Kant's Intuitionism: A Commentary on the Transcendental Aesthetic 9781442676480

Table of contents :
Contents
Preface
Acknowledgments
Bibliographical Note
Introduction
PART I. KANT'S REPRESENTATION TERMINOLOGY
Introduction
1. The Distinction between Intuition and Understanding
2. The Distinction between Form and Matter of Intuition
3. Sensation and the Matter of Intuition
4. Origins of the Form and the Matter of Intuition
Summary and Conclusions to Part I
PART II. THE EXPOSITIONS
Introduction: Purpose and Method of the Expositions
5. The First Exposition
6. The Second Exposition
7. The Later Expositions
8. The Transcendental Expositions
Summary and Conclusions to Part II
PART III. CONCLUSIONS FROM THE ABOVE CONCEPTS
Introduction
9. Kant's Argument for the Non-spatiotemporality of Things in Themselves
10. The Unknowability Thesis and the Problem of Affection
11. Kant, Mendelssohn, Lambert, and the Subjectivity of Time
Summary and Conclusions to Part III
Afterword
Notes
Sources Cited
Citation Index
Person Index
Subject Index

Citation preview

Kant's Intuitionism

A Commentary on the Transcendental Aesthetic

Ever since the publication of his Critique of Pure Reason in 1781, Immanuel Kant has occupied a central position in the philosophical world. In Kant's Intuitionism, Lome Falkenstein focuses on one aspect of Kant's Transcendental Aestheitic, namely, his position on how we manage to intuit the properties and relations of objects as they exist in space and time. It is a major problem not only in philosophy, but in cognitive science in general, to decide how much structure sensory input has of itself and how much we give it through processing. How much do our faculties do to structure our knowledge of objects and to give them their spatial and temporal existence? Recent interpretations of Kant's doctrine of intuition have emphasized the constructivist answer to this question, stressing that sensations have no structure of their own and that, for the objects of our experience to have any spatial or temporal structure at all, we must impose a structure through synthetic processes of the imagination or understanding. Rehabilitating an interpretation of Kant outlined in the nineteenth century, Falkenstein argues that our knowledge of objects in space and time is not grounded in concepts but in the quasi-physiological constitution of our senses. Falkenstein begins with a careful critique of both historical and contemporary approaches to this problem and goes on to develop a cogent and stimulating argument for his position. The dialectic that results advances the discussion into controversial new realms, revitalizing the debate about the implications of Kant's Transcendental Aesthetic. LORNE FALKENSTEIN is a professor at the University of Western Ontario.

The essential function of the understanding, according to Kant, is to combine the manifold of sensory intuition. But combination is an activity that can be understood in two ways. To assemble a number of separately given pieces into a whole, as with a jigsaw puzzle, is to combine a manifold in one of these senses. But there is also a kind of combination involved when one simply recognizes that an outline ought to be drawn in one way rather than another within a mosaic, so that one type of figure, rather than another, is depicted. In this second sense, the matters of the manifold are not moved around or arranged; rather they are taken to be presented in a spatial array to begin with. Combination consists only of deciding which pairs of already adjacent matters ought to be considered to fall on opposite sides of the outline. It does not consist of determining which matters ought to be set adjacent to one another. The adjacency relations are intuited, not constructed.

Lome Falkenstein

KANT'S INTUITIONISM

A Commentary on the Transcendental Aesthetic

UNIVERSITY OF TORONTO PRESS Toronto Buffalo London

www.utppublishing.com © University of Toronto Press Incorporated 1995 Toronto Buffalo London Printed in Canada Reprinted in paperback 2004 ISBN 0-8020-2973-6 (cloth) ISBN 0-8020-3774-7 (paper)

Printed on acid-free paper Toronto Studies in Philosophy Editors: James R. Brown and Calvin Normore

National Library of Canada Cataloguing in Publication Falkenstein, Lome, 1957Kant's intuitionism : a commentary on the transcendental aesthetic / Lome Falkentstein. (Toronto studies in philosophy) Includes bibliographical references and indexes. ISBN 0-8020-2973-6 (bound), — ISBN 0-8020-3774-7 (pbk.) 1. Kant, Immanuel, 1724-1804. Kritik der reinen Vernunft. 2. Intuition. 3. Transcendentalism. 4. Aesthetics. I. Title. II. Series. B2779.F35 1995

121'.3

C95-931934-4

This book has been published with the help of a grant from the Canadian Federation for the Humanities, using funds provided by the Social Sciences and Humanities Research Council of Canada. University of Toronto Press acknowledges the financial assistance to its publishing program of the Canada Council and the Ontario Arts Council.

in memoriam

GREG CURNOE 14 November 1992

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Allein von einem Stiicke konnte ich im obigen Beweise doch nich abstrahieren, namlich davon, dafi das Mannigfaltige fiir die Anschauung noch vor der Synthesis des Verstandes, und unabhangig von ihr, gegeben sein miisse; wie aber, bleibt hier unbestimmt. (6145)

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Contents

Preface xv Acknowledgments xix Bibliographical Note xxi INTRODUCTION i. ii. iii. iv. v.

Nativism and Empirism 5 Intuitionism and Constructivism 7 Formal Intuitionism 9 Kant's Formal Intuitionism 10 Grounds for the Popular Neglect of Formal Intuitionism

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PART I KANT'S REPRESENTATION TERMINOLOGY Introduction 17 i. The Place of the Aesthetic in the Critique of Pure Reason ii. Basic Confusions in Kant's Thought 26

21

i The Distinction between Intuition and Understanding 28 i. The Sense/Intellect Distinction in ID 32 a. The Project of the Inaugural Dissertation and Its Motivation 32 b. The Effect of the Paradoxes of Composition and Division 35 c. Kant's Theoretical Inheritance 41 d. Divergences from the Traditional Account of the Faculties 44 ii. The Argument of ID 47 iii. Strategic Difficulties 52 a. The Changed Outlook of the Critique 52

x

Contents b. Problematic Consequences of Kant's Changed Outlook iv. The Distinction between the Faculties in the Critique 58 v. The Circularity Problem 61 vi. Regressive Terminology 66

54

2

The Distinction between Form and Matter of Intuition 72 The Blindness Problem 72 i. The Two Basic Features of an Intuitive Representation 74 a. Multiplicity 74 b. Order 77 Forms as Mechanisms and Forms as Representations 79 Forms as Orders of Intuited Matters So ii. Textual Evidence against Forms as Mechanisms 81 iii. Textual Evidence against Forms as Representations 83 a. Kant's Groundless Assumption? 88 iv. Conflicting Passages 89 a. ID 91 b. The Original Acquisition Passage 91 c. Subjective and Objective Order 96 d. Figurative Synthesis 98 e. The Alteration at 634 100 v. Afterword 101

3

Sensation and the Matter of Intuition 103 i. The Epistemological Role of Sensation 107 a. Exegetical Difficulties with View i 107 b. Exegetical Difficulties with Taking Sensations Out of Space (Views 2b and 3) 109 c. Evidence for View 2a 111 d. Conflicting Passages 112 The Analogies 112 The Classification Passage and the Two Senses of 'Sensation' 113 The 'Real' of Sensation 115 ii. The Ontological Status of Sensation 117 a. The Problem 118 b. The Physiological Account of Sensation 119 c. Sensations as Sensible Qualities 123 d. An 'Intentional Object' Account of Sensible Qualities 127 Appendix: Sensations as Effects of the Intensity of Force 130 Objection 133

Contents xi 4 Origins of the Form and the Matter of Intuition 135 Summary and Conclusions to Part I 138 PART II

THE EXPOSITIONS

Introduction: Purpose and Method of the Expositions 145 i. Purpose 145 ii. Method 148 a. The Method of Conceptual Exposition 149 b. The Standard View of Kant's Methodology in the Expositions and Its Limitations 151 Appendix: An Empirical Exposition of Our Concepts of Sensible Qualities 154 5 The First Exposition 159 i. Kant's Objectives in the First Exposition 160 a. The Standard Objection and Its Standard Refutation 161 ii. Kant's Sensationist Opposition 165 iii. The Standard Objection to the First Exposition 169 a. The A Priori Status of Space and Time 172 iv. The Grounds of Kant's Rejection of Sensationism 174 a. An Excuse 175 b. A Defence 179 Appendix: Meditations on the Epistemology of Order 183 6 The Second Exposition 186 i. Analysis of the Argument 186 a. Premises 186 b. Conclusions 189 c. Appearance or Intuition? A Problem of Representation Terminology 190 d. The Two-Part Structure of the Exposition 192 ii. The Inextricability Argument 193 a. The Sense of 'Represent' 194 b. The Adequacy of the Argument 196 iii. The Third Exposition in A and the Validity of Geometry 200 iv. The Independence Argument 203 a. The Conceivability of Empty Space and Time 203 b. Arguments for the Conceivability of Empty Space and Time 205 c. The Real Possibility of Empty Space and Time 207

xii Contents d. Arguments for the Real Possibility of Empty Space and Time 210 Appendix: Empty Space and Time in Kantian Physics 213 e. Summary and Conclusions 215 7 The Later Expositions 217 i. The Singularity Argument 217 a. Justification for the Third Premise 218 b. Justification for the Second Premise 219 c. Justification for the First Premise 222 d. The Argument of the Time Section 226 e. Conclusions 228 ii. The Whole/Part Priority Argument 229 a. Premise 2 230 b. Premise 33 234 c. Premise 3b 235 d. Premise i 236 iii. The Infinity Argument 237 a. The A Infinity Argument 238 b. The B Infinity Argument 239 iv. The Completeness of the Later Expositions 241 v. The Composition of Intelligible Spaces and Times 244 8 The Transcendental Expositions 253 i. The Buttressing Argument 254 a. The Priority Argument 254 b. The Immediacy Argument 258 ii. The Subjectivity Argument 263 a. An Intuitivity Argument 265 b. The Argument for Grounding in the Subject 266 Remark: Subjective Grounding and Conditionally A Priori Truth 267 c. An Argument for Grounding in the Receptive Constitution of the Subject 268 iii. The Explanation of the Possibility of Geometry and Mechanics 269 Summary and Conclusions to Part II 275 i. The Metaphysical Expositions 276 ii. The Transcendental Expositions 279 iii. Conclusions 281

Contents xiii PART III

CONCLUSIONS FROM THE ABOVE CONCEPTS

Introduction 287 9 Kant's Argument for the Non-spatiotemporality of Things in Themselves 289 i. Substantival Space and Time 293 ii. Relative Space and Time 300 iii. Limits of Kant's Result 304 iv. Summary and Conclusions 308 10 The Unknowability Thesis and the Problem of Affection 310 i. Unknowability 310 ii. Affection 314 a. The Objectivity of Reference 316 b. 'Manifest' Idealism 318 c. The A Priori/A Posteriori Distinction 322 d. Summary 325 Appendix: The Legitimacy of Speculation about Transcendent Affection 327 11 Kant, Mendelssohn, Lambert, and the Subjectivity of Time 334 i. Kant's Subjectivity Thesis 335 ii. Mendelssohn's Objection 336 a. Kant's Initial Response 338 b. The Fallacy of Kant's Initial Response 341 c. The Representing Subject as Appearance 345 d. Kant's Critical Response to Mendelssohn 348 iii. Kant's Response to Mendelssohn and the Subjectivity Thesis 352 a. Subjectivity and Non-spatiotemporality 352 b. Subjectivity and Unknowability 353 Summary and Conclusions to Part III 356 A F T E R W O R D 359 Notes 363 Sources Cited Citation Index Person Index Subject Index

437 445 453 457

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Preface

The Transcendental Aesthetic of Kant's Critique of Pure Reason has two goals, the one explicitly recognized by him, the other never acknowledged as such but none the less achieved. The first is to give an answer to the question of how synthetic a priori judgments are possible; the second is to offer an account of the basis of our knowledge of the spatiotemporal properties and relations of things. Kant tried to achieve the first goal by attempting to demonstrate that we human beings are so constituted as to receive sensory experiences successively over time and simultaneously over two or three dimensions of Euclidean space, so that propositions describing space and time can be taken to be necessarily and universally true of all the objects of sensory experience, even in advance of having that experience, as long as our constitution does not change. He tried to achieve the second goal by offering and attempting to justify a theory of space- and time-cognition unique in the history of ideas, and radically distinct from the nativist, empirist, and sensationist accounts of space- and time-cognition that have heretofore been recognized by historians of the theory of visual perception. While the first of Kant's major conclusions has been widely recognized and intensively examined by commentators, the second has so far been ignored. It is to rectify this omission that I have written this book. It takes the form of a commentary on the Transcendental Aesthetic. Part I is an analysis of the terms Kant uses to name representations and cognitive faculties. The analysis parallels Kant's own in §1 of the Transcendental Aesthetic and is focused on four major themes: the distinction between intuition and understanding (chapter i), the distinction between the form and the matter of intuition (chapter 2), the relation between sensation and the matter of intuition (chapter 3), and the rela-

xvi

Preface

tion between the subject and the form of intuition (chapter 4). In treating these topics I have sought not only to explain Kant's frequently obscure and ambiguous use of terminology, but to present a complete and integrated picture of the working of the cognitive faculties, as envisioned by Kant. Kant's position on the role of space and time as 'forms of intuition' is front-and-centre in this picture. My major concern has been to explain what it means for space and time to be 'forms' and to be 'intuited/ and to draw out the theory of the origin of our knowledge of the spatial and temporal properties and relations of objects that these claims involve. Part II is a commentary on the Aesthetic's Metaphysical and Transcendental Expositions. The first exposition is dealt with in chapter 5, the second in chapter 6, the remaining metaphysical expositions in chapter 7, and the transcendental exposition in chapter 8. These texts constitute Kant's argument for the picture of the working of the cognitive faculties presented in Part I. Expositing them in the detail required to make them intelligible has in some cases taken me rather far afield. Thus, the second half of chapter 6 includes an investigation of Kant's views on the metaphysics and physics of empty space, and chapter 7 incorporates an account of the operations of the understanding in processing the intuitively given manifold. Part III deals with the implications of the theory presented in Part I and defended in Part II. It loosely parallels Kant's own statement of the implications of his work in the sections of the Aesthetic entitled 'Conclusions from the Above Concepts/ Chapter 9 deals with the first of these conclusions, the thesis that things as they are in themselves could not be in space and time. Chapters 10 and 11 deal with the two outstanding problems created by this conclusion: the problem of affection and the problem of the temporality of the subject. Kant's positions on nonspatiotemporality, affection, and the role of the constitution of the subject in grounding spatiotemporal order are the major tenets of what is referred to in the literature as his transcendental idealism. It is this latter theory that has heretofore captured most of the attention of commentators. If I am right, however, the major contribution of the Aesthetic is to be found in its theory of original space- and time-cognition. Part III is not the culmination of the argument of this book, but an appendix, remarking on problems with and implications of the central theory. I do not mean to deny the importance of transcendental idealism or its centrality to Kant's own thought - but that is a story that has already been told and my purpose here is not to retell it, but to show that there is more going on.

Preface xvii The book concludes with an afterword commenting on what this reading of the Aesthetic implies for the interpretation of the Analytic. In what follows, the major parts of the Aesthetic are dealt with roughly in order, and roughly in paragraph-by-paragraph fashion. Since a great deal of what Kant had to say about space, time, and representation in other works and other parts of the Critique has also been commented upon, a citation index has been added to facilitate ease of reference. I would have liked to make each chapter and section selfcontained, so that this book could be used as a reference by those wishing to look up the interpretation of a particular passage. But, though I have tried to approximate this model as far as possible (the reader who goes through it from the beginning will find a certain amount of repetition), I have been frustrated by the fact that the text I am commenting on is a single chain of argument that builds through the definitions of §1 of the Aesthetic to the arguments of the Metaphysical and Transcendental Expositions, and from there to the conclusions of the 'Conclusions from the Above Concepts.' This has made the production of truly self-contained chapters and sections impossible. However, I have tried to mitigate the result by supplying cross-references to the more important arguments.

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Acknowledgments

My thought on these matters has developed over some time, and preliminary versions of some of the points made here have been previously published elsewhere. Much of that initial work was made possible by grants from the Social Sciences and Humanities Research Council of Canada. I am indebted to Journal of the History of Ideas for permission to make use of my article 'Was Kant a Nativist?' (51 [1990], 573-97), portions of which appear in revised form in the Introduction and in chapter 2; to Canadian Journal of Philosophy for permission to make use of my articles 'Kant's Account of Sensation' and 'Kant's Account of Intuition' (20 [1990], 63-88, and 21 [1991], 165-93, respectively), which appear in revised form as chapters i and 3; to Kant-Studien for permission to make use of my article 'Kant's Argument for the Non-spatiotemporality of Things in Themselves' (80 [1989], 265-83), portions of which appear in revised form in chapter 9; and to Journal of the History of Philosophy for permission to make use of my article 'Kant, Mendelssohn, Lambert and the Subjectivity of Time' (21 [1991], 227-51), portions of which appear in revised form in chapters 8 and 11. This book has been published with the help of a grant from the Canadian Federation for the Humanities, using funds provided by the Social Sciences and Humanities Research Council of Canada. It would not have reached what state of soundness it has without the support, advice, and criticism of my friends, colleagues, mentors, and referees. I would like to thank especially Andrew Brook, Robert E. Butts, Rolf George, William Harper, Patricia Kitcher, Lothar Kreimendahl, Ralf Meerbote, Gordon Nagel, Kathleen Okruhlik, Brigitte Sassen, Eric Watkins, and Randolph Wojtowicz. I regret that, in some cases, I have repaid their valuable help in the bad coin of criticism and disagreement.

xx

Acknowledgments

It is a consequence I would have avoided if I could have seen a way, and one that makes my debt, and their generosity, all the greater. The errors that remain are a product of my own obstinacy and/or obtuseness rather than their good sense. I owe a special debt to Brad Wray, for his work on the frontispiece, and to Beverley Beetham Endersby, for an outstanding job of editing. I dedicate this book to the memory of Greg Curnoe. His contempt for jargon and technical terminology, and concern to always put the point in plain English, is a rule to which I have tried to keep, even in the strange and obscure land of Kant's critical philosophy.

Bibliographical Note

The abbreviations listed below are used to refer to standard works. Volume numbers appear in Roman, and page numbers in Arabic, numerals. Where specific paragraph (1) or section (§) numbers are relevant, these are provided in place of or in addition to page numbers. Except where indicated, all translations from Kant's German are my own. Those from his Latin follow the translations in David Walford and Ralf Meerbote, eds, Immanuel Kant: Theoretical Philosophy, 1755-1770, The Cambridge Edition of the Works of Immanuel Kant (Cambridge: Cambridge University Press, 1992), 373-416. In order to preserve the distinction between the German terms 'Gegenstand' and 'Objekt/ both of which are best translated by the English word 'object/ I have used an initial capital in translating the latter. A Ak Anfangsgrunde Anthropology AT B

Immanuel Kant, Kritik der reinen Vernunft(Riga: Johann Friedrich Hartknoch, 1781) Immanuel Kant, Gesammelte Schriften, 27+ vols (Berlin: de Gruyter and predecessors, 1900-) Immanuel Kant, Metaphysische Anfangsgrunde der Naturwissenschaft, Alois Hofler, ed. Ak, IV 466-565 Immanuel Kant, Anthropologie in pragmatischer Hinsicht, Oswald Kiilpe, ed. Ak, VII117-333 Rene Descartes, Oeuvres de Descartes, Charles Adam and Paul Tannery, eds, 12 vols (Paris: Cerf, 1897-1913; revised ed., Paris: Vrin/CNRS, 1964-76) Immanuel Kant, Kritik der reinen Vernunft, 2d ed. (Riga: Johann Friedrich Hartknoch, 1787)

xxii

Bibliographical Note

Briefwechsel De Motu Dialogues Enquiry

Entdeckung Essay Fortschritte

G

H ID Inquiry KdU Logic New Essays

Immanuel Kant, Briefiuechsel, Otto Schondorffer and Rudolf Malter, eds, 3d ed. (Hamburg: Meiner, 1986) George Berkeley, De Motu, in A.A. Luce and T.E. Jessop, eds, The Works of George Berkeley, vol. IV, 11-30 (London: Nelson, 1951) George Berkeley, Three Dialogues between Hylas and Philonous, in A.A. Luce and T.E. Jessop, eds, The Works of George Berkeley, vol. II, 163-263 (London: Nelson, 1949) David Hume, Enquiries concerning Human Understanding and concerning the Principles of Morals, L.A. Selby-Bigge and P.H. Nidditch, eds, 3d ed. (Oxford: The Clarendon Press, 1975) Immanuel Kant, Uber eine Entdeckung, nach der alle neue Kritik der reinen Vernunft durch eine altere entbehrlich gemacht werden soil, Heinrich Meier, ed. Ak, VIII185-251 John Locke, An Essay Concerning Human Understanding, Peter H. Nidditch, ed. (Oxford: The Clarendon Press, 1975) Immanuel Kant, Uber die von der Konigl. Akademie der Wissenschaften zu Berlin fur das Jahr 1791 ausgesetzte Preisfrage: 'Welches sind die wirklichen Fortschritte, die die Metaphysik seit Leibnitzens und Wolf's zeiten in Deutschland gemacht hat?' Gerhard Lehmann, ed. Ak, XX 253-351 Gottfried Wilhelm Leibniz, Die Philosophischen Schriften von Gottfried Wilhelm Leibniz, C.I. Gerhardt, ed., 7 vols (Berlin: Weidmann, 1875-1890; reprint ed., Hildesheim: Olms, 1960-1) Thomas Reid, Philosophical Works, Sir William Hamilton, ed., 2 vols (facsimile ed. Hildesheim: Olms, 1967) Immanuel Kant, De mundi sensibilis atque intelligibilis forma et principiis, Erich Adickes, ed. Ak, II 385-419 Thomas Reid, An Inquiry into the Human Mind on the Principles of Common Sense. H, I 93-211 Immanuel Kant, Kritik der Urteilskraft, Wilhelm Windelband, ed. Ak, V 165-485 Immanuel Kant, Logik, Benjamin Jasche, ed. Ak, IX i150 Gottfried Wilhelm Leibniz, Nouveaux essais sur I'entendement humain, in Gottfried Wilhelm Leibniz, Samtliche Schriften und Briefe, series 6, vol. VI, Andre Robinet and

Bibliographical Note

NTV Physical Monadology Principles (B)

Principles (D) Prize Essay Prolegomena R Traume Treatise

xxiii

Heinrich Schepers, eds (Berlin: Akademie-Verlag, 1962), 39-527. Also New Essays on Human Understanding, Peter Remnant and Jonathan Bennett, trans. (Cambridge: Cambridge University Press, 1981), which follows the same pagination as the Akademie-Verlag edition George Berkeley, An Essay Towards a New Theory of Vision, in A.A. Luce and T.E. Jessop, eds, The Works of George Berkeley, vol. 1,159-239 (London: Nelson, 1948) Immanuel Kant, Metaphysicae cum geometria iunctae usus in philosophia naturali, cuius specimen I. continet monadologiam physicam, Kurd Lasswitz, ed. Ak, I 473-87 George Berkeley, A Treatise Concerning the Principles of Human Knowledge, in A.A. Luce and T.E. Jessop, eds, The Works of George Berkeley, vol. II, 19-113 (London: Nelson, 1949) Rene Descartes, Principles of Philosophy. AT, IXb Immanuel Kant, Untersuchung iiber die Deutlichkeit der Grundsatze der natiirlichen Theologie und der Moral, Kurd Lasswitz, ed. Ak, II 273-301 Immanuel Kant, Prolegomena zu einer jeden kunftigen Metaphysik, die als Wissenschaft wird auftreten konnen, Benno Erdmann, ed. Ak, IV 253-383 Kant's reflections on Metaphysics, as numbered by Adickes and printed in Ak, XVII-XVIII Immanuel Kant, Traume eines Geistersehers, erlautert durch Traume der Metaphysik, Paul Menzer, ed. Ak, II 315-73 David Hume, A Treatise of Human Nature, L.A. SelbyBigge ed.; 2d ed., revised by P.H. Nidditch (Oxford: The Clarendon Press, 1978)

Other works are cited by the last name of the author or by last name and shortened title of the work, where reference is made to more than one work by the same author. Full bibliographic entries are provided in 'Sources Cited.'

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Kant's Intuitionism: A Commentary on the Transcendental Aesthetic

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Introduction

The history of theories of space- and time-cognition, and of visual spacecognition in particular, has traditionally been written as the story of a conflict between two opposed schools of thought: the nativist school and the empirist school.1 The schools are divided over the question of the role of sensory experience in space-cognition. When viewed from this simple perspective, Kant's allegiance would appear to be clear. Kant maintained that spatial and temporal relations are not features of things as they are in themselves and are not known as a result of how we are affected by the objects that interact with our sense organs. Only the 'matter' of intuition, according to Kant, corresponds to 'the effect of an object on the representative capacity in so far as we are affected by this object' (Ai9-2O/B34). The spatiotemporal features of intuition are instead grounded in the constitution of the subject (640-1). Thus, Kant would appear to be a nativist. In this book I set out to subvert this simple picture of Kant's position on space- and time-cognition. While the evidence that Kant took space and time to be in some sense innate is incontrovertible, his critics and commentators have generally (and especially recently) failed to grasp the precise sense of this nativism. This sense can best be indicated by considering the text of the passage I alluded to above, 640-1. Now how can an outer intuition, which precedes the objects themselves, and in which the concepts of these objects can be determined a priori, attend the mind? Obviously, in no other way than insofar as it has its place merely in the subject as this subject's formal character, whereby it comes to be affected by Objects2 and thereby acquires immediate representation (that is, intuition) of them; hence, [in no other way than insofar as the intuition has its place in the subject] only as form of outer sense in general.

4 Introduction According to this passage, what is innate to the subject is the manner 'whereby it comes to be affected by Objects.' Space, on this account, is not something the subject is innately enabled to constitute out of its most primitive sensory experiences; space is rather the manner in which the subject is innately constituted to receive its most primitive sensory experiences. Kant's nativism is, in other words, intuitionist rather than constructivist in character. Rather than take space to be actively constituted through some cognitive operation, Kant takes it to be passively received by the cognitive system in our first and most primitive experiences albeit so received in virtue of the manner in which our senses are innately constituted rather than in virtue of anything in the affecting object determining sensation. This intuitionism about space- and time-cognition is reiterated in Kant's other major works on theoretical philosophy of the Critical period. In the Entdeckung, he describes space as grounded on, 'the mere characteristic receptivity of the mind, to acquire a representation according to its subjective constitution' (Ak, VIII 222); in the Prolegomena space is grounded on 'the essential property of our sensibility, by means of which objects are given to us' (Ak, IV 287; my italics), and in the Fortschritte space is grounded on 'the way our senses are affected by objects' (Ak, XX 269; my italics). I take this intuitionism to be the most significant facet of Kant's account - one that is so significant that the nativist component of the account pales to insignificance in comparison. This is so much the case that Kant's account of original space- and time-cognition has more in common with other empirist but intuitionist accounts of the matter (notably, Hume's theory that our ideas of space and time are grounded in manners of disposition of impressions)3 than it does with the nonintuitionist, nativist accounts that preceded and followed it. Yet, to read many recent commentators on Kant, one would think that he held no such view, and that rather than take space and time to be the manners in which sensations are received by us in sense intuition, he took them to be something only first constituted through intellectual operations, such as the figurative synthesis of imagination.4 My major goal in what follows is to show the error of this current view and rehabilitate Kant's intuitionism. In doing so, I am setting myself at variance with some of the recent literature in a further way: I am postulating that, for Kant, the raw data immediately received by the cognitive system through sensory experience is structurally complex; it consists of an array of matters disposed

Introduction 5 alongside one another in space and occurring successively over time.5 Indeed, as will become clear below, I take Kant's view to be that the originally given data of sense vary not only in position, but in intensive magnitude as well. Though the general structural features of space and time (e.g., their topology, affine structure, or metric) may be determined by the way we are constituted so as to be able to receive information, the specific locations of sensations in space and time are empirically given.6 And though (for reasons Kant never really makes explicit) we may be able to anticipate in advance of any experience that the data we experience will have some intensive magnitude, the particular intensity of any datum is also empirically given. There is thus a degree of empirical determination present in Kant's theory of knowledge - and, correspondingly, a degree of empirism in his theory of original space- and timecognition. The empirical component of experience is not what Kant, in his hunt for the ground of the possibility of synthetic a priori judgments, is principally concerned to investigate, but it is definitely present in the background of his accounts of a priori knowledge in mathematics and philosophy of nature. Because Kant himself makes so little of this background, empirical component, it is tempting to read him as someone who took sensations to be mere Aristotelian prime matter for the cognitive process, and all structure and differentiation to be supplied by synthetic procedures. This book attacks that view. My reasons for taking the positions that I do on Kant's intuitionism and his empiricism are laid out more fully below, especially in chapters 2 and 3, respectively. I will not repeat or summarize them here. Instead I want to survey in more detail what I take to be the most interesting facet of Kant's intuitionism: the virtually unique position it takes on the ultimate ground of our knowledge of spatial and temporal relations. i.

Nativism and Empirism

The nativism/empirism dichotomy is a notoriously slippery one (some might even argue, a false one). One of the reasons for this is that the conflict between nativists and empirists, which is nominally a conflict just over the role of experience in cognition, has been confused with an entirely different conflict, that over the role of immediately received information (intuition) in cognition. The whole history of theories of cognition, particularly in the areas of visual perception and space-cognition, has been vexed by a failure to separate the nativism/empirism issue from the issue of what is intuited (originally given to the cognitive

6 Introduction system for processing) and what is constructed through cognitive processing. Once these issues are separated, a richer account of the history of theories of perception becomes possible - one that accords Kant a special and important place. To better understand the nature of the distinction between nativism/ empirism and intuitionism/constructivism, consider a simple information-processing device, like a calculator. The activity of this device can be represented in terms of three distinct moments: first, information is fed into the system (the keys are struck); this causes a chain of events to take place in the machine that we can refer to as 'processing of the input'; and the result is the output of a number represented on a screen or roll of paper. The calculator can be taken as a model for the brain, or the mind, considered as an information-processing device, with the senses providing the input and the output consisting of knowledge claims or 'prepositional attitudes/ The nativism/empirism issue has to do with the role of sensory stimulation (striking the keys) in the generation of the eventual output. A strict empirist will want to maintain that no knowledge is obtained that does not come from the senses (all the output is determined by how the keys are struck). This means, in particular, (i) that all the input comes from sensory experience (no original input is in the form of innate ideas, Platonic recollection, intellectual intuition, or mystical insight), and (2) that, so far as is possible, all the processes that are performed on originally given input are learned from past experience.7 A nativist, in contrast, is someone who will deny either (i) or (2). An 'innate-ideas nativist' will deny (i) and hold that there are other sources of input to the cognitive process besides stimulation of the senses (typically some form of intellectual intuition). An 'innate-mechanisms nativist' will deny (2) and hold that the processes by which a certain output is generated are inborn (typically, these processes are taken to be grounded in some sort of pure reasoning ability). An extreme case of the denial of (i), and hence an extreme example of innate-ideas nativism, can be found in Descartes's Notes on a Certain Program, where it is claimed that all the input we receive is produced by the mind itself from its own inner resources, stimulation of the sense organs providing merely the occasion for this production.8 Other, less extreme examples of innate-ideas nativism include Plato's doctrine of the reminiscence of forms9 and Reid's doctrine of suggestion.10 Examples of the opposing position, that all input does come from sensory experience, can be found in the Aristotelian dictum that nothing can be in the intel-

Introduction 7 lect that was not first present to the senses/1 as well as in Locke's doctrine of the tabula rasa12 or Hume's principle that all ideas must originate from impressions.13 Descartes's Dioptrics provides an example of denial of (2) for the case of depth perception. In this work, Descartes described four methods by which we determine visual depth, two of them - judging distance on the basis of the brightness and distinctness of the visual image and judging distance on the basis of a prior knowledge of the size, position, shape, colour, or brightness of the object - might suppose an association learned from past experience14 (at least, Descartes does not rule this out). But the other two methods explicitly do not involve learning. Descartes describes the act of accommodating the eye to focus on objects at different distances as 'ordained by nature to make our soul perceive distance/ and he describes the act of turning the two eyes to make them converge on an object as giving us a knowledge of distance 'as if by a natural geometry.'15 His point was likely not, as Berkeley was later to caricature it, that we actually see the lines and angles traced by light rays and calculate the distance of the object by triangulation; but it was at least that the mind is innately so constituted that certain muscular sensations accompanying accommodation and convergence automatically yield a cognition of the appropriate distance. The opposite, empirist position, that the process by which we infer depth from the raw data supplied in immediate visual experience is one we learn to perform through discovering by experience that certain muscular sensations in the eyes are associated with objects at certain distances (as measured by reaching or walking), was paradigmatically stated by Berkeley in NTV, 2-51. ii.

Intuitionism and Constructivism

Though histories of the theory of visual perception have been written around the nativism/empirism dispute, an entirely different set of distinctions cuts across both the nativist and the empirist camps. This set of distinctions deals with the role, not of experience, but of processing in cognition. If you believe that a certain output is already contained in the input to a processor, so that it does not require any process (other than transmission or attention) to become known, then you are what I call 'an intuitionist' with regard to that output. Aristotle, for example, gives an intuitionist account of colour perception in De Anima, II vii. According to

8 Introduction this theory, colours exist in objects, and when a transparent medium between the object and the eye is activated by light, the colour imposes its form on the medium, which in turn imposes its form on the eye. This account is intuitionist, because the colour ultimately cognized by the soul is thought to be already contained in the sensory input, and nothing needs to be done to it by the senses or the soul other than to transmit and attend to it. One can be an intuitionist without taking sensations to be the intuited items. Those who have postulated that the fundamental principles of mathematics or logic or metaphysics or ethics are simply received through some extrasensory mode of awareness, such as Platonic recollection, the Cartesian light of nature, or Reidian suggestion, are also intuitionists. We can use the label 'sensationist' to refer to the position that a particular product of the cognitive system is already present in the sensations originally given to the cognitive system as input. The alternative position, that the product, though originally given in the input, is given in some other kind of input than a sensation, can be called 'nonsensationist intuitionism.' (As will become clear in a moment, innateideas nativism is not the only kind of non-sensationist intuitionism.)16 If, in opposition to both sensationism and non-sensationist intuitionism, you believe that a given output is not already contained in the input to the cognitive system, but needs to be worked up out of that input by some process such as association, inference, comparison, abstraction, combination, or composition, then you are what I call 'a constructivist' with regard to that output. Berkeley's NTV is the classic constructivist work on the cognition of visual spatial depth. But Reid, too, was a constructivist on this question: in his view we have to learn how to associate 'visual appearances' with the innate conceptions of Euclidean threedimensional space suggested to us by our tactile sensations.17 (For examples of sensationist positions on visual depth perception one must turn to nineteenth century critics of Berkeley such as Samuel Bailey and William James.)18 The cases of Berkeley and Reid point to the importance of not confusing intuitionism, sensationism, or constructivism with either nativism or empirism. A constructivist could be an innate-ideas nativist (as was Reid), and, of course, a constructivist could also be an innatemechanisms nativist (as was Descartes). The intuitionist/constructivist and nativist/empirist camps cut across each other in both ways. There are such things as constructivist nativism and empirist intuitionism. All sensationists, for instance, are empirists, at least with regard to knowledge of the matter that they take to be

Introduction 9 directly given in sensation. Though they do not take any learned process to be involved in the production of this matter, neither do they take any processing of the raw data to be required; thus, they still adhere to the basic empirist dictum that sensory experience determines the content of all knowledge. Aristotle, for example, was no less an empirist for believing that colour sensations are directly drawn out of the input to the senses and require no processing. iii.

Formal Intuitionism

The surprising thing is that one can even be a non-sensationist intuitionist and an empirist. This might at first seem to entail an absurdity: after all, non-sensationist intuitionism, as I have characterized it, is the position that a certain output of the cognitive system is already given in an input that is not a sensation. Is there not a contradiction here? Not quite. If it could be shown that having sensory experience might involve more than just having sensations, then non-sensationist intuitionism could be consistent with empirism. To see how this might be the case, consider the model of an information-processing device introduced above. I originally described the activity of this device in terms of three moments reception or input of data, processing of data, and output of finished product - but the first moment cannot be described simply as the reception of data because it makes all the difference to the eventual output in what order the data are received. After all, 100 is a different number from 001, even though both contain the same stocklist of bits of information: two 'o's and one 'i.' The order in which the device receives these bits of information - whether it receives the 'i' before, between, or after the 'o's, or whether it receives the 'i' above, below, before, behind, to the left, to the right, or in the middle of them - makes all the difference to the output it eventually produces. In light of this model, I suggest that it is at least possible to consider sensory experience as a compound of (i) various items or bits of information and (2) an order in which these items are received: the order at least of succession in time and possibly also of disposition in space. If this is so, and if we can refer just to (i) as 'sensation,' then the presence of (2) would constitute the presence of an element over and above sensation in sensory experience. Since this element has to do with the order or form in which sensations might be received in sensory experience, we can distinguish it from sensation by referring to it as the 'formal' component of sensory experience. (Sensation can be taken to constitute the

10 Introduction 'matter' of what is received in sensory experience.) The position that sensations are received successively over time, and perhaps also at diverse locations in space, can then be described as 'formal intuitionism/ It is a distinct kind of intuitionism about space- and time-cognition, that should not be confused either with sensationism (the view that we have sensations of spatiotemporal determinations) or with innate-ideas nativism (the view that knowledge of spatiotemporal relations is already present in the mind prior to all experience). It certainly should not be confused with constructivism of either the empirist or the innatemechanisms nativist types. Formal intuitionism, as a distinct position from both sensationism (which is an empirist position) and innate-ideas nativism (which is nativist), could conceivably have either empirist or nativist variants, depending on whether one takes the form in question to be given only through sensory experience or to be grounded on some innate feature that determines the manner in which the subject is constituted so as to be able to receive sensations. The former, empirist view was held by Hume, at least in those portions of the Treatise (chiefly 1.2.3) where he described space and time as manners of disposition of impressions. The latter, nativist view is the view put forward by Kant in the Transcendental Aesthetic. iv.

Kant's Formal Intuitionism

The main consideration in favour of identifying Kant as a formal intuitionist is that this is what he says his position is. To anticipate points which will be argued more thoroughly in chapters i and 2 below, he draws a clear distinction between a receptive faculty of the mind, through which data for the cognitive process are first given, and a faculty responsible for processing - or, as he calls it, synthesizing - these raw data. He even names the former faculty 'intuition' (A5O-17674-5). And he describes space and time as 'forms of intuition' and 'manners in which sensations are ordered' (A20/B34). Moreover, his entire description of the activities of the higher, synthesizing faculty grows out of the characterization of a single, basic operation: combination, that is, the unification of the manifold (i.e., the previously given variety of bits of information) in a judgment. Thus, at A69/B94 he remarks that all acts of the understanding can be reduced to judgments so that 'the understanding in general can be represented as the ability to judge/ and a few sentences earlier he remarks that all judgments are functions of the unity of

Introduction 11 our representations. If effect, therefore, the problem of knowledge for Kant reduces to the problem of how, from an array of matters splayed out over space and occurring over time in a progressive intuition, the mind is able to produce a unified thought. And this is just the opposite of what one would have expected were Kant someone who took space and time to be constructed through synthetic operations performed upon matters that are in themselves in no way spatial or temporal. In that case, the essential problem for Kant ought to have been localization rather than combination - how to discriminate the various matters and assign them to different places and moments, not how to put them together into a unified representation. That Kant's formal intuitionism is nativist rather than empirist in character has already been evidenced by the passages cited at the outset of this introduction. However, the nativist component to Kant's theory is less significant than the fact that it is formal intuitionist, and playing up his nativism at the expense of his intuitionism is risky. Kant's 'nativism' has nothing to do with either innately given ideas or innate acts of the mind in processing immediately received data; rather, it affirms the existence of an innate structure to the receptor system, determining, not an idea or sensation or concept, but the manner in which sensations are received. Consequently, even though the distinction might not have been formally available to Kant, his position entails that the general, structural features of space and time (the 'manner' in which sensations are received - which today we would identify with the topological, affine, and metrical features of space and time) should be distinguished from the specific locations that sensations have in space and time. It is only the former that is grounded in the subject, for Kant. The latter is empirically given through receiving sensations. If the full story is to be told, therefore, then Kant cannot be called a nativist without extensive qualification. There is one further aspect of formal intuitionism, in both its nativist and its empirist variants, that is especially worthy of note. In claiming that our knowledge of spatial relations is drawn from the manner in which sensations are disposed in space, formal intuitionism spatializes sensations (at least, it spatializes those sensations, such as colours or feelings of solidity, which are taken to occur in space), treating them as physiological stimuli occurring on the surface of the sense organs rather than as ideas had by the mind. Though Kant may not trumpet this consequence, by claiming that space and time are forms of intuition he takes the responsibility for original space- and time-cognition out of the realm

12 Introduction of thought and places it in the body - in effect giving space- and timecognition an essential physiological basis.19 In what follows, especially in chapter 3 below, I show that Kant is indeed committed to this picture: that his formal intuitionism does entail that the (empirical) subject must have a body that receives stimuli at various points on its organs and that endures over time. I also expose Kant's grounds for the formal intuitionist theory of space- and time-cognition. These are grounds that are implicitly critical of the rival constructivist and sensationist accounts of space- and time-cognition.20 Kant has grounds for denying that our knowledge of spatiotemporal relations is drawn out of more primitive, given matters, that are themselves in no way spatial or temporal, but that are worked up into a representation of space or time by some sort of associative or deductive processing, as Berkeley (the empirist constructivist) or Descartes (the innate-mechanisms constructivist) would have maintained. And he also has grounds for denying that representations of pure, empty space and time antedate experience in our minds or that spatiotemporal relations are somehow directly given by sensations. These grounds are laid out in Part II, below. v.

Grounds for the Popular Neglect of Formal Intuitionism

In the whole of the history of theories of perception up to recent times, there have only been two formal intuitionists, Hume and Kant,21 and even these two have not made much of the theory. Hume hinted at it in Treatise, 1.2.3, and then dropped it from all of his later work, and Kant developed his version as a contribution to the transcendental inquiry into the possibility of synthetic a priori judgments, neglecting to apply it to the empirical questions of perception or our cognition of relations.22 With such scanty development, it is perhaps not surprising that formal intuitionism has gone unnoticed by historians. Another reason why Kant's formal intuitionism has been neglected is that the major text for the theory, the Transcendental Aesthetic, has for quite some time now been viewed as a rump of old views, incongruously patched onto the front of the book and supplanted by 'the more mature and fruitful parts of the Critique/23 (A similar fate has befallen Hume's Treatise, 1.2.3.) When the crucial text is not read with attention and with a concern for the theory of visual perception in mind - the point will not readily be discovered. Compounding these factors are two others: a dualist prejudice against

Introduction 13 physiologizing intuition and sensation (most vividly captured by the still current notion that there is a 'fallacy' in spatializing sensations), intensified by a deplorable tendency on the part of many Kant scholars to use the principle of charity unscrupulously to interpret away anything that they are antecedently convinced is absurd, on the assumption that the great man could not possibly have had an incoherent, irrelevant, uninteresting, or false thought. The most serious impediment to appreciating Kant's formal intuitionism however, is an increasingly popular position (and, I argue, a seriously mistaken one) on the nature of Kantian intuitions. Rather than recognize Kantian intuitions as distinct from thought and the representations delivered through intellectual and imaginative synthesis, and as given prior to them (the view of 6145, which is the epigraph to this book), this new view seeks to drive intuitions up into the higher cognitive faculty, and take them to be products of a figurative synthesis of imagination, or some yet higher cognitive process. Once this happens, all hope of distinguishing Kant's unique formal intuitionist position from innate-mechanisms constructivism is lost, for the intuitions themselves are no longer taken to be intuited (that is, immediately given as raw data for the cognitive process) but are, instead, taken to be products constructed by a cognitive process. Kant himself must shoulder a large part of the blame for this development because his own representation terminology is frustratingly ambiguous on this crucial point. This terminological confusion will have to be sorted out before Kant's formal intuitionist theory of space- and time-cognition can even begin to be considered. Doing so will be the business of Part I, below.

