributions of colour are perceived instantaneously that these figures are fleeting, unstable, neither planar nor solid, un-measurable and cannot be the object of geometry. It results from the above that visible and tangible ideas are different since, inter alia, visible contents are non-situated in space, are non-naturally oriented and fleeting and unstable; while tangible contents are, to the contrary, stable, oriented, movable etc. Berkeley has shown that the ideas of extension, figure, and movement as perceived by touch are structurally different, and cannot then be the objects of sight. From this, Berkeley concludes that there are no ideas commonly perceived by sight and by touch or, in other words, that ideas of sight and ideas of touch are heterogeneous.21 The opposition between the two kinds of spatial ideas thus appears to be clear. However, as I said in the introduction, in NTV there are sections that are in different ways inconsistent with this description and threaten the validity of the heterogeneity thesis. In the next section, I will consider these challenging sections.

8.4  Visible Contents and the Problems of Heterogeneity These critical sections come from different places of NTV and pursue different aims in Berkeley’s global explication of vision. The problem they raise comes from some of the elements of the description of the content of visible ideas they advance. To be more specific, I will quote here, following the order in which they appear in the text, all of the challenging passages: –– NTV 44. [the visible Moon, or that which I see, …] is only a round, luminous plain, of about thirty visible points in diameter. […] –– NTV 63. [… it is also certain] that the greater visible magnitudes might have been connected with, and introduced into our minds lesser tangible magnitudes, and the lesser visible magnitudes greater tangible magnitudes. Nay, that it actually is so, we have daily experience; that object which makes a strong and large appearance, not seeming near so great as another, the visible magnitude whereof is much less, but more faint, and the appearance upper, or which is the same thing painted lower on the retina, which faintness and situation suggest both greater magnitude and greater distance […]

 But note, however, that this conclusion is compatible with the claim we will discuss below, i.e. the claim that sight perceives in its own way some distinct alternative ideas of extension and figure.

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–– NTV 142. I answer, it must be acknowledged, the visible quare is fitter than the visible circle, to represent the tangible square, but then it is not because it is liker, or more of a species with it. But, because the visible square contains in it several distinct parts, whereby to mark the several distinct, corresponding parts of a tangible square, whereas the visible circle doth not. The square perceiv’d by touch hath four distinct, equal sides, so also hath it four distinct equal angles. It is therefore necessary, that the visible figure which shall be most proper to mark it, contain four distinct, equal parts corresponding to the four sides of the tangible square, […]. And accordingly we see the visible figures contain in them distinct visible parts, answering to the distinct tangible parts of the figures signified, or suggested by them. In these sections, Berkeley refers to different positive features of visual ideas. Visible contents are characterized in the following terms: –– at least in some conditions, visual ideas present themselves as areas having a definite, although approximate, size (“a round, luminous plain, of about thirty visible points in diameter”, NTV 44); –– portions of the visual fields present themselves as having a situation, i.e. they may be in the upper or lower part of the visual field (NTV 63); –– they may have definite figures like that of a square or of a circle (NTV 142); –– visible figures may have distinct parts, as sizes and angles; –– certain visible figures can be fitter than others to mark the parts of tangible figures without resembling them (NTV 142); Berkeley’s description here appears to correspond quite precisely to our immediate, intuitive contents of visual perceptions. Nevertheless, when we associate this description to what Berkeley writes in his proof of the heterogeneity thesis, a certain number of questions arise concerning the ideas of figure, situation, and size as possible contents of visible ideas. Here are the main challenges: –– How can Berkeley write that visual ideas are ideas of squares and circles, and, at the same time, maintain that neither plans nor solids are the immediate object of sight? Can a square, having four visible equal sides and four visible equal angles, be something else than a plane figure (or at least be an approximation of a plane figure)? (question 1) –– How can Berkeley claim that there are visible circles and squares, that have the same number of parts as tangible circles and squares, while maintaining at the same time the heterogeneity thesis, i.e., the thesis that the two kinds of figures are in no way similar? Certainly, as he says, visible figures are too fleeting and changing to be handled in the manner of geometrical figures, but is it legitimate to say that a fleeting square is heterogeneous to a definite and stable one just because it is the unstable approximation of it? (question 2) –– How can he say that visual figures are in the upper or lower part of the visual field when he denies that situation is a possible content for visual ideas? (question 3)

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–– How can he say that visible figures are fleeting and unstable and, at the same time, determine, although in an approximate way, the number of visible points that compose them? Can a fleeting and unstable figure have a size? (question 4) In the next sections, I will attempt to give a coherent answer to these questions.

8.5  Two Kinds of Extension and Figures The issue concerning the consistency between Berkeley’s heterogeneity thesis and the rest of his theory of vision has been regularly addressed and, notwithstanding the amount of literature on the subject, the interest for these nodal points of NTV does not appear to diminish. Within the wide range of interpretations, we will distinguish three main positions: the first considers Berkeley’s proof of the heterogeneity thesis invalid, and therefore maintains that Berkeley’s explanation of vision has to work without this thesis; the second accepts the validity of Berkeley’s heterogeneity thesis, claiming that only tangible ideas may have a spatial content, while visible ideas are only light and colours; the third relies the validity of the heterogeneity thesis to the possibility of two different, heterogeneous ways of being spatial, corresponding to the different, independent contents of visible and tangible ideas. My reading of Berkeley’s NTV falls within this third category. In what follows, I will briefly comment on the two first types of interpretation, and develop the latter more fully. The first group of interpretations can be illustrated by the account developed by Margaret Wilson (Wilson 1999). According to Wilson, Berkeley’s arguments for the heterogeneity thesis are ineffective, and the thesis is contradicted by Berkeley’s claim that visible squares are fitter than visible circles to mark ideas of tangible squares (Wilson 1999, 258). Wilson thinks, in fact, that Berkeley’s concepts of resemblance, heterogeneity, and fitness are too unclear to allow the possibility for a visible idea to fit a tangible one without being of the same sort as it (Wilson 1999, 268–269). The second kind of interpretation can be represented by Margaret Atherton’s argument in “What Have We Learned When We Learn to See?: Lessons Learned from the Theory of Vision Vindicated”. According to her, extension and figures may be perceived exclusively by the sense of touch, since sight has no access to ideas of distance, and therefore no access to ideas of extension, figure, and movement (Atherton 2008, 279–284). The heterogeneity thesis may then be seen as a direct consequence of this claim: since only tangible ideas can have spatial contents, while visible ideas are only of light and colours; necessarily, there are no ideas equally perceived by sight and by touch. Moreover, Atherton suggests that – and this is what we are supposed to learn when we learn to see – through experience, tangible and visible ideas can be coordinated with each other, and touch may in a sense transfer its spatial structure and organisation to visible ideas. Therefore, according to Atherton, in all sections where Berkeley refers to visible situation, extension or

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figure, he is actually referring to a special kind of ideas taken from the coordination between visible and tangible ideas (through which the tangible spatial contents have been transferred from and imposed upon visible ideas).22 The main problem of this kind of interpretation is that, since visible extension is derived from tangible extension, it cannot explain Berkeley’s claim, quoted above, that a visible square is fitter than a visible circle to mark a tangible square without being of the same sort as it. In fact, if the extension of visible ideas is derived from the one perceived by touch, a visible square – being “figured” and “extended” through the spatiality of tangible figures – must not only have the same number of parts as a tangible square, but also the same spatial nature, and therefore must be of the same kind as it.23 Interpretations of the third category maintain that, in NTV, Berkeley outlines two different ideas of extension and figure perceived respectively by sight and by touch. Lorne Falkenstein in “Intuition and Construction in Berkeley’s Account of Visual Space” and Ville Paukommen in “Berkeley and Activity in Visual Perception” defend the existence, in NTV, of this twofold nature of extension and spatiality.24 These interpretations present the advantage of supporting and explaining in simple terms the basis and foundation of the heterogeneity thesis. Both of them present a description of the features of visible and tangible extension, and both of them consider Berkeley’s description of the specific features of visual extension to be unclear and problematic. The problems Falkenstein and Paukommen point out are, however, not the same, and I will in what follows say something about their differences. Falkenstein maintains that tangible extension is “a certain qualitative kind of tangible experience” (Falkenstein 1994, 78), corresponding to the successive sensations received through the movement of the body following the surface of the objects, while visible extension is the multiplicity of visible points simultaneously present in the visual field (ibid., 79). For Falkenstein, however, Berkeley’s description of visual spatial contents remains voluntarily incomplete and ambivalent, because of the unwelcome consequences that a more precise analysis would necessarily have on Berkeley’s theories on matter and abstract ideas.25

 Atherton 2008, 284–285. Atherton 2008, 284: “What happens according to his account is that we stabilize the color we see by coming to correlate our tangible experiences of reaching up with the color that come into view when we raise our eyes up. The upshot of this process is that we come to construct a kind of Alberti-window, that is, we learn to speak of our color experiences as if they were laid out spatially on a grid. [...] If I am right, the first, Berkeley is not maintaining that the problem of situation perception is one of correlating visible situation with tangible situation. The only kind of situation that exists is tangible situation, but we learn to speak analogically of visual situation by assigning to our color ideas a tangible meaning.”. 23  In her article, Atherton do not discuss the “fitter” case of NTV 142. 24  Falkenstein 1994 and Paukommen 2014. See also Schwartz 2006b. 25  Ibid., 76–77; ibid., 83: “In the end, there does not seem to be any really satisfactory account of visual perception that Berkeley could give which would be consistent with all of his principles.” (see also ibid., 84). Furthermore, Falkenstein, at the end of his article (Ibid., 84), reverses his initial thesis assessing the intuitive, immediate character of visible bi-dimensional spatial contents and maintains that, if Berkeley would have chosen to be clearer about the content of visible spatial ideas, he would also have to make “more momentous advances in the constructivist program.” This 22

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Falkenstein’s thesis – which assesses the primitive, intuitive character of visible figures – is developed in a more recent article by Paukommen. Paukommen defends the existence of two heterogeneous ways of being spatial, and he particularizes the positive features of the tangible and of the visible ideas of extension and figure. His paper is an attempt to make the possibility of an alternative, heterogeneous, visual way of being extended and figured intelligible. Paukommen describes visible extension as having some kind of spatial organization – and this, even if visible figures are continuously changing, lacking by nature any fixed and determinate borders, so that their dimensions and proportions cannot be metrically determined.26 Unlike Falkenstein, Paukommen does not give up on explaining Berkeley’s seemingly incoherent claims about extension and spatiality. But, to get directly to the point, I believe that two problems emerge from his account. First, Paukommen maintains that visible figures lack determinacy by nature (they are fleeting, do not possess metrical features and have no determinate borders). But we can wonder whether this indeterminacy suffices to keep visible ideas separate from tangible ones. Indeed, by focusing on their indeterminacy, Paukommen seems to consider visible figures as rough approximations of tangible ones (unsuitable for geometry, because of their fleetingness and imprecision). Now, one condition for “approximation” is that the two elements share the same nature. In other words, to particularize visible figures mainly through their indeterminacy appears to undermine the possibility of their heterogeneity. Second, Paukommen distinguishes between, on one hand, the purely visual non-­ conceptual contents of ideas perceived by sight before all learning and association with the ideas of touch and, on the other, the phenomenology they acquire when visible ideas become signs of tangible ones, and he claims that, although “the proper objects of vision are still present to us since our current visual field is made up of them”, it is also true that “[…] since our phenomenology of vision has radically altered by our learning to connect ideas of touch and thus to perceive objects at distance from us, we are not able to go back to our original visual perception and to attend to our visual field as it was.”27 Now, it seems to me that, in Berkeley’s philosophy (with his reduced ontology of minds and ideas), it is difficult to find a place for a distinction between an idea and its phenomenology. As a matter of fact, Berkeley identifies the idea with the content immediately and sensibly appearing in experience, or with the contents perceivable only when a special kind of attention is program supposes that visible spatial contents result from a (cognitive) construction of visible extension and figures, starting from the elements of tangible perceptions (that is quite the opposite of the immediate intuition of visible spatial ideas defended at the beginning). 26  Paukommen 2014, 262 and 268. Paukommen lumps together Berkeley’s claims on figure as the “termination of magnitude” at the end of the part on magnitude, and what he writes about the notions of geometrical figures in the part on heterogeneity. It seems to me that this association leads to some confusions in his final discussion of the case of the idea of visible square being fitter than visible circle to mark tangible square (ibid., 270). 27  Ibid., 269. See. also ibid., 272: “and it is by application of this concept [of distance] on the visual data by which our visual field transforms and we begin to perceive (some of its elements as objects at distance).”

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given. However, these contents appear to be always immediately present to the perceiving mind. Paukommen recognizes and defends this presence, but at the same time, introduces his view that the phenomenology of the idea may change without any internal change in the visible idea. But then, we may ask, what would the phenomenology be, if not its immediately sensible content? That ideas are always contents of perception emerges in several sections of NTV where Berkeley describes either the immediate contents of visual perceptions, or a special kind of attention capable of making these fleeting visible contents known.28 This remains true although Berkeley says that, in some cases, this content is so strongly and suddenly associated with tangible ideas that to focus uniquely on the visible content “seems scarce possible”.29 I will now move on to my understanding of Berkeley’s notion of extension and figures. Like Falkenstein and Paukommen, I believe that Berkeley refers in NTV to two distinct heterogeneous notions of extension and figures, which are respectively perceived by sight and by touch. Yet, we differ on the way of understanding the features of these two kinds of extension and figures and thus, on the reasons for their heterogeneity. In the remaining part of this section, I will give a detailed account of the differences between visible and tangible extensions and figures, and I will show that the description of these differences provides us with an answer to the aforementioned questions concerning the consistency of all the propositions of NTV (questions 1–4). In my view, Berkeley keeps visible extension and figures separate from tangible extension and figures, not because the first would be the fleeting approximations of the latter, but rather, because they are composed of different ideas, and the manner in which they are composed is different: both kinds of extension have co-existent parts, but the way in which these parts co-exist is different.30 The parts of tangible extension co-exist in a diachronic way, through the movement giving rise to their perceptions, while visible parts co-exist synchronically, in one single instant. Similarly, at the level of perception, the parts of tangible extension are perceived successively, one after the other in time, while the parts of visual extension are perceived in a single instant. As a consequence of this difference, visible extension is finite and reduced to the limits of the visual field (NTV 82–83), whereas tangible extension has a temporal dimension and may be indefinitely extended. Moreover, the movements giving rise to tangible extension may be given

 See note 7 supra.  NTV 159. As we have seen before, the example used by Berkeley to illustrate this point (NTV 50–51) is clear: upon hearing a word in a known language we cannot hinder the idea corresponding to its meaning to present itself to the understanding. However, in Berkeley’s example the idea-sign, the sound of the word, becomes just associated to the idea-meaning, this association producing a quick passage from the sign to its meaning, both remaining distinct and perceivable notwithstanding their association. 30  NTV 145, quoted above, and NTV 156. 28 29