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PART I

Kant's

Representation

Terminology

(The Transcendental Aesthetic §1)

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Introduction

Only this much seems to be necessary by way of introduction or preliminary remark: that there are two sources of human cognition that perhaps spring from a common, but to us unknown, root - namely, sensibility and intellect. Through the first, objects are given to us, whereas, through the second, they are thought. In so far as sensibility may contain a priori representations that constitute the condition [A: conditions] under which objects are given to us, it will belong to transcendental philosophy. The transcendental doctrine of sense would have to belong to the first part of the science of the elements, because the sole conditions under which objects are given to human cognition precede those under which they are thought. (Ai5~i6/B29-3o)

The first obstacle confronting anyone who seeks to understand Kant's Critique of Pure Reason is the barrage of technical terminology that work contains.1 The barrage is especially intense where Kant's descriptions of the elements, objects, and modes of knowledge are concerned. There one encounters 'sensation/ 'intuition/ 'sensibility' (or 'sense'), 'matter/ 'form/ 'imagination/ 'understanding' (or 'intellect/ as I prefer to call it), 'judgment/ 'reason/ 'representation/ 'perception/ 'concept/ 'appearance/ 'object' (Gegenstand), 'Object' (Objekt), and 'thing.' In many cases, the relations between these different terms are as difficult to discern as their precise definitions, and both difficulties have resulted in protracted controversies among Kant scholars. Taking part in these controversies is inevitable, however. There is no way to understand Kant's Critique of Pure Reason without first 'coming to terms with the terms/ and anyone who pretends to do otherwise ends up begging important questions.

i8

Kant's Representation Terminology

In what follows, I present as precise an account of the meanings and relations of some of Kant's most central terms as the texts will permit. The terms I am most concerned with are those that occur in the first part of the Critique of Pure Reason: 'sense' (Sinnlichkeit), 'intellect' (Verstand), 'intuition' (Anschauung), 'concept' (Begriff), 'sensation' (Empfindung), 'matter/ 'form/ and 'appearance' (Erscheinung). These are the terms that Kant himself seeks to make precise at the outset of the Transcendental Aesthetic, and my efforts take the form of a commentary on the texts where he does so. In proceeding with this task, I have adopted and tried to follow two methodological precepts that I should reveal at the outset. The first is that, where Kant does not himself precisely define a term, its meaning is to be found in the way the cognate Latin term was traditionally employed. (Thus, for example, the meaning of the term Anschauung is to be determined by looking at traditional uses of the Latin term intuitus, not the German anscouuen.)2 It is natural to assume that, where Kant does not himself precisely define a term, he most likely took it for granted that his audience would already understand it in the correct way; in that case, the definition of the term accepted by the dominant tradition (or the dominant tradition in Kant's eyes) should be accepted. The term should, of course, be the Latin equivalent of Kant's German one (Kant himself usually supplies Latin equivalents for his terms, or did so in his own Latin works) because, at this stage in history, when German was just coming into use as a language of philosophy, and the traditions most people were schooled in were still taught in Latin, the German terms were little more than translations of the Latin, and derived all their meaning from them. The second methodological precept I have assumed is that, where Kant does define a term or specify its relations, his most oft-repeated definitions and comparisons, and those that occur in introductions, summaries, section titles, and tables of contents, are to be taken to be canonical. Definitions that occur rarely (especially in the context of argument or disputation, or as part of an obscure and difficult passage), are to be viewed with suspicion. The same holds for definitions that occur only in a letter or note. This procedure is grounded in the assumption that philosophers give the truest indication of their most solidly entrenched beliefs in their clearest, most basic, most serious, and most programmatic pronouncements, rather than when caught up in the heat of argument, when engaging in reverie, or when discussing matters with associates.

Introduction

19

In Kant's case, additional biographical considerations recommend the second methodological precept. Kant is often referred to as the 'great synthesizer.' The same point can be made, less charitably, by referring to him as the 'great coward.' Cowardice manifests itself in the details of his personal life (in small matters like his reluctance to leave his home town3 or to form intimate relationships with women,4 as well as in greater ones like his behaviour in the Die Religion affair5 and his reluctance to defend his work against any but the intellectually weakest of its attackers),6 but it manifests itself most notably in his work as a philosopher. Kant was not the sort of person who had the intellectual courage to face up to a dilemma and reject one alternative in favour of the other. Instead, when he felt himself pulled in opposite directions by conflicting imperatives, his preference was to try to work out some way of satisfying both. This intellectual 'cowardice' is not necessarily bad, any more than cowardice in practical affairs is necessarily ignoble; indeed, it is the characteristic that led Kant to his most brilliant discoveries. But when the desire to reconcile conflicting alternatives is not based on an insight into the false nature of their conflict, but, rather, springs from a character trait - a congenital inability to reject one alternative in favour of the other, regardless of whether the two really are reconcilable or not - then we can expect to find something else besides brilliant discoveries: repeated, failed attempts at a number of different solutions, and a tendency to give in to the temptation to write up something obscure that allows you to delude yourself into thinking that you have found a middle path, even if you yourself cannot quite understand what you have written, to which may be added the tendency to then excuse yourself by claiming that you do not have the time or the talent to express yourself clearly and that you need someone else to come along and popularize your point (i.e., really solve your problems) for you. If Kant ever did any of this, even some of the time, then that is all the more reason to view what he says in the heat of argument with suspicion, and look to his more programmatic and neutral texts for a statement of his fundamental position, even if that should lead to contradictions. What I have just insinuated about Kant's character and writing is harsh, and I do not want to insist that the insinuation is at all just especially at this stage. The only claim I want to make here is that our assessment of Kant - as brilliant synthesizer or cowardly obscurantist is not one that should be determined a priori. We cannot start off by assuming that Kant was a superhuman genius with some truth of enduring value to communicate to us through texts that can be assumed

2O

Kant's Representation Terminology

to be coherent and consistent. Kant's texts are difficult and obscure - no one can honestly deny that. He himself admitted as much and looked to his friends to exposit his views for him.7 His Reflexionen are filled with various, failed attempts at reconciling conflicting alternatives (freedom and determinism, simplicity and infinite divisibility, a denial of void space and an acceptance of a priori spatial form, and so on), and the history of his published works is itself a history of various attempts proposed, abandoned, replaced, and reintroduced.8 Even his personal life testifies to a character disposed to seek accommodations at all costs. It is at least possible, therefore, that he was the kind of character disposed to try to force a synthesis where there is none to be found, and that some of his writings may have sacrificed truth and coherence for a show of reconciliation between irreparably conflicting prior commitments, and been obscure, or even contradictory, as a result. No human being is immune to error, and Kant, given his predilections, may have been more susceptible to it than others. We cannot, therefore, begin our work on Kant by simply assuming that what he says must necessarily be correct, or even consistent, much less of enduring importance or relevance. It may, in fact, be all of those things, but that is something that will have to be demonstrated, not presupposed at the outset and then, when the texts prove recalcitrant, forced out of them with an overly zealous application of the principle of charity. When the texts are obscure enough, such methods are a short way to making Kant say anything - and as the history of Kant commentary shows, that has, in fact, been their result. A proper approach to the interpretation of Kant must take a different course: it must begin by isolating his clearest and most central commitments, as illustrated by his programmatic pronouncements in introductory sections, summaries, and titles, and then proceed from these principles to see whether his arguments do, in fact, lead to results that are consistent, correct, or relevant. Remarks made in letters and reflections are not to be given equal weight to those made in the published works, but are of value in so far as they support a thesis concerning the development of Kant's thought. (This presupposes, however, a reliable dating of the Reflexionen.) The principle of charity, when it is applied, is to be applied judiciously to bring the more obscure, detailed, and technical texts into line with the core beliefs repeatedly enunciated in the introductions, summaries, tables of contents, and other clear texts. Above all, the principle of charity is not to be applied in reverse, to bring the clear and programmatic texts into line with some speculative hypothesis concerning the underlying meaning of an obscure and apparently contra-

Introduction

21

dictory text or reflection. (No interpretation of Kant that starts off with a reading of a text like Bi6on, for example, deserves to be accepted. The reading may, in fact, be correct, but it is not to be relied upon when its truth is established by such short means.) Accordingly, in this work I begin with a determination of the meanings of Kant's terms, as laid out in his most central, programmatic, and unambiguous texts, and then proceed to an examination of his arguments, in so far as they employ these terms. And I let the chips fall where they may. My goal is not to prove Kant right (or wrong), consistent (or inconsistent), relevant (or irrelevant). It is, rather, to understand what Kant said on his own terms, what he meant by what he said, and why he said it. This is a mode of procedure grounded in the conviction that the history of ideas is its own excuse, and does not need to justify itself by showing that the works of past philosophers have any relevance or value for contemporary philosophical concerns. It is also grounded in the conviction that Kant studies will reach the state of maturity exhibited by, for instance, Descartes or Berkeley studies, only when scholars abandon the task of trying to defend Kant or prove the enduring relevance of his views, and focus instead on simply trying to understand what he was trying to say. i.

The Place of the Aesthetic in the Critique of Pure Reason

When following the second of the two methodological precepts laid out above, one of the first things one notices is that Kant's work in the Critique is written around a distinction between two cognitive faculties, sense and intellect. The major part of the Critique, the Doctrine of the Elements, is divided into two major parts - a Transcendental Aesthetic and a Transcendental Logic. Kant deliberately chose the word 'aesthetic' to hearken back to the classical Greek term 'aesthesis,' the term Aristotle had used to refer to the process of sensing, and the Transcendental Aesthetic is, in fact, an investigation of the nature - particularly, the structural features - of the data delivered by the process of sensing. The Transcendental Logic, in contrast, is devoted to the 'higher' cognitive functions of conceptualization or understanding (the 'Analytic of Concepts'), judgment or the formulation of propositions (the 'Analytic of Principles'), and inference or reasoning ('the Dialectic'). These latter three cognitive functions were all taken by Aristotle to be functions of intellect or nous, and Kant frequently does the same. However, Aristotle distinguished the three

22

Kant's Representation Terminology

functions in his own logic, treating of conceptualization, in the Categories; of judgment, in De Interpretatione; and of legitimate and illegitimate inference, in the Prior Analytics, Topics, and Sophistical Refutations. This practice was enshrined in the tables of contents of logic textbooks right down to Kant's day and beyond, and it is reflected in the table of contents of the Transcendental 'Logic' of the Critique. It would be wrong, however, to understand the Transcendental Logic as a logic in the traditional sense. Kant is at pains in the Introduction to the Transcendental Logic to distinguish his enterprise from what he refers to as 'general logic' ^52-64/676-88). A brief review of the nature of the distinction between transcendental and general logic will help to specify how the Aesthetic is related to the Logic and fits into the project of the Critique, as well as to give a preliminary indication of the position that is defended in chapter i, on the nature of the distinction between the lower, sensory, and the higher, intellectual, cognitive faculties in Kant's work. When we do logic, we are concerned just with the form of what is thought. We abstract as much as possible from any reference to the content of what is thought, to the non-logical syntax of the natural language in which this content is expressed, and to the peculiar quirks of our personal or cultural psychology that determine the manner in which this content is discovered. We consider just the patterns exhibited by valid inferences, and not the particular assertions made by the propositions forming their premises and conclusions. When we do consider propositions individually, we consider just the way their component variables, terms, and relations are linked by operators, and not the particular referents of the terms or anything other than the formal features of the relations. And when we consider terms or 'concepts/ as was done by early modern logicians, we consider them only with reference to such formal, structural, or quasi-grammatical features as connotation and denotation, use and mention, clarity or obscurity, distinctness or confusion, or the hierarchical relations of genus and species determined by the specific differentiae they exhibit. Kant was not unaware of this. In an age when logic and psychology (and, indeed, grammar) were not clearly separated fields of inquiry, few drew the distinction between logic (or 'general logic/ as he called it) and the related disciplines as clearly as he did. In the Introduction to the Transcendental Logic (A52-5/676-9), he carefully distinguished what he called 'general logic' both from what he called 'special' and from what he called 'applied' logic. Today, we would not call these latter

Introduction

23

enterprises logics' at all. Special 'logic' is really the result of applying the general laws of logic just to thought about a particular kind of object: it produces what are, in effect, the special canons of legitimate argumentation that might arise within a certain science because of its peculiar subject-matter. For example, the empirical facts that the efficacious cause of an effect is often regularly accompanied by a number of accidental circumstances and is often itself a product of a number of individually necessary but insufficient causes, dictates a logic' of controlled experimentation such as that outlined by Mill's methods or Hume's rules by which to judge of causes and effects. And the empirical fact that human research subjects may deliberately or unconsciously attempt to deceive a researcher, or a researcher deliberately or unconsciously signal preferred responses to the subject, dictates a special logic' for inductive reasoning in the human sciences - one describing blind and double-blind experimental procedures. The rules for controlled and double-blind experiments are, in effect, a set of additional conditions on the validity of arguments in specific sciences - conditions arising from the peculiar nature of the subject-matter of those sciences. But it is not logic itself that dictates these rules, but a kind of methodology, resulting from a combination of logic with a consideration of the specific nature of the subject under consideration and what specific problems the nature of that subject poses for arguments involving it. What Kant refers to as 'applied logic,' for its part, is really the psychological study of the human thought process, abstracted from all normative components. It examines the conditions under which we in fact reach conclusions, make judgments, and form conceptions, irrespective of whether these procedures are valid or truth-preserving. 'Real' logic, or what Kant calls 'general,' logic does neither of these things; it is neither a methodology for reasoning about a specific subjectmatter nor a study of cognitive psychology. It abstracts from all content and just considers the form of thought and, in this consideration, it, as Kant says, also abstracts 'from all empirical conditions under which our intellect is exercised, for example, from the influence of the senses, from the play of imagination, the laws of memory, the force of custom, inclination, and so on, consequently also the sources of prejudice, indeed even generally from all causes under which particular cognitions arise or may be surreptitiously introduced in us' ^52-3/677; my italics). Kant's clear appreciation of the formal and non-psychologistic nature of general logic makes it all the more important to take him at his word when he goes on to say that his own project of transcendental logic will

24

Kant's Representation Terminology

not be like this. While it will not be a 'special' logic in the sense that it will focus on our reasoning concerning a specific kind of object, it will be 'special' in the sense that it will make reference to the content of what is thought; however, this content will be the lean, a priori content that all objects of experience have in general, and not the richer, a posteriori content of any particular kind of object. Transcendental logic will consider our reasoning with an eye to this general common content. What is more, transcendental logic will be 'psychologistic' in at least the sense that it will be concerned to investigate the powers of cognition that lead us to form concepts, to connect concepts in propositions, and to draw inferences.9 General logic abstracts, as we have shown, from all content of cognition, that is, from all relation of cognition to the Object, and considers only the logical form in the relation of cognitions to one another, that is, the form of thought generally. Since, however, there are pure as well as empirical intuitions (as the Transcendental Aesthetic shows), there could well be a distinction between pure and empirical thought of objects to be uncovered. In this case there would be a logic in which we would not abstract from all content of cognition, for this [studyl, which would contain merely the rules of the pure thought of an object, would exclude all those cognitions that are concerned with empirical content. It would also consider the origin of our cognitions of objects, in so far as this origin cannot be ascribed to the objects. (A55-6 7679-80; my italics)

Kant's transcendental logic, then, is not simply a study of the form of thought in general, but a study of the form our thought has to take in so far as it results in knowledge of objects in general, given the general character of the raw materials for knowledge of objects made available to us through the senses, and the nature of our capacities for processing those raw materials into knowledge. As such, it proceeds with an eye to whatever content may necessarily have to be included in the thought of an object. As well, it proceeds with an eye to the way this content would have to be processed by minds like ours (e.g., minds that have to be explicitly conscious of or apperceive all the data they receive, and that cannot perform tasks requiring completion of an infinite series of steps) given the formal constraints laid out by general logic. Any general feature of the materials available for a certain process places constraints on the kind of product that process can yield. If you paint with watercolours, the kind of picture that can be produced will differ from what can possibly be produced when painting with oils. A

Introduction

25

structure built of wood will necessarily have to be made in a different way from a structure built of iron if it is not to collapse. Similarly, if the materials given by the lower cognitive faculty, sense, for cognitive processing have certain basic features, these features can be expected to determine the kind of epistemic product - meaningful concepts, true propositions, and valid inferences - that the higher cognitive faculty, intellect, produces. A study of the necessary features of sensory experience can therefore be expected to go beyond general logic in uncovering certain other necessary, but still formal features, of all our knowledge. The same can be said for a study of the manner in which the raw materials delivered by sensory experience are processed by the intellect. Just as the raw material (e.g., watercolours or wood) determines the nature of the product, so does the type of processing available to be performed upon the raw material. A study of the instruments available to an artisan to construct a product from raw materials can be expected to yield certain necessary conclusions about the features the artisan's products must have and will be unable to have, and, similarly, a study of the manner in which the higher cognitive faculties are able to generate concepts from sensory experiences, judgments from concepts, and inferences from judgments can be expected to uncover certain things about the necessary features of concepts, judgments, and inferences that go beyond what pure logic has to teach. Before we can draw any conclusions about what sorts of epistemic products (concepts, judgments, and inferences) the processing capacities of the mind can deliver using the methods at their disposal, however, we need to know what kinds of materials are available to them to work with. Even the crudest artisan can produce the finest work if it is present virtually ready-made in the raw materials. This is why the Transcendental Aesthetic must precede the Transcendental Logic as a distinct and separate enterprise. It is in the Aesthetic that Kant determines how crude the materials are: whether there are any features that all objects of sensory experience have in common; if there are, whether we can be sure in advance that all subsequent sensory experience will continue to exhibit them; and, if so, what these general and a priori features might be. Deciding these issues is necessary before the enterprise of the Transcendental Logic can even begin. The most important thing to note for our purposes here, however, is the underlying picture of the workings of the human cognitive capacities that this account of the relation between Transcendental Aesthetic and Transcendental Logic entails. That picture is delineated in the pro-

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grammatic passage from the close of the Introduction to the Critique ^15-16/629-30), cited at the start of this section. According to it, there are two distinct cognitive faculties, sense and intellect. In the cognitive process, sense comes first. It receives representations and delivers them to the intellect for processing into knowledge claims. Sense is, accordingly, the faculty through which representations are 'given/ whereas intellect is that through which they are 'thought/ And, as Kant stipulates, 'the conditions under which alone objects are given to human cognition precede those under which they are thought/ That is, whatever formal or necessary features the sensory faculty may be discovered to involve, those features are in no way dependent on the operation of the intellectual faculty. The question for the Transcendental Aesthetic, which is an investigation of those aspects of sense (aesthesis) that transcend empirical knowledge, is whether there may not be certain elements of sensory experience that can be known in advance to be necessary features of that experience. Of course, Kant thinks that there are such elements, and that they are space and time. But, in light of the claim that 'the sole conditions under which objects are given to human cognition precede those under which they are thought/ this means that space and time must precede all thought. What we have here, therefore, in this preliminary examination of the table of contents of the Critique (most notably, in the fact that the Transcendental Aesthetic is set outside of the Logic as a distinct and prior study) and a programmatic passage from its Introduction is an indication that no interpretation that takes spatiotemporal form to be dependent on 'thought/ that is, on imaginative or intellectual processing, can be a correct representation of Kant's position. Kant is an intuitionist about space and time. He believes that these forms are given, not made. He believes, moreover, that they are given through the sensory cognitive faculty. Tracing through his arguments for this claim in all their detail is the major burden of the work that follows. ii.

Basic Confusions in Kant's Thought

Kant's clear appreciation of the distinction between his own, at bes quasi-logical, project in the Transcendental Logic and the project of general logic is no guarantee that the realms of cognitive theory and logical theory will not be confused in his work - though when confusions do arise it is largely from Kant's employment of logical terminology within

Introduction

27

the context of his 'transcendental' inquiry rather than from his using the terminology of cognitive theory in logical contexts.10 The fault is not so much Kant's as his time's. Early modern logic was not rigorously distinguished from psychology, or even grammar.11 This is already evident from a consideration of the basic elements employed by early modern logic texts. Grammatical categories such as subject and predicate figure prominently. And the early modern logician writes of 'concepts' rather than 'terms' and of 'judgments' rather than 'propositions' - the basic elements of logic are taken to be, in effect, various kinds of thought; their ontology is explicitly psychologistic. What is more, early modern logicians were unable to refrain from identifying the standardly recognized aspects of the subject-matter of logic with distinct functions or operations of the mind doing the logic. Thus, the ability to form and compare concepts was ascribed to the understanding; the ability to connect concepts in propositions, to 'judgment'; and the ability to draw inferences, to 'reason.' Inexorably, the presence of these psychologistic interpretations of logical elements and operations leads to terminological confusion in Kant's work. The same word ('concept,' for instance) is used in certain contexts to refer to one or more different logical or grammatical elements (a universal in some cases, a subject term in others), and in other contexts to refer to the product of a cognitive activity (the output of processing by intellect). Some examples of this sort of terminological confusion are examined below.

1 The Distinction between

Intuition and Understanding

In whatever way and by whatever means a cognition may be related to objects, intuition is that way by which it is immediately related to them, and that to which all thought is referred as a means. But intuition only takes place in so far as the object is given to us. And this in turn is possible, at least for us human beings, only in so far as the object affects the mind in a certain way. The capacity (receptivity) to acquire representations through the manner by which we are affected by objects is called sensibility.1 By means of sensibility, therefore, objects are given to us, and it alone delivers intuitions to us. Through intellect, however, they are thought, and from it concepts arise. However, all thought must finally be related to intuitions, be it straightforwardly (directly) or circuitously (indirectly), by means of certain differentiae [Merkmale]. Consequently, for us, all thought must finally be related to sensibility, since no object can be given to us in any other way. (Ai9/B33)

Kant's Critical Philosophy begins with the postulate that human beings possess two, distinct cognitive faculties, sense and intellect. The Critical Philosophy 'begins' with this postulate in every sense of the word. It begins with it in time: the work widely touted as the first in which Kant's mature philosophy can be discerned, his Inaugural Dissertation (ID), is a book about the distinction between the sensible and the intelligible. It also begins with it in the order of exposition: both of the major parts of the Critique of Pure Reason, the Transcendental Aesthetic and the Transcendental Logic, open by stating that there is a distinction to be drawn between sensory and intellectual cognitive faculties. Finally, the Critical Philosophy begins with the postulate of the distinction between sense and intellect in the sense that this is the foundation on which its

The Distinction between Intuition and Understanding

29

major conclusions are erected: Kant's attack on dogmatic metaphysics rests on the claim that pure intellectual concepts need to be referred to a spatiotemporal manifold supplied by a distinct cognitive faculty, sense, before they can acquire any meaning. But, despite its undoubted importance for the rest of his theoretical philosophy, the sense/intellect distinction is not one for which Kant ever obviously argues, or even explains in anything more than the most perfunctory way. Almost the only substantive thing he has to say on the issue is that sense delivers intuitions, whereas our intellect is not capable of doing so (though not necessarily all intellects are like this). Witness A67-8/B92-3: 'The intellect was defined above merely negatively, as a non-sensory cognitive capacity. Now, apart from sensibility, we cannot acquire any intuition. Thus, intellect is not an intuitive capacity.' To make matters worse, the notion of intuition, which is so intimately connected with Kant's distinction between the faculties, is itself highly problematic. Notoriously, Kant does not always define 'intuition' in the same way, referring to it in some places as representation of particulars or singular representation ^713/6741; Logic §1), in others as immediate cognition (Ai9/B33>.2 Before any progress can be made in the interpretation of Kant's theoretical philosophy, these difficulties need to be cleared up. We need to know what intuition is for Kant, and how it differs from understanding, and we need to understand the nature of his distinction between sense and intellect.3 Otherwise, the Critique will be no more than what it appears to be from reading the introductory paragraphs of the Transcendental Aesthetic: an intricate and obscure construction built on a base of incoherently defined terms. The first thing to note when approaching these problems is the importance of reading Kant in historical context. Kant did not invent the two-faculty account of cognition or the notion of intuition. If he did not explain what he meant by sensibility, intellect, or intuition, this was, in large part, because the distinctions and the terminology were already widely in use and he took it for granted that his audience was already thoroughly versed in them. The distinction between sense and intellect goes as far back as Aristotle's distinction between aesthesis and nous (De Anima, 42.7^-15), as Kant himself notes (A2in/B35n), and was a staple of medieval cognitive theory.4 And the theory of intuitive and discursive cognition was also worked out by the Medievals.5 Indeed, far from being an innovator in this respect, Kant was a reactionary. In basing his theoretical philosophy on a two-faculty account of cognition, he was turning his back on the cognitive theory of his day and

3O

Kant's Representation Terminology

resurrecting an approach to human knowledge that his contemporaries and immediate predecessors had rejected. Ever since Descartes, who had argued that the soul is simple and without parts and has but a single faculty, the spirit of the time had been to unite, not separate, sense and intellect.6 In the generations after Descartes, theorists in both the rationalist and the empiricist camp advocated 'one-faculty' theories of cognition - albeit in diametrically opposed fashions: Leibniz, Wolff, and Baumgarten treated all representation as the more or less clear or obscure, distinct or confused, apprehension of the specific differences distinguishing species from genera and individuals within species.7 Sensory representations were taken to differ from intellectual ones only in the greater degree of confusion (confusio, Venuorrenheit) with which the collected differentiae were apprehended.8 Hume, Condillac, and Helvetius, on the other hand, treated all representations as more or less vivacious 'traces' left behind by past experience, or more or less complete replicas of the content of such experience.9 The effect of the latter approach was to treat what had previously been defined as intellectual representations as (vaguer, fainter) sensory phenomena, just as the effect of the former was to analyse sensory phenomena in a way that had been previously taken to characterize only intellectual representations - thus, Kant's famous remark in the Amphiboles (A2/i 76327) that Leibniz had intellectualized all appearances, whereas the empiricists (in the name of Locke) had sensualized them. One tentative concession to the singlefaculty point of view not withstanding,10 Kant's own approach was not to overcome but to reintroduce the distinction. The philological research that has been done on Kant by Giorgio Tonelli and Norbert Hinske lends further credence to these observations. Tonelli and Hinske have shown that Kant quite deliberately decided to use traditional Greek and Latin terms rather than forge his own philosophical vocabulary,11 and that he took this traditional vocabulary to capture most accurately what he understood to be the important features of human cognition.12 A passing reflection made by Kant himself in the Critique and cited by Hinske13 serves to show that Kant intended to trade on the commonly understood meanings of these terms. In the great richness of our languages thinkers still often find themselves at a loss for an expression that will exactly capture their concepts and in this state of deficiency are unable to make themselves really intelligible to others or even to themselves. To coin new words is to claim a right to legislate in linguistic matters that can seldom be carried off. Before one proceeds to this desperate means,

The Distinction between Intuition and Understanding

31

it is advisable to look whether the concept along with its appropriate expression might not already be found in a dead and learned language. Even when, because of a lack of care by its originators, the old usage of the term was weakened, it is still better to stick to the meaning that distinctively belongs to it (even if it remains doubtful whether exactly this meaning was originally intended) than to undermine one's work by making oneself unintelligible. (A312/B368-9)14

Tonelli's and Hinske's research carries an important moral for all Kant scholarship: that the study of Kant needs to begin with a recollection of the traditional meanings assigned to his terms by ancient and medieval philosophy.15 Konigsberg had always been a stronghold of Aristotelianism/6 and the 'meanings that distinctively belong to a term' would, therefore, for Kant, have first and foremost been the traditional Aristotelian and Scholastic ones.17 This is not to say that the explication of Kant's terminology should end with such contextual studies. Part of what I want to show in what follows is that Kant was forced, by the internal dynamics of his project and the arguments needed to establish his conclusions, to twist the traditional meanings of his terms. Often, however, he is not aware that he has done so and he reverts to traditional definitions, which continue to exist uneasily in his work alongside the revised ones. This is nowhere as much the case as it is with reference to Kant's double use of the word 'intuition' to stand for both singular representation and immediate representation. My purpose in what follows is to give a historical and strategic account of Kant's use of this term and, by implication, of his use of the closely related terms 'sense/ 'intellect/ and 'concept/ The account is historical in the sense that it pays careful attention to the traditional cognitive theory Kant adopted and to how his distinction between the faculties can be explicated and justified in the light of this tradition. It is strategic because the forces that led Kant to modify his meaning unconsciously are internal to his thought, arising from the strategy he had to employ in order to achieve certain goals - most notably, that of proving that space and time have the peculiar status of 'forms of intuition.' My argument is that Kant always accepted the standard definition of 'intuition' or intuitus as a cognition that occurs immediately, but that he also always (even in 1770 and earlier) conceived of the human intellect as a cognitive faculty that is incapable of having intuitive cognitions. As a result, he came to identify the remaining faculty, sense, as the only intuitive faculty in human beings. Since sense was traditionally understood to be a cognitive faculty dependent upon the exercise of the physi-

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cal sense organs for its realization and delivering representations of particulars, the ground was laid from the very beginning of the critical project for Kant to conflate intuitive with singular representations. However, pressures coming from the position adopted in the Critique forced Kant to revise his conception of the nature of the sense/intellect distinction. This revision made any equation of intuitive with singular representations illegitimate, something which Kant seems not to have fully realized. As a result, references to intuitions as singular representations persist in his mature philosophy, though they are, in fact, inconsistent with some of its most fundamental tenets. Demonstrating these points requires going back to Kant's original introduction of the sense/intellect distinction in his Inaugural Dissertation and then examining how his conception of the distinction changes under the force of the argument. In what follows, I, first, summarize Kant's account of cognition in ID. After examining some of the motives Kant had for presenting this account, I show that his conception of sense as delivering singular representations, which is quite evident in this preCritical work, has its roots in ancient and medieval accounts of the sensory cognitive function. I then show that certain features of Kant's argument, already incipient in ID, led him to abandon this traditional conception of the lower cognitive faculty in favour of a conception of sense as a purely receptive faculty through which the raw data for the cognitive process are directly and immediately given. Since, however, Kant had always conceived of sense as an intuitive faculty, the effect of this realignment went largely unnoticed by him, so that he continued, quite mistakenly, to think of sense as not merely intuitive, but responsible for cognition of particulars as well. i.

The Sense/Intellect Distinction in ID a. The Project of the Inaugural Dissertation and Its Motivation

In a famous reflection, Kant wrote that the year 1769 had given him "great light.'18 Ever since Erdmann discovered this remark, the question of the exact nature of the 'great light' that dawned on Kant in 1769 has been one of the most fascinating and heated topics for discussion among students of the development of Kant's thought.19 If the first thing one who has received a great inspiration does is proceed to write it down, then the 'great light' may well have as one of its major components Kant's new insight that the 'one-faculty' accounts of cognition of his day

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33

- the intellectualism of Leibniz and the sensationism of Locke - are misguided, and that the proper approach to the problems of philosophy rests with reintroducing the Scholastic, two-faculty account, with its sharp distinction between sensory and intellectual cognitive functions. The work that most immediately appeared after the dawning of the 'great light' was, after all, Kant's Inaugural Dissertation of 1770, the Latin treatise he wrote for the occasion of his election to the professoriate in Konigsberg, eleven years before the publication of the Critique. It was in this work that he first proposed that the faculties be distinguished. Indeed, 'proposed' is too weak a word, for the Inaugural Dissertation has more of the character of a manifesto. As its full title ('On the Form and Principles of the Sensible and Intelligible Worlds') indicates, the work is written around the theme of the sense/intellect distinction, and in it the author avers that, if only the distinction between the faculties is respected, we will be able to do nothing less than solve all the major problems of metaphysics. Given the dominance of one-faculty theories in Kant's day, one can easily imagine that a program of this radical and highly promising a nature might have appeared as a 'great light.' An appreciation of just how radical Kant's project in ID is immediately gives rise to a question of motivation. Why would Kant have wanted to revert to what, at the time, can only have seemed to be an outmoded and erroneous account of human cognition? The text of ID provides us with a clearly stated motive: by taking this single step, Kant found himself in a position to solve a range of distinct metaphysical problems that had come to trouble him over the preceding years. A few words of background explanation are in order.20 At least by the time of his 'Investigation into the Clarity of the Principles of Natural and Moral Theology,' the so-called Prize Essay of 1764, Kant had become convinced that a purely axiomatic mathematics, in which proofs are derived from basic definitions by appeal only to the laws of identity and contradiction, is not possible. Instead, he took recourse to 'construction' (typically involving the temporally determined act of drawing out extended figures in imagination or on paper, but more generally involving the manipulation of concrete, sensible symbols for the mathematical objects being described) to be necessary to demonstrate the evidence of mathematical propositions (Prize Essay i §2, 3 §1 [Ak, II 278-9, 29i]).21 This apparently irreducible recourse to sensory or imaginary experience in mathematics may have shaken Kant's faith in the validity of the Leibnizian intellectualist program of

34

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reducing all knowledge to a purely logical calculus performed upon certain primitive characters.22 At the same time, Kant was worried about the conflict between Leibniz and Newton over the ontological status of space. The necessity of recourse to diagram drawing in geometry indicated that space might not be reducible to anything more primitive, and hence must have some sort of reality in its own right. And this militated against the Leibnizian position that spatial relations are merely confused perceptions of the internal properties of monadic substances. But any inclination Kant might have had to side with the Newtonian account, which took space to be a real, independently existing substance,23 was stymied by his acute awareness of the metaphysical difficulties with this notion difficulties ranging from the apparent absurdity of ascribing substantiality and thinghood to something as lacking in real, positive qualities as void space,24 to the charge that absolute space and time would be rival divinities.25 His unease is clearly indicated by the conclusion of his 1768 paper 'On the First Ground of the Distinction of Quadrants in Space' (Ak, II 37583). In this paper he presented what he took to be a paradigm case of a geometrical property that could be defined only by 'construction' (that is, by exhibition in a sensory or imaginary space) and not reduced to any definition taking more primitive mathematical elements as its terms: the case of the direction of orientation of incongruent counterparts. But he still found himself unable to conclude the paper with a wholehearted endorsement of the Newtonian, substantivalist solution: [After having read the above, a] reflective reader will regard the concept of space in the way that the geometer thinks of it - the way that it has also been taken up into the basic concepts of natural science by insightful philosophers - and will not look on it as a mere thought-entity - although there is no lack of difficulties surrounding this concept when we attempt to grasp its reality - which is obviously good enough for inner sense - through rational ideas. (Ak, II 383)

The 'rational difficulties of which there is no lack' that prevented Kant from taking his conclusion to be unproblematic were the conceptual and theological difficulties just mentioned. But the solution to these difficulties is virtually stated by this amazing sentence. It is not hard to imagine Kant, some time in 1769, rereading his words here and suddenly thinking to himself that, if the concept of space is clear enough to 'inner sense' and the difficulties with it arise only when we attempt to think it

The Distinction between Intuition and Understanding

35

through rational ideas, then perhaps the problem is attributable, not to any incoherence in the concept of space, but rather to the attempt to think this originally sensory representation through reason. Perhaps space should be taken to be a strictly sensory representation - perhaps, in other words, the ancient distinction between a higher and a lower cognitive function is not all that illegitimate.26 b. The Effect of the Paradoxes of Composition and Division The conclusions of this line of reasoning - that there is a distinction to be drawn between sense and intellect, and that the objects cognized by the one faculty are radically distinct from those cognized by the other were perceived by Kant to provide more than just a solution to his problems with space and the foundations of mathematical knowledge. As the fifth part of ID (§§24-30) indicates, Kant became convinced that the surreptitious conflation of the two faculties (which he called 'subreption') was responsible for a variety of metaphysical difficulties, all of which could be solved by the simple expedient of ensuring that the sensible not be allowed to pollute the intelligible. Prime among the subreptitious problems of metaphysics to which the sense/intellect distinction could be applied were the paradoxes of composition and division. These paradoxes, which go back to Zeno of Elea's famous paradoxes and had recently been revived by Bayle,27 had by Kant's time become the subject of some debate.28 The ability of the sense/intellect distinction to resolve them was looked upon by him as strong confirmation of the legitimacy of that distinction. He mentions the paradoxes and recommends the sense/intellect distinction as a way to resolve them three tunes in ID, not only in Part V (§28 [Ak, II415-16]), where the solutions to other metaphysical problems are given, but twice more in the introductory sections (Ak, II 387-9, 391-2), where the paradoxes are invoked to illustrate and justify the distinction. No other metaphysical problem receives such close and repeated attention in ID, and no other carries, in its solution, such profound implications. I want, therefore, to consider what Kant has to say on this score in more detail. Doing so will make it easier to appreciate what he takes from traditional cognitive theory, and why. It needs to be stressed that the paradoxes of composition and division are not, as Kant sees them, attacks on the reality of space and time.29 The conceptual and theological difficulties mentioned earlier (p. 34, above) do that job. The paradoxes of composition and division are rather

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directed against the possibility of composite substances and infinite aggregates.30 In particular, they challenge any account that takes substances to be spatially extended bodies compounded of simple parts for example, atoms, physical points, or physical monads - charging that composite substances can be neither composed of spatially extended simples nor infinitely divisible into mathematical points. They cannot be composed of spatially extended simples because whatever is extended is still composite, so extended components are not truly simple. They cannot be composed of points because even an infinite number of points cannot compose the smallest finite extension. But, for the early Kant, there is no alternative to the thesis that a substance is composed of simple parts. Were substances infinitely divisible, any given part would be a composite - that is, the product of an external relation between yet smaller parts - so that there would ultimately be nothing more to the substance than just these external relations. But this, to Kant's mind, would be absurd, since external relations are purely accidental. A substance consisting only of external relations would have no essence. In other words, there can be no external relations without some things that stand in those relations, so that the being of substance presupposes something simple.31 One finds this thought expressed in the Physical Monadology of 1756: Since, however, the composition of... parts is nothing but a relation, and hence a determination which is in itself contingent, and which can be denied without abrogating the existence of the things having this relation, it is plain that all composition of a body can be abolished, though all the parts which were formerly combined together none the less continue to exist. (Ak, I 477)

And the thought gets further confirmation in ID, §14 ^4 (Ak, II 39922-7), where Kant makes the corollary point that an infinitely divisible magnitude consists of nothing but relations of composition, so that were all composition cancelled, there would be nothing left of it. Since the paradoxes of composition and division attack the notion that anything existing in space could be composed of simple parts, they in effect deny the intelligibility of spatially extended substances.32 As his remarks in ID (Ak, II 389 and 415-16) show, the Kant of 1770 is still ready to accept that substance is ultimately composed of simple parts. The distinction between the faculties provides him with a way to do this, despite the paradoxes. Kant's answer to the paradoxes is that the unintelligibility we find in the composition of substance is merely

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37

apparent - the result of a subreptitious injection of spatiotemporal (especially temporal) conditions of sensory representation into our intellectual concepts of continuity and simplicity, on the one hand, and infinity and totality, on the other. Kant's treatment opens with an inquiry into the notion of a composite substance and proceeds to explain how the 'twofold genesis of this concept out of the nature of the mind' (Ak, II 387) - that is, out of the two distinct cognitive faculties - gives rise to problems and paradoxes. He tells us that the concept of a composite substance is just the concept of an aggregate of parts. Consequently, when any composite substance is supposed to exist, we take it both that it must consist of a certain number of component simple parts, and hence be analysable into those parts, and that these parts must be such that, when combined or synthesized in a certain way, they compose the substance. This is an inference: it is something that follows from a demonstration that takes off from an analysis of the concept of the composite and concludes that this concept presupposes both a complete analysis of the composite into parts and a complete synthesis of the parts into a unified whole or totality. The problem arises when we attempt to 'follow up this intelligible definition of a whole in concrete experiences' (Ak, II 387) - that is, when we try to find this conclusion, not merely mediately, in a conclusion that we understand to follow from a process of reasoning and argumentation (i.e., rational discourse), but immediately, in an intuitive experience that would directly exhibit all of the parts of a substance and all of the coordinative relations of those parts. Exhibiting a composite in intuition is not always problematic but is so in certain cases: those where the composite we are concerned with is supposed to be continuous or infinite. Here there are, ex hypothesi, an infinite number of parts to be discriminated or coordinated. This, however, is too much for us to be able to exhibit in an immediate or intuitive experience. Kant's unspoken presupposition here - a quite natural and solid one - appears to be that our intuitive experiences are finitely complex, so that when the complexity of the object exceeds a certain limit, the only way this complexity can be intuitively exhibited is by a series of intuitions, starting from the whole and then blowing up each of its parts (like a series of successively more powerful microscopic photographs of the same object), and then starting from the smallest parts and exhibiting how they are coordinated with one another in the larger wholes. But, where the object is continuous or infinite, there could be no end to the series of intuitions, and thus, the intuition of a continuous or infinite

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substance could not be formed in any finite time. The concepts of continuity and infinity go beyond what can be exhibited in intuition. For the reason that 'whatever is unrepresentable is commonly supposed to be impossible/ continuity and infinity are accordingly commonly rejected as impossible. But, Kant proceeds to observe, those who have supposed continuity and infinity to be impossible because they cannot be represented in intuition have committed 'the gravest of errors' (Ak, II 389).33 They have confused the conditions under which an object may be intuited by us with the conditions under which an object may exist. We suppose both that the division of wholes into parts and that the aggregation of parts into a composite must terminate because we subreptitiously introduce a temporal condition on the possibility of our intuitive representations as if it were a real condition on the possibility of objects themselves. But the fact that the division or the composition must terminate if we are to be able to represent it in intuition merely shows that we cannot have intuitions of continuous or infinite objects, not that there cannot be such things. Interestingly, however, Kant has no sooner offered this argument than he hastens to add that he is 'not here pleading a case for these concepts [i.e., continuity and infinity]..., especially the concept of the continuous' (Ak, II 388) and that 'it can easily be shown by an argument, which is based on reasons deriving from the [intellect],34 that both simples and a world are given' (Ak, II 389). The remark that he is 'especially' not pleading a case for the continuity of substances is underscored by his later claim that 'the continuous is a magnitude which cannot be composed of simples' (Ak, II 39922-3)- ^ substances must be composed of simples, then they cannot possibly be continuous. Why, we might well wonder, has Kant even bothered to defend the intelligibility of the concept of the continuous if he is going to go on to insist that intellect has no use for the concept and will, in fact, reject it? His real point comes out on Ak, II 389: For whatever conflicts with the laws of the understanding and the laws of reason is undoubtedly impossible. But that which, being an object of pure reason, simply does not come under the laws of intuitive cognition, is not in the same position. For this lack of accord between the sensitive faculty and the intellectual faculty the nature of these faculties I shall explain later - points only to the fact that the abstract ideas which the mind entertains when they have been received from the intellect very often cannot be followed up in the concrete and converted into intuitions.