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in an ordered way and are reversible, whereas purely visual perception, being instantaneous, has no order. As regards figures, these differences concerning the nature of co-existence of the parts entail that visible figures are perceived all “at once” as a whole, and are “fleeting and unstable”. On the other hand, because tangible figures exist diachronically, they can be followed in an ordered way, they are stable and may be “handled” according to the operations of geometry. Moreover, since sight has an access to its contents in a single, instantaneous view, and its parts cannot be explored in an ordered way, the distinct parts of visible figures cannot be successively distinguished and precisely counted. Visible sizes and visible angles are actual sensible parts of visible figures, but they are structurally different and heterogeneous from tangible sizes and tangible figures that correspond to particular bodily sensations (i.e. ideas) linked to the movement and pressure. The classification of visible figures is then a classification of a qualitative order and therefore does not work in the same manner as the classification of tangible figures whose parts may be precisely counted. Indeed, the number of visible distinguished parts is limited (as limited as visible extension in itself). In the frame of visible ideas, a square is not a figure that has one side more than a triangle and one less than a pentagon: it is a figure having a given qualitative character that make it a visible square. The difference between visible and tangible figures does not depend on the inability of the perceiver to count the parts, as in the case of an animal or a small child that does not master the operations of counting and therefore is unable to count the sides of a square he possibly distinctly perceives: the difference between visible and tangible figures consists rather in the material or content of the ideas. In the case of visible ideas, this content is unsuitable for counting, and, more generally, it does not allow operations based on an ordered structure.31 These differences between visible and tangible spatial ideas may all be linked to a structural difference between sight and touch in relation to the movement of one’s own body. Tangible extension and situation are in fact linked to movement according to the natural directions, such as up and down (that are in turn linked to the ideas of being supported or to perceive “the body to gravitate”), while sight has no access either to movement or to direction. We may now come back to the questions concerning the internal consistency of NTV. The overview of the structural differences between visible and tangible spatial ideas allows me to explain why for Berkeley visible figures are not plane figures,  The sensation of solidity must not therefore be understood as a simple “filling” quality. In other words, I believe that the difference between figures perceived by touch and the ideas of sight does not lie in the fact that the tangible figures are filled with solidity whereas the ideas of sight can only come filled with colour. This indeed would not be a proper basis for the heterogeneity thesis. The problem is rather that tangible qualities do not behave in the same way as visible subject qualities and that only tangible ideas can bring about ideas of figure in the proper sense of the term. I thus disagree with a critic formulated by Wilson (Wilson 1999, 271) and according to which “Berkeley’s case for heterogeneity seems to come down to the view that tactual and visual shapes cannot resemble each other because they are respectively bound up with different special sensibles”.

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why they are not of the same kind as tangible figures, and yet may still have a determinate number of sides and angles. For example, a visual square is not of the same kind as a tangible square, although both have four equal sides and four equal angles. The existence of the two kinds of figures explains how Berkeley can consistently maintain that sight has no access to figures (neither planar nor solid) and, at the same time, refer to visible squares and visible circles: when “figure” is taken in its tangible sense – i.e. as an idea depending on the ideas of movement, pressure, protrusion – such an idea cannot be perceived by sight; however, when the figure is conceived as the instantaneous disposition of some coherent visual qualities, figure may be perceived by sight. It is in this visible sense that Berkeley refers to visible squares and visible circles. However, these figures are neither planar nor solid, “plane” and “solid” receiving their meaning exclusively in relation to tangible ideas of pressure and protrusion (question 1). Furthermore, since the content of visible ideas allows us to distinguish, in a single view, the existence of different parts such as angles and sides, it becomes possible to explain why a visible square is actually “fitter” than a visible circle to mark the parts of a tangible square, without being of the same sort of it: a visible and a tangible square corresponding in the number of their parts, but not in their nature (question 2).32 Contrary to what Paukommen maintains, I think that the content of visible figures is sufficiently determined to account for the relation of fitness (or, more precisely of the difference in degree of fitness) between visible and tangible figures, before and independently of any learned association with the ideas of touch. I believe then that Berkeley’s description of visible and tangible spatial contents is richer and more coherent than Falkenstein and Paukommen are ready to admit. However, this enrichment of the description of the content of visual ideas does not suffice to solve all the difficulties. The spatial features of the visible ideas listed above cannot account for the passages where Berkeley speaks of the situation of the parts of the visual field (question 3), nor for the passages about the measure (in terms of visible points) of a given visible figure (question 4). As we have seen before, visible ideas lacking the ideas of distance cannot have a content organized according to the situational directions, nor have a content structured in a way required for counting and measuring. In order to explain these references to the situation and the measure of visible parts, it is necessary to come back to the process of association and coordination of ideas of sight and ideas of touch Berkeley describes in the part on situation. This process is supposed to allow for the transfer of determinations of “up” and “down” to ideas of sight.

 I disagree here with Atherton who, if I understand her well, thinks that the ideas of sight lack any natural organization and that all structures are imposed on them by the ideas of touch (Atherton 2008, 161). I believe on the contrary that the visual ideas have natural units, i.e. definite characteristics that are independent from touch. Without these characteristics it would be impossible to maintain that visual squares have four equal sides and angles. There would not be any sense to say that visible squares are better suited to represent tangible squares than visible circles. In fact, if the ideas of sight could be numbered in any way, a circle could then have four parts and be just as “suited” as a square to represent a tangible square.

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In my view, and in contrast to Atherton’s (in Atherton 2008), there are originally visual spatial contents. However, these contents cannot account for the organization of space according to the directions of up, down, left and right properly perceived only by touch, and I believe that Atherton’s interesting idea of a transfer of spatial structure and of subsequent stabilization of visual contents is fruitful when it is applied, not to figure and extension in general, but (as we have seen before) uniquely to situation. However, since the transfer is possible only when visible and tangible contents are in a way connected and progress together, this transfer does not concern purely visible ideas, and is possible only when visible and tangible ideas are taken together and coordinated. It is by virtue of the existence of this coordination that Berkeley can, without inconsistency, maintain on some occasions that visible ideas cannot have situational order and, on other occasions, refer to the “lower” or “upper” situation of some parts of the visual field.33 The two supposedly contradictory claims do not actually apply to the same subject:34 the first claim (the one negating the possibility of a visual access to situation) applies to a purely visual content, whereas the second one (admitting the existence of a situational organization for ideas of sight) applies to ideas of sight coordinated or mixed with ideas of touch. It is then this kind of “coordinated” or “mixed” ideas that may be “seen” in the upper or in the lower part of the visual field. It is only in this “visible-coordinated” or “visible-mixed” sense that the visible moon may be seen in the upper part of the visual field, and that this mixed situation may become a sign for its tangible size (question 3). It is this same association between visible and tangible situation that explains how visible figures may be said to be fleeting and unstable and, at the same time, be composed of a fixed, apparently measurable, number of visible points. The two descriptions, in fact, do not apply to the same content and only the visible contents mixed with the tangible ones and stabilized by them (to use an expression employed by Atherton)35 may have a definite size measurable by some ordered movements. The definite size therefore characterizes the mixed (visible and tangible) figure, and not the purely visible one: purely visible figures have no fixed measurable size (question 4). Purely visible ideas may possibly be larger or smaller in comparison one to the other, but this comparison is immediate and intuitive, and does not contain any operation of measuring. Thus, in order to make the consistency of NTV as a whole manifest, it is important to distinguish three possible kinds of spatial contents, i.e. purely tangible, purely visible, and visible and tangible “coordinated” or “mixed together”. Berkeley most of time calls “visible” the ideas of the third “mixed” kind, but it is important to distinguish them from the purely visible ones.  Respectively in NTV 93–94 and NTV 63, 99, 111.  This is evident for instance in NTV 93–94 and 99 where the claims respectively negating and affirming the situational organization of visible ideas are not given in directly subsequent sections and between the two (sections 97–98) is described the process of coordination of visible and tangible ideas. 35  Atherton 2008, 284. 33 34

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To summarize, many features distinguish structurally visible and tangible extension and figures. On the one hand, tangible extension is given successively according to a spatial order and ordered directions, has no apparent limits; tangible figures (which presuppose the ideas of movement, pressure and protrusion) are stable, moveable and admit a series of operations connected to movement. On the other hand, visible extension is perceived in a single instant, without any order, and its parts are fleeting and unstable; visible figures can have definite spatial characteristics (for instance, they have qualitative features, in certain case, they have a given but small, number of visually equal sides and angles, and have a relative magnitude, i.e. they can be smaller or more extended the one than the other, etc.), but these characteristics are structurally different from the ones which belong to the ordered tangible figures. It is because of this structural difference that visible and tangible ideas may be said to be heterogeneous, even if both of them may be squares or circles, small or large, etc. Finally, ideas that are not pure visible ideas result from the coordination of the variations of the visible contents following the tangible movements of the head or of the eyes. Thanks to this coordination, visible contents, “mixed” with tangible ones, may gain a situational organization and may be said to be, for instance, in the upper or in the lower part of the visual field. Given their “mixed” or “coordinated” character, the heterogeneity thesis does not apply to them.

8.6  Extension, Succession and Motion Two writings, Philosophical Commentaries and The Analyst – the first preceding, the second following the publication of NTV – support and elucidate this reading. These texts are interesting for our subject because, in contexts different from the one provided by the theory of vision, they explicitly link extension to the manner of co-existence of its parts. First, in the entry 400 of Philosophical Commentaries, Berkeley raises the question of whether it is possible to conceive the existence of two kinds of extension, explicitly connecting their difference to the way they are perceived and to the way they are related to movement: 400 1 X 3 Qu: if there be not two kinds of visible extension. one perceiv’d by a confus’d view, the other by a distinct successive direction of the optique axis to each point.

According to Berkeley, here, spatial visible ideas of the first kind are perceived confusedly and at once, while spatial visual ideas of the second kind are perceived by the successive orientation of the optic axis. Both kinds of extension are perceived by sight, but sight is conceived as capable of working in two distinct manners: instantaneously and confusedly, or successively and distinctly. Sight is thus endowed with the capacity to perceive two distinct ideas of visible extension. It is then easy to establish a correspondence between, on the one hand, instantaneous and confused visible extension and the visible extension as described in NTV, and, on the other, the distinct and successive visible extension and the extension as perceived by touch

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in NTV. From this perspective, the main difference between the preparatory remark of the PC and what Berkeley writes in the published text of NTV would concern the definition of the limits proper to each sense, rather than a twofold way of conceiving extension and spatiality. In other words, what, in PC, is described as the extension perceived through the successive movements of the optic axis, will become the paradigm of the successive tangible extension of NTV. Indeed, according to Berkeley in PC as later in NTV, only the extension perceived through the successive movement of the optic axis is distinct and proper to mathematics: 443 1 X 3 If visible extension be the object of Geometry ‘tis that which is survey’d by the optique axis. 460 X Extension, motion, Time do each of them include the idea of succession. & so far forth they seem to be of Mathematical Consideration. Number consisting in succession & distinct perception wch also consists in succession for things at once perceiv’d are jumbled & mixt together in the mind. Time and motion cannot be conceiv’d without succession, & extension qua Mathemat: cannot be conceiv’d but as consisting of parts wch may be distinctly & successively perceiv’d. Extension perceiv’d at once & in confuso does not belong to Math.

In these entries, Berkeley associates geometrical extension (as well as time and movement) with the idea of succession. The difference between geometrical extension and the extension perceived in a single instant by sight is not a difference concerning the act of perceiving. It is more precisely a difference concerning the component parts that are “distinct” in mathematical extension and “jumbled & mixt together” in non-mathematical one: the mathematical extension consists of parts “which may be distinctly and successively perceived”. Succession and motion are therefore essential constitutive elements of geometrical extension. A similar connection between extension, movement and the succession of parts is settled in a text of 1734, entitled The Analyst (Berkeley 1979f). Berkeley concludes the text with a certain number of queries, among which the following, concerning the relation between space and movement: QU. 11. Whether many points which are not readily assented to are not nevertheless true? And whether those in the two following queries may not be of that number? QU. 12. Whether it be possible that we should have had an idea or notion of extension prior to motion? Or whether, if a man had never perceived motion, he would ever have known or conceived one thing to be distant from another? QU. 13. Whether geometrical quantity hath co-existent parts? And whether all quantity be not in a flux as well as time and motion?

There is no doubt that the two questions in point 11 must be answered in the affirmative. Yet, as they invite us to answer by suspending our initial intuitions, they also determine the answers to the other questions. Concerning question 12, despite our contrary intuitions, one has to accept that there is no notion of extension which precedes the notion of movement, and that, without the idea of movement, the idea

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of distance cannot be conceived. This claim is not as surprising as it may seem, as it fits well what we have found in NTV. Concerning question 13, Berkeley wants us to think that spatial quantities exist in succession rather than in one single instant. Again, this does not come as a surprise to anyone who reads NTV with care. The idea of distance dealt with here is the idea of a covered distance, which corresponds quite precisely to NTV’s description of tangible extension. Thus, as geometrical extension coincides with tangible extension, geometrical extension must be conceived of as a succession of parts analogous to the succession of touched parts. It seems to me that this passage of The Analyst confirms Stefan Storrie’s thesis concerning the relationship between Isaac Barrow’s conception of the foundation of geometry and Berkeley’s understanding of the nature of geometrical knowledge. According to Storrie, Berkeley takes up Barrow’s conception of the foundational role of the concept of motion in geometry in NTV. According to this view, geometrical objects should be defined through idealized generative motions (Storrie 2012, 251 and 264–267). With this claim, Storrie distances himself from a widespread interpretation of Berkeley. This interpretation associates Berkeley’s claim concerning the impossibility for the unbodied spirit to do geometry with a mechanical/ constructivist conception of Euclidean geometry, according to which the disembodied spirit would not be able to understand even the first proposition of planar geometry because he cannot use a straightedge and a compass.36 Instead, Storrie maintains that the unbodied spirit cannot understand geometry not because he cannot use tools, but rather because, having no body, he has no access to movement, and thus cannot perform the idealized operation of construction involved in the first three postulates of Euclid’s geometry.37

8.7  Conclusion In this paper, I propose a unified description of the distinct features of visible and tangible extension and figures as they appear in different and scattered sections of NTV. What emerges is a coherent description of two ways of being extended, that differ essentially in their different relation to succession and movement. The first kind of extension, which Berkeley considers, as the one perceived by the sense of touch, is composed of parts that exists in an ordered succession. This extension may be the object of geometry because it can be dealt with in a metric/quantitative way and can be handled according to the rules of geometry. Conversely, the second kind of extension consists of parts that exist all at once, and have no order, since order and distinction are essentially linked to succession and movement.