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Our intuitions, according to Kant, are the product of a distinct cognitive faculty, the sensory faculty. Pointing out the error in rejecting the concepts of continuity and infinity as unintelligible simply because they cannot be intuited is relevant because it forces us to distinguish the demands made by the sensory-intuitive faculty from those made by the intellectual-discursive faculty, and to appreciate that the conditions or laws under which the one operates cannot automatically be assumed to hold valid of the objects cognized by the other. In the case of continuity and infinity, there are two distinct sets of conditions or laws to be considered, which arise from the two distinct faculties. The intellectual faculty demands completion of the analysis (of the composite into its component parts) and synthesis (i.e., coordination of the component parts in the whole); the sensory faculty provides finite intuitions that can adequately represent large or complex objects only by occurring in a successive series. Taking the object to have to satisfy both sets of demands simultaneously is what generates metaphysical difficulties and paradoxes - difficulties and paradoxes that can be resolved by the simple expedient of not allowing the forms and principles of the one faculty to dictate the content of the representations of the other. When we do that, we see that the fact that the continuous and the infinite cannot be exhibited in intuition is not by itself adequate ground for rejecting these concepts as unintelligible (though this is not, by itself, any reason for accepting them either, especially when they are referred, not to space and time in the sensible world, but to substances in the intelligible). Keeping this point in mind can allow us to resolve the paradoxes of composition and division. Recall that Kant continues to insist, even in ID, that 'it can easily be shown by an argument, which is based on reasons deriving from the intellect, that both simples and a world are given' (Ak, II 389). The existence of both simple parts of substances and the totality of the world is thus taught by intellect - it is, in fact, a direct conclusion from the intellectual demand for completion in both the analysis of substances and the synthesis of parts. Against these conclusions, the paradoxes of composition and division are raised: if simples are points of zero magnitude in space, then how could even an infinite number of them compose any finite whole; and, if they have non-zero magnitude, then how could their analysis ever terminate in something simple? Similarly, if the parts and the past and future states of the world are represented as things in space and time, then how could the world ever be thought of as an absolute totality, since any given space or time must always be represented as a delimited portion of a yet larger whole (Ak,

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II 391-2)? But these paradoxes can be resolved by the simple expedient of identifying some subreptitious element or elements of purely sensory knowledge that are being illegitimately imported by the paradoxes into the purely intellectual consideration of the nature of substances and the world. In the case of the paradoxes of composition and division, there are such elements, according to Kant, and they are space and time. Space and time, he will go on to argue, are features only of intuitive, and hence sensory, experience. They cannot, therefore, be legitimately applied to objects as they are represented by the intellect. But this illegitimate application is precisely what we find in the attack made by the paradoxes of composition and division on the concepts of the simple and the total. It is because the parts of substances are conceived as either points of zero magnitude in space or extensions of some finite magnitude in space that they are supposed to be incapable either of summing to any finite whole or of being analysed into simples.35 And it is because the aggregate is conceived as apprehended through a successive series of intuitions, rather than taken in 'at a single glance' (Ak, II 388n. 2), that its infinitely many parts are supposed to be such that they cannot compose an absolute totality. Should it be, however, that time and space pertain only to intuitive cognition, then the point made earlier (about the illegitimacy of taking the conditions of exhibition in intuition to determine the real possibility of objects, or the conditions of the real possibility of objects to determine what must be exhibited in intuition) could be applied again to resolve the paradoxes: we could say that the paradoxes arise only when composite substances are represented in space and time, and when the intellectual demands for completion in the analysis and synthesis of those substances are subreptitiously taken to apply to their exhibition in space and time in intuition (or vice versa: when their exhibition in space and time in intuition is subreptitiously taken to be adequate to the intellectual demand for completion in the analysis and synthesis). If36 space and time could be shown to be merely conditions of intuitive cognition, then we could say that it is: (i) illegitimate to demand that intuitive representations in space and time exhibit the infinity and totality of parts demanded by intellectual demonstrations; and (ii) illegitimate to suppose that the forms of intuitive representation (which imply both infinite divisibility and infinite extension, as far as the intellect is able to determine from its demonstrations concerning the nature of space and time)37 are adequate to specify the nature of composite substances as they really are.

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As Kant puts it at the end of ID, §2: 'Let him who is to extricate himself from this thorny question [of how to resolve infinity with totality in light of the composition paradox] note that neither the successive nor the simultaneous coordination of several things (since both coordinations depend on concepts of time) belongs to a concept of a whole which derives from the understanding but only to the conditions of sensitive intuition' (Ak, II 392). The key to Kant's resolution of the paradoxes of composition and division is thus his identification of space and time as conditions just of intuitive, and thereby sensory, cognition and his claim that we have no right to assign them any role in conditioning the possibility of the real existence of objects. In giving this answer he explicitly articulates the thesis already implicit in the concluding paragraph of the 1768 paper on quadrants in space - that, while the concept of space may be good enough for reference to sensory experience, there are problems extending it to reality as represented through rational ideas - and he supplements his doctrine of the cognitive faculties in a very important way. Not only are we to suppose there to be two distinct cognitive faculties, sense and intellect, but we are - pending an identification of space and time as 'laws of intuitive cognition' with the 'forms of the sensible world' which Kant proceeds to give - to identify time (and space) as the characteristic conditions under which sense operates. Henceforth, any application of spatiotemporal predicates to the intelligible world will constitute 'subreption.' c. Kant's Theoretical Inheritance While the motivation for Kant's distinction between the faculties may be clear from ID, neither the nature of the distinction nor the justification for it is. Kant spoke of the sense/intellect distinction with the sort of confident neglect of detail and definition that can be assumed only by someone who takes it that his audience is already thoroughly versed in the terms he is using - something that, given the tradition he appealed to, he was entirely entitled to expect. Because Kant himself does not do so, it is necessary to outline the traditional tenets he is presupposing in his readers. According to the Aristotelian tradition, the lower cognitive faculty, aesthesis or sense, is a physiological one. The function of sensing is carried out by certain organs within the body of the perceiver. These organs are such that their matter can be imprinted with the forms of external

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objects (I use 'form' in the Aristotelian sense here), in much the same way that wax is imprinted by a seal (though the imprint on the senses was supposed to convey things like colour as well as spatial form). The product of this imprinting, called the 'phantasm' or 'sensible species,' is a replica of the external object. In fact, it is the form of the external object, taken to exist simultaneously in both external matter and the matter of the sense organ. But the process of perception, thus described, accounts only for the acquisition of the forms of particular objects by the perceiver, and our knowledge extends to other things: to universals, to essences, and even (for the Medievals) to necessary beings. To account for our ability to know about such things, a cognitive capacity capable of extracting the universal from the particulars delivered by sense had to be postulated. Such a task, Aristotle and the Scholastics supposed, could not be achieved by a physiological mechanism, which could at most divide or combine material phantasms to produce other material phantasms. Accordingly, the second, 'higher' cognitive function was taken to be a function of mind or intellect, not exercised through physical organs. Kant's adherence to at least the general outlines of this traditional view is evident from §1 of ID onwards, where, as noted above, he claims that the concept of a composite has a twofold origin in the mind, in sense and in intellect, and where he describes the products of intellect as 'abstract/ 'general,' and 'universal/ in contrast to those of sense, which are 'concrete.' It is also evident in §3, where the distinction between sensibility and intellect is drawn with reference to the subject's senses, intellect being a power to represent things 'which cannot by their own quality come before the senses of that subject.' But Kant's agreement with the traditional attribution of a power of extracting universals to intellect is perhaps nowhere as clear as in his doctrine of the discursivity of intellect. Here, too, Kant takes over a distinction made by his predecessors, that between intuition and discursion. 'Discursion' comes from 'discourse' and, according to medieval theory, a discursive cognition is one that requires (mental) discourse, that is, the drawing of a conclusion, not immediately evident to the mind, by a demonstration - a process of calculation or reasoning. Characteristic of discursive cognition is that it happens in stages and takes time. Intuitive knowledge is the opposite - it occurs immediately. The Medievals maintained that all God's knowledge is intuitive, since the need to infer one thing from another would imply that the inferred

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thing was previously unknown, and since the temporality of discursive cognition is incompatible with the divine attributes. God knows everything and knows it all at once. Human beings are a different matter. The Medievals supposed that information is immediately, and hence intuitively, given to us in sense. They even supposed that, once the intellect has been informed by a universal, as a result of abstracting from sense, that knowledge could be supposed to be immediately present to the intellect. But it is painfully obvious that a knowledge of general laws and principles, and sometimes even of universals, is not always directly given but is often the product of a laborious process of reasoning and inference, potentially fraught with errors - a process that Aristotle and the Medievals called 'compounding and dividing.'38 For this reason, human intellectual knowledge was taken to be largely discursive. Kant adhered to the doctrine of the discursivity of the human intellect more stringently than did his predecessors - for him, the human intellect is exclusively discursive; in principle, it is incapable of an intuitive cognition. This doctrine was a constant of his Critical Philosophy, figuring in ID (§10), in the Critique ^230/6283), in Prolegomena, §46 (Ak, IV 333), and given its fullest exposition in §§1-16 of his lectures on logic (Ak, IX 91-100), published only a few years before his death. According to Kant's version of the discursivity doctrine, intellect is essentially a classificatory function. Rather than automatically receiving universals as a natural result of the occurrence of particular impressions on the sense organs, it reflects on representations obtained from sense,39 and from these it distills or abstracts (this is where the 'discursion' comes in) differentiae (what Kant calls notae or Merkmale) (Logic, §6). Concepts, Kant's name for the representations intellect delivers, are just more or less clearly, distinctly, and adequately presented collections of differentiae. Whatever these differentiae may be, Kant's references to them make clear that a number of separate sensory experiences may all exhibit the same difference, so that the difference serves as the definition of a species, collecting a whole class of objects that share this difference under it. The more differentiae there are thought in a concept, the narrower its extension. But Kant maintains that it is impossible for the human intellect to enumerate all the differentiae to be found in any concrete particular (Ak, IX 59).40 There can be, as he puts it, no 'lowest species' (Logic, §11) - no collection of differentiae complete enough to define a concrete particular. It may turn out that a certain collection of differentiae is, in fact, satisfied by only one object, but it is always possible, at least in prin-

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ciple, that there could be a whole collection of objects satisfying these differentiae but differing from one another with respect to their satisfaction of other differentiae not yet noted. Thus, though intellectual representations may be used to pick out single objects, they always have inherent generality (Logic, §1). Only sense, therefore, can truly represent the particular. Thus, for the Kant of ID even more so than for the Scholastics, intellect is to be defined as a capacity to represent universals; sense as the capacity to represent particulars. d. Divergences from the Traditional Account of the Faculties Kant's distinction between the faculties in ID is traditional in so far as it describes sense as a physiological and intellect as a psychic faculty, and in so far as it describes the objects cognized through sense as particulars and those cognized through intellect as universals. But there are, not surprisingly, other respects in which his cognitive theory is informed by early modern views. To this extent non-traditional elements appear in the Kantian picture of cognition. One such non-traditional element is his claim that the senses represent things only as they appear, whereas through intellect we know them as they are (ID, §4). The Platonic/Augustinian denigration of sensory experience aside, the tradition tended to treat sensory experience as no less true or valid than the intellectual. The truths revealed by sense may have been about lower, meaner things, but they were taken to be truths none the less. Kant, under the influence of a new epistemological tradition that rejected sensible species and substantial forms and took the effects of the sensory process to be 'ideas' bearing no qualitative resemblance to the real world of mechanistically operating corpuscles, at least with respect to the 'secondary' qualities, is in no position to have such sanguine expectations about the ability of sense to represent the world accurately. Another, closely related point of divergence from tradition concerns Kant's postulation of what he calls the 'real use' of intellect (ID, §5). For the medieval Aristotelian tradition, nothing could be present to the intellect that had not first been given through sense. Kant, having accepted that sense gives us knowledge only of the way we are affected by things, is at this stage still unwilling to deny the possibility of knowledge of things as they are in themselves, and he is accordingly led to claim that intellect has a special 'real' use in addition to its ordinary 'logical' use. Whereas, in its 'logical' use, intellect abstracts universals and

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general principles from sense, in its real use, it can give a knowledge of 'things as they are' to itself without having to depend on sense. The concepts known by intellect in its real use are 'abstract,' not in the sense of being extracted from sensory data, like chemical compounds distilled or precipitated from a solution,41 but in the sense of being given entirely independently of all sensory data, so that to uncover them it is necessary to abstract from everything sensible rather than to abstract out of what is given concretely in sensible experience (ID, §6). None the less, Kant still insists that intellect only knows these concepts discursively. It is just that the basis for the discursion is not anything given in sensation, but intellect's reflection on its own operations in the process of cognition (ID, §8). It is tempting to see this qualification as a response to Locke's attack on innate ideas - one perhaps motivated by the influence of Leibniz's New Essays.42 This brings up a further point of divergence. Kant's stress on the exclusively discursive nature of all intellectual representations, even those arising from the 'real' use of intellect, leads him to ascribe all intuitive cognition to the remaining cognitive faculty, sense. This happens already in the first section of ID, where 'intuitive cognition' and 'the sensory faculty' are related to each other without a word of comment or justification, as if this were an obvious and unquestionable fact. Whatever is inconsistent with the laws of the intellect and of reason is undoubtedly impossible. But anything which as being an object of pure reason simply does not come under the laws of intuitive cognition is not in the same position. For this lack of accord between the sensitive faculty and the intellectual faculty the nature of these faculties I shall explain later - points only to the fact that the abstract ideas which the mind entertains when they have been received from the intellect very often cannot be followed up in the concrete and converted into intuitions. (Ak, II 389; my italics)

For the tradition preceding Kant, this was not the case. One need not mention the Platonic/Augustinian tradition of belief in extrasensory sources of immediate illumination; the empiricist Scholastic tradition, though it held that nothing could be present to the intellect that was not first given to the senses, also postulated that the presence of a universal in the intellect was, in most cases, the immediate product of affection of the patient intellect by sense (albeit as a result of the 'illumination' of sensory phantasms by the agent intellect), and not the product of any active process of reasoning or discursion ('compounding or dividing').

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Even certain fundamental principles of logic and theology were taken to be immediately seen by the intellect and not to be a result of the prior joining or separating of subject and predicate concepts.43 Despite the fact that Kant supposes all intuition to take place through sense, however, we should beware of treating sense, especially as it is described in ID, as an exclusively intuitive faculty. In at least one place, Kant tries to do this. The place is ID, §3, where Kant attempts to distinguish the faculties by denominating the one 'receptive' (i.e., intuitive) and the other 'facilitative' (i.e., discursive). Sensuality is the receptivity of a subject by which it is possible for the subject's own representative state to be affected in a definite way by the presence of some object. Intelligence (rationality) is the faculty of a subject by which it has the power to represent things which cannot by their own quality come before the senses of that subject. (Ak, II 392)

This receptivity/spontaneity distinction is destined to become the locus of a radical break with tradition in Kant's later thought. The tradition, as I have just noted, took certain intellectual representations to be intuited directly (that is, simply received), and, while it did indeed take the five 'outer' senses to also be intuitive or acquisitive, receiving impressions from external-world objects, it also took there to be certain 'inner' senses that are facilitative or productive. For the tradition, phantasms are not given, but created by a particular function of inner sense, the common sense, which has to, first, combine the particular impressions delivered by the outer senses before a phantasm can emerge. Furthermore, both Aristotle and the Scholastics postulated a certain power to alter phantasms, and even to produce new phantasms out of the bits and pieces of others that had been given. This power, imagination, was represented, not as a function of intellect, but as a special function of inner sense, exercised by physiological mechanisms. In other words, the peculiar function of human intellect was, on the traditional view, limited to extraction; the functions of combination and recombination were assigned to sense. However, while the subversive receptivity/spontaneity distinction is stated by Kant in §3 of ID, it serves as no more than a signpost of impending changes. In ID, nothing is made of the distinction, and it is, in fact, flatly contradicted almost immediately. According to ID, §§3 and 4, appearances arise from two sensory processes. The first is the process of affection. Objects in the outside world act on the subject, and because

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certain parts of the subject (its sense organs) are 'receptive' to this activity, they have an effect on the subject's representative state, an effect that becomes an immediate object of awareness for the subject. But receptivity as so far described yields only sensory data. And Kant maintains that, in addition to the data, or what he calls the 'matter of sense,' sensibility delivers awareness of a form or manner of arrangement in which the data are presented. This form, however, is no product of the objects themselves. 'Objects,' says Kant in ID, §4, 'do not strike the senses in virtue of their form or specificity.' Sensory data are, instead, 'coordinated by a certain natural law of the mind.' As Kant describes it, this is an act performed by the mind, not a datum received by it. In ID, therefore, despite the lip-service Kant pays to it, there is no distinction to be drawn between sense and intellect in terms of receptivity and spontaneity. Given Kant's emphasis on the discursivity of intellect, sense must, indeed, be seen as the only receptive or intuitive faculty. But Kant has not yet gone all the way to seeing it as exclusively intuitive. In ID, sense is facilitative as well, and, as on the traditional account, combination of the matters delivered by sense (via the act of coordination) is still seen as a sensory and not an intellectual process. ii.

The Argument of ID

So far, I have argued that Kant's position on the nature of the cognitive faculties in ID is broadly in accord with the Scholastic tradition, and that he fails to follow through on the one really subversive point of deviation from this tradition, the receptivity/spontaneity (or intuitive/discursive) distinction. I now consider how the account of the faculties figures in his argument, and I show that only in so far as Kant adheres to the tradition is he able to sustain his position. This conclusion is a philosophical rather than a historical one: that the traditional conception of the faculties is, in fact, required to sustain Kant's position in ID, not that Kant realized this requirement. As will be seen, Kant commits a serious blunder in ID precisely because he fails, at a crucial juncture, to carry through with the traditional account. I remarked above that Kant's major thesis in ID was that all the problems of metaphysics could be solved by carefully distinguishing what we know of the sensible world from what we know of the intelligible, and by not subjecting knowledge of the one world to the forms or principles of the other. Chief among the problems Kant claimed to be able to solve was that of the paradoxes of composition and division, a

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conundrum that he eliminated by claiming that space and time, as 'laws of intuitive cognition/ cannot be legitimately supposed to place constraints on the possibility of things as they are in themselves (ID, §1 [Ak, 11389]). However, to sustain this solution Kant had to argue that space and time are, indeed, 'laws of intuitive cognition' which place constraints only on the sorts of objects that may appear to us through the senses, and not also on the sorts of objects that may exist or be known through the real use of intellect. But the notion that space and time belong only to the sensory faculty and not also the intellectual is far from being an obvious or trivial point. Kant had to contend with a Cartesian tradition which took mathematics and geometry to be paradigms of intellectual knowledge (in so far as Descartes was willing to distinguish intellect from sense at all).44 He had to contend with a contingent of Newtonian natural scientists, such as Leonhard Euler, who took space to be a real thing and no mere appearance of sense.45 And he had to contend even with a Leibnizian tradition which, though it took space and time to be sensory phenomena, also supposed that these phenomena are not independent forms of the sensible world, but are, in fact, determined by the internal properties of the monads, of which they are merely confused perceptions.46 Kant may have been able to rely on tradition for an explanation of the nature of the faculties, but, given this sort of opposition, his identification of space and time as forms special to sensible experience could not pass without argument. What makes this argument all the more crucial is that Kant failed to justify his adoption of the traditional, two-faculty account of cognition (unless we take the resulting solution to the paradoxes of composition and division as a justification). In so far as the two-faculty account has any basis in Kant's work, therefore, it is only via the thesis that space and time are forms only of a sensory, as opposed to an intellectual, cognition; for this thesis forces a split between the faculties. Thus, it was not merely Cartesian epistemology of mathematics, Newtonian natural science, or Leibnizian metaphysics that stood in opposition to Kant's claims in ID, but the one-faculty cognitive theories of Leibniz, Wolff, and Baumgarten, on the one hand, and of Hume, Condillac, and Helvetius, on the other. The answer to all these opponents was the same: a demonstration that space and time are forms only of sensible experience. This demonstration is the centre-piece of ID. The demonstration occurs in what is not only argumentatively but geographically the centre of the Dissertation: Part III. There, Kant pro-

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poses to show that there are two 'formal principles of the phenomenal universe, absolutely primary, catholic, and moreover, as it were, schemata and conditions of anything sensitive in human cognition ... namely, space and time' (ID, §13). Part III consists of three sections: §13, which is introductory; §14, on time; and §15, on space. Each of the latter sections is divided into subsections that, for some very mysterious reason, are assigned numbers in §14, but letters in §15. Though there are seven numbers in §14 and five letters in §15, they do not all contribute to the demonstration. The conclusion that time is a 'pure intuition'47 is drawn at the outset of §14 13, as a conclusion from TJi and 2, and 1C for space similarly states the conclusion as a consequence of HA and B. The remaining paragraphs contain the elucidation of subsidiary principles (continuity for time, geometry for space), remarks on the errors of Kant's predecessors, and notes on implications and advantages of the theory. Thus, the basic argument is given in the first two paragraphs of each section. Kant follows a clear method in each of these pairs of paragraphs. In the first paragraph of each pair, he argues that we do not have sensations of time and space, but that all our sensations presuppose time and space (in the sense that they are originally presented to us one after another in time, and displayed alongside one another in space).48 In the second paragraph of each set, he argues that time and space are not known by intellect. From these points, the conclusion that time and space must be forms of the sensible world follows immediately. Since all our sensations are, in fact, arrayed in time and space, it follows that time and space must be orders of sensations, and since these orders are not infused by intellect, they must be products of sense itself. But since these products of sense are not attributable to sensation, the matter of sense, it remains only that they pertain to a further special element of sense, a form distinct both from sensed matter (sensation) and from all form invented by intellect.49 This conclusion is drawn in the immediately following paragraphs, B and C. The adequacy of the arguments Kant offers for these separate points need not concern us here.50 But the underlying strategy, particularly the strategy of the second argument in each pair, where Kant tries to prove that time and space are not intellectual representations, must be of concern. To make this point, Kant needs to show that there is something about time and space that renders them in principle incapable of intellectual representation. It is here that his understanding of the nature of the distinction between sense and intellect comes to be of vital impor-

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tance. For some conception of what intellect is, how it works, and how it differs from sense must be invoked in the argument. The claims Kant makes about time and space in §14 \i and §15 IB appeal to the scholastic distinction between the faculties: intellect is represented as a faculty restricted to the abstraction of universals, and sense represented as a faculty delivering cognition of particulars or, as Kant puts it here, singular objects. Accordingly, Kant's proof that time and space cannot be intellectual representations proceeds by demonstrating that they are singular representations. Thus, both the points made in §14 ^2 go to prove singularity: (i) If two times are given and they differ from each other, then one must be earlier, one later. But the earlier cannot be distinguished from the later time by any intrinsic mark or difference (per notas aliquas intellectui conceptibiles) that could be identified if the times were each considered separately, apart from the manner in which they are presented in an ongoing experience. At least, Kant claims, we could not suppose that there are any specific differences discriminating earlier and later times and abstractable by intellect without entering into a vicious circle (presumably because, in order to know which difference designates the earlier and which the later time, we would already have to have some criterion for determining which of the two in fact occurred first). Consequently, times can be ordered only through reference to a singular intuition (per intuitum singulareni) in which they are joined to each other, either immediately or by some intermediate time. Moreover, (2) were time a general rather than a singular representation, it would collect a class of objects (the various intervals of time) under it, the way 'animal' collects 'human being/ 'feline/ 'canine/ and so on. But the various times are not a scattered collection of objects with no more than a principle of resemblance determining their membership under a common genus. Each has a particular location in time, and because of this they constitute a single object when taken together, not a collection of different objects that merely resemble one another in virtue of possessing a common specific difference. Similar points are made for space. However, even assuming that these claims are defensible, they give only an incomplete answer to the question. Granting that our representations of space and time are representations of particulars rather than of general characteristics that a number of objects may have in common, why should it follow from this that they must be sensory (or intuitive) representations? Why should we suppose that intellect is incapable of forming singular representations or, as Kant would put it, of descending

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to the lowest species? Why should the fact that space and time are singular mean that they must be, as Kant claims, intuited rather than known discursively? The answer we might expect to see Kant give to this question is the one his tradition supplied for him and the one he elaborated in his Logic: that sense, being a physiological function of the human body delivering only material particulars, is inadequate to account for our cognition of universals and that, for this purpose, a second cognitive faculty must be postulated. This faculty is intellect, which works by abstracting universals from the concrete phantasms delivered by the physical sensory apparatus. Its distinction from sense is required because its products, universals, are inherently such that they cannot be represented by any corporeal faculty, but only by pure mind or nous. Because its products are abstract and general by their very nature, intellect can attain a cognition of the particular only by thinking a set of specific differentiae so large that it can be satisfied by one and only one individual. On the assumption that any particular contains an infinitely rich variety of abstractable differentiae, only an infinite spirit, not finite minds such as ourselves, could form intellectual representations adequate to particulars. However, this is not the answer Kant, in fact, gives. He attempts to explain why intellect cannot represent concrete particulars in §10 of ID a few pages before he tries to prove that space and time are the forms of the sensible world. The answer is flawed. There is not given (to man) an intuition of things intellectual, but only a symbolic cognition,51 and understanding is only allowable for us through universal concepts in the abstract and not through a singular concept in the concrete. For all our intuition is bound to a certain principle of form under which form alone can something be discerned by the mind immediately or as singular, and not merely conceived discursively through general concepts. But this formal principle of our intuition (namely, space and time) is the condition under which something can be the object of our senses, and so, as the condition of sensitive cognition, it is not a means to intellectual intuition. (Ak, II 396)

We are not capable of having intellectual intuitions or of intellectually conceptualizing singular objects, Kant tells us, because our cognition of singular objects is bound to the conditions of space and time, which figure only in sensory experience. But the point that the conditions of space and time figure only in sensory and not in intellectual experience is pre-

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cisely what is in question three pages later in §14 \2, where Kant blithely 'proves' that time is not a form of the intelligible world by appealing to the claim that intellect cannot represent singular objects. Thus, the argument ends up moving in a circle. It is not clear why Kant makes this blunder. He may have been relying on the traditional conception throughout, expecting that his readers would take that conception to justify the exclusive universality of intellectual representations in §§14 and 15, and that §§14 and 15 would in turn justify the claims about the non-spatiotemporality of intellectual representations in §10. This would be the most charitable reading. But, alternatively, he might have had some reason for wanting to retreat from the explicitly physiological account of sense that the traditional conception invokes to justify intellect's role. He might have felt, for instance, that ID, since it is ostensibly a propaedeutic to the a priori science of metaphysics (ID, §8), ought not to rest on premises garnered from empirical observation of the human body and its workings. If this was indeed Kant's concern, then it must have been redoubled for him when he came to write the Critique. The Critique is supposed to provide a justification of the very possibility of the sort of sophisticated scientific theorizing about unobservables involved in the traditional account of how the senses work, and a theory of the possibility of scientific theorizing cannot rest on an empirical theory of the functions of the sense organs. But in so far as Kant's argument in ID has any cogency, it is only in so far as it relies on the traditional physiological account of human sensory experience. If this account is rejected, then how avoid the circularity in proving that space and time cannot be represented by intellect? This, however, is only one of the problems to emerge with Kant's argument when it is transferred to the Critique. iii.

Strategic Difficulties a. The Changed Outlook of the Critique

Kant's Inaugural Dissertation and his Critique of Pure Reason are two very contrary works. The former draws such a sharp distinction between sense and intellect that it splits the cognized world in two. In denying that the forms and principles of sensory experience have any legitimate reference to the objects of intellectual knowledge, it saves the claims of pure understanding from the sceptical attacks based on the

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paradoxes of composition and division, but it also creates two distinct experiential realms, a sensible 'world' of subjective experiences and an intelligible 'world' of things as they really are. The Critique affirms the opposite of this 'two worlds' theory. Neither the products of intellect (concepts) nor the products of sense (which Kant now proceeds to call 'intuitions') are supposed to yield knowledge when taken in isolation. In the famous words of A5O/B74, 'neither concepts without intuitions in some way corresponding to them nor intuitions without concepts can give knowledge/ Far from securing the field for pure understanding by denying the admission of sensible principles, the Critique affirms that intellectual concepts and functions may be legitimately employed only with reference to the deliverances of sense. The dogmatic claims of intellect must be systematically critiqued and exploded, and all hopes to gain knowledge of a second, intelligible world must be abandoned. This change in outlook between ID and the Critique is one that occurred for the most weighty reasons.52 In ID, Kant had proposed that intellect, in its 'real' use, gains knowledge of reality through the employment of its own pure concepts (concepts like those of possibility and necessity [ID, §8]). Kant insisted, however, that these concepts are not abstracted from the materials given in sense, but discovered by intellect within itself through its reflections on its own operations. Why Kant took this view is unclear, but also unimportant for present purposes (perhaps it was the influence of Locke's account of reflection as exploited by Leibniz for his own purposes in New Essays; perhaps it was a feeling that concepts abstracted from sensory experience would, as remote results of a process of sensory affection, have to be mere appearances, not cognitions of reality;53 either way, an empiricist unwillingness to countenance Platonic recollection, Augustinian illuminationism, and other such sources of extrasensory perception is definitely paramount). What is important is that Kant came to be bothered by the question of how pure intellectual concepts could be supposed to be legitimate sources of information about the real nature of the external world. This problem comes to the fore in the much-cited passage from the 21 February 1772 letter to Marcus Herz, where Kant writes that the major question he has now come to struggle with is, 'what is the ground of the relation of a representation to its object?' - why, in particular, should pure intellectual representations be supposed to refer to real objects? This was the problem of the transcendental deduction of the categories, which was to occupy Kant for the next ten years. While there is much that is uncertain and open to speculation about

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Kant's philosophical development over the silent decade from 1772 to 1781, the outcome of his struggles is clear: in the Critique, he enunciates the position that the categories do not refer to real objects or things in themselves. Moreover, the categories, considered simply as pure intellectual concepts, are utterly meaningless - they are mere names serving as place holders for some yet to be specified content. In so far as the categories have any objective validity, or even any meaning, it is only in so far as they are employed with reference to sense (6148-9, Ai47/ 6186-7, A679/B7O7, A696/B724). Considered with this reference, they do acquire a certain meaningful content and an objective validity, though the objects they are valid for are objects considered only in so far as they appear through the use of the senses. In giving the proof that the categories have even this much meaning or objective validity, however, Kant ends up making a profound alteration to the conception of the relation of the cognitive faculties to be found in ID, and makes, thereby, a radical break with the tradition of ancient and early modern cognitive theory. He finds that the only way he can ground the legitimate employment of the categories is by reconceiving them as rules or principles responsible for the connection (the 'bringing to a unity of apperception') of the variety of items delivered by sense. It is, in fact, through being considered as such rules or principles for connection that the categories acquire meaning and content. Thus, the premises that all connection is an act of intellect (6129-30) and that a collection of matters can never be brought to conscious awareness in so far as it is merely presented through the senses but only in so far as the matters are connected in thought (6132-3) become the fundamental tenets on which the transcendental deduction rests. But these fundamental tenets just are the theses of the 'blindness' of raw sensory experience apart from intellectual connection and the 'emptiness' of all intellectual categories considered apart from their role as functions for the connection of the sensibly given manifold. b. Problematic Consequences of Kant's Changed Outlook While the Critique of Pure Reason is in this way radically different from ID, there are a number of points of similarity as well. Two of the most important are that, in the first part of the Critique, the Transcendental Aesthetic, Kant is still concerned to maintain that sense and intellect are two distinct sources of knowledge and still concerned to prove that space and time are forms of sensibility. 6ut his revised position on the

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role of sense and intellect in delivering knowledge makes the strategy used to prove this point in ID ineffective. Recall that this strategy was to exhibit some feature in our representations of space and time that intellect is supposed to be incapable of presenting. We may wonder how successfully Kant was able to give this exhibition, but, in ID, it was at least possible to propose such a project, for, in ID, sense was taken to be able to deliver a cognition of objects on its own, independently of any recourse to understanding. Thus, in ID, the only problem was to uncover the special characteristic distinguishing a sensible from an intellectual cognition, and then to demonstrate that space and time possess this characteristic. But the Critique cannot allow this. Though, in the Critique, Kant still believes that the faculties are distinct, his new belief that they are not self-sufficient means that it will now be impossible to pick out any distinguishing marks in the products of these faculties. There are no separate products of the lower faculty that we can examine - not without making them products of the higher faculty first. This is the flip side of the attack on dogmatic intellectualist metaphysics that Kant launches in the Critique. Just as there can be no knowledge gained by employing pure intellectual concepts outside of the field of experience, so there can be no purely sensory knowledge obtained prior to all application of concepts. Unconceptualized experiences may, indeed, be intuited (Ago/ Bi22), but such appearances are 'for us as good as nothing' (Am); it is only when the manifold presented in the intuition has been run through and connected in accord with concepts that any representation - even a representation of a particular - is cognized (An6, 8137-8). Prior to this connection, the intuition is 'blind.' It is suspicious that this 'blindness thesis' is stated only at the outset of the Transcendental Analytic, after Kant has proven that space and time are forms of raw (that is, immediate, preconceptual, or intuitive) sensory experience in the Transcendental Aesthetic. The thesis crops up just when it is necessary for the argument, but not earlier, where it would have posed serious questions about the adequacy of Kant's arguments for identifying space and time as forms of sensibility. It is almost as if Kant wrote the Transcendental Aesthetic without realizing that he was committed to the blindness thesis. Thus, at the outset of the Aesthetic, he blithely describes his methodology for the coming pages as follows: In the Transcendental Aesthetic, then, sensibility will first be isolated by setting aside everything that intellect thinks through its concepts, so that nothing but

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empirical intuition will remain. Second, everything in empirical intuition that belongs to sensation will also be removed in order that nothing but pure intuition and the mere form of appearances will remain - this is the only thing that sensibility can deliver a priori. This investigation will reveal that there are two pure forms of sense intuition [serving] as principles of a priori cognition, namely, space and time. (A22/B36)

This project is hopeless. Even if Kant could succeed in removing everything intellect thinks through its concepts from experience, he would be left with something that, according to blindness, would not be an object of knowledge. This blindness to the blindness thesis at least appears to infect Kant's subsequent arguments as well. In the immediately following pages of the Transcendental Aesthetic, in what he calls the Metaphysical Expositions of the concepts of space and time, Kant sets out to prove that space and time are forms of intuition, and his arguments on this score at first seem to be no more than a repeat of §§14 and 15 of ID. The same arguments occur in much the same order, and they seem to be directed to proving the same point: that we have some sort of intuition of space and time prior to all understanding (conceptualization), and that we can know this because space and time have some special feature that intellect cannot grasp. How we can know that space and time have this feature, if intellect cannot represent it and intuitions that have not been synthesized under concepts are blind, is not explained; neither is what entitles us to suppose that the feature cannot be intellectually represented. Consider the following examples: at A31-2 7647, Kant claims that time must be intuited because different times are only parts of one and the same time, and because 'that representation that can be given only through a single object is an intuition.' The argument apparently is that, because time is a particular rather than a class, it cannot be represented intellectually. But this argument comes to nothing, given the blindness thesis. If blindness is correct, there can be no cognition of particulars independently of intellectual synthesis. So if time, or the different parts of time, are not intellectually represented, we cannot say anything about it (or them); we certainly cannot say that it is a particular. But if time is intellectually represented, then we do have concepts of it, and these very concepts falsify Kant's claim that all our intellectual representations must, in principle, be class concepts either that, or Kant must either admit that time is not singular or hold

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that there are other kinds of representations grasped by the intellect besides class concepts. At A32/B48, Kant tells us that, with intuitions, the whole precedes the parts, whereas, with concepts, the 'parts' precede the whole (according to A), or perhaps concepts just are always 'partial representations' (according to B). Because the parts of time are created only through drawing boundaries within the whole, and therefore the whole of time must be given first, it is supposed to follow that time is an intuition and not a concept. But even granting that, with time, the whole precedes the 'parts' (which is granting a great deal, whatever this might mean), either the whole of time that precedes the parts is intellectually represented in which case, it is false that, with all our intellectual representations, the parts precede or fail to give the whole - or the whole time is not intellectually represented - in which case, according to blindness, we cannot know anything about it, including that it is a whole within which we may define boundaries. Finally, at A25, Kant tells us that concepts of relations can represent infinity only by referring to an unboundedness in the progress of intuition. At 640, he tells us that, even if concepts can represent infinity independently of reference to the progress of intuition, they do so only by containing an infinite number of possible representations under them (presumably, he is thinking here of species contained under a genus), whereas intuitions contain an infinity in them, as parts. Since infinity is supposed to pertain to space (A), or pertain to it in the appropriate way (B), we are apparently supposed to draw the conclusion that the original representation of space is an intuition, and not an intellectual representation. But again the dilemma posed by blindness arises: if all that we do is intuit the space, then, because intuitions are blind, we cannot know anything about it, including whether it has any parts 'in' it at all. But, if we do succeed in bringing infinite space to consciousness, then our representation is intellectual, and it exhibits precisely that feature that Kant seems to be denying to intellectual representations. In all of these cases, Kant comes to grief because, apparently, he has not revised the proof-strategy employed in ID in any way that could meet the challenge of blindness. Nor is it simply Kant who comes to grief here. Many of his commentators have proposed one or another of these features as defining the distinction between intuitive and intellectual representations. Thus, Hintikka has proposed that, for Kant, the singularity criterion is what really marks off the two classes of representation, and Kirk Wilson has clearly and cleverly worked up Kant's

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remarks on whole/part priority into a distinction drawn in terms of mereological and set-theoretical relations of membership.54 But such moves are inconsistent with the development of Kant's views on the blindness of intuition and the necessity of intellectual synthesis for cognition. These views entail that even the perception of singular objects or mereological wholes must already involve synthesis under the categories, and so cannot be non-intellectual. And, most seriously, these views make nonsense of Kant's arguments in the Metaphysical and Transcendental Expositions. If either Hintikka or Wilson is correct about what a Kantian intuition is, then Kant makes claims about intuition to which he is not entitled, given blindness, and his attempts to prove that space and time are forms of intuition fail. The Transcendental Aesthetic really does, on this view, turn out to contain a rump of old views discarded by 'the more mature and fruitful parts of the Critique.'55 In ID, Kant's argument was open merely to the charge of a possible circularity. But, if he intended to use the same argument in the Critique, then it is not just circular; it is incoherent. iv.

The Distinction between the Faculties in the Critique

It is often maintained that the Transcendental Aesthetic of the Critique merely repeats the main points of the Inaugural Dissertation proofs concerning space and time, and that Kant simply takes these arguments over without realizing that, in the changed context of the Critique, they can no longer work.56 In light of what has been said in the previous section, this assessment may not appear at all illegitimate. None the less, I have been careful in the preceding section to qualify the description of Kant's argument with words like 'seems' and 'appears.' I have done this because I think some question can be raised whether Kant, in fact, intended his argument in the Critique to be understood along the lines he had presented earlier, in ID. There are differences between ID and the Critique that extend beyond Kant's account of intellect, to his account of sense. In what follows, I draw from these differences an alternative reading of Kant's arguments for identifying space and time as forms of intuition. I noted above that, while the Kant of the Critique is concerned to deny that the cognitive faculties deliver knowledge independently of one another, he is still concerned to maintain that the faculties themselves are distinct. In keeping with his new position on the mutual interdependence of the faculties, however, he is forced to view this distinction in a

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different way. The distinction is no longer one that can be marked by the products delivered by the faculties, since the products of the sensory faculty, intuitions, are supposed to be "blind' or indescribable when considered on their own and, as I have just shown, any attempt to define a distinction that way is bound to fail. Faced with this result, Kant needs to describe the distinction between the faculties in a different way. Given blindness, this may seem to be an impossible task. After all, if we cannot 'see' what sensory experience is like prior to processing, how can we describe it? But Kant's blindness thesis, which sets such barriers in the way of identifying any particular product as sensory rather than intellectual, also forces a distinction between the manners of operation of the two faculties. It does this in tandem with the complementary thesis Kant introduces along with blindness, the 'emptiness thesis.' For Kant, sensory experience isolated from intellect is not nothing. On the contrary, it is so far from being nothing that the content it delivers is the only thing that gives meaning to intellectual concepts, which apart from it are 'empty.' Thus, while blindness might tell us that we cannot describe a raw sensory experience, the 'emptiness thesis' assures us that in so far as our thoughts are intelligible, there must none the less be some real content intuited in sensory experience (A89-9i/Bi22-3,145); it is just that, prior to all conceptualization, this intuition is unintelligible (Am, 116; Bi45).57 Thus, in accord with emptiness, sense is conceived as a function that delivers important elements to the cognitive process, but, in accord with blindness, it is supposed to deliver these elements in such a way that they are not directly usable in knowledge claims. Intellect, in turn, is conceived as a higher function that processes the elements and renders them usable. The overall effect of these consequences of blindness and emptiness is to represent sense as a faculty responsible for the operation of receiving raw data (it is through sense that things are given, as Kant likes to put it) and intellect as a faculty responsible for the operation of performing whatever processes are necessary to raise raw data to the level of consciousness (it is through intellect that what is intuited comes to be thought, as Kant likes to put it). It is with this development that the unsubstantiated remarks on receptivity and faculty in §3 of ID are finally taken seriously. In the Critique the lower cognitive faculty is truly receptive; its function is simply to present raw data to us for processing. Intellect, in contrast, is facilitative in the sense that it does all the processing required to bring these data to a cognition - including combination of various items in a singular representation, as well as the abstraction of differentiae in a concept. To

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thought belong all the processes, and all the products of processes, that can be conceived to be performed upon raw data. To sense belongs the mere act of receiving or intuiting raw data. All intuitions, as sensory, are grounded on affection, concepts on functions. By 'function' I understand the unity of the act of ordering different representations under a common one. Concepts, therefore, are grounded on the spontaneity of thought, as sensory intuitions are on the receptivity to impressions. (A68/B93)

Note that this passage begins with the words 'All intuitions, as sensory/ rather than 'All sensory experience, as intuitive.' The inversion is a subtle indication of how Kant's thought has changed between ID and the Critique. As noted above, 'intuition' was traditionally taken to refer to the act of knowing something immediately, without having to work it up through some process. Kant, following this traditional usage, now starts to refer to the products of the lower cognitive faculty as 'intuitions' - they are, after all, what is given to us prior to all processing. In fact, 'intuition' now comes to replace 'sense' as Kant's preferred name for the lower cognitive function - and quite legitimately so, because what sense now is for Kant is just the faculty that delivers intuitions to us, not the faculty of appearances or the faculty of the physiological sense organs. Calling the products of sense 'intuitions' and the sensory process 'intuition' underscores these changes to the traditional view of the faculties.58 This revision in Kant's conception of the lower cognitive faculty has a corollary effect on his account of the higher: in so far as the 'combination of the manifold' is now conceived as an activity carried out by intellect, intellect intrudes on a domain previously reserved for sense. In ID and in traditional cognitive theory, intellect was responsible only for the abstraction of universals. Now, for the Kant of the Critique, it is responsible for combination, too (6129-30, A77~8/BiO3). The functions traditionally carried out by the inner sense organs of common sense and imagination are turned into functions of intellect, carried out in accord with the categories. Thus, in Kant's Critical account of cognition, imagination is elevated out of the sensory faculty and comes to be identified as a function of intellect (8129-30,150-2). Thus, in the Critique and all later works, it is the distinction between receiving and processing that defines the separation between the faculties. Sense just is the intuitive faculty, and intuition just means 'immediate reception.' This version of the distinction between the faculties is

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captured in the first sentence of the Introduction to the Transcendental Logic, where Kant writes: Our cognition springs out of two fundamental sources of the mind of which the first is [the capacity] to receive representations (the receptivity of impressions), the second the capacity to cognize an object by means of these representations (spontaneity of concepts); through the first an object is given to us; through the second this object is thought. (A50/674; Kant immediately goes on to identify what is presented by the first capacity as intuition.)

It is also at play throughout the Transcendental Deduction, where Kant distinguishes intuition, as the capacity through which data are given, from intellect, and notably from the intellectual function of figurative synthesis, as the capacity whereby the given data are connected (6129-30, 136, 5150-2). It is even briefly mentioned in the Logic, where Kant writes that sensibility 'gives the mere material to thinking/ whereas intellect 'disposes of this material and brings it under rules or concepts' (Ak, IX 36). Nor is this account merely a later invention, to be found only in the subsequent parts of the Critique and not in the 'older' Transcendental Aesthetic. It occurs in the very first sentence of the Aesthetic, where Kant gives what must be taken (if only because of its privileged position) as the authoritative pronouncement on the nature of the distinction. In whatever way and by whatever means a cognition may be related to objects, intuition is that way by which it is immediately related to them, and that to which all thought is referred as a means. But intuition only takes place in so far as the object is given to us. And this in turn is possible, at least for us human beings, only in so far as the object affects the mind in a certain way. The capacity (receptivity) to acquire representations through the manner by which we are affected by objects is called sensibility. (A19/B33)

v.

The Circularity Problem

So far, I have argued that Kant's mature (Critical) distinction between the faculties is drawn in terms of the functions of receiving information (intuition) and connecting or unifying received information (thought). When the shift to this way of drawing the distinction happens, intellect comes to be identified as the processing faculty, responsible, not just for

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abstraction of universals, but also for the combination of matters in our cognition of particulars. As a result, the processes of imagination, recollection, common sense (perception), and cogitative or estimative power (anticipation), which for the medieval tradition had been functions of the so-called inner sense organs because they involved creation and manipulation of phantasms (images), are for Kant elevated into the higher cognitive faculty. Intellect is not just the faculty of thought (or universals), as Kant says. It is also the imaging faculty, for without synthesis under intellectual concepts, the cognition of particulars is no more possible than that of universals. But there is one further process that Kant had himself ascribed to sense in ID: the process of coordinating sensa in space and time in accord with certain innate laws of the mind. In the Aesthetic, however, the forms of space and time are most emphatically not elevated into intellect. As with all other deliverances of intuition, these forms are indeed operated upon and refined by intellect, particularly through the process of synthesis under the categories of relation, which are supposed to generate a higher-order, 'objective' space and time from the given, 'subjective' one. But Kant's position in the Aesthetic is clearly that at least the subjective order is already present in intuition, well before intellect ever comes to perform its synthetic activities. There are two ways of explaining this phenomenon: 1 Kant, carried on by the inertia of his past arguments, simply failed to realize that his conception of space and time as products constructed by a process of coordinating sensations was out of line with his new definition of sense as the intuitive faculty. In fact, when he really studied the matter in the Transcendental Deduction, he ended up treating time and space as originating from a special intellectual process, the 'figurative synthesis of imagination.' (Imagination, recall, is now an intellectual function, albeit the lowest.) The Transcendental Aesthetic is merely a piece of old work patched onto the front of the book, and its claims about spatio-temporal form being intuited need to be reinterpreted, or, better, ignored. 2 Kant deliberately intended to identify space and time as forms already present in intuition. As a result, he abandoned the thesis that they arise from any sort of process performed upon sensa and held that they characterize the manner of the subject's receptivity - the order in which sensations are received by it rather than the order in which received sensations are arrayed by it.

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In chapter 2, below, I argue that (2) is the correct option. For now, however, I want just to consider the fact that, in the Aesthetic, Kant still claims that space and time are forms of the lower cognitive faculty (now called 'intuition') and examine how, rightly or wrongly, he attempts to establish this claim. If the strategy for proving that space and time are forms of intuition is the same strategy Kant employed in ID and proposed to follow in the passage from A22/B36 cited in § iii, above - the strategy of showing that space and time possess characteristics (like singularity) purportedly possessed only by sensory products - then the project is hopeless. Given that the representations of intuition are, though not nothing, certainly 'nothing to us' prior to intellectual synthesis, we cannot possibly strip the contributions made by intellect out of experience and attempt thereby to uncover a set of essential features characterizing a sensory representation. But this is not the only way to go about the job. Though we cannot inspect our raw intuitions in order to demonstrate that they exhibit spatiotemporal form, we do have intellectual representations of space and time - what Kant refers to as 'concepts' of space and time and blindness does not forbid us from inspecting them. Perhaps, by doing so, we could gain some clue as to where these concepts originate. Do they represent something that first arises from a figurative synthesis of imagination? that is already present in sensation? in an experience of the order in which sensations are received? Despite the disappointing evidence of passages such as A22/B36, there is considerable evidence in the Transcendental Aesthetic, especially in B, that Kant, in fact, follows this alternative strategy. Throughout the sections of the Transcendental Aesthetic where Kant offers his major arguments - the Metaphysical and Transcendental Expositions he persists in referring to our representations of space and time using the term 'concept' (his preferred name for an intellectual representation). Ironically, many commentators who have noticed this refuse to take Kant at his word here, insisting that he must mean to use 'representation' rather than 'concept.'59 For them, Kant was trying to prove that our representations of space and time are intuitions and not concepts, rather than concepts of the forms of intuition. Their reading violates blindness, and so makes nonsense of Kant's position. This is, of course, no reason not to accept their interpretation (Kant was not incapable of uttering nonsense). But the indications that Kant really did mean 'concept' when he wrote 'concept' are very strong. His references to concepts of space and time occur in the titles of the sections ('Of Space:

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Metaphysical Exposition of this Concept' [537]; Transcendental Exposition of the Concept of Time' [648]; 'Conclusions from the Above Concepts' [A26/B42, A32/B49]), and they occur, perhaps most tellingly, in the definition of the activity of exposition that Kant gives in B. At A23, Kant had asked, 'What, then, are space and time?' and he had continued with the sentence 'In order to become clear about this, let us first consider space.' But in B he struck out the words 'consider space' and substituted in their stead 'exposit the concept of space' - deliberately inserting the word 'concept' where it had not before been present. What is more, he continued the passage, adding the words 'I understand by "exposition" (expositio) the clear (though not complete) presentation of that which belongs to a concept,' indicating that he saw his project not as the presentation of an intuition, but as the analysis of a concept. The Expositions are, therefore, really inquiries into the conditions that make our concepts of space and time possible; this, no doubt, is why, at A87/Bii9, Kant refers to the Expositions as transcendental deductions of the concepts of space and time. Consider now how Kant carries out this new strategy of conceptual exposition. According to Kant, all our intellectual representations spring from two sources: an original reception of material in intuition, and whatever results from bringing this material to a unity of apperception. To prove that space and time are intuited entails showing that they could not come into existence only at the second stage, as a result of the process of unifying materials that are themselves in no way spatial or temporal. Doing this is, in effect, the same thing as trying to show that a cognition of space or time could not be constructed from sensible qualities. It means attacking the way Berkeley, and successors to the Berkeleyan program such as Lotze, Bain, and Wundt, had and have tried to account for space-cognition. This may be a difficult task,60 but it is at least a coherent one. Executing it does not obviously entail violating blindness, but merely considering what, in our intellectual representations, could possibly be produced by synthesis and what must be supposed to have been originally given. Since we can identify both the products of intellectual synthesis (our knowledge) and the processes involved in generating these products from raw data (synthesis in accord with the categories), it seems at least possible that we should be able to determine what in the product could possibly have originated from processing and what must be originally given. I noted above that it has been charged that the Transcendental Aesthetic of the Critique is merely a repeat of Parts II and III of ID. In particular, the

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latter portions of the Metaphysical Expositions of space and time, with their references to essential unity, whole/part priority, and infinity, are thought to have been more or less directly lifted out of §§1412 and §§15 IB of ID. But, though the appeals Kant makes in the later arguments to essential unity, whole/part priority, and infinity are the same ones made in ID, they take on an entirely different role when seen as contributing to the strategy of conceptual exposition. Rather than serve as criteria for separating intuitive from intellectual representations, they emerge as features that raise problems for the constructivist program. Kant's charge is that Berkeley, or anyone else who takes a constructivist tack, could not account for why space is, for instance, singular (or, as he puts it at A25/ 639, 'essentially united'), for why it exhibits mereological relations of parts, or for why it is unbounded. The point is not that our intellectual concept of space does not exhibit these differentiae, but rather that no constructivist account can explain how these differentiae could come to be thought in our concept - especially in so far as we think the concept to represent correctly the space and time of the world as we experience it.61 Whether or not Kant's appeals to essential unity, whole/part priority, and infinity are successful in drawing us to this conclusion is examined in chapter 7, below. For now, I only want to note that the different role these appeals are intended to play in the arguments of the Critique is made clear by a significant alteration: throughout the Metaphysical Expositions, Kant inserts a vocabulary of ground and consequent that has no precedent in ID. Whereas, in ID, the point is simply that space and time have singularity, whole/part priority, and infinity, and therefore are intuitions, in the Critique, the point is that because the consequent, our concepts of space and time, exhibits the differentiae of essential unity, whole/part priority, and unboundedness, this consequent must be grounded on a space and time originally given in intuition. From this it follows that in respect of space an a priori intuition (one not empirical) must lie as a ground of all concepts. (A25/B39) Were there no limitlessness in the progression of intuition, no concept of relations could convey a principle of unboundedness. (A25) Space is thought as containing an infinite number of representations in itself (since all the parts of space to infinity are simultaneous). Therefore, the original representation of space must be an a priori intuition and not a concept. (640; my italics)

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Wherever the parts themselves and every magnitude of an object can only be represented as determined through delimitation, there the complete representation cannot be given through concepts, but an immediate intuition must lie as a ground of such concepts. ^32/848; my italics)

There is no such language of intuitive ground for conceptual consequent to be found in ID. The arguments are simply not the same, therefore, despite what a superficial reading might indicate. The pattern of argument of the Critical passages is that of inference from what is found in the intellectual representation back to what must have been present in the data originally given to the intellect prior to processing. Whether or not these arguments are at all successful is something we might want to question. But that Kant, in fact, intended them to be read as I have described them seems clear. Much more will have to be said about Kant's arguments against constructivism below. But I hope I have shown that the strategy Kant employs in the Metaphysical Expositions is different from that of ID, does not violate blindness, and is non-circular. This is already more than can be said for the strategy of ID, or for those interpretations that rest Kant's distinction between intuitions and concepts on the singularity or the mereological criterion. vi.

Regressive Terminology

The main conclusion to be drawn from this survey of the historical and strategic factors in Kant's account of intuition is that what in the literature is called 'the immediacy criterion' must be taken as the fundamental criterion by which Kant distinguishes intuition from understanding. This is the only way to read Kant consistent with blindness, and it is the only way his major conclusions about space and time in the Transcendental Aesthetic can have even a hope of standing as coherent, nontrivial, or non-question-begging. All the same, this reading of Kant does conflict with a number of passages (notably ^[4 of the Metaphysical Exposition for time ^31-2/847], A32O/B377, A713/B741, and Logic, §§1-16) where he appears to use singularity as the defining criterion of intuitions and generality of intellectual representations. I conclude by explaining why this regressive terminology is still to be found in Kant's mature works. Nothing that has been said so far militates against the possibility that intuitions might turn out to be mereologically structured wholes, each

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arising from sensation of, or referring to, just a single object. I have only argued that they cannot be defined that way at the outset without trivializing Kant's position on space and time. It is important to separate what is fundamental from what is derivative, what Kant starts out with from what he tries to prove. In the Critique, Kant starts out, I have argued, with the thesis that intuition is immediate reception of information, and thought the processing of information into knowledge claims. But one of the things he sets out to prove is that the data originally received in intuition are disposed in space and presented successively in time - that these are the forms in which the information is received. If we assume that he is successful in making this case, then it follows that intuitions must be spatiotemporally determined and spatiotemporally structured.62 From this it is a trivial consequence that intuitions express mereological rather than taxonomic relations of membership, and given that location in an 'essentially united' space and time is a sufficient condition for uniqueness, it is equally trivial that intuitions pick out singular objects and do not refer generally. But these are consequences of the supposition that intuitions, as the most immediate, primitive, and original elements in cognition, consist of an array of matters in space and time. They are not definitions assumed at the outset and they are not distinguishing features of intuition, as opposed to understanding. For, if intellectual representations include whatever is given through a process of combination or figurative synthesis of the immediately given spatiotemporal array, then at least some intellectual representations (namely, perceptions) will refer to particulars and to mereological relations of parts. Indeed, in so far as intellectual processing is necessary for the perception of an object, singularity and mereological structure can be seen only in the representations of intellect. Of intuitions, they must be inferred (given blindness).63 It may be objected that this is too much at variance with what Kant has to say about intuitions and concepts. Why would Kant persist in offering the singularity criterion as a distinguishing feature of intuitions (as, for instance, in Logic, §1)? Why does he so frequently claim that the products of intellectual activity are merely discursive or general representations through which we do not think singular objects, but only differentiae that a number of objects may have in common (Logic, §1; 63940, i36n; A32O/B377)? And why does he so frequently speak as if intuition by itself, apart from all reference to intellectual synthesis, might constitute the perception of a singular object? In his Logic, for instance, he remarks that 'when a savage sees a house in the distance, the use of

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which he does not know, he has the same object before him as another who knows it is a dwelling furnished for people/ But, Kant continues, the 'savage's' cognition of the house is 'mere intuition/ whereas, for the other person it is 'intuition and concept at the same time' (Ak, IX 33). The passage hints that it is possible to perceive something without synthesizing the array under concepts (we could hardly suppose that there would be a house-shaped hole in the 'savage's' visual field because intuitions without concepts are blind). This implication is seconded by Kant's claim at B422n that an indeterminate empirical intuition is perception (Wahrnehmung), and further reinforced by the classification passage ^320/6377) in which he claims that intuition is a perception (Perzeption) that not only relates immediately to an object, but is single. But if any of these claims were, in fact, true - if the 'savage's' perception of what we recognize as a house were 'mere intuition' - then synthesis under the categories would not be necessary to effect a unity of apperception and thereby become conscious of anything manifold. Thus, a crucial premise of the Transcendental Deduction - the claim that all connection is an act of intellect (6129-30) and that a collection of matters can never be brought to consciousness in so far as it is merely presented through the senses, but only in so far as the matters are connected in a single thought (6132-3) - would fail. For the argument of the Transcendental Deduction to be correct, the 'savage' must be supposed either to see nothing at all (which is implausible) or to synthesize the variety presented in intuition under some other concept (in which case perception is not 'mere intuition' but intuition rendered intelligible through intellectual processing). Assuming that the claims of the Transcendental Deduction are correct, we are left having to admit that Kant's claims about the singularity of intuitions and the generality of intellectual representations are throwbacks to the earlier position of ID and that this earlier position was never fully worked out of his later thought - particularly his thought about the basic elements of logic.64 This confusion of senses is generated, above all, by Kant's unfortunate tendency to refer to intellectual representations as concepts - a term that he then defines in the traditional way as a general or universal representation. Taken in this sense, concepts are not all that intellect produces; it also produces perceptions of particulars. But Kant uses 'concept' to refer to all intellectual representations, perceptions of particulars included. Then this terminology leads him to slip into thinking of all intellectual representations as general representations, ignoring that, by his own principles, representation of singular objects

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requires intellectual processing no less than does the abstraction of universals. At the same time, he persists in equating 'discursive' with 'intellectual' and in using 'intuitive' to contrast with 'discursive/ and this leads him to refer to non-discursive representations as singular intuitions, because the discursive representations are purportedly all general. Thus, he generates the appearance that singular representation somehow falls outside of the power of intellect. In this way, the traditional, scholastic scheme comes back to vex and confuse his account. There is a second possible cause for Kant's confusion on this matter. Occasionally, he uses the term 'intuitive' to refer, not to representations, but to the claims we make about how various representations are connected or related in propositions and judgments. One of the clearest instances of this is Prolegomena, §7, where he outlines a distinction between what he calls 'intuitive' and 'discursive' judgments. This distinction is identical to that between what he elsewhere calls 'synthetic' and 'analytic' judgments. An 'intuitive' (or synthetic) judgment is formed by noting that the truth of the proposition is instanced in some perception (or, in the case of a synthetic a priori proposition, by just the pure manifold present in all perception). A discursive (or analytic) judgment is formed by noting that the truth of the proposition follows from analysis of the component concepts. Inevitably, knowledge captured in 'intuitive' judgments ends up being referred to by Kant as 'intuition', even though the (sensory) intuitions have to first be processed into (intellectual) perceptions (and, in the case of synthetic a priori judgments, the pure elements of the perceptions have to be abstracted from the empirical by further processing) before the (so-called) 'intuitive' judgment can arise. This point is discussed more fully at chapter S.i.b, below. But once these confusions have been uncovered, they can be easily resolved with a verbal choice: either we can call all products of intellectual synthesis 'concepts/ whether singular or general, or we can legislate that the term 'concept' shall be reserved for thoughts of universals. If we take the latter route, however, we have to recognize that concepts, considered as universals, are no more than a subset of the representations delivered by intellect. If 'concept' means 'universal/ then it does not refer to the product of any intellectual process, but only to the products of a particular process: abstraction. In this sense, indeed, concepts cannot be singular or have mereological structure. But, in this sense, concepts are only one among the products of intellectual synthesis; there are also perceptions.

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Paralleling this second choice, we might also take 'intuition' to mean singular representation or perception. But if we define 'intuition' in this way, then we must recognize that 'intuitions' are not distinct from intellectual representations, but are a subset of intellectual representations: namely, products of the intellectual process of combination or figurative synthesis. However, anyone who adopts this usage must complement it by recognizing that there is another, importantly distinct sense, of 'intuition' in Kant. We cannot take Kantian intuitions to be simply singular intellectual representations. To do so would be to lose sight of other vital Kantian tenets: that pure intellect cannot deliver a cognition on its own, so that intellectual representations are empty without some content supplied by 'intuition/ and that space and time are forms of 'intuition,' and hence constitute a prior set of structures determining the form of possible intellectual syntheses. Preserving these claims requires recognizing a distinct cognitive capacity. And since Kant also refers to this capacity as 'intuition/ its separate existence must be preserved somehow in the terminology. Kant, unfortunately, did not use his terms in any consistent way. Sometimes, by 'intuition' he means intuition in what may be called the metaphysical sense: that of raw data for the cognitive process supplied by a distinct cognitive faculty. But sometimes, as in the passage about the 'savage/ he means it in what may be called the logical sense - which does not appeal to the activity of a distinct faculty at all, but merely to the (necessarily intellectual) experience of singular objects. Likewise, 'concept' sometimes means the product of intellectual processing which is the metaphysical sense - but sometimes means just a universal cognized through abstracting differentiae, which is the logical sense. Kant recognized this distinction between logical and metaphysical senses in the Introduction to his Logic (Ak, IX 36); but the body of that work, for obvious reasons, deals only with the former sense, and aside from this one instance Kant seems not to recognize the importance of distinguishing the senses, and frequently slides between them. This is why I said above (Part I) that Kant's logical terminology confuses his psychological, rather than the other way around. The mereological and the singularity criteria for distinguishing representations are not misguided, nor have Kant's commentators been wrong to raise them. But the distinctions they effect are really distinctions between different products of intellect. They are misplaced when taken as distinctions drawn between intuitions, in the metaphysical sense, and the products of intellect. The legacy of these misplaced dis-

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tinctions has been the utter confusion of Kant's purpose and method in the Transcendental Aesthetic and the Transcendental Deduction. The way to a successful reading of the first parts of the Critique begins with taking intuitions to be just immediately given data for the cognitive process.

2 The Distinction between

Form and Matter of Intuition

That which makes the manifold of appearance able to be ordered [A: be intuited as ordered] in certain relations I call the form of the appearance. (A20/B34)

Kant's argument in the Critique of Pure Reason grows out of two fundamental distinctions. The first is that between intuition and understanding (sense and intellect), the second that between matter and form. Having examined the intuition/understanding distinction in chapter i, I want to turn in this chapter and the next to a consideration of his account of, first, the form and, then, the matter of intuition. My goal in this is to establish that Kant thinks of the form of intuition as an order in which the matters of intuition occur, and that he thinks of this order of occurrence as spatial and temporal. I stress the word 'thinks' because my conclusions will be, at this stage, biographical rather than philosophical. The question of what justification he had for thinking these things can be taken up only in connection with his arguments in the Metaphysical and Transcendental Expositions. The Blindness Problem One matter bearing on justification needs to be addressed immediately, however, especially given the argument of the previous chapter. If, as Kant claims, intuitions without concepts are blind, then how could he have thought of intuitions under any rubric as specific as that of a spatiotemporal array of matters? And, even granting that he did think of them in this way, how could this be regarded as anything other than an error? These questions arise from an overassessment of the implications of blindness for Kant's thought.1 Blindness does not forbid us from saying

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anything about the representations delivered by intuition. It forbids us only from describing these representations in terms we take to be, for some reason, inaccessible to the intellect. Though intuitions without concepts are blind, intuitions with concepts are anything but. The whole function of intellect with its concepts is to raise the material given to us in intuition to consciousness, so that we will no longer be blind to it. There is no obvious impediment, therefore, to Kant arguing from the content of our intellectual representations back to their intuitive grounds. This is, in fact, what he does. Over the following sections of the Aesthetic, he proceeds by analysing our intellectual concepts of space and time and showing that these concepts contain certain differentiae that we could not have come to think in them had they originated from something originally given in the matter of intuition, from something originally supplied by intellect itself, or from something arising from an intellectual synthesis performed upon the matter of intuition. The argument is, then, that our concepts of space and time cannot be empirical concepts of the matter of intuition, pure intellectual concepts, or concepts of something constructed by intellectual synthesis of the matter of intuition. The implication is that the grounds of these concepts, space and time themselves, cannot be matters of intuition, forms of understanding, or products arising from cognitive processing of the matters of intuition. On the positive side, Kant's argument is that we can adequately account for the differentiae thought in our concepts of space and time only if we take these concepts to be of a form or order in which matters are originally disposed and presented in the act of intuiting. The implication is that the grounds of these concepts, space and time themselves, must be forms of intuition, where a 'form of intuition' just is the order in which what is intuited is presented and disposed in the intuition. Given the infinite (or indefinite) divisibility of space and time, it also follows that intuitions must consist of a multiplicity of distinguishable items what Kant calls a manifold (Mannigfaltige). This method of procedure has an unfortunate implication, however. It means that Kant's claims about the nature of an intuitive representation can be made only as the result of an argument. They cannot be simply stated at the outset. Accordingly, in §1 of the Aesthetic, when Kant defines his terms, it is not intuition that he describes as containing a manifold in space and time, but appearance. (The latter is a catch-all term that Kant uses to refer to anything that could be called an object of consciousness, whether within the mind or without - everything, that is, from raw, intuited data given prior to all intellectual synthesis [Ago/Biaz], to

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objects of perception [Gegenstande der Wahrnehmung] consisting of an array of qualitative matters barely thought under the categories of quantity and quality [as at 6207], to objects that are 'distinct from the representations of apprehension' [Objekte, Ai9i/B236], and hence from the Gegenstande der Wahrnehmung [6207].) Given blindness, he has no other choice; he has to begin by describing what is cognized by intellect. It should not be supposed, however, that simply because Kant describes 'appearance' as exhibiting an ordered manifold, he does not also hold the same about intuition. Establishing that Kant does indeed think of intuitive representations, first, as manifold and, second, as ordered is the job of the following section. i.

The Two Basic Features of an Intuitive Representation a. Multiplicity

Kant calls the representations delivered by intuition 'intuitions,' but he also has another, more descriptive name for them: he refers to them as a 'manifold.' For the reason provided above, it is merely appearance that is described as being a manifold in the passage from §1 of the Aesthetic that serves as the epigraph for this chapter. But Kant makes it clear elsewhere that 'manifold' is also appropriately applied in contexts where 'intuition' is the operative representation term. Transcendental Logic has a manifold of sensibility lying before it a priori, that is delivered by the Transcendental Aesthetic. (A76~77/BiO2) Sense, in its intuition, contains a manifold. (A97) Each intuition contains a manifold in itself. (A99) The manifold to be intuited must still be given prior to intellectual synthesis and independently of it. (6145)

These passages also make clear that it is not just intuitions in the logical sense (i.e., singular representations) that contain a manifold as far as Kant is concerned, but intuitions considered metaphysically, as the immediate representations delivered by the sensory faculty. (See chapter i, § vi, above, for a discussion of the logical and metaphysical senses of intuition.)

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'Mannigfaltig' means, literally, many-fold. A manifold is something that has many parts. When Kant characterizes intuitions as a manifold, he is saying that they are collections of many parts or items. This is the first basic feature of an intuitive representation. In opposition to the evidence I have cited, there is one well-known passage in which Kant appears to deny that intuition contains a manifold, and seems instead to endorse the contrary position that we only ever intuit one thing at a time. In this passage, A99, he writes that the manifold contained in an intuition would not be represented as such 'if the mind did not distinguish time, in the succession of impressions upon one another: for considered as contained in an instant each representation can never be other than absolute unity.' But the point Kant is seeking to make in this passage is a subtle one, and the passage needs to be considered carefully and in full. Each intuition contains a manifold in itself, that still would not be represented as such if the mind did not distinguish time, in the succession of impressions upon one another: for considered as contained in an instant each representation can never be other than absolute unity. In order therefore that, out of this manifold, unity of the intuition arise (as in the representation of space), first the summation and then the comprehension of this manifoldness is necessary, which act I call the synthesis of apprehension, because it is directed just at intuition, which indeed does present a manifold, though without an accompanying complete synthesis this [manifold] can never be brought about as such and certainly not as contained in one representation.

Note that, at both the beginning and the end of the paragraph, Kant says that intuition does originally contain a manifold: 'Each intuition contains a manifold in itself/ and '[intuition] indeed does present a manifold.' Were it indeed the case, therefore, that Kant also wanted to say in this passage that intuitions are not manifold but 'absolute unities/ then the passage would contain a clear contradiction. This fact by itself would have to disqualify A99 from the ranks of those texts that may be legitimately appealed to when attempting to found an interpretation of Kant. (The text could be subsequently explained by an interpretative theory founded on other evidence, but from a contradiction anything follows, so no contradictory text can be used to found an interpretation. Such texts can be made to justify anything.) To this needs to be added the consideration that Agg was deliberately excised by Kant from B. Thus, not only would the text contain a contra-

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diction (if Kant was indeed trying to say in it that intuitions are not in fact manifold), but it clearly cannot be accepted as canonical. Despite these problems, A99, interpreted as asserting that intuitions are not manifold (and so interpreted as foreclosing the possibility that intuitions could contain an array of distinct matters in space and time) has exerted a profound influence on a number of commentators. Perhaps no other passage expressly struck out of a subsequent edition by a philosopher has been so persistently taken to be an accurate reflection of the most central aspects of that philosopher's thought. Though the two reasons I have mentioned are by themselves adequate to justify dismissing A99 from any further consideration, it should be noted that, even were A99 taken to be canonical, the interpretation that has been placed upon it is far from obviously correct. As a careful reading of the passage shows (especially if accompanied by a reading of important prefatory material like A92-3), the passage is not, in fact, about intuited representations at all, but about representations of intuitions (note that 'of intuitions' here is intended as an objective, not a subjective, genitive: it is intuitions that are being represented, not intuitions that are doing the representing). As A92-3 indicates, Kant's whole purpose in the Transcendental Deduction is to explain how intuitions come to be thought under concepts. A99 contributes to this by remarking that, though intuitions themselves consist of a manifold of matters (incidentally arrayed in space and time), when those intuitions are thought or represented by concepts, certain special acts of mind are required to grasp this content. What happens when an intuition is thought, Kant is claiming, is that the spatial array of matters in the intuition is collapsed into an 'absolute unity.' Consider, by way of example, the image of a black triangle on a television screen. The image consists of thousands of small, black and white points disposed in a certain arrangement in space, and that is the intuition our senses deliver to us: a manifold of coloured points disposed in a certain manner. But when this array in space is brought to a unity of apperception under the concept 'triangle,' all this multiplicity is overthrown and what is represented is an 'absolute unity': a particular shape. It is not the intuition in space that is an 'absolute unity,' therefore, but the subsequent (conceptual) representation of the content of this intuition when it is thought. But, Kant notes, it is not only the spatial manifold that gets collapsed by the process of thought. With time, things are a bit more complex, but the end result is still the same. The mind seems to distinguish automatically the moments of time over which intuitions occur, and so, whereas

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it collapses the manifold in space at any instant as an 'absolute unity/ it continues to distinguish the different times over which the intuition occurs as so many successive and distinct representations.2 (This difference in the way spatial and temporal manifoldness is processed probably has to do with the fact that time is a form of inner sense.) But the temporal manifold needs to be collapsed into an 'absolute unity' under concepts, too, if anything is to be thought. (Just as an experience of thousands of black and white dots is merely an unintelligible mass until it is brought to an absolute unity under the concept 'triangle', so an experience of a successive series of 'impressions' can mean nothing to us until it, too, is unified under the concept of some event or other.) This is what necessitates the summation and comprehension of the manifold that Kant describes in the passage. In both the case of space and that of time, however, the point is that it is acts of the mind that collapse the manifold into an absolute unity when the intuition comes to be represented in thought. The intuition itself, however, consists of a manifold of component representations, as Kant is twice at pains to point out in the passage.3 Thus, those wishing to argue that spatial and temporal order first arise from intellectual or pre-intellectual (but post-sensory) acts of synthesis because intuitions are 'absolute unities' that contain no manifolds and nothing, therefore, to be ordered in space or time, will have to look elsewhere than A99 for evidence for their thesis. That passage does not establish any such conclusion, and, if it did, it would contradict itself. Either way, it is an unacceptable foundation on which to build an interpretation. b. Order There is something else Kant means to convey when he describes intuitions as containing a manifold. For him, a manifold, in addition to containing a number of parts, exhibits a certain order or form. As already implied, this is the spatiotemporal order. Once again, the problem with blindness prevents Kant from making this clear. In the lead passage from A2O/B34, he does indeed make reference to a certain order that the manifold is supposed to have. But this order is again described as present only in 'the appearance,' not in 'the intuition.' What is more, in B, Kant makes a significant alteration, that appears to take him even farther from any commitment to the notion that the order

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might actually be present in the manifold in intuition. Whereas in A he had written: 'that which makes the manifold of the appearance be intuited as ordered in certain relations I call the form of the appearance/ in B he changed 'geordnet, angeschaut wird' to 'geordnet werden kann' "that which makes the manifold of the appearance able to be ordered in certain relations/ The impression given by the change is that the order of the manifold, far from being given in the intuition, is something that merely 'can be' determined through reference to some 'form/ Apparently, 'form' here does not refer to the order itself, but rather to some ground through which this order may or may not be determined, depending on whether or not we attend to performing the task. This gives an alternative explanation of why Kant ascribes the ordered manifold to 'appearance' rather than to 'intuition/ If the order of the manifold is subsequently determined only through reference to some 'form/ then that order could not be said to be 'intuited/ that is, immediately given. These remarks are not just isolated aberrations of the A and B Aes thetic. They appear to be confirmed by a number of passages in the later Transcendental Analytic that have been read as advancing the thesis that space and time are originally generated by a synthesis of imagination or understanding. Notable in this regard are A99-ioo, 102, 120 6137-8, 151-2, 154-5, 156, i6on; and Ai43/Bi82. After what has been said above in connection with A99, many of these passages should already seem less than convincing. By and large, they claim only that imaginative or intellectual synthesis is necessary for us to generate a (conceptual) representation of a spatiotemporal order and do not rule out the possibility that a spatiotemporal order of representations is originally given in intuition. The view that imaginative or intellectual synthesis maps portions of an already given spatiotemporal manifold of representations onto a single, metarepresentation of a delimited and determinate space and time reads very well with these passages. But a number of commentators have none the less taken one or more of them to justify the more radical view that synthesis is what originally creates space or time.4 According to these commentators, Kant took the parts of the manifold to originate from sensory experience, and its form to consist in certain 'inborn laws of the mind' in virtue of which, guided by qualitative features of these parts, it imposes order on the manifold.5 On this view, sense intuition presents us with an unordered collection of matters. To put it crudely, sense dumps its deliverances on us all in a heap6 - a heap in which there is no such thing as succession in time or

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adjacency in space - and this heap of items is then subjected to a sorting and arranging process of the mind, guided by certain forms or 'inborn laws' that first produce an ordered 'manifold of appearance/ For this reason, I refer to this interpretation of Kant as the 'heap thesis.' There is some corroboration for the heap thesis to be found elsewhere in Kant's work, both early and late. Perhaps the most explicit statement he ever makes in accord with it is to be found in §4 of ID: In a representation of sense there is ... something which can be called the form, namely, the specificity of the sensibles which arises according as the various things which affect the senses are coordinated by a certain natural law of the mind ... [The form of the representation is] only a certain law implanted in the mind by which it coordinates for itself the sensa which arise from the presence of the object. For objects do not strike the senses in virtue of their form or specificity. So for the various things in an object which affect the sense to coalesce into some representational whole, there is needed an internal principle in the mind by which those various things may be clothed with a certain specificity in accordance with stable and innate laws. (Ak, II 392-3) And the position appears to be endorsed not only at the beginning of Kant's Critical career, but towards the end as well. Thus, in the Entdeckung, he writes: The Critique permits absolutely no implanted or innate representations. All whatsoever, whether they belong to intuition or to intellectual concepts; it takes to be acquired. But there is also an original acquisition (as the teachers of natural right put it), consequently also [an acquisition] of that which previously did not exist, that is, which did not belong to anything prior to this act [of acquisition]. Such is, as the Critique maintains, first, the form of things in space and time, second, the synthetic unity of the manifold in concepts. Our cognitive capacity does not take either of these things from objects, as something given in objects as they are in themselves; rather, it brings them into place a priori, out of itself. But there must certainly be a ground of this in the subject, that makes it possible that the aforementioned representations appear so and not otherwise, and can be referred even to objects that have not yet been given, and this ground at least is innate. (Ak, VIII221-2) (i) Forms as Mechanisms and Forms as Representations A slight variation on the heap thesis has it that the 'forms' are not principles or laws for generating an ordered manifold but are themselves ready-made, empty

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containers pre-existing in the mind and waiting to be outfitted with incoming matters. In light of the passages just cited, this variation might initially appear implausible. The notion that the order of the manifold exists ready-formed in the mind runs up against Kant's explicit rejection of innate representations in the Entdeckung. A similar rejection is also to be found in ID, §§8 and 15 (AK, II 395 and 406). In these works Kant's position at least appears to be that the representation of order is produced, perhaps with the help of a certain innate 'ground' or set of laws or principles, but is not itself innate. None the less, this second variant of the heap thesis (I will call it the "forms as representations view' to distinguish it from the first, 'forms as mechanisms' view) does gain a certain credence when one considers that Kant will go on to identify the 'forms' in question with space and time per se, not with some principle for producing spatiotemporal order (A39/B56, Bi6o, 202; A267/B323; A/23/ 6751; also A31/B47, A87/Bi2o), and that he will even go on to claim that space and time, as 'pure forms of intuition/ can be cognized prior to any actual perception (notably A42 7659-60, A373) - something that could hardly be the case were spatiotemporal order generated only by a lawgoverned procedure performed upon the matters of intuition. For this reason, Vaihinger, the major champion of the forms-as-representations view, maintained that Kant waffled in his position on the forms of intuition, sometimes (as in ID and the Entdeckung) maintaining that the forms are principles for generating spatiotemporal order, and at other times holding that they are ready-made spatiotemporal containers lying in us as representations in their own right and accessible for inspection independently of the sensory process.7 Despite the differences between them, however, both the forms-asmechanisms and the forms-as-representations views are agreed in taking the matters of the manifold, and the order of these matters, to arise from two quite distinct sources, the former from the activity of sensing, the latter from a separate source in the mind. On both views, the order of the manifold of appearance is the result of a process - either the process of generating order by some law-governed procedure performed on the already given parts, or the process of coordinating the unordered but already independently given parts with locations in an innate container. (ii) Forms as Orders of Intuited Matters In what follows, I argue that both versions of the heap thesis are incorrect. For Kant, the manifold is ordered in the intuition, not just in 'appearance,' and the order of the manifold originates from the same source as its matter - the reception of

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the parts of the manifold. This is not to say that Kant reduces the order of the manifold to a matter of intuition. Rather, Kant takes an ordered manifold of parts or 'matters' to be the representation immediately given in sense intuition. The representation delivered by intuition is not just a heap of matters. In intuition the matters are given in space and over time, so that the intuiting subject intuits, not just the individual characteristics and the number of these matters, but the order in which they occur as they are given before and after and alongside one another. This order is something distinct from the matters in the same sense that the ordering relation '>' is distinct from the elements of the set {i, 2, 3,... }. Just as the ordering relation is not itself an element of the set it governs, so for Kant 'that within which sensations can alone be ordered and set forth in a certain form cannot itself in turn be sensation' (A2O/B34). But, for Kant, the ordered set (the manifold) is something given in experience, so that the order in which matters or elements are disposed is just as much a piece of information immediately given in intuition as is information about the given matters or elements themselves. ii.

Textual Evidence against Forms as Mechanisms

There is a general, textual consideration that tells against the forms-asmechanisms reading. This is that, throughout the Critique, Kant calls the forms of the manifold 'forms of intuition/ But, as noted in chapter i, above, by 'intuition' Kant most often means to designate what is first given to or immediately received by us. Intuition contrasts with production, intuited form with produced form. Were Kant really of the opinion that the form of the manifold is produced by imaginative or intellectual synthesizing of sensations in accord with certain principles, he ought to have named them differently. He did not lack the vocabulary to do so. He could have spoken of forms of perception or forms of apprehension. He did not.8 Admittedly, Kant does occasionally use 'intuition' to refer, not to immediate cognition, but to the (necessarily mediate) cognition we have of particulars or singular objects. This opens the chance that by forms of intuition he might just mean 'forms of particularity7 or 'forms of singularity.'9 But this reading is challenged by the fact that Kant often further qualifies his references to the forms of intuition as forms of sense intuition (Bxxv, 137,148,160; A272/B328; A373; Prolegomena §13 [Ak, IV 285, 288]; Anfangsgriinde [Ak, IV 481], to name but a few of many occurrences), that is, as forms of the representations given through the recep-

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tive, not the spontaneous cognitive faculty. Such general and persistent use of terminology is inexplicable in the forms-as-mechanisms reading. Besides this general point, the forms-as-mechanisms reading is challenged by a number of particular texts and arguments. Notably telling in this regard are the later arguments of the Metaphysical Expositions (A24-57639-40, A31-2/B47-8).10 Kant's purpose in these passages is to argue that space and time, which he will want to identify as the forms of intuition, are not what he calls 'discursive or universal concepts' but rather are originally given in intuition. 'The original representation of space is an a priori intuition/ he writes at 640, 'not a concept.' And, at A32/B48, he notes that 'the original representation, time/ must be grounded in an 'immediate intuition.' Whether or not the particular arguments Kant uses to establish these conclusions are successful, the fact that the conclusions are affirmed at all establishes that he at least believed space and time to be forms of intuition, where 'intuition' is taken to mean immediate (i.e., original) representation. The Later Expositions are also noteworthy for invoking the claim that, with space and time, it is the whole that is first given, and the parts that emerge by a process: that of delimiting or introducing boundaries in the whole. This claim would be quite incongruous were Kant's view that space and time are generated by an imaginative synthesis of sensory matter governed by certain 'process forms.'11 If Kant really thought space and time first emerge in this way, then there would be 'parts' originally given, and then assembled by a synthesis. Kant would not insist that space and time are unities that precede their parts and that must be supposed to be originally represented in 'intuition.' And he would not say that the 'original representation' of space and time is 'immediate intuition.' A further reason for accepting that Kant took the manifold to be already ordered in the intuition comes from A2O-1/B35 and A22/B36. These are the passages at the end of §1 of the Aesthetic, where Kant claims that his project over the coming pages will be to take our ordinary human experience and isolate that element in it that is attributable to intuition, and then further remove from this result everything in intuition that is attributable to sensation, in order to prove that there is something left over namely, space and time as 'pure forms' or orders in which the 'matters corresponding to sensation' are disposed in the intuition. These 'isolation passages' were discussed in chapter i, § iii, above, and there it was noted that, considered as statements of a research project, they are in contravention of blindness, and therefore totally impracticable. The result of

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actually removing 'everything that intellect thinks through its concepts from experience' would be something that, as Kant himself says elsewhere, 'would be for us as good as nothing' (Am). None the less, the passages do have value when read, not as statements of a proposed research project, but as a description of the genetic relations Kant conceived space, time, sensation, intuitions, and concepts as having to one another. Seen from this perspective, the isolation passages tell us that space and time are so far from being constructed by synthesis that it would ideally be possible to find them already contained in an intuition considered in abstraction from any contribution of intellect (in abstraction, notably, from any 'transcendental synthesis of imagination/ if we follow 6152 in taking this synthesis to be 'an action of intellect on sensibility'). The implication is that raw sensation already exhibits spatiotemporal form before intellect or imagination make any contribution to it. Aside from the Aesthetic, there is at least one other outstanding confirmation of this view to be found in the Kantian corpus. This is Entdeckung (Ak, VIII203), a passage that appears to start off by admitting that space and time are produced by a synthesis of the higher faculties, but then completely undercuts this view by claiming that the material these faculties are given to work with must already be spatiotemporal: One can and must admit that space and time are mere thought entities and things of the imagination. This is not to say that they are invented by the latter, but rather that they lie as a ground of all its combinations and inventions. This is because they are the essential forms of our sensibility and the receptivity of our intuitions, through which all objects are given to us.12

Space and time are not the products of some unnamed ground in the cognitive faculties. As forms of sensibility, they are the ground of all subsequent imaginative or intellectual processing. iii.