 See for instance Atherton 1990, 205 and Jesseph 1993, 80.  The first three postulates of Euclid’s Elements are the following: “Postulate 1. To draw a straight line from any point to any point; Postulate 2. To produce a finite straight line continuously in a straight line; Postulate 3. To describe a circle with any center and radius.” (Euclid 1908, 1:154)

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This difference between two kinds of extension is evidently connected to the ways they are perceived, but it cannot be reduced to a difference of perception, since it is primarily conceived of as a difference between the ways the spatial parts co-­ exist. The existence of this twofold nature of spatiality allows us to make the heterogeneity thesis consistent with all sections of NTV, and to connect in a natural way Berkeley’s developments on tangible and visible extensions with his considerations about geometry and geometrical spaces.

References Atherton, M. 1990. Berkeley’s Revolution in Vision. Ithaca\London: Cornell Univ. Press. ———. 2008. What Have We Learned When We Learn to See?: Lessons Learned from the Theory of Vision Vindicated. In Contemporary Perspectives on Early Modern Philosophy, ed. P. Hoffman, D. Owen, and G. Yaffe, 273–288. Toronto: Broadview Press. Belfrage, B. 1987. George Berkeley’s Manuscript Introduction. Oxford: Doxa. Berkeley, G. 1979. In The Works of George Berkeley Bishop of Cloyne, ed. A.A.  Luce and T.E. Jessop, vol. 9. Nelden: Kraus Reprint [abridged Works]. ———. 1979a. Philosophical Commentaries. In Works, vol. 1, 9–104. [abridged PC]. ———. 1979b. An Essay toward a New Theory of Vision. In Works, vol. 1, 171–239. [abridged NTV]. ———. 1979c. Treatise Concerning the Principles of Human Knowledge. In Works, vol. 2, 41–113. ———. 1979d. Works. Vol. 3. Alciphron. ———. 1979e. Theory of Vision Vindicated and Explained. In Works, vol. 1, 249–279. ———. 1979f. The Analyst, in Works 4: 63–102. Euclid. 1908. The Thirteen Books of Euclid’s Elements, Sir T. L. Heath transl. and commentaries, 3 vols. Cambridge: Cambridge Univ. Press. Falkenstein, L. 1994. Intuition and Construction in Berkeley’s Account of Visual Space. Journal of the History of Philosophy 32 (1): 63–84. Jesseph, D.M. 1993. Berkeley’s Philosophy of Mathematics. Chicago\London: University of Chicago Press. Paukommen, V. 2014. Berkeley and Activity in Visual Perception. In Active Perception in the History of Philosophy, ed. J.F.  Silva and M.  Yrjönsuuri, 255–273. Cham\Heidelberg\New York\Dordrecht\London: Springer. Pearce, K.L. 2017. Language and the Structure of Berkeley’s World. Oxford: Oxford University Press. Schwartz, R. 2006a. Seeing Distance from a Berkeleian Perspective. In  Visual Versions, ed. R. Schwartz, 13–26. Cambridge, MA\London: MIT Press. ———. 2006b. What Berkeley Sees in the Man Born Blind. In Visual Versions, ed. R. Schwartz, 71–89. Cambridge, MA\London: MIT Press. Storrie, S. 2012. What is it the Unbodied Spirit cannot do? Berkeley and Barrow on the Nature of Geometrical Construction. British Journal for the History of Philosophy 20 (2): 249–268. Wilson, M.D. 1999. The Issue of ‘Common Sensibles’. In Berkeley’s New Theory of Vision, in Ideas and Mechanism: Essays on Early Modern Philosophy, ed. M.D.  Wilson, 257–275. Princeton: Princeton Univ. Press.

Chapter 9

The Ideality of Space in Enlightenment Empiricism: The Idéologues’ Contribution Elisabeth Schwartz

Abstract  Last representatives of the French movement of ‘construction’ of space starting from unextended sensory elements, the idéologues played an important role in the movement of metaphysical construction of space in the mind. Succeeding Kant, they offer a sort of obscure and little-known alternative to the usual way the history of the evolution of the way space was conceived during the Enlightenment is told, a story whose main thread is that this evolution culminated with Kant, whose philosophy alone was capable of synthesizing the knowledge acquired by the empiricists and Leibnizian idealism. On the contrary, the idéologues tried to defend the idea that there was an alternative future to that offered by nascent German idealism. The object of this article is therefore to demonstrate in what way Condillac’s philosophy can be thought of as an ‘empiricist’ alternative to Kantianism with regards to space and in what way, after Kant and Condillac, the idea of space and movement were related. This article will more particularly focus on how the idéologues replaced the classical empiricist analysis of the idea of space with one proposing that forming the idea of space is based on the sensation of movement. In that, they initiated a way out of the limits set by an analysis of signs. Their very loyalty to the idea of a genesis of a space of signs, in their immediate aftermath, however, was at the origin of a split between a sensory and an intellectual ideal of space, whereas the aim of their empiricist idealism was to propose their fundamental union. Keywords  Idéologues · Space · Movement

E. Schwartz (*) Laboratoire PHIER – MSH Clermont-Ferrand, Clermont-Ferrand, France e-mail: [email protected] © Springer Nature Switzerland AG 2020 L. Berchielli (ed.), Empiricist Theories of Space, Studies in History and Philosophy of Science 54, https://doi.org/10.1007/978-3-030-57620-2_9

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9.1  Introduction In this essay, we propose to examine the position held by the idéologues on the question of what we may call ‘space in the mind’ and, more particularly, on the passage from a theological and metaphysical approach of space to an empiricist approach to the construction of space and its ideality.1 The idéologues’ position concerning this passage is peculiar both for its content and its chronology. Regarding the content: the idéologues received the empiricist legacy of the French Enlightenment, and primarily the Condillacian heritage;2 however, it seems difficult today to place Condillac’s philosophy under the sole empiricist banner and consider his thought as developing only against the “metaphysicians” under the sole inspiration of the Enlightenment and of the “Philosophers” of the Encyclopédie.3 As regards the chronology, these authors are the last witnesses in France of the movement to construct space from sensory elements, but they come a century too late to actually contribute to the philosophical shift from a theological and metaphysical approach to an empiricist one. The late chronological situation and the ambiguity of the ideological testimony in relation to the empiricist tradition has interesting implications. Centered on the reinterpretation of Condillacism, the philosophy of the idéologues is anchored in a corpus where metaphysical tradition and Lumières are are tied and opposed at the same time. This philosophy participates in the movement of the metaphysical construction of “space in the mind”, which marks the contribution of classical empiricism to what may be seen as the progressive constitution  – in the period from Descartes to Kant via Malebranche, Locke, Leibniz and Berkeley – of the problem of idealism.4 Now, the once-standard history of the evolution of the concept of space, in the wake of Cassirer’s work, presents Kant’s philosophy as the culmination of Enlightenment thought on space, and as the only philosophy capable of synthesizing – through the new transcendental approach to idealism and its conditions of possibility of experience – Leibnizian idealism and the achievements of the empiricist century. It then appears that the idéologues, who were Kant’s critical

1  “Space in the mind” is the expression used in the framework of the Pneuma project (project directed by L. Jaffro and P. Hamou and financed by the Agence Nationale de Recherche (ANR) entitled: Pneuma: L’espace de l’esprit: theories de l’espace, pneumatologie et physico-théologie à l’époque newtonienne  - The Space of Spirit: Theories of Space, Pneumatology and PhysicoTheology in the Newtonian Age), to refer to the transition at the turn of the 17th and 18th centuries from a theological and metaphysical approach to space to the empirical thesis of a construction of space and its ideality. Our research concerning space among the idéologues was conducted within the framework of our collaboration in this project. 2  They claim, praise and cultivate the British Enlightenment, however, but always with a certain distance. 3  The agreed vision of Condillac’s work had not convinced all the specialists; it became untenable after L. L. Bongie edited Condillac’s anonymous text Les monades in 1980. In the introduction, Bongie recalls the concordant views of Knight 1968. 4  See Beyssade 2001, 174.

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readers, offer a little-known variant within this mainstream history of the concept of space in the Age of Enlightenment. Far from following the “red line” that leads to Kant,5 the idéologues tried to defend, in the name of what they invoked as “the French era”,6 a future they wanted, alternative to that of the “German era” that was open then. Therefore, in the name of their analytical methods, they did not stop criticising both Kant’s work and his legacy in German idealism. It is precisely this little-­ known answer to the question of the “space in the mind” developed by these “last idealist empiricists” that we would like to examine in this essay. In the first part, we will attempt to clarify the meaning of this late empiricist alternative to the Kantian conception of space as a form of the external senses. More particularly, we will describe the modalities of Condillac’s “analytical” construction of space in the mind, and the original articulation between space and movement that this construction supposes. In the second part, we will show how, over the course of reading the different versions of the Traité des sensations, the idéologues (who read Condillac), up to Biran (who read Tracy), replaced the classical forms of empirical analysis of spatial ideas with a new type of space construction through the sensation of movement. In this part, we will also study the risk that such a departure from the limits of the framework of the analysis of ideas and signs entails for their own program. In the last part, we will show that it is indeed their fidelity to the idea of a genesis of a space of signs that  – distinct from the question of the conditions of possibility for spatial mathematics as a part of the sciences of nature  – led their immediate posterity, such as Babbage for instance, to a disjunction between an intellectual ideality and a sensitive ideality of space, while their empirical idealism had nevertheless wanted to propose an original conjunction.

9.2  S  pace in the Mind: Condillacism as an “Empiricist” Alternative to Kantian Idealism? The idéologues recognized in Condillac’s philosophy a founding act.7 Tracy, when presenting the future of the “French era”, said that Condillac can be “seen as the founder of the idéologie” (ibid.). Despite the diversity of their approaches – which forbids a confusion of styles between the two central figures, Cabanis and Tracy, and the less integrated styles of Gérando or Sicard, and especially Maine de Biran – the disciple who became a dissident – all these philosophers considered their own philosophy as a Condillacian form of the answer to the problem of idealism. Condillac had raised this problem, inherited from the British tradition, from the  Cassirer 1932, ch. 3, §2.  Destutt de Tracy 1970a, Introduction, 10. Destutt de Tracy 1802 (De la métaphysique de Kant) is Tracy’s clearest text concerning the opposition to German idealism. F.  Azouvi and D.  Bourel republished some of these texts accompanied by a commentary in Azouvi - Bourel 1991. For a more detailed study of the idéologues’ Kant, see Schwartz 1986, vol. 1, chap. 7. 7  Destutt de Tracy 1970a, 9. 5 6

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Essai sur l’origine des connaissances humaines of 1746, focusing on the famous Molyneux problem. Notably due to the internal difficulties of the Essai, in the Traité des sensations (1754) he challenged his first answer.8 The analysis of ideas method gives Condillac the program for a construction of space in the mind, where the genesis of space arises from sensible ideas. These ideas are elementary because minimal. However, if by space we consider the object of the geometer, the geometer being the theoretician of the science of the material objects of the external sense and the science of space as a sensible knowledge, these ideas are at the same time non-spatial because they are “ideal”.9 The issue is therefore one of finding a way of making the spatial character of the material sensible world compatible with the ideal nature of sensation. This is all the more important since the hypothesis of the animated statue in the Traité adopts the extreme ‘idealist’ definition of sensations as mere modifications of our mind.10 It is indeed a good way of defending empiricism, first by disjoining the ideality of sensation from the content represented to the senses, and second, deploying, within this extreme idealism, the totality of ideas as resulting from sensations thus idealized. For the first part, Condillac writes in the Traité des sensations (which goes beyond the definitions considered too Lockean in the Essai concernant l’origine des connaissances humaines): “Philosophy takes a new step: it discovers that our sensations are not the properties themselves of objects and that, on the contrary, they are only modifications of our mind”;11 and for the second: “judgement, reflection, desires, passions, and so forth are only sensation itself differently transformed”.12 But this implies coping with the problem posed to the ideality of space by the existence, and the success, of a geometry defined as the science of the material sensible datum. Condillac deals with this problem in the Extrait raisonné, in the text of the posthumous edition of 1798, admitting the inadequacy of the solution he proposed in the first edition of the Traité:

8  The correspondence between Condillac and Cramer (Bonnot de Condillac 1953) testifies to this reflection during the years 1745–1750. 9  Kant also argues (in Kant 1770, Section II, §7) that space science must be thought of as sensible knowledge, thus freeing the sensible representation from the imputation of confusion. 10  See Bonnot de Condillac 1947b, I, xi, §1, 244A and Précis de la seconde partie, 329B; 1982, 212 and 163. We will refer here to the 1947b Traité edition (hereafter referred to as Traité) that gives in two full-page columns (which we will indicate as A and B) the text of 1798 and at the bottom of the full page of the first edition text (to which we refer by the page number not followed by any letter). The English translation, refers only to the text of 1798; the English translations of the first edition are our own. 11  Traité, I, xi, §1, 244A; 1982, 212: “La philosophie fait un nouveau pas: elle découvre que nos sensations ne sont pas les qualités mêmes des objets, et qu’au contraire elles ne sont que des modifications de notre âme.” 12  Traité, Dessin de cet ouvrage, 222B; 1982, 171: “Le jugement, la réflexion, les désirs, les passions, etc. ne sont que la sensation même qui se transforme différemment.” Same wording in ibid., Précis de la première partie, 326A; 1982, 159).

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On the one hand, all our knowledge comes from the senses; on the other, our sensations are only ways of being. How thus can we see objects outside of us? Indeed, it seems that we ought only to see our minds variously modified. I agree that this problem was poorly resolved in the first edition of the Treatise on Sensations.13

This is the general aporia, or challenge, raised by empiricist idealism. It is also the challenge that Diderot had proposed to Condillac, in 1749, in his Lettre sur les aveugles. But it is obvious that the challenge is sharpened, at least since Newton, and for a contemporary of D’Alembert, when it is posed more precisely about space. And in the first edition of the Traité, Condillac refers precisely to D’Alembert as having given an original formulation to the problem of idealism, to which Condillac intended to answer: I do not know of a Philosopher who has solved this problem. None made the attempt and M. d’Alembert is the first to propose it: “It is up to them (i.e. to the Metaphysicians) – he says – to determine, if it is possible, what gradation observes our soul in the first step it takes out of itself, pushed, so to speak, and at the same time held back by a host of perceptions, which on the one hand lead it to external objects, and on the other seem to circumscribe it into a narrow space from which they do not allow it to go out.”14

D’Alembert doubted the possibility of finding an answer to this problem, while Condillac claims that his method of analysis can easily come to a solution: He had only to analyze the sensations of the soul, and he would have easily discovered those who carry him outward, and those who hold him within itself.15

This discovery is described in the second part of the Traité, where Condillac shows that the sensations of touch link the sensation of oneself with that of external bodies in a peculiar way16 and thus bring the statue outside of its own self: His hand moves and goes to different bodies; at once the sensation of solidity or resistance joins the sensations of hot and cold. As soon as these sensations are united, this man can no

 Traité, Précis de la seconde partie, 329B-330A; 1982, 163): “D’un côté toutes nos connaissances viennent des sens; de l’autre nos sensations ne sont que nos manières d’être. Comment donc pouvons nous voir des objets hors de nous? En effet il semble que nous ne devrions voir que notre âme modifiée différemment. Je conviens que ce problème a été mal résolu dans la première édition du Traité des Sensations.” 14  Traité, Précis de la seconde partie, 329: “Je ne connais point de Philosophe qui ait résolu ce problème. Aucun n’en a fait la tentative et M. d’Alembert est le premier qui l’ait proposé: ‘C’est à eux, dit-il, (aux Métaphysiciens) à déterminer, s’il est possible, quelle gradation observe notre âme dans le premier pas qu’elle fait hors d’elle-même, poussée pour ainsi dire, et retenue tout à la fois par une foule de perceptions, qui d’un côté l’entraînent vers les objets extérieurs, et qui de l’autre n’appartenant proprement qu’à elle, semblent lui circonscrire un espace étroit dont elles ne lui permettent pas de sortir.’” This passage will be revised and replaced in the posthumous edition by the admission that the problem had been badly solved in the first edition. 15  Ibid, 330: “Il n’avait qu’à analyser les sensations de l’âme, et il aurait découvert aisément celles qui l’entraînent au dehors, et celles qui la retiennent en elle-même.” 16  This way remains inaccessible to, for instance, the sensations of hot and cold when the body is in contact with the surrounding air. 13

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longer feel himself, that he feels at the same time some other thing than himself: hot and cold continuing to be modifications of his soul, become also modifications of something solid. From then on, they belong both to the soul and to objects external to it, they go on these objects, and drag the soul with them.17

This is the general solution. Its application to space may be naturally inferred: “The sensation of solidity is all that forces this man out of himself; and it is with this sensation that his body, objects and space begin for him”.18 Without this sensation he will perceive, along with the compared sensations, at best the dual properties of unicity and multiplicity of self: “He will feel that he is multiplying, that he is repeating himself, that he is reproducing, so to speak, out of himself. He will judge that he is one because in every sensation he recognizes his self; he will judge that he is multiple, because the self varies from one sensation to another”.19 Before opening to the sense of touch, this self – being himself confused with the content of sensation, which varies from diverse to unity – he does not have the means to unify from himself the relational diversity that constitutes space:20 These are several coexisting sensations, and it is already a precondition to the phenomenon of extension; but it is not enough to produce it. The idea of extension supposes not only that several things coexist, it supposes also that they bind themselves, terminate each other, and circumscribe each other. Now it is a property not possessed by the sensations to which we limit this man; they present themselves to him as isolated.21

In the ideality of spatial relations, the Leibnizian meaning of idealism appears. Surprisingly enough, Condillac in the anonymous Monades (1748), almost at the same time as he published the anti-Leibnizian pages of the Traité des systèmes (1749), had not only presented, but also far enough defended the party of this idealism against the partisans of Euler.22 However, the Traité des sensations placed itself  Ibid., 330: “Sa main se meut et se porte sur différents corps; aussitôt aux sensations de chaud et de froid se joint la sensation de solidité ou de résistance. Dès que ces sensations sont réunies, cet homme ne peut plus se sentir, qu’il ne sente en même temps quelqu’autre chose que lui: le chaud et le froid continuant d’être des modifications de son âme, deviennent encore des modifications de quelque chose de solide. Dès lors elles tiennent tout à la fois à l’âme et aux objets qui lui sont extérieurs, elles portent donc sur ces objets, et entraînent l’âme avec elles.” 18  Ibid., 330: “La sensation de solidité est donc la seule qui force cet homme de sortir hors de lui; et c’est à elle que commencent à son égard son corps, les objets et l’espace.” 19  Ibid., 330: “La sensation de solidité est donc la seule qui force cet homme de sortir hors de lui; et c’est à elle que commencent à son égard son corps, les objets et l’espace.” 20  For the Leibnizians, the necessity of a subjective unification of relational diversity is seen as a mark of the ideality of space. 21  Ibid., 330: “Voilà plusieurs sensations coexistantes, et c’est déjà une condition préalable au phénomène de l’étendue; mais ce n’est pas assez pour le produire. L’idée de l’étendue suppose non seulement que plusieurs choses coexistent, elle suppose encore qu’elles se lient, se terminent mutuellement, et se circonscrivent. Or c’est une propriété que n’ont point les sensations, auxquelles nous bornons cet homme: elles se présentent à lui comme isolées.” 22  Bonnot de Condillac 1980, II, v and vii. In the Traité des Animaux (1755) dealing with the question “How man acquires the knowledge of God” (which is the title of Chapter VI of Part II), Condillac reuses the text of the Monades and more precisely almost the entire last chapter of the Second Part of the Monades. 17

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on the different ground of the generation of spatial ideas and, in this text, Condillac thought he had solved the puzzle of space, here discrediting the purely intellectual explanation of the idea of space that he advanced in the Monades.23 Note that, in a similar way, the first thesis of the “Metaphysical Exposition of Space” in the Critique of Pure Reason – resuming the analysis already given in the Dissertation of 1770 – reverses the order of transition from the experience of relations between external phenomena, perceived as distinct, to the representation of the content of the concept of space. But if Condillac, in the Traité, operates such a deep change, it is not with the intention of substituting the hypothesis of space abstracted from the empirical representations by the original character of the pure form of space. Condillac’s intention is rather the opposite, since he aims to describe the effective genesis of space, which must be born of the sensible to be built analytically in the mind, without requiring an original power of synthesis. It remains that this construction must supplant a purely intellectual (and ineffective) genesis of space as an order of difference, and that the sensations of hearing, smell and sight are incapable of leading beyond the simple difference of the identical, to the specificity of spatial representation. In fact, spatial representation requires the intervention of touch: “But if we give it the feeling of solidity, its ways of being immediately resist one another. They exclude each other, terminate each other, and the man feels the different parts of his body in them.”24 The resistance felt then gives a direct equivalent of the properties of objective space. The analyses of the Traité, Part One (chap. xi), had deemed these properties inaccessible to the exercise of the sense of sight alone. In fact, it was not possible to pass from the sensation of color as extended, and from the distinction of the objectively contiguous colors with which the statue identifies itself successively, to the sensation of extension. In the first edition, Condillac said that the feeling of the statue of its own extent when limited to the only sense of sight is vague, and that it contains no representation of figures or determinate quantities.25 The corrected text insisted on the impossibility of passing from the perception of contiguous things – perception that indeed leads to an idea of externality – to that of surface and determined size: “it [the statue] thus feels itself a colored extension, but this extension has neither a surface nor a definite size.”26 Things will radically change when the statue is opened to the sense of touch, and this difference is even more radical when posthumous corrections are taken into account. Why? This is because Condillac, seeking to determine the representative content that constructs the idea of objective space, brings movement – of which he finds an ideal correspondent only in sensations of touch – into play and presents it  Bonnot de Condillac 1980, Part II, chap. v, 169 and 173.  Traité, Extrait Raisonné, 330: “Mais si nous lui accordons le sentiment de solidité, aussitôt les manières d’être résistent les unes aux autres. Elles s’excluent, se terminent mutuellement, et cet homme sent en elles les différentes parties de son corps.” 25  Ibid., I. xi, § 8, 247–248. 26  Ibid. 248A; 1982 217: “Elle se sent donc une étendue colorée: mais cette étendue n’est pour elle ni une surface, ni une grandeur déterminée.” 23 24

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as essential for the constitution of the ideas of contiguity and continuity. In fact, handwritten corrections add the sensation of resistance, which is then said itself to be extended, to the sensation of double contact and impenetrability perceived, in the first edition, through the touch of the mobile hand. Chapter 4, which is an addition to the last edition, opens up a number of corrections, by observing the impossibility of a genesis of extension from what is un-extended: “It is only with extension that we can make extension as it is only with objects that we can make objects; for we do not see how there can be contiguity among several non-extended things nor how as a result they can form a continuum.”27 The Leibnizian solution – of a purely phenomenal reality of space and of access to the simple that is reserved to the imagination alone  – adopted in the Monades, had already been rejected in Traité des systèmes as unable to explain phenomena positively.28 In the Traité des sensations, the point of view of the genesis of the ideas of extension and of material bodies requires further inquiry: It is thus evident that we will not proceed from our sensations to a knowledge of objects except insofar as those sensations produce the phenomenon of extension; and because an object is a continuum formed by the contiguity of other extended objects, the sensation that represents it must be a continuum formed by the contiguity of other extended sensations. We have not found this property in any of the sensations that we have observed: it remains to inquire whether we will find it in yet others.29

The sensations of touch, limited to what Condillac called “basic sentience”30 and its modifications, are not sufficient to give the idea of extension. To acquire it, it is necessary to be able to pass from the feeling of my body to that of the external bodies. In the text of the first edition, the key to this passage was the sensation of double

 Ibid., II, iv, § 1, 253B; 1982, 230: “Nous ne saurions faire de l’étendue qu’avec de l’étendue, comme nous ne saurions faire des corps qu’avec des corps: car nous ne voyons pas qu’entre plusieurs choses inétendues, il puisse y avoir contiguité, ni que par conséquent elles puissent former un continu.” 28  Bonnot de Condillac 1947a, VIII, ii, §1, 160B; 1982, 65. See also Bonnot de Condillac 1980, II, v, lines: 126–150. On this withdrawal, see also the editor note 135. 29  Traité, II, iv, §1., 253B-254A; 1982, 230: “Il est donc évident que nous ne passerons de nos sensations à la connaissance des corps, qu’autant qu’elles produiront le phénomène de l’étendue, et puisqu’un corps est un continu, formé par la contiguité d’autres corps étendus, il faut que la sensation qui le représente, soit un continu formé par la contiguité d’autres sensations étendues. Nous n’avons trouvé cette propriété dans aucune des sensations que nous avons observées: il nous reste à chercher si nous la trouverons dans d’autres.” 30  Ibid., II, i, §1, 251A; 1982, 225: “Our statue, deprived of smell, of hearing, of taste, of vision, and limited to the sense of touch, exists first by its sensitivity to the action of the various parts of its body on each other, and above all to respiratory movements: and there you have the lowest degree of sentience to which it can be reduced. I will call this “basic sentience”, because animal life begins and depends uniquely on this activity of the machine”; “Notre statue, privée de l’odorat, de l’ouïe, du goût, de la vue, et bornée au sens du toucher, existe d’abord par le sentiment qu’elle a de l’action des parties de son corps, les unes sur les autres, et surtout des mouvements de la respiration: voilà le moindre degré de sentiment où l’on puisse la réduire. Je l’appelerai sentiment fondamental, parce que c’est à ce jeu de la machine que commence la vie de l’animal: elle en dépend uniquement.” 27

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contact and the sensible access it gives to the properties of contiguity and continuity. It was the first answer to the doubts that D’Alembert had formulated as follows: “since there is no relation between each sensation and the object which causes it, or at least to which we relate it, it does not seem that we can find by reasoning a possible passage from one to the other: there is only a species of instinct, surer than reason itself, which can force us to bridge so great a gap […].”31 For Condillac, a body touching another body bridges a gap: “It seems to me that to discover this passage, it is not necessary to reason; to touch is enough. The feeling of solidity having two relationships at once, one to us and the other to something outside. The feeling of solidity is like a bridge between the soul and objects, sensations pass and the gap is nothing. ”32 The corrections of the last edition will take up the idea, which is a leitmotiv of all the last philosophy of Condillac, that “nature begins everything in us”.33 As we said, the corrections accentuate the role of bodily movement in the effective exercise of touch: We have proven that with the sensations of smell, hearing, taste and sight, man would believe himself to be smell, sound, taste, color; and that he would acquire no knowledge of external objects. It is equally certain that with the sense of touch he would be in the same state of ignorance if he remained immobile.34

 Ibid., Précis de la seconde partie, 330, quoting D’Alembert, Discours Préliminaire de l’Encyclopédie: “n’y ayant aucun rapport entre chaque sensation et l’objet qui l’occasionne, ou du moins auquel nous la rapportons, il ne paraît pas qu’on puisse trouver par le raisonnement de passage possible de l’un à l’autre: il n’y a qu’une espèce d’instinct, plus sûr que la raison même, qui puisse nous forcer à franchir un si grand intervalle [...].” 32  Ibid: “Il me semble que pour découvrir ce passage, il n’est pas nécessaire de raisonner; il suffit de toucher. Le sentiment de solidité ayant tout à la fois deux rapports, l’un à nous et l’autre à quelque chose d’extérieur, est comme un pont jeté entre l’âme et les objets, les sensations passent et l’intervalle n’est rien.” 33  Ibid., II, iv, 254A; 1982, 231: “la nature commence tout en nous”. The text refers to Condillac’s Logique, I, i. The posthumous text of the Extrait Raisonné du Traité des Sensations will insist on the idea that “If we suppose then that the statue reasons in order to proceed from itself to objects, we suppose wrongly; for certainly there is no reasoning that can make it leap this hurdle, and moreover, it cannot begin by reasoning. But nature reasoned for it: she constituted it to be moved, to touch, and to have in touching a sensation that makes it judge that there are, outside of its sentient being, continua formed by the contiguity of other continua, and consequently, extension and objects.” Ibid. 331B; 1982, 164: “Si on suppose que la statue raisonne, pour passer d’elle aux corps, on suppose faux; car certainement il n’y a pas de raisonnement qui puisse lui faire franchir ce passage, et d’ailleurs elle ne peut pas commencer par raisonner. Mais la nature a raisonné pour elle: elle l’a organisée pour être mue, pour toucher, et pour avoir, en touchant, une sensation qui lui fait juger qu’il y a, au dehors de son être sentant, des continus formés par la contiguité d’autres continus, et par conséquent de l’étendue et des corps.” 34  Ibid., Précis de la Seconde Partie, 331A; 1982, 164: “Nous avons prouvé qu’avec les sensations de l’odorat, de l’ouïe, du goût et de la vue, l’homme se croirait odeur, son, saveur, couleur; et qu’il ne prendrait aucune connaissance des objets extérieurs. 31

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It is the movement produced in the statue by nature, which will make it pass from solidity to resistance or impenetrability, which are now properties of matter: “Impenetrability is a property of all bodies; several bodies cannot occupy the same place: each one excludes all the others from the place that it occupies.”35 Thus, the statue feels differently the solidity of her own body, which it touches, and that of the bodies that the movement of her hand explores. Condillac expresses this in almost Fichtean terms: As long as the statue places its hands only on itself, it is from its point of view as if it were the only thing that existed. But if it touches a foreign body, the I that feels a modification in the hand does not feel itself modified in this foreign body. If the hand says I it does not receive the same response in turn. Thus, the statue judges that the body’s existence is entirely external to it. As it formed the concept of its own body it now forms that of all other objects. The sensation of solidity which gave them consistency in the one case gives it to them likewise in the other; with this difference that the I that responded previously ceases to respond.36

It is then and only then that the statue discovers the space constructed in itself by its judgment, but as external. It now appears more clearly in which sense Condillac’s idealism is an alternative to Kant’s, since Kant promotes a notion of space that is both sensible and ideal in its relation to the faculty of knowing. To develop this idea, it may be useful to question the status of Condillac’s notion of space, a status that he leaves ambiguous according to whether he insists either – as an heir of the monads – on the purely phenomenal ideality of space, or – as an heir of the English century – on the impossibility of reducing the sensible source of the representation of space to the “contemptible occupation of confusing and upsetting the representations of the understanding.”37 This double legacy of the monads and of the English century can also be found in Kant. But Condillac’s and Kant’s philosophies can notably come together in an (ambiguous) conception of the mathematical space as the space of the Mechanics – that is, of a space whose truth is only reached in mechanics. Actually, for D’Alembert’s contemporaries, it was unthinkable to leave this kind of objective Il est également certain qu’avec le sens du toucher, il serait dans la même ignorance s’il restait immobile”. 35  Ibid., II, v, §3, 256A; 1982, 233: “L’impénétrabilité est une propriété de tous les corps; plusieurs ne sauraient occuper le même lieu; chacun exclut tous les autres du lieu qu’il occupe.” 36  Ibid., §5, 257A; 1982, 234–235: “Tant que la statue ne porte les mains que sur elle-même, elle est à son égard comme si elle était tout ce qui existe. Mais si elle touche un corps étranger, le moi, qui se sent modifié dans la main, ne se sent pas modifié dans ce corps. Si la main dit moi, elle ne reçoit pas la même réponse. La statue juge par là ses manières d’être tout à fait hors d’elle. Comme elle en a formé son corps, elle en forme tous les autres objets. La sensation de solidité qui leur a donné de la consistance dans un cas, leur en donne aussi dans l’autre; avec cette différence, que le moi, qui se répondait, cesse de se répondre.” 37  This is Kant’s formula in his criticism of “Leibniz’s famous doctrine of space and time” in the Kritik der reinen Vernunft, (Kant, A276/B331-B332; 1998, 374–375). Neo-Kantism deplored the ambiguity of the concept of space, whose truth it proposed to find by purifying the concept from all the elements that, according to H. Cohen and his friends, remain too dependent on the heritage of the English century.