Textual Evidence against Forms as Representations

Even though Kant calls space, time, and the forms of the manifold 'sense intuitions,' it remains a question how these forms come to be present in the intuition. One possibility is that they originate along with the matters as the manner in which the matters occur. Another is that they originate in distinct 'pure' intuitions, with which intuited matters are only subsequently coordinated. On this latter, 'forms as representations/ view, sense intuition is merely a generic label for two distinct kinds of

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intuition: pure intuition of spatiotemporal form and empirical intuition of matters. The spatiotemporal manifold of matters is taken to be the product of a coordination of the two. On the former view, the situation is reversed: all sense intuition is originally of a spatiotemporal manifold of matters, and both pure 'intuition' of space and time and pure sensation are abstractions from this originally given manifold. The major piece of evidence for the 'forms as representations' view is A20/B34, where Kant describes the form of intuition as 'lying ready a priori in the mind/ and its major proponent has been Hans Vaihinger. In the section of his Commentar devoted to the sentence 'the form of intuition lies ready a priori in the mind' (A2O/B34)/3 Vaihinger attacked Riehl, Meyer, Lange, and (of course) Cohen for maintaining that Kant takes the forms of intuition to be merely logically distinct from sensation and not also temporally prior to it, given through a distinct act of mind. According to Vaihinger, 'a priori' means 'given prior to sensation in time.' Space and time actually exist as complete, infinitely extended and infinitely divisible 'representations' lying in the mind and accessible to cognition even prior to our first sensory experience. This view Riehl, Cohen, et al., took to be obviously absurd.14 So did Vaihinger, but he realized (quite correctly) that the obvious absurdity of a view is no reason to suppose that Kant did not hold it, and he went on to cite in excess of fifteen passages from the Aesthetic, the Prolegomena, the Analytic, the Fortschritte, and the Reflexionen which he took to be clear indication that Kant did hold it. But though Kant was not incapable of maintaining an absurd position, we should carefully weigh the evidence that he did so against the evidence that he did not. In this regard, there are six considerations to bear in mind. First, Kant explicitly says in the B Introduction that 'there is no cognition to be found in us that precedes experience with respect to time, and it is with experience that all cognition begins' (Bi). He goes on to remark, of course, that it does not all arise out of experience, but the point is made that our a priori cognitions are not prior to experience in time but prior in another sense. Second, Kant refers to the spatiotemporal sensory manifold as 'empirical intuition' (for instance, 6146-7, A239/ 6298), though he had the terminology available (for example, 'perception' [Wahrnehmung], appearance, experience), had he wished to indicate that this manifold is not intuited but is the product of a synthesis.15 Third, Kant repeatedly stated that what he variously referred to as 'empty space' or 'time' are not objects of a possible experience for us.16 Given this, how could representations of pure space and time exist in us

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prior to all sensation? Fourth, the 'original acquisition passage' from Entdeckung (Ak, VIII 221-2; cited earlier) indicates that Kant was no friend of innate representations and went to some lengths to distance his theory from any such associations (though he was willing to posit innate cognitive mechanisms or innate dispositions). Fifth, there is at least one passage where the forms-as-representations view is explicitly rejected: Empirical intuition is thus not put together out of appearances and space (perception and empty intuition). One is not the correlate of the other in a synthesis; rather they are bound together in one and the same empirical intuition, as matter and form of this intuition. (A429n/B457n)

Finally, besides the textual evidence that may be cited against it, there is a problem with the view, considered on its own merits. (While the fact that a view is problematic is by itself no reason for supposing that Kant did not hold it, such considerations cannot be entirely dismissed. This is especially the case if the problem is an obvious one that Kant did not address but could reasonably be expected to have tried to address had he, in fact, held the view.) The innate-representations view generates a localization problem. It demands an account of our ability to correlatively apprehend space and the matters due to sensation. Why should I represent one collection of matters as square, another as triangular; one as oval, another as round?17 There could be no ground of this in the pure intuition of space because it makes no reference to any matter. But the matters themselves are only supposed to acquire their order through being placed in space. Kant is left having no way to explain why we place matters in one location rather than another18 - no answer, that is, if he takes form and matter to originate from distinct sources. But the textual evidence cited above indicates that Kant took the locations of matters to be given in empirical intuition along with those matters, not to be subsequently assigned by the mind. This, in turn, indicates that his failure to address the localization problem might be attributable, not to oversight, but to the fact that he did not hold the view that generates such a problem. Vaihinger was not unaware of the textual evidence against ascribing the forms-as-representations view to Kant. His response,19 one typical for him, was to claim that Kant simply contradicted himself. In his Inaugural Dissertation and in the Entdeckung, Kant is supposed to have propounded a forms-as-mechanisms view. But, in the Transcendental Aesthetic, he is supposed to have been forced to advocate a forms-as-

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representations view instead. The note from the Antinomies (A^2^n/ B475n) is dismissed as a position that might possibly be intended to represent the antithesis view of the Antinomy rather than Kant's own view,20 as, in any case, applying merely to cosmological space rather than to epistemological (erkenntnistheoretischem) space,21 and as an isolated statement that clearly contradicts what Kant says in the Aesthetic.22 But Vaihinger's case for 'clear contradiction/ his more than fifteen citations, with their boldface treatment of the words 'ohne/ 'vor/ 'ehe/ and 'vorher/ merely begs the question against Cohen, Riehl, and the others who read these passages as merely metaphorical descriptions of the independence of space and time from determination by the matter of intuition. It is here that we come to the real linchpin of Vaihinger's position. He claims that the 'spirit' and not just the 'wording' of the Transcendental Aesthetic requires that space and time be genetically distinct from the matters attributable to sensation, and temporally prior to them. The reason the spirit of the Critique requires this is that space and time, as forms of intuition, are supposed to be a priori representations. And, Vaihinger claims, this could be possible only if space and time originate from some source other than sensory experience. Were they given in sensory experience, they would be empirical and not a priori.23 This argument is not one that can be quickly or easily dismissed. Dealing with it properly requires a short digression to look back at Kant's views on the nature of experience and empirical knowledge. In the B Introduction, Kant remarks that, while all cognition may begin with experience, part of the content we end up cognizing as a result may be spontaneously injected by the mind into the material we properly 'sense through impressions' (Bi). While Kant does not, at this stage, want to affirm that there must be such extrasensory elements in our cognition, he does pause to define an 'a priori' cognition as one that would indeed be 'independent of experience and especially of all impressions of the senses/ Later, of course, he goes on to insist that space and time are a priori representations (A42/B6o). At A19-2O/B34, he also goes on to define 'that which we sense through impressions' (or 'the effect of an object on the representative capacity so far as we are affected by it,' as Ai9-2O/B34 puts it) as sensation, and to note that the matter of intuition 'corresponds' to sensation. Putting these remarks together, we can see that Kant paints a picture of cognition as originating from two distinct sources - sensory impressions and spontaneous contributions made by the mind on the occasion of sensory impression - and that he identifies

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the matter of intuition as the product of the former, and space and time as products of the latter. There are at least two ways in which this picture can be interpreted, however. One of them would take impression of the sense organs and certain characteristic features of the subject's 'constitution' to be the joint causes of a single, complex intuition, a representation containing both sensory matter and spatiotemporal form in an immediately given spatiotemporal sensory manifold, but with it understood that the subject's constitution is the ground determining the spatiotemporal form of the manifold whereas impression of the sense organs is the cause only of its matter. The other way of interpreting Kant's picture would take there to be two distinct intuitions: one an a priori intuition yielding representations of empty space and time, the other an empirical intuition resulting from impression of the sense organs by external objects and yielding sensations. On the first view, the sensory mechanism that first presents raw data, that is, intuitions, to us would already present an integrated manifold, though two distinct causes would have concurred in its creation. On the second, a cognitive process would be required to synthesize two distinct types of primitively given data.24 Unlike the second view, the first view allows Kant to claim that there are a priori forms 'lying ready in the mind' without having to commit himself to the existence of two distinct kinds of intuition. On the first view, though all intuition is originally empirical intuition (of a spatiotemporal sensory manifold), this original, empirical intuition has a non-empirical component that can be isolated from the only properly empirical component in the intuition and identified as a necessary aspect of all intuition whatsoever. Vaihinger opts for the second reading, but the texts in no way force us to choose it in preference to the first. On the contrary, the range of texts cited above as evidence against the forms-as-representations view indicate that the first reading ought to be preferred: Kant explicitly says in the note to the Antithesis of the First Antinomy that space and time are originally given along with the matter of intuition in an empirical intuition, he repeatedly denies the possibility of an experience of empty space and time, he rejects innately originating representations in the Entdeckung, and he refers to the spatiotemporal sensory manifold as empirical intuition. Furthermore, were sensory impression and subjective constitution jointly responsible for the production of a spatiotemporal manifold, then the manifold as a unit would be originally given and the task would be, first, to establish that space and time, as forms of this

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manifold, do not arise just from impression of the senses, and, second, that they are attributable to the subject's constitution. And we find that Kant does indeed concern himself with these tasks, undertaking the first in the earlier paragraphs of the Metaphysical Expositions, and the second in the Transcendental Expositions and the 'Conclusions from the Above Concepts.' Had Kant's position rather been that pure spatiotemporal form and pure sensation are separately intuited, then he should have been concerned to explain how the two come to be coordinated in perception - a worry that he seems never to have had.25 There is one final consideration I want to bring up in this regard. It is not conclusive, but it is telling. Above (chapter i, introductory section), it was noted that careful attention needs to be paid to the ancient and medieval meanings associated with the technical terms Kant employs. 'Matter' and 'form' are two such terms. They have not only great antiquity but also a fairly clear and widely accepted meaning. They refer to two aspects of one substance - aspects that, while they may be distinguishable by the mind, cannot exist separately in nature. Given this usage, it would have been incongruous for Kant to adopt the terminology of form and matter to describe the relation between spatiotemporal order and the matter of intuition. The terminology of matter and form indicates that matters, on the one hand, and spatiotemporal form, on the other, are intellectual abstractions from an originally given sensory manifold, not distinct components, compounded in an empirical intuition. a. Kant's Groundless Assumption? There is a classic objection to Kant, motivated by the forms-as-representations view, that deserves some mention in this connection. This is the objection that Kant quite arbitrarily assumes 'that sensations cannot have spatial properties,'26 that he excludes, 'from the very beginning, the possibility that the temporal manifold might be given with the material of sensibility/27 and, in general, that he contends falsely that the relations of sensations cannot themselves be sensed.28 There is a way in which this objection ascribes to Kant a view he does not, in fact, maintain, and there are a couple of ways in which it correctly represents him but misses his argument and the groundwork he carefully lays for his conclusions.29 In one sense, the objection misrepresents Kant because he does not, in fact, believe that space and time are given to us apart from the matters that correspond to sensation. On the contrary, his position is that space

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and time are given together with the matters of the manifold in one and the same sensory experience, which he calls an 'empirical intuition.' Of course, Kant does want to say that, though spatiotemporal form and sensory matter are given together in a single sensory experience, space and time may, as forms, be distinguished from the matters of the manifold. In this sense the objection does ascribe to Kant a view to which he is committed. But the view is hardly a groundless one. Rather, it is grounded on the observation that the order in which the elements of an ordered set are arranged can be described independently of specifying exactly what elements are placed in that order - something that is practised in any textbook on topology, number theory, or the logic of relations. In so far as Kant's position on this issue stands in need of justification, it is only with reference to his claim that space and time are indeed the orders in which the matters or elements that are intuited are presented in the intuition. This, far from being something he arbitrarily assumes, is something he at least tries to prove in the Expositions. Finally, it has to be admitted that Kant wants to say more than just that space and time are distinct from the matters that are intuited. He also wants to say that they originate from a distinct source. Though space and time are given together with matter in one and the same empirical intuition, the spatiotemporal component of this intuition is supposed to be attributable to the constitution of the subject, and the various matters to impression of the senses. The matters of the manifold are therefore 'sensed' (they are products of stimulation of the sense organs) whereas the order of these matters is not given in sensation but is only 'intuited.' Whatever we may think of this claim, it is far from being one that Kant arbitrarily assumed. The arguments he gave for it may not be very good ones, and they may even turn out to violate his own restrictions on making claims about things in themselves, but unquestionably he did struggle to prove the subjectivity of spatiotemporal form and the non-spatiotemporality of things in themselves. There is no sense, therefore, in which Kant makes a groundless assumption about the distinction between space and time and the matter of the manifold. iv.

Conflicting Passages

It remains to consider a number of passages often cited as indications that Kant intended to propound a forms-as-mechanisms or formsas-representations view.30 Some of these passages can be dismissed

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because of their ambiguity. Among these are the passages cited by Vaihinger. Though Kant does refer to space and time as existing prior to and apart from sensation, this does not entail his having taken space and time to be independently originating representations. Were space and time originally given along with the matter of sensory impressions, but not determined by that matter, then, too, they would be 'prior' to sensory impression - in the sense that they are the way they are independently of what specific sensory impression may happen to occur. In this case we could know in advance that no datum uncovered in the matters we experience could ever undermine or falsify any knowledge we might have of the formal features of the manifold. We would know this in advance because we would know that the content of the matters in the manifold is simply irrelevant to the manner in which they may be ordered in the manifold. Under such circumstances it would not be an abuse of language to refer to the form of the manifold as 'lying ready in the mind for the matter.' On the contrary, this would be an effective metaphor for getting the point across. A similar ambiguity infects Kant's occasional references to space and time as pure or formal intuitions given in isolation from all matter (for instance, at Prolegomena §7 [Ak, IV 281]). If what I have said is correct, then Kant's position is that space and time are never intuited as pure, empty forms existing apart from matter. But this does not preclude him from referring to them as 'pure intuitions/ provided that he means thereby only to refer to them as the pure or formal aspect of the originally given sensory manifold, or as the pure or formal aspect that has been obtained from the originally given sensory manifold through the (necessarily intellectual) act of abstracting the content from the intuition and thinking the form that remains. However, other passages call for more detailed consideration: §4 of ID, Kant's references to innate grounds in the original acquisition passage from the Entdeckung, his remarks on objective and subjective spatiotemporal orders in the Analogies, those places in the Transcendental Deduction where he seems to indicate that the spatiotemporal order might be the product of a figurative synthesis of imagination, and his alteration to A2O at 634. In what follows I consider each of these texts in turn. Those already familiar with this debate will remark that there is one classically cited text which I do not consider: Bi6on. This passage must be relegated to that group of texts that are explained by an interpretation of their author's thought. It cannot belong to that group of texts that jus-

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tify such an interpretation. It cannot do so for the simple reason that it is so obscure that it can be made to serve the needs of any interpretation whatsoever. From a contradiction, anything follows, and any text that contains two assertions like (a) 'this unity [of space and time]... presupposes a synthesis ... through which all concepts of space and time are first made possible/ and (b) 'the unity of this intuition [of space and time] belongs a priori to space and time and not to the intellectual concept' is close enough to exhibiting a contradiction that it makes it possible to get virtually any conclusion one pleases out of the passage with only minor effort.31 a. ID

The evidence that Kant adhered to a forms-as-mechanisms view in ID is simply too pervasive and unambiguous to permit any other reading. But ID is not the Critique, and, despite the superficial similarities between the Aesthetic and Section III of ID, it is a mistake to affirm any similarity in aims, arguments, or presuppositions between the two works without good reason. Chapter i, above, has already exhibited a number of respects in which Kant's position and arguments in ID differ from those in the Aesthetic. ID cannot, therefore, be taken as strong evidence for Kant's later views. If he held a version of the heap thesis in the Critique, that will have to be established by what he says in that work. b. The Original Acquisition Passage Next to ID, the strongest indication of an inclination towards a forms-asmechanisms view comes from the original acquisition passage in the Entdeckung, already cited above: The Critique permits absolutely no implanted or innate representations. All whatsoever, whether they belong to intuition or to intellectual concepts, it takes to be acquired. But there is also an original acquisition (as the teachers of natural right put it), consequently also [an acquisition] of that which previously did not exist, that is, which did not belong to anything prior to this act [of acquisition]. Such is, as the Critique maintains, first, the form of things in space and time, second, the synthetic unity of the manifold in concepts. Our cognitive capacity does not take either of these things from objects, as something given in objects as they are in themselves; rather, it brings them into place a priori, out of itself. (Ak, VIII221)

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This position is familiar from Kant's claim in the B Introduction (Bi) that, though all knowledge begins with experience, not all need arise out of experience - it might be that 'even our experiential cognition is a composite of that which we receive through impressions and that which our cognitive capacity (merely occasioned by sensory impressions) brings out of itself.' However, the claim from the Entdeckung is more sophisticated than the Introduction passage. The Introduction lends itself to the reading that space and time are innate images pre-existing in the mind. The Entdeckung passage makes clear that this is not intended. Space and time are instead 'originally acquired' - acquired, that is, in the way a builder acquires a house - by working on the given raw materials to create something that did not exist prior to the act of building. Unfortunately, in offering this qualification, Kant appears to be steering his boat around the Scylla of the forms-as-representations view only to have it swallowed by the Charybdis of the forms-as-mechanisms view. For, by putting the point this way, Kant hints that space and time are originated or produced - originated or produced, moreover, by the mind itself, out of something that it brings, as he puts it at the end of the passage cited, 'out of itself.' The position appears to be that, even if space and time are not themselves innate ideas, there is something else in the mind in virtue of which it originates or produces space and time on the occasion of experience. This position is endorsed by the immediately following sentence in the Entdeckung: But there must certainly be a ground of this in the subject, that makes it possible that the aforementioned representations appear so and not otherwise, and can be referred even to objects that have not yet been given, and this ground at least is innate. (Ak, VIII221-2)

However, just a little farther on in the 'original acquisition' passage, Kant makes an important qualification that recasts the whole passage in a radically different light. The innate ground that determines the appearance of space and time is, he tells us, not a mechanism for producing spatiotemporal order out of sensory experience; rather, it is a ground for receiving sensory experience: The ground of the possibility of sensory intuition is ... the mere characteristic receptivity of the mind, to acquire a representation according to its subjective constitution when it is affected by something (in sensation). This first formal ground, for example of the possibility of the intuition of space, is alone innate, not the representation of space itself. (Ak, VIII222)

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This is no isolated, accidental turn of phrase. Whereas, in ID, Kant had written that the mind coordinates its sensa and clothes things with a certain specificity in accordance with stable and innate laws, in all his later works there is a striking change to this description of what is going on. He never uses the vocabulary of sorting or producing to describe the relation between the order of the manifold and its ground. In the Entdeckung, the order of the manifold is grounded on 'the mere characteristic receptivity of the mind, to acquire a representation according to its subjective constitution'; in the Critique, it is 'the formal constitution whereby [the subject] comes to be affectedd by objects' (641; my italics); i the Prolegomena, it is 'the essential property of our sensibility, by means of which objects are given to us' (Ak, IV 287; my italics); and, perhaps most ominously (for the heap thesis), in the Fortschritte, it is simply 'the way our senses are affected by objects' (Ak, XX 269; my italics).32 The difference here is crucial for understanding Kant's position on the forms of intuition. To make it more perspicacious, consider once again a point made earlier, in response to Vaihinger's assertion that Kant's commitment to a separate source for the form of intuition (the 'constitution of the subject' as opposed to 'impression of the senses') demands that space and time be recognized as pure intuitions existing in the mind prior to all sensory experience. The answer to Vaihinger was that there are at least two ways in which Kant could be read. One reading is Vaihinger's and is shared by the forms-as-mechanisms view. On this view we have either two quite distinct kinds of intuitive representation that are then coordinated by a cognitive process (or, if we follow Vaihinger, left uncoordinated owing to oversight) or one type of purely empirical intuition, and the spatiotemporal order of the matters in this empirical intuition is created entirely by cognitive processing. The second view, in contrast, takes sensory impression and the constitution of the subject to be joint causes operating prior to any cognitive processing to deliver an integrated spatiotemporal sensory manifold as originally intuited representation. In other words, whereas the first view takes some spontaneous act of the mind, operating on its immediately given representations, to produce the spatiotemporal sensory manifold, the second takes this manifold to be originally received as the immediate effect of impression of the senses of a subject with a certain sensory 'constitution.' But it is just this shift, from a vocabulary of active sorting and arranging to a vocabulary of receiving, that characterizes Kant's later pronouncements on the form of intuition. Kant's shift in vocabulary designates a shift from the first to the second view.

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The passages from Kant's later works still maintain that there is some 'ground' of spatiotemporal order existing in the subject prior to all experience. But Kant has retreated from the view that this ground consists of a mechanism or a set of principles for the synthesis of incoming matters. Instead, he has placed this ground in the lower cognitive faculty, in the 'constitution' of the subject's senses. Rather than arise from a cognitive process (be it the drawing of an inference from previously given data in accord with rules of judgment or the mere association of previously given data in accord with principles grounded in our nature), the spatiotemporal sensory manifold arises through the precognitive, sensory process that originally delivers data to the cognitive system. Some examples might help to make clearer just how this might happen. Consider a computer set up to do word processing. The computer receives input when its keys are struck - striking its keys is what brings it to receive information. But the information received by the computer does not exhibit just 'matter' (which is different, depending on which keys are struck); it also exhibits a certain 'form' - the form, namely, of succession in time. While the computer may store the information it has received in spatial arrays or display processed products as a manifold of alphanumeric characters in two dimensions on a screen or on paper, it can receive information only successively in time. (Indeed, the fundamental task performed by a word processor is just to transform a temporal array of keyboard impacts into a spatial array of characters on paper.) Because of the way it is built, the computer cannot accept simultaneously entered input. When the keys are struck simultaneously, it jams (it has an 'unintelligible experience'), or it ignores the input, or it arbitrarily selects one character and presents it alone or first. This is not a 'software' feature - it has nothing to do with the manner in which the received data are processed by the program. It is a feature grounded in the machine's 'hardware' - the physical 'constitution' of its 'receptor system/ The constitution of the computer's 'receptor system' does not entirely determine the information that it originally receives, however. While the spatial array of alphanumeric characters on paper, which is produced by the computer, is constructed by 'applying certain rules/ to put it broadly, to the given input, and while the temporal form this input takes may be structured by certain features of the machine's hardware, the specific order the originally typed bits of information take is in no way determined either by processing or by the machine's hardware. That is the prerogative of the typist and not of the machine. Thus, in so far as

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the computer's 'constitution' determines that time is the 'form of its receptivity/ it determines only the most general topological features of the order; it in no way determines the specific locations of the input elements in this order. Other information-processing devices are differently constituted and accordingly have different 'forms of receptivity/ An animal's eyes, for instance, can simultaneously receive a two-dimensional array of data.33 But these processing devices have their own limitations, imposed by their own 'constitutions.' Eyes cannot discriminate data below a certain degree of fineness; they cannot receive data that are too small or too faint, and they cannot simultaneously represent data at more than a certain angular separation. We could say, therefore, that the 'constitution' of the eye determines that it will receive data both successively in time and arrayed in a two-dimensional, discrete, bounded space, just as the 'constitution' of the computer determines that it will receive data successively in time. But, as with the word processor, the constitution of the eyes in no way determines the specific locations of visual stimuli. These locations are rather the result of the way external objects are disposed in ambient space and the way light travels from them to the eye, so that the spatial pattern of receptor stimulation merely maps the spatial array already present in the light rays immediately before the eye. My purpose in giving these mechanical and physiological examples is not to suggest that Kant had exactly these sorts of cases in mind. It is simply to illustrate that, when Kant shifts from the active voice to the passive and starts to talk about the way the subject is constituted so that it can be affected by objects rather than the way it is innately disposed to sort and order incoming sensa, a certain latitude for interpretation is created. It would be a mistake to read the Entdeckung passage, or any of the other passages in the Critique, the Prolegomena, or the Fortschritte, where Kant discusses the ground of the forms of intuition, as reaffirmations of the forms-as-mechanisms view of ID. In the later works it is no longer obvious just what role Kant sees even the receptor system (that is, our sensibility), much less the higher processing functions of the mind, playing in the determination of the spatiotemporal form of the manifold. That the subject's 'constitution' determines certain structural features of the order of intuition - those we appeal to when doing geometry by line and compass drawings, for instance - seems clear from what Kant will go on to say about the nature of geometrical knowledge. But to determine the local structural features of space and time is not the same thing as to determine the specific locations input elements are seen to have

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within these structures. There is no 'coordination language' in Kant's Critical works strong enough to attribute that view to him. (Extreme caution is called for before labelling Kant a 'nativist' about space-cognition, therefore. When carefully considered, those aspects of intuited space that are grounded on something innate in us may turn out to be very lean indeed.)34 Of course, just because, in his later works, Kant is reticent about the nature of the contribution our 'constitution' makes to space-cognition, it does not necessarily follow that he changed his beliefs. Failure to voice a previously stated belief does not necessarily mean that one no longer holds it. But it is extraordinary, none the less, that the language of active sorting and ordering of sensa that one finds in ID is not to be found anywhere in Kant's later work. A clear, consistent shift from the active language of innate principles for coordinating incoming sensa to the passive language of a constitution for being affected by objects is a phenomenon that calls for some explanation. The best explanation is that, over the years between ID and the Critique, Kant changed his beliefs about the manner in which spatiotemporal order comes to be present in experience and adopted a more reticent and ambiguous method of stating his position. c. Subjective and Objective Order There is an internal reason why Kant may have changed his views about the manner in which spatiotemporal order comes to be present in experience. In ID, he had speculated that the mind spontaneously arranges sensations in space and time in accord with certain stable and innate laws. Between 1770 and 1781, when the first edition of the Critique appeared, Kant tried to describe just what the 'stable and innate laws of the mind' for coordinating sensations are. The fruit of this inquiry, which has no precedent in ID, was the Analytic of Principles of the Critique, particularly the Analogies - that section of the Analytic of Principles in which Kant describes how the mind works up the given data of sense into a recognition of objects: objects with location, extension, and duration in an 'objective' space and time. Kant's examples in the Analogies instantiate the claim he had made earlier in the Inaugural Dissertation that 'objects do not strike the senses in virtue of their form or specificity.' The parts of a house all exist simultaneously, but we see them one after another. The heating of a room follows upon the lighting of the stove, but we perceive the lit stove and the

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heat in the room simultaneously. The position of a ship downstream follows from its earlier positions upstream but we, looking at the ship from the portholes of our own vessel, are uncertain whether it is the ship that is in motion past us, or we who are moving past the ship. To determine the true or real spatiotemporal relations of objects, certain laws or rules of evidence are required that allow us to infer, from the given data we have at our disposal and from the tests we can go on to perform, what these objective states of affairs are. But, in attempting to uncover what the laws or rules of evidence are, Kant discovered that the originally given data, to which the mind first applies the laws, must already be supposed to be presented in spatiotemporal sequence.35 It is just that this spatiotemporal order of data does not correspond to the real spatiotemporal relations of the underlying objects. These real relations have instead to be sifted out from the given ones with the aid of the principles. Kant expresses this insight in the general 'proof of the Analogies, and again in his specific proof of the Second Analogy, where he explicitly recognizes the existence of a subjective order, present as an originally given datum of experience. Kant's investigation into the 'stable and innate laws of the mind' taught him, therefore, that the mind does not itself produce space out of sensations, through its own spontaneous acts of coordination. Rather, the mind produces (or, more properly, discovers) the objective spatiotemporal relations underlying the given subjective ones. This discovery forces a reassessment of any blithe claims to the effect that the mind 'produces' space 'out of itself.' And this, I suspect, is the real ground of the Critical shift in emphasis from spontaneity in original space- and time-cognition to receptivity. Ironically, this point has been turned inside out by many commentators who read Kant's claim that, 'in this case, I must derive the subjective succession of apprehension from the objective succession of appearances' (Ai93/B238) as entailing that all spatiotemporal order must be derived from synthesis under the categories. After all, they reason, the objective spatiotemporal order is obviously so derived, and if the subjective order is derived from the objective, then all cognition of spatiotemporal order must ultimately be obtained from categorical synthesis. But those who argue in this way miss the subtlety of Kant's point. While the objective spatiotemporal order underlies and determines the subjective, the subjective is what is given first, as the fundamental, original datum from which the objective is reconstructed. To use an Aristotelian metaphor, while the objective order is first in the order of being, the subjec-

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tive is first in the order of knowing. In the order of being, the subjective order is thought to be caused in the perceiving subject by the objective order. But, in the order of knowing, the objective order is inferred, with the aid of the principles, from the subjective order, which is originally given in experience as the fundamental datum for the inference. Because the inference takes the form of inference to the best explanation - that is, a supposition about what must have brought the subjective order about - Kant describes us as deriving the subjective order from the objective. But the subjective order is originally given in intuition, and the objective is inferred by determining what it must be like for the subjective order to have been derived from it. d. Figurative Synthesis There are passages in the Transcendental Analytic where Kant appears to pick, not on synthesis under the relational categories, but on imaginative or figurative synthesis as the source responsible for our cognition of space and time. Perhaps the strongest statement of this view is 6151-2, where Kant describes figurative or imaginative 'synthesis' as being able to 'determine sense a priori with respect to its form, in accord with the unity of apperception.' Such passages lend credence to the forms-asmechanisms view, since they appear to represent the order of the manifold as the product of construction. But they are not unambiguous. The essential role played by synthesis is that of 'combination of the manifold' (6136). It is important to be clear about what this means. To assemble a jigsaw puzzle is, in one sense, to combine a manifold in space and time. The many pieces are the manifold and, by assembling them, we construct a particular set of spatial relations for them. But this is not the only sense of 'combination.' Consider a child's picture-book where the game is to find certain objects cleverly camouflaged in a line drawing - a knife, say, outlined in the bark of a tree, or a train in its leaves. When the child sees the knife or the train, there is a sense in which it, too, 'combines' the manifold - it takes the various points and lines in the picture and combines them under the concept 'knife' or 'train' rather than under the concept 'tree/ Only here the combination of the manifold does not involve actively arranging parts in spatiotemporal relations, as we do when we build jigsaw puzzles. Instead, the spatiotemporal order of parts is already given in the first glimpse the child has of the line drawing and is preserved unchanged through the process of 'combination.'36 The child's task is not to construct the order of the

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parts of the manifold but merely to describe or outline or trace it. But the child is still, in a very important sense, 'combining' the manifold. The child takes the various items presented and brings them to a unity of apperception by thinking or recognizing in this multiplicity an instance of one thing - a knife or a train or a tree. This is certainly combination - a combination of the many into one - and it is an essential component of cognition.37 Were the child not to combine in this sense, it would not recognize anything in the manifold and its cognition would be, as Kant puts it at Am, an intuition that, being without thought or knowledge, is for us, as good as nothing.38 This latter sense of 'combination' is what Kant means by 'figurative synthesis of imagination/ It is the recognizing of a single figure instantiated by the spatiotemporal manifold presented by intuition. Consider by way of evidence, 6154: inner sense contains the bare form of intuition [already!], but without combination of the manifold in it, and consequently without yet containing any determinate intuition.

Combination does not produce the forms of intuition; it merely outlines the boundaries of a determinate space or time. 8137-8 seconds this: Thus the bare form of outer sensory intuition, space, is not yet any kind of cognition; it only gives the manifold of an a priori intuition to a possible cognition. To cognize something in space ... I must draw it and thereby synthetically bring into being a determinate combination of the given manifold, (my italics)

Combination of the manifold and figurative synthesis are essential aspects of Kant's account of space- and time-cognition. But, as these passages make clear, they are processes Kant conceived to be carried out on input that is already spatiotemporally articulated. Their existence does not mean that Kant held a forms-as-mechanisms view. The most that could be said is that Kant takes determinate spatial shapes or temporal intervals to be constructed, not that he takes space and time as such to be constructed. Even this, however, says too much. For the sort of process involved in generating a cognition of determinate spaces and times does not involve active sorting or ordering but merely the recognition of the unity of boundaries that have been already defined by the way various qualitatively similar items are disposed in the intuition. The determinate spaces and times cognized through combination or

ioo Kant's Representation Terminology figurative synthesis may themselves become the input for a higher-level cognitive process that is responsible for sorting and rearranging the various determinate spaces and times conceptualized through figurative synthesis. This is what is going on in Kant's examples of the house and of the stove-heated room in the Analogies ^190/6235, A202/8247-8).39 While in our subjective experience the parts of a house occur successively, and the fire and the heat simultaneously, we think that objectively the parts of the house simultaneously inhere in some enduring substance, and the fire precedes the heat in time as its cause. This higher-level synthesis is extremely important for Kant. But, as noted in the previous section, it itself accepts a spatiotemporally ordered manifold as originally given datum for the processes it goes on to perform. e. The Alteration at 634 As I noted above, this alteration seems to imply that Kant wanted to remove the implication that spatiotemporal order is present in intuition. It hints that order comes to be present only when intellect constitutes an object of 'appearance' for itself. This is strong evidence for the forms-asmechanisms view, but it is made less so by the fact that the position of A2O, that the manifold is intuited as ordered, is still explicitly sustained in B. Just two sentences after the 634 revision, there is a second reference to the manifold of the appearance as being intuited in certain relations ('worinnen alles Mannigfaltige der Erscheinungen in gewissen Verhaltnissen angeschaut wird'), and this reference was retained in B. Nor is this obviously a case of oversight. B also contains revisions to the A text that make the same point. At 6136, for instance, Kant writes: The highest principle of the possibility of all intuition in relation to sensibility was, according to the Transcendental Aesthetic, that the manifold of intuition stand under the formal determinations of space and time ... This principle governs all the various representations of intuition so far as they are given to us.

If the principle that the manifold of intuition stands under the formal determinations of space and time is a principle that governs how the various representations of intuition are given to us, then the manifold must be intuited (given) as ordered, just as Kant claimed in A. A different motive for Kant's alteration at 634 can be gleaned by considering it in the context of his remark in the Entdeckung that there must be some innate ground of spatiotemporal order in the constitution of the

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subject's receptor system. It could be that, at 634, Kant is waffling between using the term 'form of intuition' to refer, on the one hand, to the innate ground determining the reception of matters in space and time, and, on the other, to the spatiotemporal order itself. Given that he wants to go on to say that the 'form lies ready a priori in the mind' for incoming sensations, it is the first sense he should use (since that is all that is really prior to sensation), and that is what the B edition reflects. But Kant does not stick to this meaning, and most often uses 'form' to refer to the order that results from affection of the receptor system, rather than the ground in the receptor system determining the characteristics of the order. Thus, even before the next paragraph has ended, he is back to using 'form' to refer to space and time themselves, rather than to their grounds. If Kant in fact intended the revision at 634 as I have suggested, then the revision does not imply a forms-as-mechanisms view, since the 'form' being referred to in the revised sentence is a precognitive cause determining the features of the data originally given to the cognitive system, not a cognitive process applied to already-given data. The modal reference in the revision (to what makes the manifold of the appearance able to be ordered ['geordnet werden kann'l) would then not imply that the order is in any way contingent on a spontaneous act of the mind, but only that it is through the innate ground in the subject's receptor system that the existence of a spatiotemporal order among intuited matters is, in fact, made possible. v.

Afterword

The main problem with the forms-as-mechanisms and forms-asrepresentations readings is not that they invoke cognitive data processing or innate features of the mind. Kant's account does appeal to processing (though only for the higher-level, objective representation of space and time, and for our intermediate-level representations of unified, delimited portions of the spatiotemporal manifold). It also appeals to our innate constitution (though the 'constitution' in question is one that determines the manner in which information is received through the senses, not one that imposes an innately existing idea of space or time on previously given materials). The main problem with the forms-asmechanisms and forms-as-representations view is that they obscure the existence of a primitive spatiotemporal order given in sense intuition. As a result, they blind us to the most important feature of Kant's account of

1O2 Kant's Representation Terminology space- and time-cognition: his claim that space and time are the orders in which data are presented to us. Over the previous pages, I have tried to show that Kant does indeed intend to make this claim and that he accordingly takes the representation originally delivered in intuition to be, not just a manifold of various parts, but a manifold articulated in space and time. In the remainder of this work, I underscore this result by referring to the representation delivered by intuition as an 'array/ This is a very free translation of Kant's 'Mannigfaltige/ but by now it is a justified one, and it will serve as a reminder of what Kant really thinks an intuition is like.

3 Sensation and the Matter of Intuition

The effect of an object on the representative capacity, so far as we are affected by it, is sensation. That intuition that is related to the object through sensation is called empirical. The undetermined object of an empirical intuition is called appearance. I call that in the appearance that corresponds to sensation its matter. (A19-20/B34)

These words could have been written by Kant's contemporary Thomas Reid (though Reid would have written 'perception' or 'memory' where Kant writes 'intuition'). Had that been the case, there would have been no question how they ought to be interpreted. Reid was explicit that sensation is entirely distinct from perception and memory. He was also explicit about the nature of the relation between perception and its object. Sensations are feelings had by a mind. They exist only in the mind and continue to exist only for as long as they are felt. Perceptions and memories are beliefs in the present or the past existence, respectively, of an external object. While perceptions and memories are mental states in their own right, they are states that refer to something distinct from the mind and existing independently of it. Sensations, in contrast, refer to nothing other than themselves, and they do not resemble the objects that are perceived or remembered in any way. They serve at most to suggest perceptions. One of the central errors of past philosophy, as Reid saw it, was the conflation of the first of these two distinct states of mind with the objects of the second in the 'ideal philosophy/ which takes the view that external objects are known, not directly through acts of perception, but by means of intermediary sensory impressions - 'ideas' - that resemble or at least represent these objects.

1O4 Kant's Representation Terminology Had Reid written the passage, 'sensations' would be feelings had by the mind as a result of the way it is affected by objects, 'intuitions' would be the perceptual beliefs it forms as a consequence of being stimulated, and 'appearances' would be the intended objects of those beliefs. But the passage was not written by Thomas Reid, but by Immanuel Kant, and the distinction between sensation and belief about which Reid was so emphatic and explicit is very far from the surface in Kant's writings.1 It is not immediately obvious from what Kant says whether appearances, as the 'undetermined objects of an empirical intuition/ are intentional objects distinct from (though perhaps 'suggested' by) sensations, or just some aggregate of spatiotemporally disposed sensations. My task in the first part of this chapter is to try to determine precisely what role sensation plays in cognition for Kant. This is not a question that he himself ever explicitly answers, though an answer can be pieced together by considering the implications of a number of his scattered pronouncements. In the passage cited above, Kant claims that sensation is that to which the matter of appearance 'corresponds.' This is far from being an unambiguous statement of the manner in which sensation figures in appearance, much less in intuition, but, as noted at the outset of chapter 2, above, it is rendered inevitable by Kant's blindness thesis. Since intuitions without concepts are blind, Kant is forced to begin his accounts of intuitive representations by referring, not to the structure of intuition itself, but rather to the appearances that emerge when the intuitive array is synthesized under concepts. Inevitably, this introduces complications. What, we must ask, is the relation between a matter of appearance and a matter of intuition? And what is the force of saying that sensation 'corresponds' to the matter of appearance? Does this mean that sensation just is the matter of appearance? Or is it something distinct from the matter of appearance but related to it in some way? In the latter case, is sensation the same thing as the matter of intuition, or does it merely 'correspond' to that, too? The thesis that sensation just is the matter of intuition is conveyed by passages such as A42/B6o, where Kant writes that sensation 'is that in our cognition in virtue of which it is called a posteriori cognition, that is, empirical intuition' (my italics). It is also entailed by Kant's claims that it is through sensibility or sense that we acquire intuitions (for instance, A19/B33, A51/B75), as well as by the historical and philological reflections of the previous two chapters, which have shown that the Kantian

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concept of intuition has its origin in the traditional Aristotelian notion of a lower, sensory, cognitive function. Even the title of the Transcendental Aesthetic, recalling aesthesis, Aristotle's name for sense, sets forth an intimate connection between sense and intuition. But there are other places where Kant seems to treat sensations and intuitions as two separate kinds of representation. At A32O/B3y6-7, for instance, he describes sensation as 'a perception that relates only to the subject as a modification of its state/ and he contrasts sensation, so understood, with objective cognition, which is either 'intuition' or 'concept.' If this is, in fact, his considered view, then sensations are not 'in' intuitions at all - or, at most, only in some intuitions: those we have of our own inner states. Thus the 'matter' of intuition would have to be something other than (or largely other than) sensation, and its relation to sensation - if any - would require further explanation.2 Kant's tantalizing reference to sensation as 'corresponding' to the matter of appearance at A2O/B34 (see also Ay23 76751 and A581/6609) comes to be of crucial importance in this regard. Just how does sensation 'correspond' to the matter of appearance? At A20/B34, Kant defines 'appearance' as the undetermined object 'of an empirical intuition (the 'of is conveyed by the genitive case). This leaves it ambiguous whether an appearance is some sort of impression or idea created in the subject as a result of the process of sensory or empirical intuition, or whether an appearance is the referent of a belief induced in us as a result of this process, and hence possibly an external, mind-independent object. (Those familiar with the history of early modern philosophy since the days of Malebranche and Arnauld will find nothing new in this 'object/act' ambiguity - it is the same one that challenges our interpretations of the work of almost every early modern philosopher with the exception of Reid.)3 If we take the latter view and suppose that Kantian appearances are the intended referents of beliefs, then the claim that sensation 'corresponds' to the matter of appearance would have to mean that there is some sort of correlation between what exists in us as sensation and the matter or stuff of which any intentional object would consist - a relation of sign to signatum, perhaps, or of effect to cause, or of resemblance. But it might also be that 'corresponds' just means 'is.' Were this the case, then we would have to read Kant's references to appearances in the first way, as designating impressions or token entities literally 'in' the mind. Appearances would be collections of sensations or constructs built on sensations and, as such, they would have the status, not of external or

106 Kant's Representation Terminology even intended objects, but just of phantasms or images created in us by the cognitive process. In light of this, there are three different positions one could take on the role Kant sees sensation playing in cognition. In order of decreasing significance, sensations might figure in cognition not only as intuited data, but as the very stuff out of which appearances are constituted. Alternatively, they might figure in cognition as intuited matters that merely assist us in coming to know appearances (considered as either higher-order representations in us,4 or as intentional objects,5 or even as actually existing external objects that are still - in some technical sense - 'appearances' and not things in themselves).6 In these cases, sensations would merely 'correspond' to the actual content of the objects referred to in our knowledge claims, and the precise nature of this correspondence relation would have to be further specified.7 They would, however, not merely correspond to, but be the matters of intuition. As a final alternative, sensations might be supposed to be not even matters of intuition but merely 'feelings' in the subject that stand in some unspecified relation - if any - to the matters of intuition (whatever they might be). Let us refer to these as views i, 2, and 3. View i: Sensations are the matter of appearance. View 2: Sensations are the matter of intuition but not of appearance. View 3: Sensations are feelings that refer to nothing other than themselves and by which the subject is merely aware that it is affected. They only correspond to the matters represented in intuition but are not themselves matters either of intuition or of appearance generally. View 2 comes in two flavours, one of which approaches View 3 more closely by taking sensations to be matters only of the subject's intuitions of its own inner states in time: View 2a: Sensations are matters of 'outer' (spatiotemporal) as well as 'inner' (strictly temporal) intuition. View 2b: Sensations are matters only of inner intuition. In what follows, I argue that Kant's position on sensation is best captured by View 2a. Kant takes sensations to be matters of intuition presented in space and time, though he takes sensations to designate or symbolize (but not constitute) a particular content in appearances.

Sensation and the Matter of Intuition i.