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space – whether it is a construction or a form of the external sense – to the classical forms of idealism.38 And both Condillac and Kant use the minimal data of motion to construct the ideality of space as empirical realism. This common call to movement, however, is also linked to a common difficulty and to a common risk of bursting which will become manifest in Kant’s and Condillac’s successors. In a famous expression, Jules Vuillemin asserted that, in Kant, pure thought really applies to the constructible object under the a priori conditions of space and time only under the supposition of movement: “In the critical system, the thought of movement directs the movement of thought.”39 Now, even if the new mathematization of the sensible by modern science is not the first preoccupation of an empiricist philosophy like that of Condillac and of the Ideologues, the fact remains that the construction of the space of pure geometry presupposes – for them as for Kant – the intervention of movement. This is even more obvious in the case of the space of mechanics, from which all borrow the concepts of impenetrability (versus coexistence) and of fulfillment (versus occupation). The fulfillment/occupation opposition was mobilized in the debates of the Berlin Academy to try to resolve the conflict between the monads’ simplicity and the infinite divisibility of space. This same conflict appears in the works of Kant’s pre-critical period (see for instance his Physical Monadology) and in Condillac’s Monades. The objective, representative properties of space are indeed to come from this space filled with moving bodies (and whose mechanization is completed by D’Alembert’s move from solids to fluids.) This is the case both for the ideas for which the empiricists wanted to construct the genesis, and for the anticipations that the critical method posed to the foundation of the relation between our knowledge and our faculty of knowing. This space filled with bodies, while being the ideal object of pure geometry, involves an existence external to our representation, an external existence leading to D’Alembert’s aporia and therefore to the challenge that the Condillacian genesis intended to meet. It is also from this space that arises the aporia that Kant considers insoluble without the difference between the “thing in itself” and “phenomenon”, which he expresses in terms that echo the Enlightenment vocabulary: If we let outer objects count as things in themselves, then it is absolutely impossible to comprehend how we are to acquire cognition of their reality outside us, since we base this merely on the representation, which is in us. For one cannot have sensation outside oneself, but only in oneself, and the whole of self-consciousness therefore provides nothing other

 In Prolegomena, Kant identifies two classical forms of idealism (as opposed to his critical idealism): the first is “visionary” idealism which transforms actual things into mere representations (Berkeley), the second form is “dreaming” idealism, that makes mere representations into things (Descartes). In the second edition of the Kritik der reinen Vernunft, Kant opposes formal idealism (transcendental idealism) and material idealism (skeptical or dogmatic). 39  Vuillemin 1955, 41. The author aims to show the role of movement data in the constitution of the system of categories, the precession of the system of principles over that of categories, and the presence of a dialectic for specification of matter as movement. This specification should respond in advance to the Fichtean and Hegelian objections to the system of categories presented as an inert exposition, cut off from the conditions of genesis of the thing, as well as to the Platonic suggestions of Marburg’s intellectualization. 38

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than merely our own determinations. Skeptical idealism thus requires us to take the only refuge remaining to us, namely to grasp the ideality of all appearances [Erscheinungen], which we have already established in the Transcendental Aesthetic […]40

Now, in Kant and among D’Alembert’s contemporaries, the aporia from which one has to go out to refute idealism is, in the case of the knowledge of space, redoubled by the reference to a content that is at the same time a purely ideal content – because mathematical – and a sensible one – since it is inherited from the external world. For all these authors, the aporia is solved by considering material movement as a datum. This is the case even with Kant, who in Transcendental Aesthetics does not resort directly to the datum of movement but presupposes it through spatiotemporal continuity. To the question “[…] how can I expect an a priori cognition and thus a metaphysics [mithin Metaphysik] of objects that are given to our senses, thus given a posteriori?,”41 the answer is unambiguously about the object of the external sense: “The answer is: We take from experience nothing more than what is necessary to give ourselves an object, partly of outer and partly of inner sense. The former is accomplished through the mere concept of matter (impenetrable lifeless extension), the latter through the concept of a thinking being (in the empirically inner representation “I think”).”42 Similarly, Condillac and his successors intended to build this space of material, mobile, perceptible bodies in the mind. Condillac in the Dictionnaire des Synonymes defines “space” in the following way: “The extension in all directions, in which all bodies move, and which embraces the Universe”.43 It seems difficult, however, to further reconcile Condillac and Kant with regard to the issue of movement in the construction of space in the mind. The enduring severity of the idéologues’ reaction to the Kantian revolution may testify to this claim. The idéologues saw in Kant’s philosophy not only a denial of their analytical method, but also the German resurgence – against all the optimistic expectations of a “French era” as the culmination of the spirit of the Enlightenment – of the shortcomings of metaphysical systems, which Condillac had definitively discredited. In a similar way, they praised the “English” for having preserved themselves from these shortcomings, as if by instinct. The idéologues read the Kantian revolution at a time when its author had to defend it against the suggestions of his “friends” (and, first, of Fichte). In general, they knew little about the Kant Aufklärer, and opposed supporters of the system and adepts of the method en bloc.44 For Tracy and his friends, the debate between German and French philosophy was not a question of “opposing a system received in Germany to a system received in France […]”, since

 Kant 1781, Book II, chap. 1, A378 (Transcendental Dialectic); Engl. Ed., 430–431.  Kant 1781 and 1787, Book II, chap. 3, A 847/B875 (Transcendental Doctrine of Method); Engl. Ed., 699. 42  Ibid., A 848/ B876; Engl. Ed. 699. 43  Bonnot de Condillac 1950, 258: “Est l’étendue en tout sens, dans laquelle se meuvent tous les corps, et qui embrasse l’univers.” 44  Destutt de Tracy 1802, 547. 40 41

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in France “we do not adopt any”45, it was rather a question of “bringing the German system closer to the French method”46 and see if it supports the test. The method of the analysis of sensations and ideas gave its name to the section of the idéologues in the Second Class of the Institut national des sciences et des arts until its elimination by the imperial power. For the idéologues, this method was so closely associated with the program of an era to come – alternative to the German future – that they put the English heritage in the background. In the polemical urgency produced by the introduction of Kantianism in France, they wrote: “It is, I believe, what is still done in Germany, and what one would do perhaps in England, if strong habits of reason, more felt than thought, did not oppose it powerfully and happily.”47 A note apologizes for the cursory character of this remark: “No doubt, I will not be suspected that I mean to say that English philosophers are preserved from metaphysical errors only by a sort of instinct, and that they do not know human intelligence. Immortal glory to the nation to whom we owe Bacon, Hobbes, Locke, and Newton.”48 Tracy presents the analytical method as “a universal touchstone,” which he however considers “as a national property”. He defends it against the challenge of his age, criticizes German philosophy, and relegates  – because of the historical legacy of the French Revolution – the English “great men” to the rank of founders: “These great men certainly have left deep traces and excellent habits of mind […] I only claim that it is in France that, in recent times, we have worked with the most success to perfect the ideologist theory of which they have laid the foundation, and that we are the nearest to succeed completely.”49 This philosophy is thus presented as a militant philosophy centered on method, ostensibly directed against all traditional forms of metaphysics and particularly against the supposed German metaphysical resurrection. It also presents itself as the philosophy capable of transcribing almost all of Condillac’s ideas in the form of a positive, even naturalized, description of the facts. However, there is a considerable gap between these characteristics and the ambiguity of Condillacism, more properly grasped as a synthesis between English empiricism and Leibnizianism. This gap developed from the question concerning the role of movement in the construction of space in the mind and justifies the continuation of the comparison between  Ibid., 550: “d’opposer un système reçu en Allemagne à un système reçu en France, où on n’en adopte aucun.” 46  Ibid: “rapprocher le système allemand de la méthode française.” 47  Ibid.: “C’est, je crois, ce que l’on fait encore en Allemagne, et ce que l’on ferait peut-être en Angleterre, si de fortes habitudes de raison plus senties que réfléchies ne s’y opposaient pas puissamment et heureusement.” 48  Ibid, 550 note (1): “On ne me soupçonnera pas sans doute de vouloir dire par là que les philosophes anglais ne sont préservés des erreurs métaphysiques que par une sorte d’instinct, et qu’ils ne connaissent pas l’intelligence humaine. Gloire immortelle soit à la nation à qui nous devons Bacon, Hobbes, Locke et Newton.” 49  Ibid. 605, note (1): “Ces grands hommes certainement ont laissé de profondes traces et des habitudes d’esprit excellentes… Je prétends seulement que c’est en France que l’on a travaillé avec le plus de succès, dans ces derniers temps, à perfectionner la théorie idéologique dont ils ont jeté les fondements, et que l’on est le plus près d’y réussir complètement.” 45

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post-Condillacism and post-Kantianism. It is in fact this question that was to lead, on the side of post-Condillacism, to Biran’s bursting, which amplifies the empirical ideality of body consciousness, and in Fichte’s post-Kantianism, to a radicality of the ego’s activities internal to transcendental ideality, presented as being more in keeping with the spirit of the Kantian revolution.

9.3  S  pace in the Mind and Thought of Movement. Post-­Condillacism and Post-Kantianism? Destutt de Tracy – whose thought is strongly connected to that of his friend and physician Cabanis  – interpreted Condillac’s genesis of space from a naturalistic standpoint. And it is very precisely this naturalistic bias that was to highlight the tensions between the contrary inspirations internal to Condillac’s genesis. These tensions bore a risk of bursting, and this risk became reality with Maine de Biran’s philosophy. Although the coherence and subtlety of Condillac’s concept of space was based on the co-existence of the two facets, the unilateral reading of his idéologue pupils – increasing the distance between the movement of the mathematician and the movement of the analyst of sensations, physiologist and psychologist  – actually brought out the tensions. We assume then that the idéologues interpreted the evolving character of the Traité (in the parts concerning the articulation of space to movement) as a mark of the tension between, on the one hand, Condillac as the inheritor of the mathematical conception of space  – a concept accepted in the Monades  – and, on the other, Condillac the ‘empiricist’, who is here urged on by the requirements of his genetic analysis to overstep the mere sense of touch by introducing the sensation of movement. We can, however, suppose that Condillac did not assess all the implications that the introduction of the sensation of movement may have had on the pursuit of the initial idealist empiricist program. That the surface is not an idea accessible to the statue limited to the sense of sight appeared, we have seen already, in Part I, chapter XI: the text of the first edition describes as ‘vague’ the idea of the extension when the statue is limited to the sense “of sight”;50 the text of the second corrected edition accentuates this ‘vagueness’ and specifies a bit further: “Since the statue has only a confused and indefinite idea of extension, without any idea of shape, place, arrangement, and movement, it feels only that it exists in many ways”51. The explanation of this ‘vagueness’ does not vary from one edition to the other and both suppose that the vagueness will disappear with the introduction of the sense of touch and with the access to the notion of

 Traité, I, xi, §8, 248.  Ibid., §9, 249B; 1982, 218–219: “N’ayant qu’une idée confuse et indéterminée d’étendue, privée de toute idée de figure, de lieu, de situation et de mouvement, la statue sent seulement qu’elle existe de bien des manières.”

50 51

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solidity. Although the sensation of color “does convey extension to the mind experiencing it”52, since the sensation is itself extended, “[…] this extension neither is a surface nor has a definite size.”53 It is not a surface because the idea of a surface presupposes the idea of a solid; and it has not a definite size since “any such size is an extended thing enclosed within circumscribing limits. Now the statue’s I cannot feel itself circumscribed within limits.”54 This idea of extension as a definite magnitude is borrowed from the geometer, and from an objective definition of space, and it is possible to generate this idea of space precisely with the sensation of solidity and of double contact starting from lived sensations or, at least, from what the idéologues, and especially Biran, were to take for lived sensations. The connection that we have already underlined between the space of the geometer and the space of mechanics, and the role of the concept of movement in determining the concept of space, appears here, on the one hand, in the definition of the parts of the extension as continuums formed by the contiguity of other bodies and, on the other, in the definition of the continuum as formed by the contiguity of other continuums. Aristotle, in Physics (V, 3 and VI, 1), had established, already under the assumption of a primitive datum of motion as a common sensible, a mathematical definition of the continuum from the concepts of contact, intermediary and contiguity.55 And as Aristotle, at the foundation of the system of mathematical objects, lays down the concept of continuity studied in Physics56, Condillac, for at least partially similar reasons, was interested in space as it is filled by bodies. According to Condillac, the statue perceiving color lacks “a distinct and precise idea of a magnitude”, and it has no way of “seeing how the things seen one out of the other bind together, terminate each other, and how all together they have boundaries that circumscribe them”.57 Therefore, at this level of analysis, Condillac relies on the mathematical concept of term, boundary and delimitation, without making explicit (or grasping) the full scope of it. This is the case, for example, when he merely indicates without further justification that the statue limited to the sense of sight feels itself like a colored extension but an extension which is not a surface and that does not have a definite magnitude.