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The Epistemological Role of Sensation a. Exegetical Difficulties with View i8

Because of a number of remarks Kant makes, especially in the Fourth Paralogism (A366-8o, later excised from B), to the effect that appearances are 'mere representations in us/ View i has long been considered the correct account of Kant's position on sensation.9 But View i fails to find unambiguous support in the text and it is undermined by certain remarks Kant has to make that suggest that the relation between sensation and the matter of appearance is one of an effect to its postulated cause rather than one of identity. Rather than claim that appearances are constructed out of sensations, Kant is normally careful to distinguish sensations from the parts or the properties of appearances. He describes sensations as the matter of experience (A223/B270; Ak, XX 276) but not as the matter of the objects that we experience. They are the matter of perception (Ai67 76209) or of our manner of perceiving ^42/659-60) but not of the objects that are perceived. And they are described as the qualities by means of which empirical intuitions are specifically distinguished (Ak, IV 309) and the properties of sense intuition (Ak, XX 268) but not the qualities or properties of the objects known through intuition. Instead, Kant merely correlates sensations with the objects that appear to us. This view comes out most clearly in the Anticipations (Ai66~76/ 6207-18), the section of the Critique of Pure Reason that is the primary source for his views on the role of sensations in cognition. There he tells us that sensation (or, more exactly, what he calls the 'real' of sensation, which for the present we can take to be the particular sensory quality that the sensation expresses),10 is 'a mere subjective representation, from which we can only be aware that the subject is affected, and that we relate to an Object11 in general' (6207-8). Later on in this same paragraph, Kant speaks as if our perceptions and the objects of these perceptions are two different things. After explaining that our sensations possess a degree of intensive magnitude, he goes on to remark that, corresponding [to the intensive magnitude of sensation] intensive magnitude, that is, a degree of influence on the sense, must be ascribed to all the Objects of perception, in so far as the perception contains sensation. (6208)

Here the objects of perception are taken to be distinct entities to which

io8 Kant's Representation Terminology we ascribe a degree of influence or force corresponding to the intensity of our sensations. Rather than being a relation of identity, the 'correspondence' represented between sensation and the objects of perception is a relation of a given effect to an unseen object, postulated as the cause of this effect.12 This picture of the objects of perception as distinct from sensation is already implicit in some examples from A. The pleasant taste of a wine does not belong to the objective determinations of the wine, and so to an Object even considered as appearance, but rather to the particular constitution of the senses in the subject who tastes it. The colours are not characteristics of the bodies, to the intuition of which they are attached, but also only modifications of the sense of sight, which is affected in a certain way by light... [Taste and colour] are connected to the appearance only as contingently introduced effects of the particular organization. This is why they are not a priori representations but are based on sensation - or in the case of the pleasant taste, on the feeling of pleasure or displeasure, which is an effect of sensation. (28-9; my italics)

However, Kant is not always careful to distinguish sensation and appearance. There are places where he speaks of sensation or the real of sensation as being contained in 'appearance.' The passage cited earlier from 6207, for instance, comes out of a longer sentence that begins: 'Besides intuition, they [appearances, as objects of perception] also contain the material for [Kant here uses the preposition zu (to, towards), not the genitive case] some Object in general... that is, the real of sensation ...' And Prolegomena, §11, refers to the matter in appearance as 'that which is sensation in it' (Ak, IV 284). But, even here, we have to wonder exactly what Kant meant. His reference to the matter of appearance as 'that which is sensation in it' could be a careless way of saying 'that which is due to sensation in it.' And the use of the preposition zu at 6207 appears to imply a distinction between what Kant here calls 'appearance' and 'some Object in general.' The 'appearance' referred to here might not be an 'Object' but some more primitive representation from which the presence of the 'Object' is inferred. Kant's use of the term 'appearance' is very indiscriminate. Certain passages make clear that he uses it only to designate raw, intuited data given prior to all intellectual synthesis (A9O/B122). Elsewhere, he uses it to designate objects of perception (Gegenstande der Wahrnehmung) consisting of an array of qualitative matters barely thought under the categories of quantity and quality

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(as at 6207). And, in yet other places, it is clear that he uses it to designate objects known through even more sophisticated cognitive processing, Objekte, that are 'distinct from the representations of apprehension' (Aigi76236), and hence from the Gegenstande der Wahrnehmung (6207). For View i to be sustained, it would have to be shown that Kant meant 'appearance' in this last sense when he said that sensations are 'in' appearance (otherwise there would be some sense of 'appearance' in which sensations are not the matter of appearance), and the evidence is simply lacking to make such a case. b. Exegetical Difficulties with Taking Sensations Out of Space (Views 2b and 3) The ambiguity of 'appearance' cuts against View 2 as well. If sensations merely 'correspond' to the matter of appearance, and 'appearance' might just mean 'intuited array/ then could Kant be saying that sensations are not the matter of intuition or that they are at least not the matter of spatial intuition? There are places where he claims that sensation merely 'designates' what he calls 'the real in intuition' (Prolegomena, §24), and there are also places where he remarks that sensations have no magnitude and do not contain space (Ai67/B2O9, Prolegomena, §§24 and 26). But any approach that takes sensations out of intuition raises its own difficulties. At A42/B6o, Kant says that sensation is that in our cognition in virtue of which it is made empirical or a posteriori and, at Ai67/ 6208-9, he describes sensation as that which properly distinguishes empirical from a priori cognition. Were sensation to play absolutely no role in intuition, therefore, there could be no such thing as an a posteriori intuition. All our intuitions would have to be a priori. But, at A2O/B34, Kant claims that there are empirical as well as a priori intuitions and, moreover, that what makes these intuitions empirical is that they are 'related to their objects through sensation.' If sensations are not actually in empirical intuitions, therefore, they must at least be taken to play some sort of guiding role in generating them. This alternative has been championed by Rolf George: It is evident that Kant took the spatial and extended nature of objects to be the result of an interpretation placed upon certain sequences of sensations, which are themselves without extension ... Initially only the succession of sensation is present, and we may speak of a generation of the spatial features of objects by

no

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putting the sensations in relation to each other ... The aggregation and coordination of sensory impressions produce objects ... Through these synthetic activities intuitions are generated.13

On George's view, the spatial form of intuitions is a product of the cognitive processing of sensations. In this he has been followed by Kitcher, who has extended the view to include temporal as well as spatial intuitions.14 But after what has been said in the previous two chapters about the immediacy of intuitive representations, Kitcher's approach cannot be accepted. It simply does not square with what Kant means by 'intuition' and 'form of intuition.' For Kant, intuitions are the most immediate representations we have, not the product of any sort of process performed upon sensations considered as yet more primitive representations. George's approach, which recognizes that sensations occur successively in time (and so, in effect, recognizes the presence of an originally given sensory experience articulated in time, even if it does not call this experience an 'intuition'), evades this objection (in effect, if not in words). But, if George is right that Kant took only time, and not space, to be the form of our immediate experience of sensations, then it is odd that Kant would so consistently have treated space and time together, as phenomena of precisely the same sort, and not have done anything to indicate that space is any more derivative or any less original a representation than time.15 A related point can be made against Richard Aquila's recent suggestion that the spatiality of the objects towards which we are intentionally directed is a correlate of some sort of intuited 'form' that is not strictly a spatial form, though it results in the representation of space in these objects.16 While there are references in Kant to a subjective ground of spatial order, these references are best interpreted, as chapter 2 has shown, as being to the constitution of the subject's receptor system, in so far as this system determines the character of its intuitions. Thus, the ground of spatial form is not itself anything that is sensed, but a pre-cognitive cause of our original intuitions. This ground, moreover, can be taken only to determine the general features of the spatial order (i.e., its topology, affinity, and metric) and should not be supposed to fix the particular locations of the matters that are intuited. Aquila would go far beyond this and have us postulate the existence of sensory representations that not only are prior to spatial intuitions, but contain some pre-spatial form determining their locations in space (or those of corresponding matters of intuition). But, if Kant thought that there were such representations, why did he nowhere refer to them?

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Be this as it may, the ultimate test of the textual accuracy of Aquila's interpretation - as of the other alternatives considered in this section must be whether Kant himself says that sensations are presented in space in intuition. If he does, then however cogent these alternatives may be as accounts of space-cognition, they cannot be Kant's account. c. Evidence for View 2a The texts do indicate that Kant took sensations to be spatially arrayed components of intuitions. At A42/B59~6o, he remarks that space and time are the pure forms, and sensation in general the matter of our mode of perceiving objects, thereby implying that, be they intuited or not, sensations are at least modified by both spatial and temporal form. More explicit evidence is to be found at A23/B38, where Kant claims that sensations are presented 'outside of and next to' one another and are 'not merely different but in different places.' Again, at Prolegomena, §24 (Ak, IV 306-7), he implies that sensations fill space to a certain degree (though they do not fill it by extension). Correspondingly, at 6208, he notes that when the magnitude of a sensation vanishes to zero what remains is pure intuition, that is, the bare form of space and time. But, if pure intuition is what is left over when the intensity of sensation diminishes to nothing, then the sensations must have had a location in space and time to begin with. Even those passages from the Anticipations and the Prolegomena in which Kant insists that sensations are not spatial (Ai67/B2O9, Prolegomena, §§24 and 26) do not really undermine this picture. In these passages, Kant never goes farther than to deny that sensations have extensive magnitude - that is, size, shape or, for that matter, duration. But he never denies that sensations have location. Indeed, sensations are explicitly described as successive, hence located in time, even though Kant insists they can no more have temporal magnitude than spatial. If there is no contradiction in sensations, with no extensive magnitude in time, none the less succeeding upon one another in a temporal sequence, then by the same token there can be no absurdity in sensations, with no extensive magnitude in space, none the less being presented alongside one another in the intuition. The overall view implied by the Anticipations and Prolegomena, §§24 and 26, is that sensations are entities that occur at locations in space and time but that themselves neither contain nor determine any spatiotemporal predicates, being completely indifferent to where they are located. This is just what Kant needs to take sensations to be if his views on the

112 Kant's Representation Terminology relation between matter and form of intuition are to be sustained. The matters of intuition must be such that they are always localized in space and time, since space and time are the forms in which these matters are presented, but there must be nothing in a matter of intuition that determines it to a particular location or set of locations in space or time, otherwise the independence of the form of intuition from its matter, to which Kant commits himself when he calls the form 'pure' and 'a priori,' would not obtain. The given features of the sensations cannot determine the topology or other general structural features of the form of intuition; instead, the structure of the form of intuition must place a priori restrictions on the possible locations of sensations. d. Conflicting Passages (i) The Analogies At places such as Ai82/B226 and Ai89/B234, Kant asserts that our apprehension of the array of appearance is always successive in time and that the representations of the parts of the manifold follow upon one another. This might be taken to lend credence to the view that we only ever intuit one datum at a time and that spatial order is a construct on a purely temporal order of apprehension. But to take such a view is to read more into the texts than they contain. As noted in chapter 2, above, at §iv. c, Kant's project in the Analogies is to uncover the principles by which we discover the objective spatiotemporal relations underlying the subjective succession of our experiences. This investigation is necessary because, in a world of objects and perceivers arrayed in space and time, changes in experience can be attributable to alterations in a stationary object, to local motion of objects in the stationary field of view, or to perceiver-induced motion of the field of view. Consequently, any given alteration in the subject's experience may or may not correspond to an actual alteration in the object of experience, and many may result instead from perceiver motion. The actual alterations must be uncovered from the evidence provided by the subjective succession of experiences. In this investigation, principles or rules of evidence need to be invoked to discriminate the cases where an alteration in the subject's experience results from alteration in the state of an object (such as the warming of a stove-heated room), from a shift in the position of an enduring object (such a ship moving downstream), or from a sweep of the perceiver's sense organs over a continuously existing collection of objects or parts of an object (such as the successive sightings of

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parts of the side of a house). In the Analogies, Kant sets out to describe what these principles are and to investigate what they are grounded on. But this project - determining how, from successive alterations in subjective experience, we go on to make inferences concerning the real spatiotemporal relations of objects, their parts, their states, and ourselves with respect to them - takes as its subject-matter alteration in the apprehension. Whether that which is apprehended, and undergoes change, is also apprehended as spatially articulated at each moment is neither denied nor affirmed. Even though the apprehension of the array of appearance is always successive and 'the parts follow upon one another,' as Kant puts it at Ai89 76234, it may be that the 'parts' of the array are not individual atoms of sensation, but rather successive apprehensions of a spatially articulated manifold of sensations. (ii) The Classification Passage and the Two Senses of 'Sensation' There is, however, one well-known passage where Kant appears to explicitly deny that sensations are matters of intuition. This is the 'classification passage' from A32O/B376-7, a point halfway through the Critique, where Kant finally gets down to defining the terms he has been using thus far: The genus is representation in general (repraesentatio). Under it is representation with consciousness (perceptio). A perception that relates solely to the subject, as the modification of its state, is sensation; an objective perception is cognition (cognitio). This is either intuition or concept (intuitus vel conceptus). Here Kant appears to set sensation altogether outside of intuition as a separate kind of representation. But this is not the whole story. In the Critique of Judgment, Kant contradicts this position, claiming that sensations do figure in 'objective perception': But all reference of representations, even that of sensation, can be objective (and then it signifies the real in an empirical representation). (Ak, V 203) As well as the mere subjective aspect of our representations of things outside of us, sensation ... properly expresses the material aspect (the real) of these things (whereby something existing is given). (Ak, V 189) The fact of the matter, as Kant goes on to remark, is that the term 'sensation' has 'a double meaning' (Ak, V 205):

114 Kant's Representation Terminology When a determination of the feeling of pleasure or displeasure is called 'sensation/ this expression means something quite different than when I name the representation of a thing (through sense as a receptivity of the cognitive capacity) 'sensation.' For, in the latter case, the representation is referred to the object, but, in the former, only to the subject and serves for no cognition whatsoever, not even that by which the subject cognizes itself. (Ak, V 2o6)17

In the classification passage Kant uses 'sensation' only in the subjective sense.18 It may seem surprising that Kant should employ the term 'sensation' in the 'classification' passage in an entirely different way than it has been employed throughout the earlier part of the Critique, particularly as this is the place where he is ostensibly laying down the law about how representation terminology ought to be used. But, consider the context in which the passage occurs. The passage is placed at the end of an eight-page sermon bemoaning the loss of the concept 'idea/ through loose use of the ancient Greek terminology. After explaining what 'idea' really ought to mean, Kant implores his readers to use the term correctly and closes with the 'classification' passage - the primary purpose of which is to demonstrate how narrow the employment of 'idea' ought to be with respect to the denotations of other representation terms. Thus, the passage continues beyond the portions I have cited above to describe three more rungs in the ladder that have to be traversed before one can legitimately employ the term 'idea.' The moral is that 'idea' should be used neither to refer to an unconscious experience, nor to a pure concept of the form of intuition, nor even to a pure intellectual concept used within the bounds of experience, but only to a pure intellectual concept employed outside of those bounds. Thus, the 'classification' passage has little to do with explaining the role of sensation, intuition, or concepts in cognition. It was not written for that purpose, but for the purpose of correcting the tendency - most vicious in Locke and Hume - of employing the term 'idea' to designate almost any mental representation. In accord with this purpose, one of Kant's concerns is to point out that 'idea' should not be employed to designate a state of feeling in the subject, and to this end he distinguishes 'idea' from 'sensation.' It is just that 'subjective feeling' is not the only sense of 'sensation.' But Kant does not remark on that here because his purpose is to explain, not what sensations are, but what ideas are. Had he gone on to divide intuitions into matter and form, or pure and

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empirical, or had he gone on to divide empirical concepts into concepts of substances and concepts of properties, modes, and attributes, the question would no doubt have arisen, but because he is concerned with ideas and because there is no point in pursuing branches of the tree that do not lead to the appropriate node, he does not make these divisions. The point that there is also a sense in which sensation is objective perception is entirely peripheral to the purpose. (in) The 'Real' of Sensation There are places where Kant writes that what he calls 'the real' in empirical intuition 'corresponds' to sensation (Ai68/B2O9) or that sensation 'signifies' 'the real of intuition' (Ak, IV 306). These passages might lead one to ask whether something other than sensation - namely, 'the real' - is the true matter of intuition for Kant. In order to answer this question it is necessary to inquire into the relation between sensation and 'the real' as Kant saw it. Did he take sensation to be 'the real,' or did he suppose that sensation is something distinct from 'the real/ that serves merely as a sign for its presence? Kant appears to have understood 'the real' in the way it was understood in German school philosophy and in Descartes's Third Meditation proof of the existence of God.19 According to this conception, 'the real' designates whatever there is in a thing that distinguishes it from sheer nothingness. Reality (Realitat) and actuality of existence (Wirklichkeit) are therefore two quite different things. Existence means that a thing can be encountered in experience. But a thing that is encountered in experience may have very little 'reality' in the sense that it has very little content or is described through predicates that are largely privative (that is, that refer to a lack or absence of content of a certain kind, such as, for example, colourlessness, tastelessness, immobility, and lack of resistance), whereas a purely imaginary entity may, in its concept, mention a number of positive (or 'real' attributes). In his Third Meditation proof of the existence of God, Descartes made notorious use of this distinction by arguing that the content or objective reality of the idea of God that I find within myself exceeds the content or reality I am able to ascribe to myself in so far as I consider myself to be an actually existing being, so that this idea must be supposed to be the effect of some cause outside of myself. When Kant talks about 'the real' in our representations, he correspondingly means to refer to that in our representations that arises from or designates some positive (or, in Kant's case, 'real' negative) content in objects - as opposed to that which results from or designates nothing at

n6 Kant's Representation Terminology all. That there may even be such things as representations of nothing or representations arising from nothingness may appear to be impossible, if not absurd, but Kant was at pains to argue otherwise. In a 1763 essay on 'negative magnitudes' (Ak, II 165-204), he attempted to explain the possibility of representations of this latter sort (representations of nothingness) by appealing to the existence of negative magnitudes (such as opposed forces) that, when present with equal, opposed, positive magnitudes in a thing, would cancel one another out and so produce a kind of nothingness or zero-sum effect in the object and in our representations of it. Later, in the Anticipations and the corresponding §§24 and 26 of the Prolegomena, he claimed just that any given positive quality can always be continually diminished to the point of absence, with diminishing degrees of the positive quality corresponding to decreased 'reality': So therefore every sensation ... however faint it might be, has a grade, that is, an intensive magnitude, that can always be further diminished and between reality and negation there is a continuity of ... possible fainter perceptions. Any given colour, for example, red, has a grade that, however faint it might be, is never the faintest, and so it is in all cases, with temperature,... and so forth. (Ai69/B2ii) Between reality (the representation of sensation) and nothingness, that is, the complete emptiness of intuition in time, there is still a difference that has a magnitude, since between any given degree of light and [complete] darkness, between any degree of warmth and total coolness, any degree of heaviness and absolute lightness, any degree of occupancy of space and completely empty space, it is always possible to think of a yet smaller degree. (Ak, IV 306-7)

What is especially instructive about these passages is that, in them, Kant explicitly identifies reality with sensation. It is sensation that is described as having a degree of reality, and the specific examples Kant uses to illustrate cases where continuously diminishing degrees of reality are conceivable are the same cases that he elsewhere cites as examples of sensation.20 The short answer to this section, therefore, is that sensations are 'the real' for Kant, or, more properly, that they have (a degree of) reality and designate or denote the real in intuition by being that in intuition that has reality. It should be noted, however, that Kant does not just talk of a 'real' of intuition. He also speaks of the real of appearance (A58i/B6o9), of our representations of things outside of us (Ak, V 189), and of empirical rep-

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resentation (Ak, V 203). In these contexts he describes sensation as that which 'designates/ 'expresses/ or 'denotes' the 'real.' Here, however, the relation is not one of instantiation, but of signification. The Anticipations again make this clear: So therefore every sensation and consequently also every reality in appearance, however faint it might be, has a grade, that is, an intensive magnitude, that can always be further diminished and between reality and negation there is a continuity of possible realities and possible smaller perceptions. Any given colour, for example, red, has a grade that, however faint it might be, is never the faintest, and so it is in all cases, with temperature, with the moment of gravity, and so forth. (Ai69/B2ii; my italics)

This passage was cited elliptically above. The omitted passages, which have here been reinserted and italicized, indicate that Kant took there to be a 'real' not just of sensations like red or warm, but of features of objects (appearances) such as the moment of gravity. He took our knowledge of this reality, moreover, to be in some sense a consequence of our experience of the reality of sensation. 6208, cited earlier, hints at what this sense of epistemological 'consequence' might be: corresponding [to the intensive magnitude of sensation] intensive magnitude, that is, a degree of influence on the sense, must be ascribed to all the Objects of perception, in so far as the perception contains sensation. (6208)

The real of appearance is a 'consequence' of the real of sensation in the sense that we ascribe a certain degree of reality (a certain attractive force or impenetrability) to the appearance corresponding to the degree of reality (the intensity of sensible quality) evidenced by the sensation. We make this ascription because we take the reality of the appearance to be the cause of the reality of the sensation, so that, in ascribing reality to the appearance as a consequence of the reality of sensation, we are reasoning back from effect to cause.21 ii.

The Ontological Status of Sensation To suppose that our soul apart from the body and as spirit should intuit other things, that is, intuit outwardly, is to go beyond the limits of the data.

n8 Kant's Representation Terminology For we know the soul only as the object of inner sense, and the body as the means of outer sense. Our intuition is physical and not mystical; the physical is not pneumatic, but organic. (R4863; Ak, XVIII13)

a. The Problem Kant's remarks on sensation are not entirely unambiguous, but on the whole they indicate that it is View 2a, not Views i, 2b or 3, that should be recognized as his position on the relation among sensation, intuition, and appearance. Sensations are the matters that are given in intuition, though they only 'correspond' to the matter of appearance. As such they are the 'real' of intuition, though they merely designate or express the real of external objects through their intensive magnitude, which is taken to reflect the intensity of whatever affective power there may be in the external object. It is in this way that sensation 'corresponds' to the matter of appearance. Thus, whether Kant was influenced by Reid or not, one of the characteristic doctrines of the Scottish school, the doctrine that the objects of knowledge are not made up of sense impressions, is also to be found in his work.22 But, for all this, Kant is no common-sense philosopher of the mind. While he believes that sensations only correspond to the matter of appearance, he also maintains that they are the matter of intuition, and this leads to a conclusion that Reid would never have accepted: that at least some of our sensations occur alongside one another in space. For Kant, space, like time, is a form of intuition and, as such, like time, it is an order in which the matters of intuition - sensations - are presented. This makes inevitable a question that so far has not been addressed: what exactly is a Kantian sensation (aside from being a matter of intuition)? For Reid, a sensation is a state of feeling induced in the mind by the effects of external objects on the senses. Were this Kant's view as well, then his position on the forms of intuition would lead him to accept that the mind's states do not simply occur one after another in time but one alongside the other in space. This is a rather surprising conclusion. It is also one that Kant would likely have viewed with dismay. For most philosophers of the seventeenth and eighteenth centuries, extension is a characteristic of material substance, or at least a characteristic incompatible with spiritual substance.23 And Kant was antipathetic to the view that the substance that is conscious of sensations is material, and wanted to at least maintain that his critical philosophy left the question of the materiality of the soul open.24 Either, therefore, Kant was a

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materialist malgre lui, who was perhaps unwittingly driven to this position by his accounts of the matter of intuition as sensation and the form of intuition as a spatiotemporal manner of disposition of the matter, or he did not hold to the view that sensations are states of mind. But then what are Kantian sensations? b. The Physiological Account of Sensation To begin to address this question, let us return to Kant's original definition of sensation as 'the effect of an object on the representative capacity, so far as we are affected by it' (A19-2O/B34). Here Kant obviously agrees with at least one part of Reid's view: that sensations are effects that objects have on us.25 This account is seconded by passages such as A32O/B376: 'A perception that refers merely to the subject, as a modification of its state, is sensation,' and 6207: 'Besides intuition, appearances, as objects of perception, contain the material for some object in general, that is, the real of sensation, through which one can only become conscious that the subject is affected.' But what exactly is it that is being affected, and what is the nature of the effect? Kant simply says that it is our 'representative capacity' that is being affected, but there are at least two ways to take this. We could take the representative capacity to be a psychic capacity, in which case what is being affected is the mind and the effect is the alteration of a mental state, or we could take the representative capacity to be a physiological capacity that makes representation possible, in which case what is being affected is the body of the subject and the effect is a physiological alteration of some kind. Taking the latter view would give Kant the option to preserve neutrality on the question of the materiality of the soul, because it would remain an issue whether the higher stages in the cognitive process (all the functions of apperception through which intuitions are synthesized and 'thought' through concepts) are carried out by an immaterial mind. It would also, however, commit Kant to the view that there is a body and that physiological alterations in this body form the first stage of the cognitive process. In so far as this entails rejecting immaterialism (or pneumatism, as Kant called it) but preserving the possibility of dualism, it is hardly an un-Kantian view, and in any case we have seen that Kant's position on the matter and form of intuition, as sensation and spatial manner of disposition, respectively, inexorably commits him to the thesis that, whatever intuitions turn out to be, they have to be extended and, whatever sensations turn out to be, they have to

12O Kant's Representation Terminology be located. If sensations are in addition specified as 'effects' on the representative capacity (rather than as the intentional objects of those effects),26 then there is inevitably going to have to be something in us that counts as an extended intuition. The only question is whether to take this intuition to be a physiological first stage in the cognitive process, thus preserving at least the possibility that an immaterial mind might be responsible for the higher cognitive functions, or whether to concede the argument to the materialist right away and grant that cognition is, through and through, a physiological process. Either way, immaterialism is just not in the cards.27 But then, this is not a result with which Kant would have any quarrel.28 Granting, then, that taking sensations to be physiological effects on the body of the intuiting subject (and, by implication, intuitions to be extended and enduring physiological states) would still allow Kant to preserve his metaphysical predilections on the topic of the materiality of the soul, we need to ask whether he actually held this view. There is strong (but unfortunately not uncontested) evidence that he did. This does not come out in the major Critical works, though they entail that sensations must be in space in so far as they identify space as a form and sensations as matter of intuition. For the fullest account of Kant's position on sensation, we must turn to §§15-21 of the Anthropology of 1798 (Ak, VII153-7), a collection of notes Kant lectured from for twenty years in his classes on that subject and finally published after he had retired from teaching. Here, though Kant is reluctant to go into much detail, we find an explicitly physiological account of sensation: the senses can be divided into outer and inner sense (sensus internus). The first is that, where the human body is affected by corporeal things; the second that where it is affected by the mind. (Ak, VII153)

Remarkable here is the reference to sensing as involving affection of the body of the subject (including, so it appears from this passage, even inner sense, which results from the backwards affection of the body by the mind).29 A few sentences later, Kant is more explicitly physiological: the senses that give us bodily sensations (die Sinne der Kdrperempfindung) are 'all only to be found in those places where nerves are' (154). There are five senses that are 'fixed' to certain physical organs (Organempfindung, sensus fixus). The sensations of these senses 'affect only the nerves that belong to a certain part of the body' - the eyes; ears; the mouth, nose, and palate; and the skin (especially the fingertips) - which

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are 'so many external, prepared entrances that nature has provided the animal so that it can distinguish objects.' There is also a 'vague' or 'vital' sense that has to do with sensations that 'affect the whole system of nerves' (154). We are told that sensations come about because of mechanical and chemical interactions between the affecting objects and our sense organs. The sense of taste, for instance, is aroused when the tongue, throat, and palate are touched by the outer object. In smell, the odoriferous object emits particles that interact with the organ (157). The sense of touch is 'the most immediate of the outer senses' (155) because 'it lies in the fingertips and the nerve endings of the fingertips (papillae)' (154), which are in direct contact with the shape of the object. In hearing and sight, in contrast, the object affects the organ through a vibrating medium (155) or by means of radiation (156). But sensations are not just connected with parts of the body or originally caused by physical interactions between certain bodily parts and objects. Kant goes so far as to say that when we experience a sensation, what we are experiencing is a state, not of the mind, but of the sensory organ itself. The sensation just is the effect the object has on the sensory organ - the state it puts it into. (In the case of dreams and illusions, that is, 'inner' sensations, it is the mind itself that is the affecting object that acts on the sense organ.30 Paradoxically, 'inner' experience can exhibit spatial form - a point that Kant underscores when discussing the 'mental disease' of 'enthusiasm' - a condition that he describes as grounded in the inability to distinguish 'inner sense' from 'outer' [Ak, VII 161].)31 Thus, Kant tells us that three of the organ-senses are 'more objective than subjective' because they bring us more to a cognition of outer objects than to a 'consciousness of the affected organ' (154). The subjective organ-senses, in contrast, involve a 'delectation' of the state of the affected organ. But even the sensations from the objective senses can be converted into subjective sensations if the affecting object is very powerful. Bright lights that make our eyes blink, shrieking voices that hurt our ears, and objects with strange textures that distract touch from noting their shapes are mentioned as particular examples of this (156-7). Thus, even the sensations from the objective senses must really be alterations of the organs - it is just that when the effect is relatively mild we do not notice it as an effect on the organ but identify it with the affecting object. As a consequence, the senses 'teach us less [about objects] the more they feel themselves affected' (158), and sight is the noblest of the senses because 'its organ feels itself least affected' (156).

122 Kant's Representation Terminology This is not to say, however, that sensation can occur only in the five sense organs, so that in dreams and vivid imaginings these organs would have to be supposed to be worked upon by the mind. It is most likely that Kant intended 'sense organ' widely, to refer to the central nervous system and the brain as well as to the external receptors. He thought that imagination could produce or reproduce spatially organized sensory data in the absence of affecting objects (Ak, VII 167-8) and, as noted, he also thought there were pathological cases where the data of inner sense could be confused with outer appearance (Ak, VII 161). Thus, the presentations of outer sense, for Kant, are such that they can be produced by, or at least confused with, the products of systems that do not involve the external sensory receptors. The denotations of terms like 'outer sense,' Vital sense/ 'feeling/ 'inner sense/ and 'representation of imagination' are very obscure in Kant, and the question of what precisely it may be in the workings of the body - or mind - that might distinguish them is an even darker one. It is also a question that Kant carefully left untouched. The physiological knowledge of human beings rests on the investigation of that which nature has made out of them ... Whoever broods over natural causes of, for example, what memory might be based on, can rationalize about remaining traces of impressions left over in the brain by the sensations we have sustained (as Descartes did). But it has to be admitted that he was a mere spectator to this play of our representations and he had to let nature have its way, since he did not know the central nerves and fibres or understand how to use them for his purposes. Consequently, all theoretical rationalizing over these subjects is a pure waste. (Ak, VII119) we have no knowledge of the brain and the places in it where the traces of the impressions left by representations might be brought into sympathetic harmony with one another. [Ak, VII176]

But the fact that Kant left questions such as these unanswered because of the inadequacy of the empirical science of physiology of his day (the lack of knowledge of the central nerves and fibres and their manner of operation) only goes to show that he thought of them as empirical questions that would have to be answered by empirical studies. As the passages cited above show, even questions about memory and association, which are functions of imagination, were taken by Kant to be physiological questions whose answer rested on an investigation of the workings

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of the brain and central nervous system. (This, incidentally, is what really lies behind the notorious claim that the schematism and the workings of human imagination are arts concealed in the depths of the human soul (Ai4i/Bi8o-i). Kant uses 'soul' loosely. Imagination and schematism are not concealed in the human psyche but in the human brain, and what conceals them is the difficulty of examining the workings of the central nerves and fibres.) In any case, the picture that emerges from the Anthropology is that sensations, be they outer or inner, be they such that they lead to cognition of external objects or such that they involve cognition only of ourselves, and be they produced by affection by external objects or instead produced by memory, by dreams, or by some other function of imagination, are, one and all, physical states of the nervous system in the sensing subject. It may be that outer sensations of affecting objects have particularly to do with the states of the external sense organs or their adjoining nerves or certain connected places in the brain. And it may be that imagination, memory, and dreams are differently located states of the nervous system. But these are questions that do not need to be answered for Kant's purposes. There is strong evidence, therefore, that Kant did indeed take sensations, as 'effects on the representative capacity' arrayed in space as well as time, to be physiological states of the body of the perceiver. Following this line, it can be concluded that intuitions, which for Kant consist of sensations as matter, must, first of all, be effects on the subject and not objects the subject intends in so far as it is affected (since the sensations that make up the matter of intuition are effects on the subject and not intentional objects), and, second, be physiological effects (since space as well as time is a form of intuition). The distinction between the intuitive and the intellectual in Kant is properly to be seen as a distinction between the physiological and the psychic or, more exactly (if we do not want to presuppose dualism), between the physical and the cognitive. c. Sensations as Sensible Qualities Unfortunately, this account of Kantian sensations and intuitions cannot easily accommodate everything Kant says about sensations. What causes the problem are a number of the specific examples Kant gives of sensations. These are not, as one might expect, of physiological phenomena, such as Cartesian mechanical impressions on the corporeal imagination or Hartleyan vibrations of the nerve fibres. Instead, Kant tends to take

124 Kant's Representation Terminology sensations to be exemplified by classical, Aristotelian 'proper sensibles' such as the red of a rose or the taste of a wine. Thus, at 644, he refers to colours, sounds, and feelings of temperature as 'mere sensation/ In the parallel passage at A29, he speaks of the taste of a wine and of colours as grounded on sensation. R3958 (Ak, XVII366) speaks of 'red, black, sweet, hard, warm, etc/ as being set forth by sensation. Ak, XX 268-9, instances colours, sounds, and acidic tastes as examples of sensation. At Ai/5/ 6217, colour and taste are given as examples of 'the quality of sensation/ In Prolegomena, §24, colour, temperature, and heaviness are the examples. Ak, IV 290, refers to the sensation of red excited by cinnabar. In the note to Prolegomena, §26 (Ak, IV 3O9n), temperature and light are described as having grades of intensity that vary independently of the space they occupy, and so are called magnitudes 'in the manner of sensation rather than intuition, or magnitudes of the ground of intuition/ And, perhaps most tellingly, in the first of the 'isolation' passages (A2O-1/B35), Kant lists hardness and colour as examples of what must be removed when we abstract what belongs to sensation from experience. The evidence that Kant took sensations to be sensible qualities such as pains, smells, and tastes may be what has led to charges that he committed the 'fallacy' of spatializing sensations (in the minds of commentators who accept that he took sensations to be the matters of intuition or of appearances generally)32 and to claims that he took at least spatial intuitions to be products of construction (in the minds of commentators who want to absolve him from this charge).33 But the problem posed by these examples is not that there is something inherently absurd in taking sensible qualities to be spatially located. Some sensations - if not tastes or sounds, then certainly colours and tactile feelings - do seem to be located in space. And to hold that they are indeed so was not entirely unprecedented in the eighteenth century. Hume clearly did so in Treatise, 1.2 and 1.4.5. And Kant's own claims in the Anthropology could be read as entailing that even tastes, smells, and sounds are located in the particular sense organs that receive them, and that the only sensible qualities not experienced as having any location are the generalized bodily sensations delivered by the 'vital sense/34 But Hume's spatializing of visible and tangible impressions was carried out against the background of a larger sceptical attack on the notion of a soul-substance in which these impressions might inhere (executed in Treatise, 1.4.5). Kant's contrary desire to rehabilitate the concept of substance in the face of Hume's critique, and to at least preserve agnosticism on the question of the substance of the soul, means that he would insist

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that there is something permanent of which all our representative states are predicated. This brings up the real problem with Kant's examples of sensible qualities: combined with his view that sensations are effects on the subject, they lead to the conclusion that, when the subject is affected and so has a sensation, there is something (some substance) that literally becomes red or warm or wine tasting. This, however, is untenable, regardless of whether sensations are taken to be psychic or physiological effects. It would be untenable were sensations taken as psychic effects because, as Hume pointed out, some of the instanced examples of sensations (colours and tangible qualities) are located in space and aggregated into spatially extended composites, and ex hypothesi no psychic state is extended. But it would also be untenable were sensations taken as physiological effects, because that would be to suppose that the so-called secondary qualities are real features of bodies (at least of those bodies composing the physical sense organs of the subject), a view that few early modern philosophers, Kant not excepted,35 took seriously. Interestingly, however, not all of Kant's examples of sensations are of classical Aristotelian sensible qualities. One passage that is especially interesting in this regard is Ai69/B2ii: Any given colour, for example red, has a grade that, however small it might be, is never the smallest, and so it is with temperature, the moment of gravity, and so forth.

Note that Kant's German here is not 'Farbe, Warme, Schwere' (colour, temperature, weight), but Tarbe, Warme, der Moment der Schwere/ Weight, considered as a feeling of strain in the muscles, or pressure on the skin, hence as a kinaesthetic or haptic sensation, is a sensible quality. But the moment of gravity is no such thing. It is a technical term of classical mechanics used to designate a force - something that, unlike red or the taste of wine, we suppose really does inhere in bodies. And temperature is something in between. Depending on whether we understand temperature to be the phenomenal feeling of warmth, the state in the affecting object that produces this feeling, or the physical state induced in the affected sense organ as a result of being affected by the object, it could designate a feeling had by the mind, a state of an external object, or a physiological state of the sense organ. The first isolation passage (A2O-1/B35) contains a similarly anomalous reference. The list of examples of 'that which belongs to sensation' includes not just colour and hardness, but impenetrability (Undurch-

126 Kant's Representation Terminology dringlichkeit) - a term that no student of the physics of Leibniz or Boscovitch, or, for that matter, the early Kant, could interpret as standing for anything other than the force of repulsion. Had Kant meant merely to refer to the kinaesthetic or haptic sensations of resistance in the muscles of the squeezing palm or painful pressure in the skin crushed against the bones, he would have started the list with 'hardness' (Htirte), not 'impenetrability.' Faced with this sort of evidence, we have two alternatives. We can conclude that Kant was hopelessly confused about what sensations are so confused that he was able to list states of mind like determinations of the feeling of pleasure and displeasure, sensible qualities like colours (commonly thought to exist neither 'in' the mind as its qualities nor 'outside' of it as qualities of things as they are in themselves), and properties of physical objects such as gravitational force and impenetrability as examples of sensation. Or we can look for some underlying explanation of what it might be that unifies these diverse phenomena. One text that is particularly provocative in the latter regard is the Anticipations. The Anticipations open with a preliminary remark (A 166-7 / 6208-9; in B this remark is ineptly sandwiched between a newly added proof and a repetition of the original proof) in which Kant notes that an 'anticipation' is properly to be defined as that which can be said of an experience in advance of having it. He then goes on to remark that this might lead us to believe that sensation must be that in our experience that cannot be anticipated. (The reason for this probably goes back to his original definition of sensation at Ai9/B34- If we take sensation to be that in the effect an object has on us that is attributable to the activity of this object [as opposed, say, to what our cognitive faculty might inject into this effect on its own initiative], then we would expect that no sensation could be known in advance of being affected, and no sensation could therefore be anticipated.) But, he goes on to add, were we to suppose that there is something in every sensation that must belong to it in so far as it is a sensation, then this would deserve to be called 'anticipation' in a very special sense. 'And this is in fact the case/ he says at the end: there is something else or something more to sensation than just the content, 'that is always merely empirical and can in no way be represented a priori' - something that can be anticipated in advance. The remainder of the text of the Anticipations leaves us in no doubt as to what this special feature might be: any sensation, Kant claims, can always be conceived to be subject to remission, so that (quite apart from changing its location or size) it can gradually be diminished until it fades

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out altogether and only the empty manifold of pure intuition remains (Ai68/B2O9-io).36 This is something that is indeed common to all the phenomena Kant lists as examples of sensation. Subjective states of feeling, which refer to nothing other than themselves and by which the subject is only made aware that it is affected, states such as pain or joy, have a degree of force or strength and can be intensified (up to a point) or remitted. Colours, tastes, smells, and other proper sensibles come in varying shades of vivacity, from bright to dark, vibrant to insipid, loud to soft. And the gravitational force and impenetrability of objects can be conceived to increase or diminish to infinity even though the volume of space the body occupies is not changed. We can say, therefore, that if sensation is any one thing for Kant, it is something that can come in varying degrees. This still does not help, however, to explain what exactly a sensation is 'of or 'where' it is to be found. Sensations still seem to be in different 'places/ to speak loosely; some qualify objects as their properties; others stand somehow 'before' the mind without either inhering in it as properties or belonging to the external world, and yet others qualify the mind as its states. In the end, there are three Kantian theses about sensation that just do not sit well together. 1 Sensations are the matter of intuition (hence, phenomena at least some of which are arrayed in space). 2 Sensations are effects on the subject's representative capacity (hence, not intentional objects). 3 Sensations are exemplified, on the one hand, by colours, tastes, and other proper sensibles and, on the other, by attractive force and impenetrability. Taken together, (i) and (2) entail that sensations must be physiological phenomena, since being extended and being an effect on the subject can be taken to be jointly sufficient for being a physiological phenomenon. But (3) locates sensations anywhere but in the body; indeed, (3) is problematic all on its own, since it locates sensations in very different 'places/ Kant nowhere explains how to reconcile these claims. In what follows, I offer a speculative solution that, while not grounded in anything he says, is Kantian in spirit. d. An 'Intentional Object' Account of Sensible Qualities There is no way to reconcile the thesis that sensations are any sort of

128 Kant's Representation Terminology effect on the subject with the claim that they are exemplified by sensible qualities. The only route open, therefore, short of ascribing inconsistent views to Kant, is to take sensations and sensible qualities, such as colours and smells, to be two different things. Sensible qualities are 'secondary qualities' which could not plausibly have been taken to be real qualities of any physical object, including the human body, by any early modern philosopher. But it is equally implausible to suppose that they could be effects on the mind, so that the mind would literally become red or wine-tasting when it has these sensations.37 And even if this strange possibility were admitted, some sensible qualities (colours and tactile sensations, at least) are located and arrayed in space, which would entail the even more unacceptable thesis that the mind, in taking on these qualities, must also take on extension and shape. The only route open, short of ascribing inconsistent views to Kant, is to take sensations as effects on the subject and sensations as sensible qualities to be two different things. Sensible qualities are best accounted for, not as effects on the subject, but as the intentional objects of such effects, that is, as the things the subject thinks of or believes in when it is in a certain state. Given that Kant is in general insensitive to the issue of intentionality, it is not implausible to suppose that he would have conflated these two really distinct things under one term. If this supposition is correct, then the effect on the representative capacity can be taken to be, really and properly, a state through which the subject eventually comes to perform an act of thinking or believing, and the sensible quality can be taken to be something else: the object intended or referred to by that state.38 There is room in Kantian cognitive theory for the notion of an intentional object. As was seen in §i, above, this room is provided by Kant's notion that the matter of appearance merely 'corresponds' to the matter of intuition (as opposed to being composed of this matter). Appearances can consequently be taken to be objects that are thought of or intended rather than objects that result from aggregating or rearranging effects on the representative capacity - though the acts of thinking or intending that are involved here must be somehow determined by effects on the representative capacity, indeed, determined in such a way that the matter of the appearances will in some way 'correspond' to the matter of the intuition. Therefore, we could provide a Kantian account of sensible qualities as intentional objects by taking them to be matters of appearance rather than matters of intuition. Despite the fact that Kant uses sensible quali-

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ties as examples of sensation, this is quite in accord with the general outlines of his account of cognition. After all, if sensation is the matter of intuition, and intuitions that have not been conceptualized are blind, then sensation should not be the sort of thing that can be exemplified. Any example of a sensation would have to be an intellectually processed version of what the sensation really is; it would have to be a concept of a sensation or, more exactly, it would have to be a sensation the way it appears to us through intellectual processing. What has been said about sensible qualities holds equally for the properties of physical objects such as gravity and impenetrability. These properties could not properly exemplify sensation either. Like sensible qualities, they could only be the matter of some appearance, a matter that at best 'corresponds' to sensation. While it is strange that one and the same term for an effect on the subject, sensation, should be applied to phenomena as various as the properties of physical objects and sensible qualities, it is not strange that the appearances we come to think of or intend as a result of being affected should be manifold and various, depending on how they come to be cognized or processed by the mind (e.g., in naive 'common-sense' or perceptual experience, or as the objects of more sophisticated scientific theorizing). Some objects may appear to us simply as colour patches or other 'sense objects/ that is, barely as qualia extended and arrayed in space and time (these are the sorts of 'objects' we attend to when doing perspective painting, for example, or when confronted with an ambiguous or 'unintelligible' experience that we cannot describe in any other terms). Others consist of bodies in three-dimensional space, thought as existing unperceived over time and making up a common world that other subjects see, each from their appropriate perspective. Yet others appear as the theoretical entities postulated in scientific explanations, such as the forces of impenetrability and gravitation or, alternatively, the 'solid, massy, moving particles' Newton speculated might have been originally formed by God at the moment of creation as the ultimate mechanical causes of all these effects). If it is asked how the 'matter' of all of these different appearances could 'correspond' to the matter of intuition, then the Anticipations provide a ready, Kantian answer: they correspond on the basis of their intensive magnitude. A sensation occurs. We may suppose in light of the researches of this chapter and Kant's claims in the Anticipations that, whatever this sensation is, it is some sort of effect on the body of the subject and has some intensive magnitude. Corresponding to this intensive

130 Kant's Representation Terminology magnitude, there is the brightness of a colour (the 'matter' of a senseobject or physical object) or the intensity of a force (the 'matter7 of a physical or theoretical object). One and the same intensive magnitude of sensation, in other words, is thought of or intended in one way in perception, in another way in objective experience. Thus, the colour quality thought in perception is not an effect on the subject, but an object of appearance that the subject thinks of or intends as an ultimate result of being affected. (As it turns out, this object does not actually exist in the world as described by the science of Kant's day.) But the colour quality also expresses a certain intensive magnitude, and this intensive magnitude corresponds to something actually given in intuition as sensation. The case is similar with forces like attraction and impenetrability, except that there is no 'quality' that is attached to the force (unless we think of the feelings weight or hardness, which are inexact representations of these forces) and the intensity of the force is thought to actually exist in the world (though again, only in the world considered as appearance). To sum up: the inconsistency between claims 1-3 above can be resolved if we allow that Kant's examples of sensations in claim 3 are not examples of sensations considered as the matter of intuition, but examples of how sensations appear to us when the intuited sensory array is processed in various ways into percepts and objects of appearance. Or, which is the same thing, that they are examples of the matter in various kinds of appearance that corresponds, in virtue of its intensive magnitude, to sensation. Because these appearances are various, the corresponding matters are various in quality and nature. Some are matters of sense-objects such as colour patches, others matters of physical objects. But there is no real anomaly in this, since sense objects and physical objects are equally objects that appear to and are intended by us. In so far as the matters of these objects correspond to the matter of intuition, however, they all exhibit a corresponding intensive magnitude. This explanation of claim 3 is Kantian in spirit and it allows us to preserve the implication of claims i and 2, that sensations are physiological effects, while accounting for how it is that Kant gives the examples of sensations that he does. Appendix: Sensations as Effects of the Intensity of Force I have argued in this chapter that Kant takes sensations, considered as matters of intuition, to be physiological effects on the subject. I have also observed that, while Kant is extremely reticent to say very much about

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the physiological processes of sensation, imagination, or memory that are responsible for delivering, compounding and dividing, and storing these effects (witness Anthropology [Ak, VII 119]), he is convinced that whatever the effects are, they are capable of remission. I want here to introduce some further considerations in support of these claims and at the same time to address a question that must arise spontaneously to any reader of the Anticipations: why is Kant so convinced that sensations must all have intensive magnitude? In his original definition at A19-2O/B34, Kant defines sensation as 'the effect of an object on the representative capacity so far as we are affected by it/ The qualifying clause, 'so far as we are affected by it/ is obscure, but what Kant probably intended was to convey that not everything in the effect of an object on our representative capacity should be considered to be sensation. When an object acts on the sense organ, the resultant effect may contain elements that arise from another source than the activity of the object (e.g., a disposition in the subject to inject a certain element into the effect on the occasion of being affected). Recall, in this connection, Bi-2: But even if all our cognition arises with experience, it still does not exactly all spring out of experience. For it could well be that even our experiential cognition is an aggregate of that which we receive through impressions and that which our own cognitive capacity (merely occasioned by sensory impressions) brings forth out of itself - an addendum that we cannot distinguish from the former basic matter, before long practice has made us aware of it and given us a facility for abstracting it.