 Ibid., I, xi, 8, 248A; 1982, 216: “offre de l’étendue à l’âme qu’elle modifie [...].” This is not the case, for instance, for the sensations of sound. 53  Ibid.: “... cette étendue n’est pour elle ni une surface, ni aucune grandeur déterminée.” I propose here a different translation from Traité 1982, 217. 54  Ibid.: “Une pareille grandeur est une étendue renfermée dans des limites qui la circonscrivent. Or le moi de la statue ne saurait se sentir circonscrit dans des limites.” 55  For an accurate and in-depth analysis of this conception in relation with the contemporaneous one, see Granger 1976, 304–308. 56  Granger (1976, 304), for instance, claims that “the very root of the mathematical object can only be physical.” 57  Traité des Sensations, I, xi, § 8, 247: “l’idée distincte et précise d’une grandeur”; “voir comment les choses aperçues les unes hors des autres se lient, se terminent mutuellement et comment toutes ensembles elles ont des bornes qui les circonscrivent.” 52

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These concepts have a history that refers to the Aristotelian conception of magnitudes, and to the distinction of three types of figures according to the three possible dimensions of divisibility: the line as divisible in one way, the plane in two, and the solid in all dimensions (Metaphysics, livre Δ, chap. 6 and 13).58 Prefiguring one of the modern definitions of the topological dimension by means of cuts, this classification of figures gives a precise meaning to the idea of delimitation (πεπερασμένον) and allows a distinction between area (πλάτος) and delimited area or surface (ἐπιφάνεια). This conception was not forgotten in the eighteenth century, it persists in Wolff’s work59 and it appeared without change in Kant in the De mundi sensibilis atque intelligibilis forma et principis, (1770), in the note that attempts a demonstration of the tri-dimensionality of Euclidean space from its continuity.60 Condillac puts into play this concept of term (terminus) first in the distinct idea of extension, which requires conjunction and mutual determination, delimitation within bounds, and second, when he claims (without being able to identify the reason) that it is necessary to start from solid and from the continuity of the three-­ dimensional space to think of the surfaces that are their terms (and not their constituent parts). However, if this mathematical conception is used by Kant to promote the idea that the intuitive space is sensible but pure,61 this is not the case in Condillac, who considers that the object of geometry is immediately sensory and material, instead of sensory and pure. He describes empirical genesis by appealing to the data of the movement of bodies external to ours starting from the sensations themselves extended. In Condillac, bodily movement is the – finally reached – solution given to

 For a commentary, see Granger 1976, 303.  Condillac may have found in Wolff’s Philosophia prima sive Ontologia (1730) the definition of this concept of continuity, as well as the indications of its Aristotelian source. This text forms part of a common basis of the mathematical culture for the readers of d’Alembert, the articles in the Encyclopédie and the work of the Berlin Academy. On this common basis and its relation to Wolff, see Carboncini 1987. 60  See Kant 1770, §15 note. C. J. Vuillemin (Vuillemin 1962, 447n) noted that this demonstration evokes Poincaré’s formulation of the link between continuity and dimension through the concept of cut. 61  We evoke here the Kantian conception only for comparative purposes and in order to illustrate a general ambiguity of the relationship between the definition of space and that of movement in Kant and Condillac. Kant’s thought is on this point of formidable complexity, which we simplify here. Both, M. Fichant (Fichant 1997 and 2004) and B. Longuenesse, (Longuenesse 1993 and 1998) defend two distinct and partially irreconcilable interpretations of Kant on this point. The two interpreters distance themselves from Marburg’s interpretation, but they oppose each other on the meaning to be given to the relationship between aesthetics and transcendental logic on this point. We do not fully agree with either interpretation. Vuillemin (Vuillemin 1954 and 1955) had already taken, in a very detailed way, this distance from Marburg’s interpretation proposed a reading just as opposed to the neo-Kantian intellectualizations of sensitivity as to the Fichtean idealizations of transcendental subjectivity. The author deals in a new way with intuitive space which, to be “much more primitive and general than the metric space” and thus distinct from the one mobilized by transcendental logic in the theory of intensive quantities, is not, however - as it is proper to Kant’s first Aesthetics - presented as a concept external to mathematical conceptualization. 58 59

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the problem of exteriority already at the level of the sensation, whereas in Kant the movement – excluded from Aesthetics but supposed by it – will be meaningful for the construction of space only through the reinterpretations internal to the different parts of the Logic. Condillac, coming back on his first solution founded on the sense of touch (without movement), was led to introduce movement and the history of this rethinking brings into play not only the work’s internal coherence, but also its relationship with its ideologist posterity. This reinterpretation remains internal to the senses, however, and rather takes the risk of compromising the ideality of the sensible space by directly connecting the concept of extended sensation to material movement. The history of Condillac’s interpretation by the idéologues, which crosses Condillac’s interpretation by himself over the corrections made to the posthumous edition, is here particularly instructive. Marked with twists and multiple retractions, this story is played out in three moments – or four if we add to Tracy’s interpretation that of Biran, reader of Condillac and of Tracy on the question.

9.3.1  Moment 1 The first moment takes place in the Mémoire sur la Faculté de Penser, published under the date of the Destutt de Tracy’s first lecture at the Institute on 2 Floréal Year IV (April 1796) in the Volume I of the Mémoires de la Classe des Sciences Morales et Politiques, Year IV, published in Thermidor Year VI (August, 1798), 283–451.62 This mémoire is like a first draft of the system of the Eléments d’Idéologie, the first part of which, entitled Projet d’Eléments d’Idéologie à l’usage des Ecoles centrales de la République française, appears in 1801-Year IX, and will become, under the title Eléments d’Idéologie, Première Partie, Idéologie proprement dite, the first of the four volumes published from 1803 under the general title of Eléments d’Idéologie.63 In this mémoire, the author introduces the term “idéologie” as a substitute for the old name of “métaphysique” rendered obsolete by the renewal of the method of the “analysis of sensations and ideas.” This new name “designates the work to be done, and not the science that results from this work.”64  The published text reproduces the text of the second lecture delivered the 22 Germinal of Year VI, after recasting of the previously read mémoires. The short chronology of Tracy’s mémoires in Tracy 1992 contains some inaccuracies regarding the dates on which the mémoires are read and published. 63  The three parts, Idéologie proprement dite, Grammaire, and Logique appeared between 1801 and 1805, followed ten years later by a volume entitled Traité de la volonté et de ses effets. 64  Tracy (Destutt de Tracy 1798, 322) writes this remark giving (or delivering) his title within the Classe des Sciences Morales et Politiques of the new Institut created by the Revolution in the section where sit those who will be called the idéologues, and first and foremost Destutt de Tracy and his friend Cabanis. The justification for this new name is very detailed, and Tracy apologizes for the digression, on behalf of the importance of the issue for the science of thought: he devotes more than five pages to it. 62

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In this mémoire, Tracy illustrates this science “so new, that it has no name yet”,65 by the examination and discussion of “an opinion of Condillac, the brightest and the most exact of the metaphysicians.”66 At this preliminary level of the text, Tracy means by “metaphysics” the “science of human understanding” which has ceased to be hypothetical and based on “frivolous suppositions”, to be finally based on “a first, well established and well proven fact” that is the origin of all our ideas in our sensations. Locke is praised for having shown the truth of this first fact and Condillac is said to “have been even further in his admirable Traité des sensations.”67 Condillac’s opinion, which we are going to discuss here, is very precisely the answer to the question that he claimed to have inherited from D’Alembert. According to Tracy, this question is a consequence of the second fact about ideas: “But since – as shown by Condillac – our sensations and all the resulting ideas are nothing but interior modifications of our being, given that in themselves they have nothing that tells us where they come from, how do we learn to relate them to beings who are their occasional causes? How do we acquire the knowledge of these beings? This is a second fact to explain.”68 Tracy believed the question was “not yet resolved” and offered a two-step answer. The first step established, against Condillac, that “It’s not to the sense of touch that we owe the knowledge of bodies”69; the second advances that “It is to the faculty of moving us that we owe the knowledge of bodies”.70 Tracy’s analysis is an almost linear commentary of the Traité’s first edition, of which he cites the passages we quoted above concerning the limits of the sense of sight with regard to ideas of surface and extension. He notes all the clues of Condillac’s hesitation as to the attribution or refusal of the sensation of extension to the statue provided uniquely with the sense of sight and as to its capacity (or incapacity) to have the notion of extension from the sensation of different colors. This hesitation is indeed at work throughout the entire text of Part I, Chapter 11, §8, which Tracy follows line by line. He remarks that “here Condillac seems to me to start deviating from his ordinary accuracy”71, since he appears in turn to grant and to refuse to the statue the perception of extension and of surface. Indeed, to the statue, on the one hand, feeling green would feel out of the red, and feeling red would feel out of the green, but on the other, “it is not even a surface” and it has no idea of any figure or size determined. Tracy considers that the attribution of the perception of extension through color plainly contradicts the text which, a few lines later, claims that sight may perceive the sensation of extension only once it has been trained by touch.72  Ibid.; “si neuve, qu’elle n’a point encore de nom”; the formula is repeated on the next page.  Ibid., 290; “une opinion de Condillac, le plus lumineux et le plus exact des métaphysiciens.” 67  Ibid.; “un premier fait bien constaté, bien avéré.” 68  Ibid., 289–290. 69  Ibid., 291 (title of Part I, chap. ii). “De la manière dont nous acquérons la connaissance des corps extérieurs et du nôtre”. 70  Ibid., 300 (title of Part I, chap. ii) “C’est à la faculté de nous mouvoir que nous devons la connaissance des corps”. 71  Ibid., 292: “Ici Condillac me paraît commencer à s’écarter de son exactitude ordinaire.” 72  Ibid., 293; Tracy quotes here Condillac (Traité, 247). 65 66

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While reserving the right to later prove that the sense of touch alone cannot suffice, Tracy specifies: “At present I just conclude that the author was wrong to say, the page before, about the statue seeing red and green “Insofar as it is red, it senses that it is outside green; insofar as it is green, that it is outside red, and so forth”.73 According to Tracy, to see red and green together does not give the feeling of externality from one to another: “No. When it sees red and green together, the statue does not feel them out of each other; it feels itself red and green at the same time, or if you want to express this state by a single word, it feels itself ‘varied’, that does not derive from the idea of extension (that the statue does not have), as would the expression ‘speckled’ or ‘spotted’.”74 Then Tracy takes up a concession from Condillac who admits that, repeated or not, the feeling of a piece of color is never but one way of being, and that he does not imagine in these conditions how the statue could feel extended and he emphasizes: “Neither do I imagine it [i.e. How the statue could feel itself extended] or rather I am sure it cannot be; and I am astonished that Condillac comes back again, the next moment, to his first idea and says: “We have to conclude that the sensation it has of its extension is vague”75. He writes then that, with all the due respect to Condillac: “I will say clearly that it is not the feeling of the statue that is vague, and that it is the author’s idea that is shady and badly determined; and that, finally, this excellent analyst, who has so perfectly demonstrated to us how we learn to see, has not yet clearly explained to himself how we acquire the notion of extension. But that is what we will better see later.”76 The remainder of the chapter continues the statement of this hesitation even at the heart of the analysis of the sense of touch, analysis from which Tracy intends precisely to stand apart: “I have insisted somewhat on Condillac’s hesitation about the notion of extension, because it is the germ of the error that I claim to refute, which consists in believing that it is to the sense of touch that we owe the knowledge of external bodies and of our own.”77 According to Tracy, this same difficulty

 Destutt de Tracy 1798, 293: “Actuellement je me borne à conclure de cette décision que l’auteur a eu tort de dire, la page auparavant, quand elle voit du rouge et du vert: […].” 74  Ibid. “Non. Quand elle voit du rouge et du vert ensemble, elle ne les sent pas hors l’un de l’autre; elle se sent rouge et vert en même temps, ou si vous voulez variée, pour exprimer cet état d’un seul mot qui ne dérive pas de l’idée d’étendue qu’elle n’a pas, comme ferait l’expression mouchetée ou tachetée.” 75  Ibid., 294, quoting Condillac (Traité, 247–248): “Ni moi non plus, je ne l’imagine pas, ou plutôt je suis certain que cela ne se peut pas; et je suis bien étonné que Condillac revienne encore, le moment d’après à sa première idée et dise: ‘Il faut convenir que le sentiment qu’elle a de son étendue est vague’[...].” 76  Ibid., 294: “[...] je dirai nettement que ce n’est pas le sentiment de la statue qui est vague, que c’est l’idée de l’auteur qui est louche et mal déterminée; et qu’enfin cet excellent analyste, qui nous a si parfaitement démontré comment nous apprenons à voir, ne s’était pourtant pas clairement expliqué à lui-même comment nous acquérons la notion de l’étendue: mais c’est ce que nous verrons mieux par la suite.” 77  Ibid., 295: “J’ai un peu insisté sur cette hésitation de Condillac au sujet de la notion de l’étendue, parce qu’elle est le germe de l’erreur que je prétends réfuter, et qui consiste à croire que c’est au sens du toucher que nous devons la connaissance des corps extérieurs et du nôtre.” 73

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emerges again when Condillac deals with the sensations of a man limited to the sense of touch alone. According to Tracy, Condillac’s assertions that a man opened solely to the sense of touch has a “basic sentience” as a minimum degree of sentiency and that yet he has “no idea of extension or of movement” – as emerge even in the titles of the chapters 1, 2 and 3 of the second Part – are at odds with the analyses that concede that once the feeling has changed, ceasing to be uniform, the statue can pass from the feeling of distinction to that of externality.78 He notes that here as well Condillac testifies to an “embarrassment in his ideas”, which is the same, even by Condillac’s own admission, as for sight and extension. Condillac wrote: “Besides, this idea [of extension], as we have noticed elsewhere, is quite vague […] For the statue, it is only the perception of several ways of being which coexist and which are distinct from one another, perception in which it cannot find any notion of a body.”79 According to Tracy, the root of this hesitation lies in what he considers a “false idea of the notion of extension – as well as that of bodies – that has prevented Condillac from discovering how we acquire it.”80 To “this false idea of the notion of extension”, which conceives the idea of extension as formed by the coexistence of several sensations, he opposes what, in his eyes, is the correct conception that is an idea of extension derived from that of body: extension is a property of bodies, but the idea of extension is not a part of the idea of body; it is rather derived from it, as we have already seen for the idea of surface.81 It is this “derivative” character that, according to him, “Condillac should never have lost sight of” and which would have preserved him from the error of imagining “that his statue could have formed the idea of extension by the only coexistence of several sensations, without having any notion