Cognizant of this, when Kant defines a sensation at the outset of the Aesthetic, he is careful to stipulate that it is not just the effect of an object on us, but that in the effect of an object on us that is really attributable to the activity of the object. Sensation is thus 'the effect of an object on the representative capacity so far as we are affected [by that object]/ It is that which strictly results from the object's impression of the organ and is to be distinguished from that which, because of our cognitive constitution, would have been present in the intuition regardless of what object happens to be present or how it affects the organ. But, if this is the case, then sensation would appear to be precisely that in our experience that can in no way be anticipated in advance. There ought to be no telling, in advance of encountering an object, just what sort of sensations it will bring about in us. Yet, Kant insists that there is some-

132 Kant's Representation Terminology thing we can anticipate about all sensations: that they are subject to remission. How can he be so sure? Not having experienced all the possible qualities of sensations that there are, and not being able to anticipate those he has yet to encounter, what makes him certain that there could not be some as yet unexperienced quality lurking somewhere in the wide reaches of the sensible world that exists only in digital or quantum states, or simply cannot undergo diminution? Second, why does Kant make his claim just about remission and not also about intensification? If we grant that a quality of sensation can always be further diminished, why not say as well that it can always be further intensified, and if we refrain from making the latter assertion, what entitles us to make the former?39 One way to approach this question is to go back to Kant's original description of sensation as 'the effect of an object on the representative capacity, so far as we are affected by it/ and drop the reference to 'the representative capacity' in order to ask a more primitive question: what, in general, is the effect of one object on another, for Kant? The answer to this question is a straightforward one, and it is supplied by Kant's philosophy of nature. Objects, for Kant, physical objects at least, are centres of force. Extension, shape, and motion are not essential properties of matter but derivative ones (Anfangsgrunde [Ak, IV 49714._28]). All bodies have an internal repulsive force that, left unhindered, would cause the smallest particle of fluff to expand to occupy the volume of the universe (Ak, IV 508). Because the different parts of bodies also attract one another, as well as surrounding bodies, this does not happen (Ak, IV 508-9). Rather, the internal repulsive force, continually weakening as the body expands, sooner or later gets stopped by the attractive force, and perhaps also by mechanical forces that Kant thinks might possibly be exerted by the impacting of particles of a pervasive ether. Since the repulsive force not only decreases to zero as the body expands to infinity, but increases to infinity as the body contracts to a point (Ak, IV 501 ^X there is no danger that the attractive force will overcome the repulsive. Instead, the superficies of a body is defined as the place where the attractive, mechanical, and repulsive forces balance one another or, which is the same thing, as the place where the body has been compressed so far that its force of repulsion becomes strong enough to hold off any further compression (Ak, IV 5i718_24)Given such a physics, there is no problem identifying the effect of one body on another. The effect of one body on another is to attract or repel it and, through attracting or repelling it, to bring about a redistribution in the intensity of the repulsive forces between its parts, or even to

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deform its surface, quite literally giving it an 'impression.' Since the forces vary continuously in intensity (Ak, IV 499 and 516-17) - this is a function of the fact that they extend over space and so can be supposed to vary as the size of the space or distance from the centre increases or diminishes - these effects will do so also. This general view of physical affection as a product of the activity of forces leads easily to a view of sensation that can answer the questions posed at the outset. Sensation, as the effect of one body, the affecting object, on another, the sense organ, just is an alteration in the forces of attraction and repulsion in a body resulting from the attraction or impact of another body. In so far as these forces are subject to continual remission, the same must hold for the sensations. A continual intensification of sensation, on the contrary, cannot be possible for the simple reason that there is an upper bound on the intensity of sensation: that at which the degree of force in the affecting object is so great it starts to destroy the organ. Objection It might be objected that to appeal to Kant's natural philosophy when attempting to explicate his account of affection is to start at the wrong end. Kant's account of bodies as centres of force, and his science in general, are supposed to be grounded in, among other things, the metaphysical principles established in passages such as the Anticipations. The natural philosophy cannot, therefore, in turn be taken to explain the underlying conceptions that make the Anticipations work - at least, not legitimately.40 I am not sure that this objection is entirely fair. It rests on an interpretation of the argument in the Dynamics chapter of the Anfangsgriinde that would have to be made more explicit. Before the charge of arguing in a circle can be justly levelled, it has to be shown exactly where and how Kant's account of dynamics presupposes the principle of the Anticipations, and it is not obvious that this can be done. The Dynamics begins with the supposition that body, considered as the real in space, exists. That it fills space by repulsive and attractive forces is then proven over the next six propositions and five explications, and the proofs make no obvious reference to the Anticipations. Thus, it may in fact be the case that Kant's Anticipations presuppose the Dynamics of the Anfangsgrunde, and that there is no circle because, in this respect, the Anfangsgrunde is more fundamental than the Anticipations.

134 Kant's Representation Terminology Regardless of how these priority relations might work out, however, this much is clear: there simply is no justification, either in the Anticipations chapter itself or in the earlier parts of the Critique, for the premise of the Anticipations that sensations are intensity values or, as Kant puts it, 'intensive magnitudes.' There is only an explanation for why he may have so confidently made this unsupported assertion, not even noticing that a justification was called for. That explanation is that he was antecedently convinced by his account of affection (the outlines of which he had already worked out at least as early as the Physical Monadology of 1756) that sensation, considered as an awareness of the effect of an object, must be a feeling of the intensity of a force rather than some sensible quality that can in no way be anticipated in advance. As far as the argument of the Anticipations is concerned, it is Kant's physics which ends up determining his epistemology, rather than the other way around - as was the case with Descartes, as was the case with Locke, as was the case with Leibniz, and (arguably) as was the case with Hume.

4

Origins of the Form and the Matter of Intuition

I call all representations pure (in the transcendental sense) in which there is nothing to be found that belongs to sensation. Since that in which sensations can alone be ordered and set forth in a certain form cannot itself in turn be sensation, it follows that, while the matter of all appearance is indeed given to us a posteriori, its form must lie ready a priori in the mind for all sensations and for that reason can be considered apart from all sensation. Thus, the pure form of sensory intuition in general can be found a priori in the mind, wherein all the manifold of appearance is intuited in certain relations. (A2O/B34)

There is one further complication to Kant's preliminary survey of the sensory cognitive faculty in §1 of the Aesthetic: namely, his claim that the formal and material aspects of an intuitive representation originate from distinct sources - that the form lies ready a priori in the mind of the subject, prior to all sensation, whereas the matter arises only a posteriori, through 'the effect of an object on the representative capacity so far as we are affected by it.' So far, these claims have been alluded to in passing, though not discussed in any detail. In chapter 2, above, Kant's claim that the form of intuition is somehow already present in the mind, in the sense of being grounded on the constitution of the subject, was simply taken at face value. In chapter 3, likewise, his claim that the (a posteriori) effect of an object on the representative capacity is restricted to just the matter of intuition was also accepted without comment. But, again in passing, there have been indications that the distinc-

136 Kant's Representation Terminology tion of origin may not be as neat as Kant presents it here. While the general structural features of the forms of intuition (e.g., their topology and, if they have it, their affine structure and metric) may be a priori, it may also be that the specific locations of sensations in these structures are determined a posteriori. And, while sensations, for their part, may be given a posteriori, it turns out that they have a certain feature (being capable of remission) that can be anticipated a priori. However, despite the fact that there may be a posteriori aspects to the form of intuition (localization) and a priori aspects to sensation (remission), Kant takes it that the former 'lies ready a priori in the mind/ in the sense that it arises from the constitution of the subject, whereas the matter first arises only as a product of experience. But what reason does Kant have for supposing that the matter of intuition may not be as much a product of the subject's 'constitution' as its form? On the other hand, what reason does he have for insisting that the spatiotemporal form of intuition may not be as attributable to the effect of an object on the representative capacity as the matter? In so far as Kant has an answer to give to these questions in §1 of the Aesthetic, it occurs in the second of the three passages cited above. There he tells us that the form of intuition must lie ready a priori in the mind because it is that in virtue of which sensations come to be presented in a certain order, and the order in which sensations are set forth cannot itself in turn be a sensation. This argument is a failure. Obviously, the order in which the elements of an ordered set are arrayed is not itself an element of that set. But, even granting this premise, it does not follow that the order in which the matters of intuition are arrayed must lie ready a priori in the mind and not be given a posteriori, as the result of affection. The argument would follow if Kant had already established that what I will call the 'proper effect' of an object on the representative capacity (that is, what is properly attributable to the action of an object on the representative capacity as opposed to what the subject's cognitive capacity would inject into this effect of its own accord, regardless of the manner in which it is affected) supplies us only with a collection of intensity values, that is, distinct and independent 'matters/ each capable of continual remission towards zero (i.e., with what Kant calls 'sensation'). Then, indeed, it would follow that the forms of intuition, space and time, cannot arise through affection, and hence must be a priori. But the thesis that affection can supply us only with such 'matters of intuition' is precisely what is in question. Why should the proper effect of an object on the representative capacity

Origins of the Form and the Matter of Intuition 137 not be taken to include the orders as well as the intensities of sensations? Kant's argument in fact rests on an equivocation on the term 'sensation.' In the premise, when he writes: 'that in which sensations can alone be ordered and set forth in a certain form/ he treats sensations as if they were by definition just the elements that occur in an order - in this case, the intensity values that are ordered in space and time in intuition. But, in the conclusion, he treats sensation as 'the effect of an object on the representative capacity so far as we are affected by it/ This is what is implied in his claim that what is not a sensation must be determined by the constitution of the sensory capacity itself, that is, cannot be the proper effect of an object on that capacity. And that 'the effect of an object on the representative capacity so far as we are affected by it' should consist just of sensations considered as a collection of intensity values is simply not obvious. That Kant should fail in his initial effort to establish separate origins for the form and the matter of intuition may not seem at all inappropriate. As noted at the outset of chapters 2 and 3, above, the attempt to describe what an intuition is like prior to all intellectual synthesis is a difficult matter because of the blindness problem. But an attempt to take the regress a step farther and describe the grounds of an intuition is even more difficult. The former task demands merely that we be able to identify and describe intuitive representations prior to the intellectual synthesis that renders them intelligible to us. The latter, however, demands that we identify distinct causal agents responsible for producing distinct effects (the 'constitution' of the cognizing subject, on the one hand, the effects of an external object, on the other). For many commentators this has seemed not only a difficult but, within the context of the Critical Philosophy, an incoherent endeavour because the notion of an affecting object cannot in principle be well defined within the Critical system, and because only the nature and activities of what Kant calls the 'empirical subject' (that is, the subject in so far as it appears to itself through the cognitive process, as distinct from the subject that undertakes cognition) are supposed to be knowable by us.1 The materials are not available to decide this question now. This topic will have to wait for Part III, where I am in a position to look back on what Kant's real arguments in the Aesthetic, the Expositions, are able to establish. For now, Kant's claims in §1 of the Aesthetic are best treated as the goals of a research project - goals that the immediately following sections of the Aesthetic will seek to realize.

Summary and Conclusions to Part I

The investigations of the previous chapters have led to the following picture of Kant's account of cognition: Kant, following Aristotle, postulates the existence of two distinct cognitive powers or faculties, sense and intellect. Unlike Aristotle, however, Kant does not ground the distinction between these faculties in the kind of knowledge they supply (knowledge of particulars versus knowledge of universals) or in the constitution of the associated organs (the physiological sensory system versus an immaterial mind) but in the functions that they perform in the overall cognitive process. Sense and intellect are not distinct knowing powers but first and second moments of a single activity. Sense receives representations immediately; intellect produces higher-order representations in the light of sensory input. Sense is thus the intuitive faculty, intellect the discursive faculty. However, Kant will also occasionally use the term 'intuition/ which by the time of the Critique had come to be his preferred name for the sensory cognitive faculty, to designate a certain kind of intellectual representation: the representation of particulars, resulting from synthesis of the originally given sensory array. In this case 'intuition' is opposed to 'concept/ the representation of universals, and intuitions and concepts are two distinct types of intellectual representation. This ambiguous usage is a holdover from the Aristotelian tradition, reinforced by the terminology of the logic of Kant's day, which was never worked out of his theory of knowledge (though in his published notes on logic, he at least recognizes the distinction between a 'metaphysical' and a 'logical' sense of 'intuition'). A further feature of Kant's account of cognition is his thesis that the original deliverances of sense are unintelligible or 'blind' prior to intellectual processing, which first brings them to the unity of apperception,

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apart from which nothing can properly be said to be experienced by a subject. None the less, Kant thinks that it is possible to argue backwards from the content evident in intelligible experience (from 'appearance') to draw conclusions about the characteristics of sense intuitions. This does not involve literally separating 'everything that intellect thinks through its concepts' from experience, as Kant proposes in the isolation passages, but it does involve considering what in appearance could possibly be attributable to intellectual processing and what must be a raw datum for any such process. In §1 of the Transcendental Aesthetic, Kant does not actually perform this abstractive exercise. His representation terminology none the less presupposes its results, so in order to give a preliminary indication of how Kant uses his terms I have had to anticipate arguments and present a set of claims about the definitions of and relations between representation terms that are grounded in historical and philological considerations. This investigation has shown that Kant takes the original deliverances of sense to be something complex - what he calls a 'Mannigfaltige' but what is best described as an array. The array consists of a variety of parts - that is, separable items of information, that occur in a certain order as they are presented. Kant claims that he will be able to go on to demonstrate that the items occur in spatiotemporal order. The items of information, whatever they may turn out to be, are sensations. Both aspects of this account call for comment. In making the claim that space and time are 'forms of intuition/ Kant is rejecting the thesis that the spatiotemporal order is constructed by any sort of process, innate or learned. Subsequent processing may refine our experience of the originally given spatiotemporal sensory array, perhaps even to the point where we come to think of that originally given array as being 'second in the order of being' (i.e., a product of perceiver and object motions in the objective space and time we have inferred from it). But the originally intuited array remains first in the order of knowing. It is the fundamental datum for all subsequent processing. This 'formal intuitionist' position on our cognition of space, in particular, is one that Kant shares with Hume, but that so far as I know is otherwise unprecedented in the early modern period (as well as largely ignored by historians of that period). The other aspect of the intuited sensory array is sensation. Besides identifying sensations as the items of information ordered in space and time in an intuition, Kant makes three further important claims about

140 Kant's Representation Terminology them. First, sensations are described as effects on the representative capacity, and hence as modifications of the state of the subject. From this it follows that sensations, and hence the intuitions of which they are the material components, must be physiological states of the body of the subject (supposing that being extended in space is a sufficient criterion for being physical). This result does not commit Kant to materialism (that would follow only if it could also be proven that the higher, intellectual cognitive processes are also physical). It does, however, commit him to the view that the lower cognitive faculty, sense, is exercised by material organs. In this way, the old, Aristotelian distinction between sense as a physiological and intellect as a (perhaps) psychic faculty resurfaces in Kant's account. Kant's second claim about sensations is that they are intensity values, that is, 'matters' that, whatever else they may be described as involving, have a degree of intensity that may be continually diminished towards zero. In our intelligible experiences of percepts and objects, these intensity values are instantiated by the intensive magnitudes of sensible qualities and forces. This is why the classic Aristotelian proper sensibles qualia like colours, tastes, and feelings of heat or cold - as well as physical properties like gravitational force and impenetrability, appear in Kant's examples of sensations. These phenomena are not sensations per se; rather, they are examples of how sensations are thought of by us in our representations of various kinds of objects - in our representations of sense objects, sensations are thought of as sensible qualities; in our representation of physical objects, as physical properties; and in our representations of ourselves, as feelings. Kant's idea appears to be that when we think of or intend an object, certain features in the intentional object' correspond to the effect that physically exists in us as intuition. In particular, what we think of as the 'matter' of the appearance is some quality or property that is capable of intensification or remission and corresponds in intensive magnitude to the intensive magnitude of our sensations. (And, though occasion has not arisen to develop this conclusion, Kant also believes that the matters of appearance are arrayed in space and time in a way that is a function of the locations of the corresponding matters of intuition, though here the mapping is by no means neat.)1 Kant's third claim about sensations is highly problematic. Not only did he want to draw a distinction between sensations, considered as intensity values, and the orders in which these intensity values are disposed and presented in intuition (this is quite unproblematic), he also

Summary and Conclusions 141 wanted to claim that these two aspects of intuition are determined by distinct grounds. The effect of an object on the representative capacity, so far as this effect is determined just by the object, is supposed to be just sensation. The form or manner in which sensations are disposed is supposed to 'lie ready for them a priori in the mind.' It is not only difficult to find an argument in Kant for these claims, it is difficult to follow him at all sympathetically here. The claim is especially hard to argue in the case of time. If the matters of intuition are a posteriori, that is, knowable only after the fact of affection, then already there is a tacit reference made to the notion that the subject must wait for the object to act on it before a matter of intuition can be known. But, from this it follows that the temporal locations of matters of intuition must be at least partially dependent upon the affecting object. The point cannot be made as forcefully for space (because the term 'a posteriori' refers only to a temporal index), but with the case of time as a precedent we can still ask why the particular locations of sensations should not be supposed to be determined by some feature of the objects affecting the sense organs. This is not the worst of the problems with Kant's account of affection, however. The charge that spatiotemporal order could be determined by the affecting object is undercut by another line of criticism that draws its support from the conclusions Kant himself draws about the bounds of human knowledge. According to this charge, Kant is not entitled to say anything whatsoever about the entities, be they external objects or features of the subject's cognitive system, that determine what the senses deliver. Indeed, the very notions of an affecting object or an innate disposition in an affected subject are supposed to be rendered incoherent so that Kant cannot even so much as mention these things without violating his own position on the bounds of knowledge. For, the principles of Kant's Critical Philosophy clearly state that things as they are in themselves, be they external objects or the subject considered as a thing in itself, cannot be said to affect the cognitive process because this requires thinking them under the category of cause, which the Critique shows to be illegitimate. If the objects that affect us are not things in themselves, then the only remaining alternative recognized by the Critique is that they are the entities that Kant calls 'appearances.' But appearances, at least on one standard interpretation, are only objects that first come to exist through our being affected, receiving intuitions, and synthesizing these intuitions under the categories. As results of the cognitive process, they could hardly be responsible for determining the raw data that process operates upon.

142 Kant's Representation Terminology This is a devastating objection, but it is important to remember that it arises only because Kant attempts to isolate distinct grounds for the matter and the form of intuition. Before he ever gets to that, he says a great deal about the elements of human cognition: about the distinction between sense and intellect, the distinction between matter and form of sense intuition, the spatiotemporality of the form of intuition, and the nature of the matter of intuition. This work - particularly his distinction between matter of intuition considered as a collection of intensity values and form of intuition considered as a manner in which these intensity values are disposed and presented - stands independently of his theory of affection, so that even if we should decide that Kant went too far in attempting to identify specific grounds for the formal and material aspects of the intuited array, we can still inquire into the nature of his distinction between form and matter of intuition, the grounds for it, and the consequences of it. There is a cognitive theory and, in particular, a theory of space- and time-cognition to be found in the Critique of Pure Reason. This theory is more fundamental than the theory of affection, and stands independently of any problems there may be with the theory of affection.

P A R T II

The Expositions

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Introduction: Purpose and Method of the Expositions

i.

Purpose

In Part I, it was shown that Kant is committed to a certain account of cognition. This account has four main features: (i) It postulates a distinction between a higher and a lower cognitive faculty - the latter, sense, responsible for the reception of data; the former, intellect, for its processing. (2) It postulates a distinction between form and matter of sensory intuitions grounded in the distinction between order and ordered elements. The form is the order in which elements are received; the matter consists of the elements themselves. (3) It postulates that there are two forms of intuition, space and time, and that the matters of intuition are physiological effects that vary in intensity. (4) It postulates that the matter of intuition arises as the effect of external objects on the sensory capacity, whereas its form is attributable to the constitution of the senses in the subject. By the time of the Critique, the first of these claims had been weakened from the reactionary thesis that we possess two, distinct cognitive powers, operating in accord with distinct principles and delivering distinct objects, to the uncontroversial position that the data that are originally given in experience need to be subjected to a certain amount of processing to yield knowledge, so that whatever it might be in us that is responsible for first receiving data can be usefully distinguished from that which is responsible for processing it. The remaining claims were, however, quite controversial. The claim that the matters of intuition are originally presented and disposed in space as well as time ran counter to a tendency to see spatial relations as derived, be it from innate operations of the mind (Descartes) or associations learned from past experience

146 The Expositions (Berkeley). The implied identification of sensations with physiological intensity values was subversive of the traditional notion that sensations are 'ideas' standing 'before' the mind. And the claim that the spatiotemporal features of intuition are contributed by the subject, whereas the intensive magnitude of sensation is determined by the degree of force in the affecting object, reversed the standard view that it is the spatiotemporal features of experience that correspond to features of objects and sensible qualities that are purely subjective effects arising on the occasion of affection. There is a single source to which Kant looks to establish the controversial features of his account: an investigation of the nature of space and time. If Kant can establish that the raw data that are first received by our cognitive systems occur successively in time and simultaneously in clusters arrayed in space, then he will have shown that space and time are original forms in which our representations first occur, not merely derivative representations. Assuming that sensations are effects on the subject, and that the spatiality of an effect on the subject is a sufficient condition for considering it to be physiological, he will, moreover, have shown that sensing and intuiting must be physiological functions carried out by bodily organs. Finally, if he can assume that our knowledge of space and time (expressed in the propositions of geometry and certain axioms regarding time) is valid prior to any reference to the specific sorts of effects objects have on us, and hence independently of any particular experience, then he will establish that our representations of space and time must be grounded on our own subjective constitutions. Establishing these three things is the job of the Transcendental Aesthetic's Metaphysical and Transcendental Expositions. (The Metaphysical Expositions are directed to establishing the first two, the Transcendental to the last.) They are accordingly the centre-pieces of the Transcendental Aesthetic. Unfortunately, Kant is anything but explicit about this purpose. After a preliminary remark on the characteristic differences between space and time, the Expositions open with the following statement: What then are space and time? Are they actual entities? Or are they only determinations or also relations of things, though of a sort that would still belong to them even if they were not intuited? Or are space and time rather of such a sort as to adhere only to the form of intuition and thereby to the subjective constitution of our mind, without which these predicates could not be ascribed to anything whatsoever? In order to inform ourselves on this matter, let us first exposit

Introduction

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the concept of space [A: first consider space]. [B adds: Now I understand by exposition (expositio) the distinct (although not complete) representation of that which belongs to a concept. The exposition is metaphysical when it contains that which presents the concept as given a priori.] (A237637-8)

Reading this statement, one gets the impression that the ensuing passages are to constitute an investigation into the question of what space and time are.1 One gets the further impression that Kant has in mind four distinct alternatives that he will proceed to weigh against one another: the Newtonian position that space and time are independently existing entities; the Cartesian position that there is no real distinction to be drawn between body and space, so that space simply is the extension of body; the Leibnizian position that space and time arise from the way things are related to one another; and the position Kant himself will press, that space and time are in no sense features of the external world but rather are just the orders in which, in virtue of our subjective constitution, we are determined to receive data in intuition.2 However, when one turns to the actual arguments Kant proceeds to give, these expectations are disappointed. The Metaphysical and Transcendental Expositions never address the possibility that space and time might exist independently in their own right, or be determinations or relations of independently existing entities.3 Instead, the first argument of the Metaphysical Expositions is concerned to show that our concepts of space and time are not drawn from experience;4 the second that the representations of space and time are conditions of the possibility of the representation of any other objects or appearances;5 the last two arguments that the 'original representations' of space and time are not discursive or general concepts, be it of relations or of anything else;6 and the Transcendental Exposition that our representations of space and time are grounded on the manner in which the subject is constituted so as to be able to receive data in intuition.7 In short, the Expositions are not about what space and time are at all. They are about what sorts of representations we have of space and time and how these representations arise in us. If they have any common theme, it is the thesis that our representations of space and time cannot be supposed to be derived from anything more primitive. To this end they argue: (i) that our representations of space and time cannot be supposed to be drawn from the matters given in space and time, and (2) that they cannot plausibly be supposed to be products of intellectual processing. This is, however, just what Kant needs to prove if he is to defend the

148 The Expositions controversial aspects of his picture of cognition. The ontological question, about whether space and time are just forms of intuition or whether they may not also be relations or determinations of things in themselves or independently existing entities in their own right, is not pertinent to this issue. And, as a matter of fact, it falls entirely out of Kant's argument until, at the end of the Expositions, in the 'Conclusions from the Above Concepts/ he makes his notoriously sudden claims about the nonspatiotemporality of things in themselves.8 It is as if Kant embarks on a project of investigating the nature of space- and time-cognition without realizing that this is what he is doing, imagining instead that he is somehow still engaged with a question about the ontology of space and time.9 Instead of considering the Newtonian, Cartesian, and Leibnizian options, he directs all his efforts towards determining just what kind of representation space and time might be. Then, when he reaches a conclusion and determines that they are representations of the form of intuition, rather than of the matter of intuition or the products of intellectual processing, he takes this result to be somehow relevant to the ontological question, and imagines himself to have established that space and time are nothing more than representations in us and not properties, relations, or self-subsisting entities. But, regardless of what Kant may say, the real purpose of the Expositions is not to answer the ontological question but to defend a certain picture of human cognition by proving that space and time are forms of intuition. Whether there are also ontological implications to be drawn from this thesis is examined in Part III, below. ii.

Method

There is one place where Kant does seem to realize that the Expositions are really an investigation into our cognition of space and time. This is the isolation passage from the immediately preceding §1 (A22/B36): In the Transcendental Aesthetic, then, sensibility will first be isolated by setting aside everything that intellect, in passing, thinks through its concepts, so that nothing but empirical intuition will remain. Second, everything in empirical intuition that belongs to sensation will also be removed in order that nothing but pure intuition and the mere form of appearances remain - this is the only thing that sensibility can deliver a priori. This investigation will reveal that there are two pure forms of sense intuition [serving] as principles of a priori cognition namely, space and time - the examination of which will now be undertaken.

Introduction 149 But this passage, too, gives a misleading impression of what Kant will actually proceed to do in the Expositions. For one thing, it gets the order of the argument wrong. In the Metaphysical Expositions, Kant does not proceed by first removing everything that intellect thinks through its concepts and then everything that is supplied by sensation. The term 'sensation' figures only in the first numbered paragraph of the space section, and even references to appearance, which might be supposed to involve something corresponding to sensation and in this sense derivative from it, do not occur after the second numbered paragraph. It is, rather, the later numbered paragraphs that are specifically directed to demonstrating that space and time are originally intuitions rather than discursive or general intellectual concepts. More significantly, however, the isolation passage outlines a method that, given other things Kant wants to conclude about the nature of our cognitive capacities, it would be impossible to execute. Knowledge of any sort requires, not just intuition of the spatiotemporal sensory array, but the intellectual synthesis of this intuition under concepts, so that intuitions that have not been synthesized by the intellect are 'blind/ as Kant puts it at A51/B75- Kant cannot intend to draw this conclusion about the nature of intuition in the Analytic, but then blithely ignore that it is on the way in the Aesthetic, and talk as if it is actually possible to remove everything that intellect thinks through its concepts from experience and still be able to describe what remains. a. The Method of Conceptual Exposition Kant's remarks on the blindness of raw intuition might make it seem impossible to isolate that in our experience that is attributable to intuition. But this pessimistic conclusion follows only if we tacitly assume that the intellect necessarily transmutes or alters what is given to it in intuition, so that the original raw materials can no longer be recognized in the processed result. However, the principal thing that the intellect needs to do to experience, according to Kant, is just to unify it (Ayy/ 6102-3, 6130-1). It takes the variety that is presented in intuition and collects it together in a single thought (for example, thousands of minimally visible coloured points arrayed in space might be collected together in the single thought, 'triangle'). There is no reason, therefore, why the content of the intuited array should be in principle inaccessible to us. Whatever content there is in intuition can be unified under some concept or other. Thus, just as there

150 The Expositions ought to be (i) concepts of objects, resulting from intellectual synthesis of the manifold of intuition, so there ought also to be (2) concepts of properties of objects (concepts of sensible qualities), resulting from intellectual abstraction and synthesis just of the matter of the intuited manifold, as well as (3) concepts of the order in which matters are originally presented in intuition, resulting from intellectual abstraction and synthesis just of the pure form of the intuited manifold - as, indeed, there ought to be (4) pure intellectual concepts, whereby intellect represents just its own forms of synthesis. Given that this is the case, Kant does not need to strip 'everything that intellect thinks through its concepts' out of experience in order to prove that space and time are forms of intuition. Instead, he needs simply to prove that our concepts of space and time are concepts of the form of intuition rather than of the matter of intuition, of the objects of appearance, or of the functions of intellectual synthesis. As a matter of fact, this is what Kant does. Kant is explicit about this method of procedure only in the Introduction to §2 of the B Aesthetic (538). There he makes a significant alteration to his statement of the nature of his project. Whereas in A he had asked the question 'What, then, are space and time?' and then gone on to list the four ontological options mentioned above, concluding: 'In order to inform ourselves about this matter, let us first consider space,' in B he crosses out the words 'first consider space' and inserts, instead, 'first exposit the concept of space.' Then he proceeds to add a sentence explaining what he means by 'exposition': 'I understand by "exposition" the distinct (although not complete) representation of that which belongs to a concept.' Kant is here proposing the opposite of the project described in the 'isolation' passage: not to remove what intellect thinks through its concepts and try to isolate a pure intuition of space and time, but rather to analyse our (necessarily intellectual) concepts of space and time.10 Kant's vocabulary is very explicit. He is going to 'exposit' the concept of space. And this exposition is going to consist in the distinct, though not complete, representation of that which belongs to this concept. Both 'distinct' (distinctus, deutlich) and 'complete' (suffectus, ausfiihrlich) were technical terms of the logic of Kant's day,11 and 'exposition' (expositio, Ero'rterung) was a technical term of Kant's own logic. A concept was called 'distinct' when the differentiae (Notae, Merkmale) that characterize it could be clearly identified and separated from one another. A concept was called 'complete' when all of its specific differences, the specific differences of those specific differences, and so on to infinity, are distinct.

Introduction

151

For Kant, 'exposition' was a certain kind of exhibition of the content of a concept, to be contrasted with 'definition' ^727-30/6755-8; Logic, §§99 and 105). The terminology indicates that Kant sees himself to be engaged in the project of explicating at least some salient differentiae of our concepts of space and time. At this point Kant's own description of what he is up to ceases, but he has brought us far enough to permit a conjecture: that he hopes, by expositing the differentiae exhibited by our concepts of space and time, to uncover something that will indicate their origins in the cognitive system: some specific difference that could be supposed to characterize the concept only on the assumption that the concept originates from something supplied by a form of intuition as opposed to a matter of intuition or a form of intellectual synthesis. Kant's concluding remark on exposition in the Introduction to §2, 'The exposition is metaphysical when it contains that which presents the concept as given a priori' (B38),12 lends support to this reading. This remark indicates that Kant sees the purpose of exposition to be the exhibition of some conceptual content that indicates a specific origin in the cognitive system. Thus, metaphysical exposition shows that the concept contains something that simply could not be there were the concept supposed to arise from sensation (a posteriori). (It certainly has nothing to do with exhibiting that space and time have a peculiar ontological status.) But, if I am correct, then Kant's project of expositing the concepts of space and time also takes a step beyond what is here described as metaphysical exposition: it seeks to establish, not only that these concepts originate outside of sensation, but that they presuppose something that antedates any intellectual contribution to cognition - namely, the representation of an order in which sensations (irrespective of their specific content) are originally presented in intuition. This may be what Kant was really trying to get at in the 'isolation' passage, when he talked of removing everything that intellect thinks through its concepts from experience. What he meant may have been not so much removing what intellect thinks through its concepts from experience as trying to isolate, in what intellect thinks through its concepts, that which is attributable to intuition from that which is attributable to the synthesis of intuitions. b. The Standard View of Kant's Methodology in the Expositions and Its Limitations The position I have sketched so far on Kant's method in the Expositions falls roughly in line with a view that has long been standard among

152 The Expositions commentators, though there are subtle and important differences. According to this view, Kant devotes the first two numbered paragraphs of the Metaphysical Expositions to proving that space and time are a priori. He then devotes the last two numbered paragraphs to proving that space and time are intuitions. These arguments are supplemented by the Transcendental Exposition, which further undergirds the a priori status of space and time by showing that this status is presupposed by the sciences of geometry and mechanics. The Transcendental Exposition also explains the a priori status of space and time by grounding them in the constitution of the subject's receptive faculty. Thus, the Metaphysical Expositions establish that space and time are a priori intuitions, the Transcendental that they have to do with the constitution of the subject. From these points, Kant is then supposed to draw the conclusion (more or less legitimately, depending on which commentator one consults) that space and time are subjective forms of sense intuition.13 This standard view gets Kant's method broadly correct. Kant does indeed argue that space and time are a priori in the first two numbered paragraphs of the Metaphysical Expositions, that they are intuitions and not concepts in the later two numbered paragraphs, and that they are subjective in the Transcendental Exposition. But to summarize the steps of Kant's project in this way is to invite certain significant misrepresentations. Though I have tried to avoid these misrepresentations in the account of Kant's method that I have presented so far, a quiet revision can also be an unnoticed revision. I want, therefore, to list those features of the standard account of Kant's method that I take to be misleading and remark upon how the account I have presented revises the standard one. i Kant's immediate purpose in the Expositions is not to draw a conclusion about space and time, but, rather, to draw a conclusion about the origin of our concepts of space and time. To represent Kant as arguing that space and time are a priori intuitions (rather than that our concepts of space and time are not based on sensation) is to present his project as an ontological rather than an epistemological one: as an inquiry into what space and time are rather than into how we come to know them. As noted above, Kant himself wants to cast his project in an ontological light, but the ontological conclusions Kant wants to draw are the remote consequences (if, indeed, they follow at all) of arguments for more immediate points, and these more immediate points are what should first call our attention.

Introduction 153 2 Kant does not simply claim that space and time are intuitions and not concepts. He claims that the original representations of space and time are intuitions, that is, that our (necessarily conceptual) representations of space and time must be based on something originally presented in intuition rather than being constructed by intellectual synthesis out of more primitive elements that are themselves in no way spatial or temporal. 3 Though Kant claims that space and time are a priori intuitions, his claim needs to be taken with a grain of salt. What he proves (in the First Exposition) is just that our concepts of space and time are not drawn from the matters that are observed in space and time in our experience, and (in the Second Exposition) that these concepts are formed prior to our concepts of other appearances. This is a sense of 'a priori': being independent of the matter of appearance and prior to appearances. However, for our concepts of space and time to be 'a priori' in this sense is not the same thing as for them to be given independently of any experience whatsoever, independently of how we happen to be affected by objects, or independently of a posteriori observation. These stronger claims are argued by the Transcendental Exposition and the Third Exposition as it appears in A (when there was no distinction between Metaphysical and Transcendental Expositions). However, the weaker claims are themselves a significant result, and we should not allow an obsession with the stronger, which unfortunately has infected all of Kant commentary up to now, to blind us to it. The weaker claims establish Kant's unique intuitionist position on the question of spacecognition, and are in their own right a significant though neglected contribution to the history of the theory of visual perception. 4 The conclusion that space and time are forms of intuition is not some further conclusion that needs to be worked out of the Metaphysical and Transcendental Expositions (as if the latter established only that space and time are a priori intuitions, not that they are forms of intuition). It is precisely what the Metaphysical Expositions immediately establish in so far as they show that our concepts of space and time originate from something given a priori in intuition. One point for which Kant should not have to argue is that our concepts of space and time are concepts of two manners or forms in which a (not necessarily denumerable) collection of elements can be arrayed. Space and time are forms of ordering - this follows immediately by analysis of their concepts. But then the Metaphysical Expositions (assuming that they are successful) establish (a) that our concepts of these forms of ordering must be taken

154 The Expositions to represent something that is already present in what is given in intuition prior to any intellectual processing (non-intellectual), and (b) that the locations of sensations in these orders are not determined by any properties discernible in the sensations themselves and so are not based on what is given in sensation (non-empirical). This is just what it means for space and time to be pure forms of sense intuition. These revisions to the standard picture of Kant's method in the Expositions are significant because they entail a very different picture of how the arguments of the Expositions work. What is required to prove that space and time are intuitions and not concepts is different from what is required to prove that our concepts of space and time originate in intuition rather than in intellectual construction. Similarly, what is required to prove that we have intuitions of space and time existing in us independently of all sensory experience is very different from what is required to prove that our concepts of space and time are not drawn from the matter of sense intuitions. And all are very different from what would be required to refute the Leibnizian view that space and time are relations of independently existing things, or the Newtonian view that they are independently existing entities in their own right. Kant's arguments in the Metaphysical Expositions have long been viewed as something less than paradigms of persuasive or successful argumentation.14 But perhaps part of the problem rests with what Kant has standardly been supposed to be trying to do with these arguments. Perhaps, with a different assessment of Kant's purpose and method in mind, the Metaphysical Expositions can at least be seen to be plausible and well-directed (if not successful) arguments, rather than a collection of non-sequiturs, contradictions, and irrelevancies. So I argue in what follows. Appendix: An Empirical Exposition of Our Concepts of Sensible Qualities Granting that Kant's project is one of conceptual exposition, directed at establishing that our concepts of space and time contain some content that presupposes an origin in a form of intuition, it is still a serious question how such an exposition might proceed. What sort of differentiae might be taken to indicate an origin in this or that function of the cognitive system and why? In order to approach this issue it might be helpful to begin with a counterpoint to Kant's 'metaphysical' exposition of the

Introduction

155

concepts of space and time - an 'antimetaphysical' or 'empirical' exposition of our concepts of sensible qualities. This exposition is directed to establish that our concepts of sensible qualities could not arise in an a priori manner, and so be known prior to our being affected by specific objects. If successful, it will back up Kant's claim that sensation, or at least the matter of appearance that we conceptualize as sensation, is to be understood as 'the effect of an object on us, so far as we are affected by it' (A19-2O/B34). It will not rule out that there might be other things that ought equally to be considered effects of objects on us (the form of intuition, for instance, though Kant would never have agreed), but it will establish that the matters of appearance certainly do belong in this class. Empirical expositions of our concepts of sensible qualities antedate Kant. They are foundational for the empiricism of Locke and Hume. In Enquiry, II, and Treatise, 1.1.1 (p. 5), Hume offers two reasons why our concepts of sensible qualities presuppose specific effects on specific sense organs: (i) people whose sense organs have never been affected in a specific way can form no concept of certain sensations (one who has not eaten pineapple, for example, cannot conceive of the taste of pineapple), and (2) people who lack specific sense organs are unable to conceive of any of a whole circle of sensible qualities (the blind can form no concepts of colour, for example). Locke gives the same two arguments at Essay, 2.2.3and 2.1.6 (cf. 3.4.11), right down to the example of the taste of pineapple, further embellishing the point about the inconceivability of colours for the blind with a story of a blind man who, after long investigation of others' reports of colour phenomena, declared that the colour red was like the sound of a trumpet. The moral of both cases is that our concepts of sensible qualities presuppose, not just activity of the sensory faculty, but specific types of effects on specific sensory organs, in the absence of which the concepts simply cannot be formed. Even the most detailed verbal communication with others who have had the requisite experiences is inadequate to supply a concept to those who have not had the experience, so that in its absence they can only substitute other concepts from their own experience that they take to be analogous.15 Sensible-quality concepts could not, therefore, be based on something that the intellect necessarily brings with it to all its cognitive tasks (a concept of a function of synthesis), since then no special effect and no special sense would be requisite indeed, it might even be the case that no effect whatsoever would be required and the intellect would be able to form the concept just by con-

156 The Expositions templating its own 'logical functions/ Similarly, our concepts of sensible qualities could not represent anything like an order in which all matters are received in intuition since then again no specific action on specific organs would be required.16 Some sensory activity would be necessary to supply a concept of a form of arrangement of matters in the first place, but what activity on what organs would be irrelevant.17 What is more, sensible-quality concepts should even be distinguished from complex empirical concepts such as motion, alteration, inertial mass, impenetrability, viscosity, or brittleness, which, while they presuppose the idea of something given through sensation as object, also include determinations of space and time (granting, for the moment, that these latter are indeed the forms of intuition and not sensible-quality concepts in their own right).18 Kant is sensitive to these points/9 and though he does not anywhere dedicate a part of the Critique to giving an empirical exposition of our concepts of sensible qualities, he does remark on the empirical characteristics of sensible-quality concepts in passing, at A28-9, 644, and A2930/645 - texts specifically devoted to demonstrating that our spatial concepts ought not to be compared with our sensible-quality concepts: The pleasant taste of a wine does not belong to the objective determinations of a wine and so to an object, even considered as appearance, but rather to the particular constitution of the senses in the subject who tastes it. The colours are not characteristics of the objects to the intuition of which they are attached, but rather also only modifications of the sense of sight, which has been affected by light in a certain way ... Taste and colour are hardly necessary determinations, under which objects can alone become Objects of the senses for us. They are only bound up with the appearance as contingently included effects of the particular constitution of the organs. Consequently they are also not a priori representations but rather are grounded on sensation - indeed, the pleasant taste is rather grounded on feeling (of pleasure or displeasure) as an effect of sensation. Hence no one can have a representation of a colour or any sort of taste a priori. But space concerns only the pure form of intuition and therefore does not include any sensation (nothing empirical) in itself, and all the kinds and determinations of space can and must be represented a priori if concepts of figures as well as of relations are to arise. Through this alone is it possible that things are outer objects for us. (A28-9) But besides space there is no other subjective representation referred to something outer that could be called objective a priori. For we can derive synthetic

Introduction 157 a priori principles from no other subjective outer representation, as we can from intuition in space (§3). Consequently these other subjective outer representations, to speak exactly, possess no ideality,20 though they agree with the representation of space in belonging only to the subjective constitution of the sensory mode, for example, of sight, sound, and feeling through the sensations of colours, sounds, and temperatures, which, however, since they are merely sensations and not intuitions themselves, permit the cognition of no object, much less its a priori cognition. (644) The intention of this remark is just this: to prevent anyone from getting the idea of illustrating what I have called 'the ideality of space' by means of such thoroughly inadequate examples as colours, taste, and so forth [which are] properly to be considered, not as characteristics of things, but merely as alterations of our subject, which could even be different for different people. ^29/645)

These texts draw our attention to four salient differentiae possessed by our concepts of space, but not by our concepts of sensible qualities: (i) our concepts of space are objective: they refer to objects, at least considered as appearances, whereas those of sensible qualities refer to some thought in the subject that is so far from being objective that we are willing to allow that what the subject thinks of could be different for different people, so that only the common names used in common circumstances insure commonality of reference; (2) our concepts of space are necessary: they refer to something that must be included if we are to cognize an object; (3) our concepts of space are a priori: we can form them in advance of having any specific sensation whatsoever, and they are the basis for principles (of geometry) that we can know in advance will hold valid for all sensory experience; and (4) our concepts of space are public: we cannot wonder whether different people might think something different from what we do under these concepts. Considered as claims about our concepts of space, these remarks will have to be considered below. At the moment, however, I am particularly interested in what they both explicitly and tacitly imply for Kant's views about the nature of our concepts of sensible qualities. The remarks indicate that Kant takes sensible-quality concepts to be empirical because (i) they refer to specific effects had on specific organs. Thus, the taste of a wine is supposed to be attributable to the particular constitution of the senses in the subject who tastes it; colours are modifications just of the sense of sight, which has been affected in a certain way by light; and sensible qualities in general are contingently intro-

158 The Expositions duced effects of the particular constitution of the organs. Furthermore, (2) and (3), our concepts of sensible qualities cannot be formulated in advance of having the appropriate experience. Someone who has never seen a simple geometrical figure can form a concept of it on the basis of a description, but no one can form a concept of the taste of pineapple in advance of actually having the experience of tasting it. Finally, (4) because our sensible-quality concepts arise from specific effects on specific organs, the same object could, for all we know, affect different people with different sensible qualities, so that, for example, they would think something different under the concept red from what we think, though they would refer to it by the same name. But these are just the characteristics Locke and Hume remark upon in arguing for the origin of these concepts in affection of the sense organs (for remark [4! see note 15, above). It should be noted, however, that it would not be legitimate to run this empirical exposition of sensible-quality concepts in reverse. Showing that a specific effect on a specific organ is required before a certain concept can be formulated certainly suffices to prove that this concept is empirical, originating from affection of the senses. But showing that a certain concept can be formulated independently of having to wait on any specific way in which the senses might be affected does not suffice to prove that this concept is not empirical. The concept may still arise from affection of the sense organs, though from some effect that is very widespread and pervasive, so that any specific experience will tend to exhibit it, or from some effect that is very old and memorable as well as inevitable, so that all of us will have experienced it at an early age and will retain the concept though we have forgotten the specific circumstances that provided the material for its formation. Before our ability to formulate a concept prior to any specific experience can be taken to establish anything about its origin outside of the senses, its priority must be established in a very strict sense: the concept must be such that it is not prior, simply to this or that experience, but to the content supplied by any and all experience whatsoever. Though sensory experience may have to take place (in the background, as a necessary concomitant of the process) before the concept can be formulated, the concept must be absolutely indifferent to the content of this experience, so that in its formulation we abstract from sensory experience rather than abstract it from out of the sensory component of experience.21 It must be, as Kant puts it, 'pure.' But these are matters to be dwelt upon in the exposition of our concepts of space and time, to which I now turn.