 Ibid., 295–298. The author quotes - as usual, without giving a precise reference to the pages of the text - extracts from Part Two, Chap. I, II and III whose titles are respectively (ibid., 251A, 251B, 252; 1982, 225, 226, 228): “Of the Least Degree of Sensation to which a Man Can be Reduced Who is limited to the Sense of Touch Alone”, “This Man Limited to the Lowest Degree of Sentience has no Idea of Extension or of Movement”and “How this man, remaining motionless, begins to feel somehow extended” (in French: “Du moindre degré de sentiment où l’on peut réduire un homme borné au sens du toucher”, “Cet homme borné au moindre degré de sentiment n’a aucune idée d’étendue ni de mouvement.” and “Comment cet homme, demeurant immobile, commence à se sentir en quelque sorte étendu”). The last title will be changed in the posthumous edition in “Of the Sensations that are Attributed to Touch and Nevertheless Give no Idea of Extension” (“Des sensations que l’on attribue au toucher et qui ne donnent cependant aucune idée d’étendue”. 79  Ibid., 1798, 298, quoting Condillac’s Traité (II, iii, §2, 253): “Au reste cette idée [d’étendue], comme nous l’avons remarqué ailleurs, est tout à fait vague […] Elle n’est pour elle que la perception de plusieurs manières d’être qui coexistent et qui se distinguent, perception dans laquelle elle ne saurait trouver la notion d’aucun corps, [...]”. 80  Ibid., 298: “fausse idée de la notion de l’étendue qui l’a empêché de découvrir comment nous l’acquérons, ainsi que celle des corps.” 81  Ibid., 298–299; at ibid., 292, Tracy discussed about the idea of surface, answering the question of whether the sensation of varied colors would give that of colored surface: “I would dare decide that no: because the idea of surface is a derivative of that of body and that it does not have”; (“j’oserai décider que non: car l’idée de surface est un dérivé de celle de corps qu’elle n’a pas”). 78

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of bodies.”82 And, in fact, Condillac, in the posthumous edition, makes the derivative character of the notion of surface clear: “it [the statue] thus feels itself a colored extension, but this extension has neither a surface nor a definite size. It is not a surface because the idea of a surface presupposes the idea of a solid, an idea that it does not and cannot have.”83 However, the more precise details that the second edition brings here mainly concern the articulation of the notions of contiguity, continuity (taken according to the mathematical concept) and the idea of continuous sensations.84 It is possible that Condillac uses the ambiguity that surrounds the concept of extension – which the statue has without having it, or without noticing it – to establish the relation between the properly aesthetic level of subjective sensitivity, and the logical level of spatial ideas in the mind. Far from seeing this, Tracy immediately jumps to the data of movement – in our own bodies or in external ones – as a condition for thinking of space. Paradoxically, however, it is Tracy who analyzes the continuity of space less finely than Condillac, who also brings to light this property of derivation of the surface from the solid given to sensitivity. By creating an opposition between the parts of an idea and derivation, however, he actually aims to grasp not mathematical space, but rather material space directly, which is full of bodies opposing the action of our own body in the movement. The second chapter of the Mémoire aims to establish that “we owe the knowledge of bodies to the faculty of moving us.”85 According to Tracy, we owe this knowledge neither to sight, nor to any of the five senses, but rather to the faculty of moving. He reproaches Condillac again for having approached – but missed – the great truth that, in the end, remains ambiguous in his analyses of touch. Referring to various passages of the Traité, in Chapter IV,86 which establish a connection, for the statue provided with the use of its hands, between mobility and the sensations of resistance and solidity, and finally concludes that it is to the sensation of solidity that the body, objects and space begin to emerge, Tracy exclaims: How is it! Condillac says formally: “It is to the sensation of resistance that the body, objects and space begin for the statue. […] As long as it was motionless, it could have no idea of this resistance. […] As soon as it moves, it feels it […]”, and he does not immediately conclude that it owes its knowledge of bodies to the faculty of movement alone! Surely we could not be closer to a truth without touching it.87  Ibid., 299: “[...] que sa statue ait pu se former l’idée d’étendue par la seule coexistence de plusieurs sensations, sans avoir aucune notion des corps.” 83  Condillac, Traité, I, xi, §8, 248A; 1982, 217: “Elle se sent donc comme une étendue colorée: mais cette étendue n’est pour elle ni une surface, ni aucune grandeur déterminée. Elle n’est pas une surface parce que l’idée de surface suppose l’idée de solide, idée qu’elle n’a pas et ne peut avoir.” 84  Kant will later develop the same kind of articulation. 85  Destutt de Tracy 1798, 300 (title): “C’est à la faculté de nous mouvoir que nous devons la connaissance des corps”. 86  The chapter in question was to become chapter II, v of Condillac’s posthumous edition, amended with substantial corrections, after a new chapter had been inserted which was the new chapter II, iv. 87  Ibid., 301: “Comment! Condillac dit formellement: ‘C’est à la sensation de la résistance que commencent pour la statue son corps, les objets et l’espace … Tant qu’elle a été immobile, elle n’a 82

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According to Tracy, the sensation of resistance or solidity did not become truly meaningful until Condillac clearly accepted its dependence on mobility and detached all five senses, including touch, from what he names “motility”: “Only the faculty of making movements and of being aware of them teaches us that there are what we call bodies, and it teaches us by resistance that these bodies oppose our movements. This faculty, which I will call, to make it short, motility, is then the only link between our self and the sensible universe.”88 In response to D’Alembert’s aporia, a difference is thus established on the level between the five senses and this “sixth sense, which has not been distinguished so far, because it has no particular organ, because it merges with all the others, especially with touch”; this sixth sense is “the only intermediary that establishes communication between the interior modifications of our ego and the sensible universe”.89 So, according to Tracy, we know space and extension from movement, and not the opposite: it is not movement that can be defined as the passage of a body from one place to another. The word space is “the general expression of all that can or cannot be crossed by movement.”90 Extension is then a property of bodies, which one can indeed say to have parts that are outside each other, occupying different points in space, but “I would prefer it if we said: An extended being, a body, is a being that we feel continuously while we have the sensation of a certain amount of movement.”91 This means that the definition of extension refers directly to the space of Mechanics, and that, like that of time, refers to the measure of motion: “The extent of a body is therefore for us the permanent representation of the amount of

pu avoir aucune idée de cette résistance … Dès qu’elle se meut, elle le sent’ … et il n’en conclut pas immédiatement que c’est à la faculté de se mouvoir qu’elle doit uniquement la connaissance des corps! Assurément on ne pouvait être plus près d’une vérité sans la toucher”. 88  Ibid., 302.: “La faculté de faire des mouvements et d’en avoir conscience nous apprend seule qu’il existe ce que nous appelons des corps, et elle nous l’apprend par la résistance que ces corps opposent à nos mouvements. Cette faculté, que pour abréger, je nommerai la motilité, est donc le seul lien entre notre moi et l’univers sensible.” 89  Ibid., 303: “Sixième sens, que l’on n’a point distingué jusqu’à présent, parce qu’il n’a point d’organe particulier, parce qu’il se confond avec tous les autres, surtout avec le tact”, qui pourtant peut et doit en être distingué, et qui est “l’unique intermédiaire qui établisse une communication entre les modifications intérieures de notre moi et l’univers sensible.” A note states: “We’re so used to confusing tact with motility, that I’ve seen a man of an excellent mind have some trouble conceiving one separate from the other; however it does not seem more difficult to me to suppose Condillac’s statue moving with all the skin of the body completely insensible than to assume it moving with a sensitive skin and the organs of sight, hearing, smell and taste, insensitive.”; “On est si fort accoutumé à confondre le tact avec la motilité, que j’ai vu un homme d’un excellent esprit avoir quelque peine à concevoir l’une séparée de l’autre; cependant il ne me parait pas plus difficile de supposer la statue de Condillac se mouvant avec toute la peau du corps parfaitement ladre, que de la supposer se mouvant avec cette même peau sensible et les organs de la vue, de l’ouïe, de l’odorat et du gout, insensibles.” 90  Ibid., 309: “l’expression générale de tout ce qui peut ou ne peut pas être traversé par le mouvement.” 91  Ibid., 310: “j’aimerais mieux que l’on dit: Un être étendu, un corps, est un être que nous sentons continuement pendant que nous avons la sensation d’une certaine quantité de mouvement.”

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movement necessary to cross it.” 92 The same is true of time as a measure of duration and a measure requiring movement: “Time is for us the representation of a movement completed.”93 Before trying to understand why, on this last point, Tracy thinks he needs to distance himself advantageously from Condillac, we must discuss the second moment of the ideologist reading.

9.3.2  Moment 2 This second moment corresponds to the text of Tracy’s mémoire entitled Dissertation sur quelques questions d’Idéologie contenant une nouvelle preuve que c’est à la sensation de résistance que nous devons la connaissance des corps, et qu’avant cette connaissance l’action de notre jugement ne peut avoir lieu, faute de pouvoir distinguer les unes des autres nos perceptions simultanées, published under the reading date of the 7 Prairial Year VIII (27th of May, 1800). The new proofs were brought in the context of an analysis of the text of the last edition of Condillac’s works, published in 1798 (Year VI), of which Tracy recommends the reading to his colleagues at the Institute. This new edition is an opportunity to discover the still unpublished text of La langue des calculs, and especially the changes brought to the Traité des sensations, published in accordance with the manuscripts of the author, who died in 1780, and who had worked the last two years of his life on a new, corrected edition of his complete works. Tracy discovers that, while discussing, in his first mémoire, Condillac’s opinion concerning sensation which gives us knowledge of the bodies, he had “much less the appearance of commenting on Condillac than of combating him”, the last edition gives him “the pleasure of seeing that the last thoughts of this famous man are […] closer to my opinion in this respect”, since “it is only on this point and on all that relates to it that he has made considerable changes.”94 Tracy notes that “this question always had something that bothered him [Condillac]”95 and discovered that Condillac had already provided answers to his objections, since he rewrote all the passages that the mémoire considered “shady”, especially in chapter III of the Second Part (which had become Chapter IV of the  Ibid.: “L’étendue d’un corps est donc pour nous la représentation permanente de la quantité de mouvement nécessaire pour la parcourir.” 93  Ibid., 312: “un temps est pour nous la représentation d’un mouvement fait.” 94  Destutt de Tracy 1801, 496: “... beaucoup moins l’air de commenter Condillac que de le combattre”; “donne le plaisir de voir que les dernières pensées de cet homme célèbre se rapprochent encore plus de mon opinion à cet égard”; “Ce n’est que sur ce point et sur tout ce qui y a rapport qu’il a fait des changements considérables.” 95  Ibid.: “... cette question a toujours quelque chose qui lui fait peine”; according to Tracy, the proof is in Condillac’s admission at the beginning of the Précis de la seconde partie/Précis of the Second Part, (Bonnot de Condillac, Traité  329B-330A; 1982, 163) where Condillac writes concerning D’Alembert problem: “I agree that this problem was poorly resolved in the first edition of the Treatise on Sensations.”; “Je conviens que ce problème a été mal résolu dans la première édition.” 92

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new edition since a new chapter III had been inserted), as well as what follows. These changes go in the direction desired by Tracy. However, even if Condillac no longer attributes even a vague idea of extension to a statue that has no access to the movement of its body, the impenetrability of other bodies, and therefore the sensation of solidity, Tracy rightly notes that Condillac still seems contradict himself and maintains the ambiguity in the text of the second edition as well. Tracy deems it necessary to give a different formulation of the question of the knowledge of bodies. In order to remove all ambiguity, he rewrites the text of the last paragraph of IV, § 3, as follows: We learn that a body exists only because it obstructs our movements and gives us the sensation of resistance. We have this sensation only because we first are aware that we are moving, and we learn that this obstacle is extended only because by sliding on it we feel it continuously while we feel that we are moving. This is precisely what it is for us to exist and be extended; and that is why we cannot know nor even conceive of anything but resistance and extension.96

Tracy also gives the reasons why Condillac missed this straightforward radicalization and stopped at the threshold of the sensation of obstacle and resistance: “I think that what has prevented Condillac from going so far is that, in his explanation, he loses sight of what he has established himself, that when we move, we feel it. In the last edition he is still talking about movements that the statue makes, and he does not mention the consciousness, the feeling that it has of them.”97

9.3.3  Moment 3 The third moment of the idéologues’ reading (still in the Eléments d’Idéologie) of Condillac’s theory of space – alone, or linked to what would be a fourth, Biranian, moment – seizes the precise point at which Tracy’s criticism of Condillac applies. Tracy probably did not fully appreciate the threat this point carried within itself for the coherence of the philosophy of the analysis of sensations, ideas and signs. With Biran, this criticism will lead to the end of the philosophy of analysis.98

 Destutt de Tracy 1801,  498–499. The author has just quoted Condillac (Traité, 256B; 1982, 233–234): “Nous n’apprenons qu’un corps existe que parce qu’il fait obstacle à nos mouvements, qu’il nous donne la sensation de résistance; nous n’avons cette sensation que parce que nous avons auparavant la conscience que nous nous mouvons, et nous n’apprenons que cet obstacle est étendu, que parce qu’en glissant dessus nous le sentons continuellement en sentant que nous nous mouvons. Voilà proprement ce qu’est pour nous qu’être existant et étendu; et voilà pourquoi nous ne pouvons rien connaître ni même rien concevoir que de résistant et d’étendu.” 97  Destutt de Tracy 1801, 499: “Je pense que ce qui a empêché Condillac d’aller jusque là, c’est que, dans son explication, il perd de vue ce qu’il a établi lui-même, que quand nous nous mouvons, nous le sentons. Dans cette dernière édition encore il parle toujours de mouvements que fait la statue, et il ne fait pas mention de la conscience, du sentiment qu’elle en a.” 98  On this issue, which goes far beyond the problem of space, see Schwartz 1986, vol. 1, 448–547. 96

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In the Mémoire, Tracy criticizes Condillac for having lost sight of the nature of the sensation of movement (after having established it), and its irreplaceable role in the formation of the idea of body, and therefore of extension and space.99 It is always as an analyst that Tracy wanted to correct Condillac. From the Mémoire to the Eléments, the correction is done in two stages. In the first stage, Tracy discusses the analysis of the idea of space starting from the sensation, proposes to develop Condillac’s thought without contradicting him, and emphasizes that “when we move we feel it”.100 In the second stage, he discusses the manner in which Condillac connects sensation and judgment. This implies a comparison between Condillac’s and Tracy’s approaches that goes far beyond the question of space.101 On this point, he declares “for the first time, I differ essentially from Condillac”.102 Tracy’s First Critical Stage As for the first stage of his criticism, Tracy maintains that the neutralization of the consciousness and of the feeling of movement has led to a confusion in the analysis of the sensations of resistance and solidity. Condillac made it clear that impenetrability was not a sensation, but a property of bodies, and therefore that we judge bodies to be impenetrable rather than to feel them as such. The judgment of impenetrability is the consequence of the sensation of solidity, which the statue experiences when it touches its own body through the double contact of its hand and, for instance, its chest, or when it touches other bodies, which it feels differently than when it touches itself.103 To this Tracy opposes the empirical hypothesis of a motionless statue pressed by a foreign body: according to him, this statue will have a sensation of solidity, as strong as its pain, but not the judgment of externality. Here he especially recognizes an error of analysis: the confusion between the simple sensation, which is – like the sensation of solidity – a pure internal modification, on the one hand, and the judgment of externality, on the other. But the question here is not yet of reproaching Condillac for having forgotten consciousness, or the activity of thought, in the analysis of representations; rather, the question is of showing that he did not assign the right feeling as the basis of the judgment of externality: “it is not therefore the sensation of solidity that allows this judgment, for this sensation is simple like all others; it is rather the feeling of resistance, because it is composed of that of solidity and that of movement, and that two simultaneous and distinct  In turn, Biran was to apply this same interpretive scheme to Tracy. The same thing, on the same dates, led Kant’s “friends” to remind him of the radicalism of a Copernican revolution, for which they credited him. It would be wrong indeed to see in this insistence on consciousness and motility as feeling, the announcement of a future to be sought either in the future psychology, and in the feeling of effort as the feeling of ego in Biran, or in a more critically idealistic rewriting of the thought of space, such as that of Kant, of which Fichte meant to radicalize the spirit. 100  Destutt de Tracy 1801, 499: “[...] quand nous nous mouvons, nous le sentons.” 101  Ibid., 502. 102  Ibid., 504: “Ceci m’amène naturellement au point où, pour la première fois, je diffère essentiellement de Condillac.” 103  Traité, II, v, §§3–6, 256A-257A; 1982, 233–235. 99

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perceptions are necessary to give rise to a judgment.”104 Tracy points out, in passing, that the recourse to impenetrability – which, he says, Condillac had not mentioned in other editions – is inaccurate since it is not this property of bodies that produces the sensation of resistance. In the Mémoire, he wrote, “it is more exactly the inertia – or opposition that each body raises against receiving movement – that causes us this sensation.”105 The Eléments d’Idéologie was to renew these details, which are in agreement with the analysis of the principles and theorems of dynamics and mechanics in Kant’s Metaphysische Anfangsgründe der Naturwissenschaft106, with solidity, impenetrability, resistance and inertia corresponding to the principles by which D’Alembert’s Traité de Dynamique (1743) rewrote Newton’s laws. Here, as already in the mathematical concept of continuity, the authors probably draw on a scientific fund common to all the Enlightenment philosophers, who read the works of the Berlin Academy and the articles of the Encyclopédie. A difference then emerged between Condillac, or Kant, on the one hand, and the Ideologues or post-Kantians on the other, at a moment when the latter already maintained that they wanted to continue without contradicting the thinking of their predecessors. Kant, for instance, in the precession of the moments of the Science of Nature in relation to the system of metaphysical principles – as well as in the teleology exerted by the complete analysis of the material movement on the categorical system – created the necessary duplicity of a transcendental idealism as an empirical realism, whereas it seems that Fichte wanted to retain only the initial data of a shock causing the consciousness of movement, thus determining the principles starting from the concepts without mathematical mediation. This is the meaning of the Fichtean suggestion, which Kant refused, to conflate Grundsatz and Lehrsatz, or, in other words, a metaphysical condition and a mathematical determination.107 Something similar could be found in the relationship between Condillac, on the one hand, and Biran and Tracy, on the other. In emphasizing this analogy, we do not mean that Condillac has succeeded in proposing an articulation between the content of sensations of continuity in the mathematical sense and the analysis of space and extension of bodies. Rather we would like to suggest that he tried to find this  Destutt de Tracy 1801, 500. “Ce n’est donc pas la sensation de solidité qui fait porter ce jugement, car elle est simple comme toutes les autres; mais la sensation de résistance, parce qu’elle est composée de celle de solidité et de celle de mouvement, et qu’il faut deux perceptions simultanées et distinctes pour donner lieu à un jugement.” 105  Ibid.: “c’est plus exactement l’inertie, ou l’opposition qu’apporte tout corps à recevoir du mouvement, qui nous cause cette sensation.” 106  Note that M. Friedman translates the title of this works as Metaphysical Foundations of Natural Science (Kant 2004). However to translate “Anfangsgründe” with “Foundations” involves the risk, on the one hand, of confusing the vocabulary of the “Anfangsgründe”‘of Mechanics (“First Principles”‘, or even “Elements”) with that of the “Foundations”‘(“Grundlagen”, “Grundzüge”‘), which the German mathematicians and logicians Frege, Hilbert, Ackermann, Bernays, etc. will adopt in the very different and later context of the new axiomatics and the new mathematical logic; and, on the other hand, of confusing Mathematical Mechanics with all the physical and natural sciences. 107  See Vuillemin 1955, 13–25. 104

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articulation, without ever arriving at a result that would be satisfactory, even for himself. On the contrary, his successors immediately gave themselves a solution to the problem of the objectivity of space that ceases to rely on the analysis of the mathematical concept. More specifically, they find this solution in the sensations of resistance and continuous movement (of the human body). Tracy, for example, did not hesitate to use D’Alembert’s principle and the constancy of material movement (conflated with the permanent sensation of this quantity of movement) to define the extension of a body108 thus going further than Condillac in the use of Mechanics to define the concept of space. Similarly, when Tracy indicated that the newly inserted Chapter III of the Traité made use of “the idea of continuity and contiguity which he had not spoken of in previous editions”, this claim should not contain the suspicion that Condillac was not aware of the definitions of mathematical space. As we have said, the mathematical definition of continuum and contiguity, which is mobilized here, may have been borrowed from Wolff. This definition does not immediately imply the measurement of a material space infinitely divisible, nor the metaphysical conflict between the ideality of mathematical space and the real simplicity of monads.109 Tracy, on the other hand, seems to take the problem within the Academy posed by the system of monads as the solution, and was clearly in favor of the mechanics.110 More particularly, he did not see that his arguments were neither unknown to Condillac nor likely to convince him. He writes, for example, that with his own definition of an extended being as “a being that we feel continuously while we have the sensation of a certain amount of movement […] we would never have had the idea of making extended beings starting from un-extended being, from monads; we would never forget that the idea of extension […] is only a consequence of that of movement, which alone is a sensation.”111 By this claim, he seems not to realize that a Wolffian can admit the imaginary nature of geometric space and refute the reality of simple parts in matter, while affirming the possible, non-actual, nature of the parts of the pure mathematical space whose parts are terms and not components of its idea. What Condillac was trying to introduce in the second edition of the Traité, however, was not a concept – such as that of the continuity of mathematical space – which would have been hitherto unknown to him, but rather the genesis of a type of  Destutt de Tracy 1798, 310.  This is attested by the massive use made by Condillac, in the Monades, of the idea that “In any quantity we accumulate simple beings, we cannot form an extension”, and that “the modifications of extension are only produced by the movement.” Condillac 1980, Les Monades, II, chapter V, 202, our translation; in French as follow: “en quelque quantité qu’on accumule des êtres simples, on n’en saurait former de l’étendue” and “les modifications de l’étendue ne sont produites que par le mouvement.” 110  This question divided the Leibnizians, such as Wolff and Formey, and the Newtonians, such as Euler and Maupertuis. 111  Destutt de Tracy (1798, 310): “être que nous sentons continûment pendant que nous avons la sensation d’une certaine quantité de mouvement [...] on n’aurait jamais eu l’idée de faire des êtres étendus avec des êtres inétendus, avec des monades; on n’oublierait jamais que l’idée d’étendue [...] n’est qu’une conséquence de celle de mouvement, laquelle seule est une sensation.” 108 109

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sensation, productive of the phenomenon of extension. Therefore, since “it is only with extension that we can make extension […]; for we do not see how there can be contiguity among several non-extended things nor how as a result they can form a continuum”112, it must itself be “a continuum formed by the contiguity of several other extended objects.” (ibid.) It is not, therefore, the mathematical definition of the continuum that is new here, but rather the effort to construct an articulation of its ideal nature with the reality of external objects. Note, however, that the continuity of the sensations necessary to have access to external objects will be sought in the movements of the statue’s body, provided with a movable hand. It is a postulate that the hand’s motion is continuous in both the geometric and the physical sense.113 Tracy thinks he does not need this postulate since he only considers the mechanic’s movement; conceives continuity as the absence of obstacle or resistance to a movement; and, under the influence of his friend Cabanis, considers sensations both as representative of external objects114 and as sensations of movement that are not representative of objects. Tracy’s Second Critical Stage This kind of conjunction between two meanings of movement is employed in the second – critical – part of the third moment of Tracy’s reading of Condillac (and of Biran’s reading of Tracy). In this part, the body progressively replaces the statue and the functioning of the central nervous system replaces the five senses. In the Mémoire, Tracy claimed “to differ essentially” from Condillac on the question of judgment. According to Tracy, it is impossible to attribute judgement to the motionless statue, which is thus deprived of the faculty of distinguishing and comparing, and of the sensation of resistance which alone relates the contents of our sensations to their causes.115 In the Eléments, however, he corrects his criticism, admitting “to having gone too far”116 in the connection between the sensation of movement with judgement and the knowledge of external objects. Biran took this statement for a disavowal of the method initiated by Tracy, but actually it is rather the expression of the tension between the Condillacian model of the genesis of ideas by the analysis  Traité, II, iv, § 1, 253B; 1982, 230; quoted by Tracy (Destutt de Tracy 1801, 497): “puisque nous ne saurions faire de l’étendue qu’avec de l’étendue……car nous ne voyons pas qu’entre plusieurs choses inétendues il puisse y avoir contiguité, ni que par conséquent elles puissent former un continu.” The rest of the text takes up exactly the analysis of what Condillac in the Monades presented as the role of the imagination representing us even the infinitely small (and therefore non-sensible) as extended. 113  To continue the comparison with Kant, we should look for an analog of this articulation, not in Aesthetics, but in the theory of intensive magnitudes. That continuity comes from the sensation of the movement marks an important difference between an empiricist genesis, even if ideal, and a transcendental deduction. 114  These sensations are representative of external objects insofar as they are sensations of movement. Only such sensations can offer the equivalent of Kant’s Analogies and Kant’s Refutation of Idealism. 115  Destutt de Tracy 1801, 510: “être allé trop loin.” 116  Destutt de Tracy 1970b, chap. vii, 126 and 141: “être allé trop loin.” We proposed an analysis of these reversals and of the correspondence with Biran in Schwartz 1986, vol. 1, chap. 6–7. 112

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of sensations (relayed by signs) and the consideration of sensations of movement felt without access to an externality.117 Tracy’s “retreat” here does not mean, as Biran understood, a denial of the distance taken from Condillac’s method because of the active principle of motility. By stating that the voluntary movement of the body is the condition behind the judgment of external existence, and not just its material or organic movement, he failed to acknowledge that the alliance between the methods of the analyst ideologists, on one side, and those of the physicians-­ philosophers, inventors of the concept of the central nervous system, on the other, was something difficult to reconcile with the data of the pure science of bodies’ movement in the space of mechanics.

9.4  Space in Mind or Space in Signs? Biran and Fichte introduced a distinction between ideas and sensations based on the active-passive opposition by which they went beyond the limits of Condillac’s analytical method and of Kant’s critical method, respectively. The construction program for the space in mind was then redefined by passing from the content of the sensations to the experience of a movement of the organic self, which becomes a real operator of the thought of space. With this shift, the program progressively moves away from both the question of pure space of the Mechanic in Kant, and the question of mathematical space produced by an empiricist genesis of ideas from the sensations relayed by the signs in Condillac. As we have tried to show, Condillac’s idealism, with its ambiguity, could offer a kind of pure empiricist alternative to what remains essentially empiricist in Kant’s transcendental idealism, while his idéologue disciples miss this ambiguity and its import. Lastly, we would like to suggest that their rejection of German philosophy depended on the frame of reference in which they developed the constructions of the thinking of space. This frame, which the idéologues took to be immediate, was the experience of the movement of bodies and, in Condillacism at least up to Tracy, was the science of signs expressive of ideas. This science was indeed that “secret operator”118 that Biran had detected, but which he felt was incapable of grasping the activity of thought. This “science of the signs”, however, was yet another face of the idéologues thought of spatial ideas, which was not the least modern. Gérando, in his Essai sur les signes et l’art de penser considérés dans leurs rapports mutuels,119 followed Condillac in reinterpreting the Lockean theory of the complex ideas of simple  The sensations of the fetus moving in its mother’s womb illustrate this kind of sensations.  The expression comes from Maine de Biran in the correspondence with Tracy (Biran 1930, vol. VII, 259), undated letter to which Tracy answers on 17 Prairial Year XII.  On this point, see Schwartz 1999. 119  De Gérando 1800, is the published version of the Mémoire crowned by the Institut on 15 Germinal Year VII, as an answer to the question put into competition on this issue by the Classe 117 118

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modes in terms of signs. He thus joined this other aspect of Condillac’s Leibnizianism, which freed the mathematical sign from the constraint of expressive representations of a sensible material extension. This took place at the very moment when not only the century of D’Alembert and of the mechanization of the continuous was coming to an end, but also the century of algebra and analysis applied solely to the service of the ideas of quantity. The English Analytical School – that of Peacock, Gregory, Hamilton, Cayley, Boole and Babbage – read the ideologues, just when they discovered – beyond the weight exerted on English mathematics of the eighteenth century by Newtonianism – the virtues of algebra and analysis.120 Thus, it was possible to find in Gérando’s signs – which are “signs of signs” and no longer refer to finished operations – a kind of philosophical confirmation of the operational calculus (precursor of abstract algebra and the theory of vector spaces).121 This science opened up a completely different conception of space, and this space was no longer the object of mathematics understood – as was the case with Kant, Condillac and the idéologues – as the science of the sensible.122 And indeed, it is this adherence to the empiricist vision of space that is maintained in the program of the idéologie.123 These last idealist empiricists sought to develop an integrated conception of space – one that articulates a mechanical, physiological and algebraic approach to the notion. In conclusion, it might be appropriate to explain why this integration did not resist time. It is possible that, at the birth of analytical philosophy, when Bertrand Russell, in his early works, looked for an articulation between the new forms of geometry and what he called ‘idealism’  – meaning by ‘idealism’ Kantian and Hegelian idealism124- he unwittingly equated this kind of ‘idealism’ with the various forms of empiricist idealism that had continued to move, more or less obscurely, into the English tradition, even if, at that time, empiricist idealism and the German forms of idealism had nothing in common. This was certainly not the case during the Enlightenment and that is what we have tried to show in this article by comparing the answers given by Condillacism and Criticism to the challenges of the science of their time – answers that their posterity illuminates and prolongs, linking space and movement, thought of space and movement of thought. (English translation and revision by L. Berchielli and D. Andru)

d’analyse des sensations et des idées, Year V. These letters are parts of his posthumously published manuscripts. 120  On the relationship of the Cambridge School with the continental tradition, see, for instance, Koppelman 1971. 121  C.  Babbage, in a paper read at a meeting of the Cambridge Philosophical Society on 16 December 1821 entitled “On the influence of signs on mathematical reasoning” (Babbage 1989), quotes the Gérando’s text in French. In a passage where he discusses the generalizing power of algebra he writes that Gérando’s writings supported and enriched his theses. 122  This appears in Destutt de Tracy 1802, 604. This adherence is common to the Kantians and to the French heirs of Condillac. 123  Ibid. 124  Russell 1897.

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