5 The First Exposition

Either space contains the ground of the possibility of the compresence of many substances and their relations, or these contain the ground of the possibility of space. (R 3790; Ak, XVII 293) It is an essential and distinguishing characteristic of spatial relations that they are variable but do not depend on the quality or quantity of the substances related, while all other relations between objects depend upon their properties.1 i. Space is no empirical concept that has been drawn from outer experience. For, in order that certain sensations be referred to something outside of myself (that is, to something in another spatial location than that in which I find myself), the representation of space must already lie as a ground. Similarly, in order that I be able to represent certain sensations as outside of [B adds: and next to] one another (and consequently in order that I be able not merely to differentiate them, but to represent them as being in different locations), the representation of space must already lie as a ground. As a result the representation of space cannot be derived from the relations of outer appearances through experience. Rather, this outer experience is itself only first possible through this representation. (A23/B38) i. Time is no empirical concept that has somehow been drawn from an experience. For neither simultaneity nor succession would figure in perception did the representation of time not lie a priori as a ground. Only when it is presupposed can things be represented as being at one and the same time (simultaneous) or different times (subsequent). (A3O/B46)

160 The Expositions i.

Kant's Objectives in the First Exposition

In these passages, Kant observes that space must be presupposed in order to represent sensations as outside of myself or alongside of one another, and that time must be presupposed in order to represent perceptions as simultaneous or successive. He concludes in light of this that our concepts of space and time could not be derived from sensations or perceptions. We need to make allowance for a certain slovenliness in Kant's statement of this observation and of the conclusion that he draws from it. Strictly, the conclusion should be that our concepts of space and time are not derived from the things that we experience as being related to one another in space and time. Kant identifies these relata as sensations and perceptions, but neither expression is very apt. Sensations are matters of intuition, and intuitions without concepts are blind, so we might ask how Kant could know what our sensations are like without first conceptualizing them, and how he could be so sure that, in the process of conceptualizing them, the intellect does not draw something from them that leads it to assign them to certain locations relative to one another and so, in effect, to construct a representation of them as arrayed in space. In this case, our concepts of space would be based on what is given in sensation, contrary to Kant's conclusion. Kant should not be begging this important question at this stage, and he does not, in fact, need to do so. It would already be a significant result if, starting just from the appearances that intellect works up out of intuitions and to which we are not blind, he were to demonstrate that the things that are given as related to one another in space in appearances do not exhibit anything that grounds their spatiotemporal relations, so that our concepts of space and time, considered as concepts of relations, could not be supposed to be derived from these things, considered as relata. In what follows, therefore, I do not follow Kant in speaking of 'sensations' as being what are arrayed in space. I instead use the expression 'matters of appearance.' Kant takes the matters of appearance to 'correspond' to sensation, but I do not want to go even that far. Throughout this chapter, I want the expression 'matter of appearance/ to be understood to refer just to whatever it may be in our experiences, as they appear to us through intellectual processing, that plays the role of relatum in spatial relations, regardless of how these matters may be supposed to be related to what Kant calls 'sensations.' In chapter 6, I begin to relate what Kant establishes concerning the 'matter of appear-

The First Exposition 161 ance/ so defined, to sensation considered as matter of intuition and as the properly empirical element of intuition. The term 'perception/ which Kant uses in the time argument, gives rise to a different problem. Kant occasionally (e.g., at 6297) defines 'perception' very narrowly as consciousness of what is given empirically, and hence as consciousness just of sensation (if we follow A42/B6O in taking sensation to be the properly empirical element of experience). In this case, the time section exhibits the same problem as the space section and stands in need of the same reformulation. But Kant also uses the term 'perception' more broadly (e.g., at Aii9~2O, Bi6o), to refer to any kind of consciousness that contains something empirical (whatever else it might contain). But, if space and time are indeed the forms of intuition then such a consciousness could exhibit spatiotemporal structure in addition to empirical content. And then it would be wrong to say that perception could not exhibit time, or that time could not be 'derived' from perception. What Kant really wants to claim is that our concept of time is not derived from the matter that is given in perception, that is, from the relata that are perceived as standing in temporal relations. So Kant's point again appears to stand in need of the more rigorous formulation proposed above for the space passage. Let us proceed, therefore, by taking Kant's point in both sections of the First Exposition to be just that our concepts of spatiotemporal relations are not derived from the relata that appear or are perceived to stand in these relations. a. The Standard Objection and Its Standard Refutation There is a standard objection to Kant's argument in the First Exposition, and a standard reply to this objection. The objection is that the conclusion, that space and time are a priori representations, does not follow from the premises, that space is required for me to be able to represent matters as outside of myself or alongside one another and that time must be presupposed in order to represent matters as simultaneous or successive. That space should be required in order for me to be able to represent matters as 'outer' is true. Indeed, it is a tautology, and the same holds for the claim about time. But this does not prove space or time to be a priori. If all that we had to do to prove something a priori were show that it must be represented in order to be attributed to anything, then everything would have an equal title to be a priori. For, just as space must be represented in order to represent matters of appearance as outside of myself or alongside of one another (in other words, as

162 The Expositions located in space), so colour must be represented in order to represent matters of appearance as of a lighter or darker shade than one another, and sound in order to represent them as of a higher or lower pitch, and so on. But, as Kant himself would admit, our representations of colours, sounds, and the like are empirical, obtained by comparing and contrasting the kinds of effects objects have on our various senses. Why should space and time not be the same?2 The standard response to this objection is that Kant's real point is more subtle. When he says that space is required in order for me to be able to represent matters of appearance as outside of myself or next to one another, he is not just saying that space is required in order to represent these matters as located in space; rather, he is saying that space is required in order to distinguish these matters as belonging to some object other than myself. Only in so far as I represent my sensations as located in space, so the defence goes, am I able to tell them apart from my own inner states.3 Furthermore, once I have distinguished these objects from myself, only in so far as I represent them as being in different places in space can I distinguish them from one another.4 Time, in contrast, is supposed to be the form particularly of those matters that I take to belong to the appearance of my own states,5 though derivatively this makes it a form of all sensations (since all representations, be they of myself or of other objects, are supposed to be inner states of the mind and, as such, subject to temporal form, as Kant claims at A34/B5O). And only in so far as I represent my inner states as located at different points in time am I supposed to be able to distinguish them from one another.6 This reading of Kant's premises gains support from the way the notion of outer sense was understood in Kant's day. The distinction between outer and inner sense goes back at least as far as Locke's distinction between sensation and reflection. For Locke, sensation is not simply defined as spatial representation, nor is reflection defined as temporal representation. Rather, sensation is defined as the source of those ideas that we perceive as a result of the action of objects on our sense organs (Essay, 2.1.3), reflection as 'the Perception of the operation of our own minds within us' (2.1.4). There is a connection between space and sensation, and time and reflection in Locke, but it is genetic rather than tautological. Our ideas of space are supposed to arise from sensation (2.5 and 2.13.2), those of time from reflection (2.14.3)7 Similarly, in the work of Kant's contemporaries, outer sense is not by definition the sense of what is in space. Rather, it is defined as the sense

The First Exposition 163 through which we represent everything distinct from our minds, including our own bodies as a special case. Thus, Crusius writes: We call outer sensation that by which we represent things as outside of that thing that thinks in us, and these [outer sensations! are in accord with the state of certain extremities of our bodies. But they are called inner sensations when through them we represent something as in the very thing that thinks in us. Through these latter we are aware of ourselves, our thoughts, and our states of mind. (§426)

And Baumgarten, §535, states that 'sense represents either the state of my soul (as internal sense) or the state of my body (as external sense)/ From these definitions, it in no way follows that 'outer' sense need necessarily be spatial. What makes a smell or a pain an 'outer' sensation is that it is referred, in the one case, to some other object than myself and, in the other, to the physiological state of my body. An imagined smell or hypochondriacal pain, however similar to outer sensations, would be states of the soul and, as such, inner sensations. Kant takes this distinction over. But he also embellishes it with his doctrine of the forms of intuition, describing space as the general form of 'outer' sense, and time as the form of in inner sense: By means of outer sense (a feature of our minds), we represent objects as outside of us, and all of these as in space ... Inner sense, by means of which the mind intuits itself or its inner state, admittedly gives no intuition of the soul itself, as an Object, but there is still a determinate form under which the intuition of its inner state is alone possible, so that everything that belongs to its inner determinations is represented in temporal relations. Outwardly time cannot be intuited,8 any more than space can be intuited as something in us. (A22-3/B37)9

In Kant, however, this is still not a definition, but a synthetic claim about the nature of the representations of 'outer' and inner sense. Unfortunately, because the sense through which we represent objects distinct from the mind was traditionally called 'outer sense/ Kant's claim that objects 'outside' us are represented in space takes on an appearance of tautology that is quite foreign to his true meaning. Thus, those who offer the standard defence of Kant's First Exposition make a point that is quite correct. This does not, however, alter the fact that their point is also quite irrelevant to the context of the First Exposition. While, for Kant, outer sense is defined as the ability to sense objects

164 The Expositions distinct from my mind, so that the equation of space with the form of 'outer' sense is not true by definition, there is simply no indication that this is at all relevant to what he is trying to prove. In the text of the space exposition, Kant explicitly defines the words 'outside me' as meaning 'in another place in space than that in which I find myself.' The representation of space must already lie as a ground in order that particular sensations be referred to something outside of me (that is, to something in a different place in space than that in which I find myself)' (A23/B38; my italics). As this pronouncement makes clear, 'outside me' does not mean 'numerically distinct from me'; it means 'located in a different space than me.' To read Kant as actually intending to say that I must locate objects in a different space than myself in order to numerically distinguish them from myself is to ignore the parentheses and the 'that is,' which demonstrate that the reference to other places in space is a definition or explication of what 'outside' means, and not a condition for something to be 'outside.' Kant is even more explicit about the phrase 'outside of or next to one another.' Here he says quite plainly that by 'outside of or next to' he does not mean 'distinct from' but rather 'being in a different location.' The representation of space must already lie as a ground in order for me not merely to distinguish [certain sensations] as outside of [and next to] one another, but represent them as being in different places' (A23/B48; my italics). Those who read Kant as saying that we need space in order to distinguish mind-independent objects from one another read him as saying precisely what he claims not to be saying.10 Again, in the section on time, Kant nowhere says that time is needed simply to distinguish perceptions numerically from one another. He is quite emphatic about saying that time is needed, instead, to locate perceptions at earlier or later or coincident points in a series. 'Simultaneity or succession would not figure in perception were the representation of time not present a priori as a ground' ^30/646; my italics). Those who read him as really meaning to say that locating perceptions at different points in time is the only way to distinguish perceptions numerically are attributing a premise to Kant that is simply not to be found in the text. In fact, they are running contrary to the spirit of the text, which mentions simultaneity, as well as succession, as a possible relation of perceptions. Were the response correct, there could be no simultaneity of perceptions unless the perceptions were identical, and Kant gives us no indication that he thinks this. On the contrary, he treats the possibility that different perceptions might be represented as being at the same time (while

The First Exposition 165 still remaining different) as no less likely than the possibility that they might be represented as being at different times.11 Contrary to what the standard defence maintains, the theme of the First Exposition is not object recognition - how we differentiate between objects in the external world, or between ourselves and an external world, or between our own states in the internal world. The theme of the First Exposition is spatiotemporal localization - how we are able to refer our sensations and perceptions to locations in ambient space and fix their relations in time. As Kant makes clear in the first sentence of both the space and the time passages, he intends to attack a certain view of localization, that can be called the 'empirist' or, better, 'sensationist' view. According to this view, our concepts of space and time, and thereby of the spatial and temporal relations and locations, are obtained simply from inspection of the matters of appearance.12 It is in this sense that they are what Kant calls 'empirical concepts' that have been drawn out of experience. ii.

Kant's Sensationist Opposition

Just what sort of view might Kant consider himself to be attacking when he directs himself against the theory that space and time are empirical concepts that have been drawn out of experience? Locke's account of how we obtain our idea of time can provide an entry to consider this question.13 §3. To understand Time and Eternity aright, we ought with attention to consider what Idea it is we have of Duration, and how we came by it. 'Tis evident to any one who will but observe what passes in his own Mind, that there is a train of Ideas, which constantly succeed one another in his Understanding, as long as he is awake. Reflection on these appearances of several Ideas one after another in our Minds, is that which furnishes us with the Idea of Succession: And the distance between any parts of that Succession, or between the appearance of any two Ideas in our Minds, is that we call Duration ... §4. That we have our notion of Succession and Duration from this Original, viz. from Reflection on the train of Ideas, which we find to appear one after another in our own Minds, seems plain to me. (Essay, 2.14)

According to Locke, the idea of time is not innate in us but arises from a certain kind of experience, specifically from an experience of inner sense or reflection. We get this idea by, first, having various other ideas of

166 The Expositions sensation and reflection (in Kant's terminology, various sensations from outer and inner sense) and, then, reflecting on these other ideas. When we do so, we discover that our ideas stand in certain relations of simultaneity and succession, and it is from these relations that we first abstract our concept of time. Kant's time exposition contains a counterpoint to this view. 'Simultaneity or succession would themselves not come into perception were the representation of time not present a priori as a ground/ he writes. 'Only under its assumption can something be represented as at one and the same time (simultaneous) or in different times (subsequent).' Clearly, there is a disagreement here. Locke believes that our idea of time is based on reflective or inner-sense experience of the temporal relations of other ideas, whereas Kant believes that our ideas of temporal relations are based on what he calls 'a prior representation of time.' However, more needs to be said to expose the substance of this disagreement. In the end, Kant is propounding not so much the opposite of what Locke says as a more profound analysis of the presuppositions of Locke's theory. Locke's account of time is deficient in an important respect: it does not explain just how the ideas of simultaneity and succession are obtained from reflection on the other ideas that we have (though, as I note in a moment, there are hints at a possible explanation which perhaps inadvertently slip into Locke's account). But this much is obvious, even from what Locke does say: our ideas of simultaneity and succession are ideas of relations. As such, they presuppose relata. Reflection cannot spontaneously supply us with ideas of simultaneity or succession; we must be supplied with certain other ideas in which reflection can discover these relations (though perhaps, subsequent to this experience, we may go on to form an abstract idea of the relations of simultaneity or succession). Thus, Locke goes on to note that, were there no other ideas actually standing in relations of succession in our minds, we would not experience the passage of time and would have no ideas of the relations of simultaneity or succession (Essay 2.14.4). But now, granting that various other ideas of sensation and reflection are given to us, how precisely do we come to find upon further reflection that these ideas stand in relations of simultaneity and succession? A strict sensationist - someone who believes that absolutely nothing is given to us in experience over and above ideas of sensation and reflection, would say that our ideas of relations must one and all be somehow drawn out of our other ideas. This is, in fact, the case with many of our

The First Exposition 167 ideas of relations. The way we form the idea that one colour is brighter or more saturated or differently shaded than another is by holding the two colours before our eyes and comparing the sensations they give us. The way we scale sounds is similarly based on a comparison of various sounds. A truly sensationist account of the relations of succession and simultaneity would hold that they likewise are obtained by reflective acts of comparison and contrast of our various ideas. The classical version of such a theory of time perception has it that our different experiences exhibit a certain scalable quality (often called Vivacity')14 that serves to designate their relative position in time. On this account, simultaneous experiences are those which exhibit the same degree of Vivacity' when they are compared with one another on reflection, whereas, if experiences are successive, one will be more Vivacious' than another, increases in Vivacity' corresponding to increasing proximity to the present moment.15 Locke, however, simply does not say enough at Essay, 2.14.3-4, f°r us to be able to attribute this view to him.16 Even more interestingly, however, he says something that, perhaps quite inadvertently, endorses a very different account of time perception: there is a train of Ideas, which constantly succeed one another ... Reflection on these appearances of several Ideas one after another in our Minds, is that which furnishes us with the Idea of Succession ... we have our notion of Succession and Duration ... from Reflection on the train of Ideas, which we find to appear one after another in our own Minds, (my italics)

Note the occurrence of the little word 'after' in these sentences. The implication, whether Locke intended it as such or not, is that the ideas upon which we reflect actually occur one after another in time, so that the basis for our cognition of temporal relations is not some reflective act of comparison or contrast of ideas but this original fact of their succession. It might be thought that the account of memory that Locke added to the second edition of the Essay (2.10.2) mitigates this implication somewhat: But our Ideas being nothing, but actual Perceptions in the Mind, which cease to be any thing, when there is no perception of them, this laying up of our Ideas in the Repository of the Memory, signifies no more but this, that the Mind has a Power, in many cases, to revive Perceptions, which it has once had, with this

i68 The Expositions additional Perception annexed to them, that it has had them before. And in this Sense it is, that our Ideas are said to be in our Memories, when indeed, they are actually no where, but only there is an ability in the Mind, when it will, to revive them again; and as it were paint them anew on it self, though some with more, some with less difficulty; some more lively, and other more obscurely.

On this account, what enables us to order our ideas in time in the way that we do is not that these ideas actually occur in temporal succession, but rather that they are regularly accompanied by certain other ideas of reflection by which we think of the first ideas as earlier or later. This is a sort of vivacity criterion, except it is not the vivacity of the idea itself that supplies the temporal index but what is thought in the accompanying idea of reflection. But, far from explaining time-cognition, this account merely begs the question in a new way. What, we may ask, is it that determines that one idea rather than another should be had 'with this additional Perception annexed to it, that it has been had before'? And what it is it that determines how much earlier an idea of memory is thought to have occurred? Is it that the mind is so constituted that ideas that, in fact, occurred earlier in sensation are thought to be older in memory? But then a real succession of ideas is presupposed as the actual ground of our cognition of time. Worse, on this account, when we recall ideas, we are supposed to recall them 'with this additional Perception annexed to them, that [we have] had them before.' But the little word 'before/ like the little word 'after/ designates order in time. If all our ideas occur in the solipsism of the present moment, so that temporal succession is merely an appearance resulting from the fact that some of our (presently had) ideas are accompanied by a further (presently had) idea to the effect that the first ideas have been had 'before/ then where are we supposed to get this idea of 'before' from? Is it an innate idea originating in us on the occasion of the act of recalling past perceptions? Locke remains silent. These reflections on Locke's problems explaining the origin of our idea of time make particularly apt a comment Kant included in ID, §14 li (the parallel in ID to the Critique's 'First Exposition of the Concept of Time'): And thus the concept of time, regarded as if it had been acquired through experience, is very badly defined, if it is defined in terms of the series of actual things which exist one after the other. For I only understand the meaning of the little word after, by means of the antecedent concept of time. For those things come

The First Exposition 169 after one another which exist at different times, just as those things are simultaneous which exist at the same time. (Ak, II 399)

Were it not for the fact that Kant speaks here of the series of actual things rather than the series of ideas, it would be hard not to see this remark as addressed specifically to Locke's account of time-cognition in Essay, 2.14.3-4. (ID, §14 ^5 [Ak, II 400-1] makes clear that Kant did not have Locke in mind but the Leibnizian definition of time as the order of successive things.)17 But, regardless of whether Kant had Locke specifically in mind, the point both ID, §14 1i, and the 'First Exposition of the Concept of Time' seek to make is that, if our perceptions (or 'the things that come before the senses,' as an earlier sentence of ID, §141i puts it) were not already in time to begin with, no notion of the temporal relations of simultaneity and succession could be drawn out of any reflection upon our experience or any comparison or contrast of perceptions or of the things that come before the senses.18 Kant's account therefore does not so much oppose Locke's as run deeper. Where Locke says that our ideas of time are based on reflection on the temporal relations of simultaneity and succession exhibited by our other ideas of sensation and reflection, Kant asks, 'What is the basis for our knowledge of these relations?' and he picks on the little word 'after,' which infiltrates into accounts such as Locke's and says that our ability to discover temporal relations of simultaneity and succession itself presupposes that our ideas of sensation and reflection have originally been presented after one another in time. Locke's ideas of sensation and reflection are therefore not all there is to experience. Over and above these ideas, the properly empirical element in experience, there is something else: a temporal order in which ideas of sensation and reflection are presented so that an experience of a temporal array of representations lies at the basis of all concepts of temporal relations - rather than it just being the case that reflection upon the comparative relations evidenced by representations serves to supply us with our ideas of time. iii.

The Standard Objection to the First Exposition

Having made this elucidatory remark on what it is Kant is trying to claim in the First Exposition, I now return to an issue raised earlier. I said above that it is frequently charged that Kant's argument in the First Exposition reduces to the trivially true claim that we need a concept of space in order to be able to represent things as outside of us and next to

170 The Expositions one another - and that this is hardly sufficient to prove that this concept is of a priori origin. I also said that it is wrong to try to defend Kant by taking his point to be that space is required for us to be able to distinguish objects from ourselves and from one another. Kant's point in the First Exposition has to do with spatiotemporal localization, not with object recognition. The preceding presentation of Kant's views in contrast to Locke's has illustrated and strengthened this point. Does this mean that we must accept the validity of the standard objection? I think not, and in what follows I explain why. Those who propound the standard objection have Kant's basic point right. Kant does indeed claim that time must be represented in order for us to represent our perceptions as being simultaneous or successive, not in order for us to be able to distinguish them from one another. And he does claim that space must be represented in order for us to represent matters of appearance as outside of ourselves or alongside one another, not in order for us to be able to distinguish them from ourselves or from one another. But the standard objection misses the import of this claim. It is only very crudely rendered as the claim that the representations of space and time are required in order for us to be able to represent the spatial and temporal locations of objects. What Kant means more exactly is that, in order for us to be able to represent spatiotemporal relations, such as simultaneity, succession, or adjacency, among the matters of appearance, these matters must first have been presented to us in a spatiotemporal order. This is not, as the crude rendering makes it appear, a merely trivial claim. It is very seldom the case that we have to be presented with an ordered array of elements before we can determine the relevant relations between those elements. Indeed, this is almost never the case. Most often, all we need to do is inspect and compare the elements with one another. Thus, we do not have to be presented with a three-dimensional colour map, in which all the distinguishable hues, shades, and tones of colours are laid out alongside one another on little swatches, in order to be able to determine that crimson and scarlet are more like each other than either is like green. We can determine the relevant proximity relations merely by inspecting the three colours. Indeed, it is our acts of comparing and contrasting various colours (in effect, of relating them to one another) that originally determine the locations of colours in colour space, rather than the other way around. Kant is saying that the locations of objects in space and time are not like their locations in colour 'space.' Where colour is concerned, we

The First Exposition 171 experience the elements first and then determine their ordering relations by comparison and contrast. Then, as a final step, we may actually arrange the elements in terms of these relations and so generate the colour 'space/ But, with location in space and time, Kant is claiming, it is rather an articulated experience of the elements already arranged in the order that comes first and serves as a ground of our perception of the relations (of position), not relations (of similarity and difference) that determine the order. This is what Kant means by saying that space literally lies as a ground of the spatial relations of externality and adjacency and that time lies as a ground of the temporal relations of simultaneity and succession.19 The relations of the elements are determined by the manner in which they are originally presented in experience, so that, were there no temporal order already structuring the way our perceptions occur, there would be no basis for discriminating relations of simultaneity or succession, and, were the elements not disposed alongside one another in any given perception, there would be no basis for ascribing spatial proximity relations to them. ID, §14 ^[5, is especially explicit about this point: For it is only through the concept of time that we coordinate both substances and accidents, according to both simultaneity and succession. And, thus, the concept of time, as the principle of form, is prior to the concepts of substance and accident. But as for relations or connections of any kind: in so far as they confront the senses they contain nothing which tells us whether they are simultaneous or successive to each other, apart from their positions in time, and those positions have to be determined as being either at the same or at different points of time. (Ak, II 400)

This is hardly a trivial claim, as the standard objection would have it. It is one that is even open to empirical testing of a kind. If our cognition of space and time were actually based on something given in the matter of appearance, then it ought be possible to induce experimental subjects to misperceive the order in which stimuli are actually impressed by careful manipulation of the kinds of stimulation. If, on the other hand, our cognition of space and time comes from the order in which stimulation occurs, then the only way to change a subject's experience of the spatiotemporal relations of matters of appearance would be to actually change the locations and times of stimulation, and changes in the nature of the stimulus ought to have no effect on judgments of location.20 Not only is Kant's position one that can be challenged, it is one that

172 The Expositions was (in its spatial form) vigorously opposed by a whole school of nineteenth-century visual theorists (the empirist school), who tried to explain how our experience of the spatial locations of objects could be derived from mental operations performed upon 'sensations'21 that themselves are in no way spatial. The standard objection merely makes the claim appear trivial by glossing over the distinction between spatial order and spatial relations, on the one hand, and temporal order and temporal relations, on the other, and by ignoring the priority to which Kant is calling our attention. Kant is saying that an array of elements in space and time must be given before spatiotemporal relations between those elements can be perceived. Spatiotemporal relations cannot be independently drawn from the elements merely by qualitative comparison. In this respect space and time are not 'empirical concepts of relations that have been drawn out of the matters of appearance/ as are colours or sounds. They are, as Kant concludes in the First Exposition, a priori with respect to those matters. That is, they have their origin, not in anything we can draw out of these matters themselves, but in something else: a form or manner of disposition in which they are presented. a. The A Priori Status of Space and Time This final point is one that I want to pause to remark upon in more detail because it shows up a variant way of pressing the standard objection that has been popular ever since Feder and Maafi formulated it in 1787 and 1788. According to this variation on the objection, even if we were to grant Kant the point that there is some non-trivial22 sense in which a representation of space must be presupposed before the matters ultimately perceived as being in space can be localized, it still would not follow that space is an a priori concept. Space would not have to be a priori because, even if space has to be present in our experience before the matters of appearance can be localized, it does not follow that it has to be present in experience prior to these matters. It could be the case that it is always given in experience along with the matter of appearance, never prior to or independently of it, so that our concepts of spatial determinations are abstracted from outer experience no less than our concepts of sensible qualities. Feder, who so far as I have been able to determine was the first to raise this objection, also puts it best: And indeed it is admittedly beyond doubt that, without having the representation of space already within our power, we could not with clarity and awareness

The First Exposition 173 either distinguish ourselves from things outside us or distinguish things outside us from one another, as we now can. But no one is conscious of this distinction from the first beginning of their life and sensation, so that, before the representation of space may be admitted to be present in us prior to all sensation, it must first be asked whether this representation could not have been drawn from out of the confused chaos of our first sensory impressions or worked up from the power of thought of the human spirit23 before the ability to distinctly distinguish bodies in space developed: an ability of which we only became conscious after thousands of sensory impressions. (Feder, 25)^

The answer to this objection is that it is no objection at all and that it does not say anything that Kant could not accept with complete equanimity. It may well be the case that space is only ever given to us along with the matter of appearance in an empirical experience. It may well be the case that our concepts of pure space and sensible qualities are both concepts abstracted from this originally given experience. The real question is: from what in empirical experience are these concepts abstracted? Are they abstracted from the matter of appearance? Or are they abstracted from something that is given in sensory experience over and above this matter? If the latter, then they are given independently of this matter, notwithstanding the fact that they are only first given along with it in an experience. There can be no doubt that all our cognition begins with experience/ writes Kant at Bi. 'No cognition precedes experience in time ... But though all our cognition arises with experience, all does not come out of experience. For it could well be that even our experiential cognition is a composite of that which we sense through impressions and that which our own cognitive capacity (merely occasioned by sensory impressions) brings out of itself.' In the First Exposition, Kant does not draw any conclusions about whether the orders in which matters are given in an appearance, or for that matter the matters themselves, are occasioned by sensory impressions or contributed by the subject.25 But he does conclude that our knowledge of the order in which matters are given is not derived from the matters themselves. Our knowledge of this order is, to this extent at least, not posterior to our knowledge of the matters. And if we take 'a priori' in a preliminary, negative sense to designate just that which is not a posteriori, then we can say that our knowledge of the order is a priori. In the analysis of the concept 'nothing' appended to the Amphibolies, Kant is even more explicit. There, far from rejecting Feder's position on

174 The Expositions the genesis of our concept of space, he explicitly accepts it. 'Were light not given to the senses, and were extended objects not perceived, then it would also be impossible for us to represent any darkness or any space' (A292/B349). The burden of Kant's First Exposition has been to claim that our concepts of spatiotemporal relations like adjacency and succession, and hence our concepts of spatiotemporal determinations in general, are not, in fact, drawn out of an inspection of the relata but presuppose an experience of something over and above the relata: a form of arrangement or manner of disposition in which the relata are originally presented. From this it follows that our concepts of space and time originate independently of reference to the context of the matters of appearance, and thus that these concepts are a priori in the negative sense.26 It is not necessary that Kant go on to establish some extravagant sense of priority involving being given prior to any sensory experience whatsoever.27 Our concepts of spatiotemporal relations, and hence of space and time, do not have to be innate ideas antedating sensation or pure intuitions given all on their own.28 They just have to be drawn from something given in experience over and above the matters of appearance or what results from comparison of those matters.29 iv.

The Grounds of Kant's Rejection of Sensationism

In the First Exposition, Kant articulates an alternative to the sensationist view that our concepts of space and time may be drawn from what is given in the matter of appearance. He claims that the matters of appearance must instead be supposed to be already presented to us in a spatiotemporal order and that it is this order of presentation, and not anything that can be found in the matters themselves, that is the ground of our cognition of space and time. This view undercuts Locke's account of time-cognition by presenting a more sophisticated analysis of the presuppositions Locke appears to make about our ability to obtain ideas of spatiotemporal relations by reflection on our other ideas. It also avoids the 'circle' in the Leibnizian definition of time. But one wonders if more may not be said on behalf of a sensationist account of space- and timecognition than Locke provides, and whether Kant's alternative looks good merely in an ad hominem context. Aside from exposing Locke's hidden presuppositions and attacking Leibniz's alternative position, does Kant articulate any independent, positive reason for accepting his view? Is there any such reason?

The First Exposition 175 a. An Excuse The answer to the first of these questions is 'no/ Kant does not present any independent, positive reasons for accepting his view. The First Exposition simply states that spatiotemporal relations cannot be apprehended unless the relata, sensations or perceptions, are presented in a spatial and temporal order. There is no argument for this claim. It is presented simply as if it were an obvious fact of our experience. At the time Kant wrote, it may well have been. Locke's account of space- and timecognition had, as has been seen, tacit Kantian presuppositions. Leibniz's was an ontological theory that did nothing to address the question of how space and time are cognized. The revolution in the theory of vision initiated by Berkeley's New Theory of Vision, a revolution that was to culminate in the mid-nineteenth century with the development of sophisticated empiristic theories of space-cognition, had only just begun to take hold. Berkeley himself had gone only so far as to identify four components of space-cognition - depth perception, size constancy, orientation, and our ability to coordinate visual and tangible space - which could be drawn from the matter of appearance. He had not questioned the thesis that we have a prior representation of the spatial relations between visual data in two dimensions or tried to effect a similar derivation of what he called 'apparent magnitude' (two-dimensional spatial relations) from features of sensations. On the contrary, he had supposed that minima visibilia are presented in a two-dimensional spatial order in visual experience.30 In 1787, Feder tried to make good this lack by appealing to the Berkeleyan notion that our primitive idea of space just is the feeling of entirely unimpeded motion31 and claiming that some sort of intellectual synthesis of visual images with feelings of motion is what generates our concepts of visual spatial relations: For the essential content of [the idea of space] lies in that feeling that arises in us along with our motions and by setting these feelings together we also develop this idea out of every image that appears to the eye. Getting the content of the concept of space out of these two types of sensory impressions is admittedly something that belongs to a power to develop ideas, that is, that belongs to human intellect.32

But Feder failed to give any explanation of just how the intellect is supposed to be able to achieve this. This is especially important as some of

176 The Expositions the language he employs seems dangerously circular. Is there a tacit presupposition that visual images consist of parts already presented in a spatial array in the original visual experience? If so, then our cognition of spatial order is not explained but presupposed; if not, then how do sensations of motion fix the spatial locations of a collection of disparate, aspatial visual experiences? What is a feeling of motion? Does it involve the presentation of the moving limb at successively different positions in tangible space? Then, again, the cognition of spatial order is not explained but presupposed. But if, alternatively, the feeling of motion is a mere muscle sensation, then the question of how it is supposed to assist the mind in generating what we think in our concept of space becomes even more perplexing. How are successive, purely qualitative muscle sensations supposed to assist us in localizing the parts of visual images in space? Feder has nothing to say. Berkeley's nativist opponents were no more successful at effecting a complete reduction of spatial phenomena to aspatial elements than were his empirist successors. William Porterfield assumed that the mind is so constituted that its judgments about the spatial arrangement of the parts of objects reflect the order in which the light coming from those parts falls on the retina.33 In taking this position, Porterfield stressed that the mind does not actually see the 'picture' on the retina (this he regarded as a vulgar error),34 and neither does it learn to interpret what it sees in such a way that its judgments come to reflect the order that is, in fact, present on the retina.35 Rather, the correlation is brought about in virtue of 'an original, connate and immutable Law to which our Minds have been subjected from the Time they were at first united to our Bodies.'36 There is no real causal connection between the 'picture' on the retina and the judgments the mind makes (Porterfield was an occasionalist on this topic); rather the 'original, connate and immutable law' describes what is no more than a 'Humeian' constant conjunction.37 Despite these qualifications, however, the fact is that Porterfield's law takes the physiological location of the stimulus in the body, not anything in the sensations received by the mind, to be what determines space-cognition, if only 'occasionally.' Were the stimulus not already articulated in space to begin with, there would be nothing to serve as even an occasional cause of space-cognition, and nothing to be correlated in a law-like fashion with our judgments of location. In this sense, Porterfield's account presupposes a primitive ground of space-cognition that is already spatial in structure - it is just that this ground is a physiological impression rather than an idea.

The First Exposition 177 Much the same point can be made about Porterfield's disciple in these matters, Thomas Reid. Reid was a committed dualist who supposed that nothing extended in space could qualify the mind.38 One might think that, if anyone would have a way of explaining how the mind works a perception of space up out of originally given elements that are not themselves spatial, he would. And indeed, the broad outlines of Reid's cognitive theory are very promising in this regard. The basic Reidian doctrines are as follows: Minds can have sensations, but these are merely feelings that are in no way spatially extended. Minds can also have perceptions, but, while the object of a perception can be something extended in space, the perception itself is only an act of the mind whereby the mind acquires a belief in the present existence of an object possessed of certain features; the perception is not itself anything extended.39 Objects stimulating the sensory organs can bring about sensations in the mind and the mind can be innately so constituted that the occurrence of certain sensations leads it to form a belief in the present existence of an object of a certain kind,40 but in this process nothing extended migrates into the mind. But, when the time comes for Reid to talk about visual space-cognition, this neat picture gets muddied. Objects affect the eye, and we are so constituted that, when the eye is affected in different sorts of ways, the mind experiences different sorts of sensations. These sensations are sensations of colour. When they occur they suggest to the mind the present existence of an external object thought to be qualified in a certain way (the mind is so constituted as to think that objects or parts of objects that cause identical colour sensations themselves have the same colour quality).41 But colours can occur anywhere on the visual field and can be arranged in any order. So our colour sensations cannot by themselves suggest anything about the locations of their causes. What, then, gives us our knowledge of the locations and manner of arrangement of colours? Reid's answer is that there is no sensation that is suited to suggest a perception of location to the mind. Location is, rather, directly suggested by what he calls the 'material impression' on the retina, that is, by the physiological stimulus.42 And here Reid invokes Porterfield's principle: the mind is innately so constituted as to judge the causes of the colour sensations it receives to be disposed in space in the way in which the parts of the material impression are ordered on the retina. Like Porterfield, Reid denies both that the mind sees the 'picture' on the retina and that it learns to impose a spatial interpretation on its sensations.43 Rather, it is simply innately so constituted that stimulation of different parts of the retina

178 The Expositions leads it to make a judgment that a stimulus source exists at a corresponding location in space (and again, the only kind of causality claimed here is Humeian constant conjunction).44 In effect, each part of a material impression is supposed to both cause a colour sensation and suggest to the mind that the cause of that sensation is located at a certain place on the visual field.45 Thus, for Reid as for Porterfield, space is not so much constructed as presupposed. Were the parts of the material impression not already articulated in space, there would be nothing for the mind to draw on in forming its beliefs about visible figures. The observations that have been made about Berkeley, Feder, Porterfield, and Reid are indicative of a general problem with theories of space-cognition in Kant's day. Between Berkeley's time and Kant's, no one was able to successfully effect a complete derivation of all three dimensions of spatial relation from purely qualitative properties of the matter of appearance.46 The situation with the theory of time-cognition was little better. There was, as mentioned earlier, a theory attributed to Hume by Reid that temporal relations might be based upon the relative intensity relations of some quality, analogous to vivacity, in our current ideas. But this theory is not obviously Hume's,47 and it certainly was not Reid's, since he subjected it to withering attack,48 and I have not been able to determine whether Kant was aware of it or, if he was, whether he took it seriously. He had, in 1770, encountered a quite different theory of time-cognition in a letter from Mendelssohn: If A and B are both real and are the immediate (or even the remote) consequences [rationata] of a ground, C, I call them hypothetically compatible things [compossibilia secundum quid]: if they are unequally remote consequences, or rationata, I call them hypothetically incompatible. I continue: Hypothetically compatible things (things that in this world are compossibilia) are simultaneous; hypothetically incompatible real things [Actualia], however, are successive, to wit, the nearer rationatum precedes, and the more remote one follows.49

This is a Leibnizian ontological explanation, however, which begs for an account of how we are able to determine whether one thing is the consequence of another. If 'consequence' means 'effect,' and the only way we are able to determine cause-effect relations is by observing that A and B constantly occur 'after' C, then the account of time-cognition is begged.50 If, on the other hand, 'consequence' means something like 'logical consequence,' then time-cognition ends up being a privilege

The First Exposition 179 reserved for God or a similarly endowed being, able to discern all the relevant laws and states determining the succession of events in the universe - and this leaves the basis for human time-cognition unexplained. It may be unfair, therefore, to charge that Kant should have done more than he did to support the claim of the First Exposition. A philosopher cannot be expected to be sensitive to the need to provide a defence for principles that have never been effectively opposed, or to be able to provide an adequate defence when strong or convincing arguments to the contrary have yet to be formulated. Kant was within his rights to suppose it simply obvious that, with space and time, an experience of the order precedes the determination of relations, rather than vice versa. b. A Defence While Kant may have had no effective opposition to work against in the 17705 and 17803, this situation rapidly changed. A mere seven years after his death, in 1811, a sophisticated theory of space-cognition was presented in Johann Steinbuch's Beytrag zur Physiologic der Sinne.51 I want to pause to consider Steinbuch's theory in some detail. Gary Hatfield has claimed that, considered as an attempt to derive the concept of space exclusively from mental processing of aspatial sensations, it was unsurpassed.52 Though Kant had no opportunity to be apprised of it or to comment upon it, an assessment of the strengths and weaknesses of Steinbuch's theory can put us in a better position to determine whether there was anything more Kant could have said in defence of his position in the First Exposition - and perhaps even whether there was something more to what he did say. Steinbuch postulated that the mind is conscious of certain sensations when it wills the contraction of the rectus muscles in the eye. He took these muscle sensations to be qualitatively graded so that contraction of the same muscle would always produce the same sensation, and this sensation would have a degree of intensity proportional to the degree of contraction of the muscle. The four rectus muscles on the top, bottom, left, and right of the eye would thus each produce its own series of qualitatively graded sensations, corresponding to the four lines of motion of the eye upward, downward, leftward, and rightward from the centre. Steinbuch also supposed that directing the eye inside the quadrant defined by any two of these lines of motion - which would require contraction of two muscles (the upper and left rectus muscles for the upper left quadrant, and so on) - would produce feelings in which the sensa-

180 The Expositions tions of contraction from the two rectus muscles involved would be presented simultaneously, but fused into a single, simple unit, in much the way that blue and yellow are fused in green. Different degrees of rotation of the eye would thus produce sensations that shade off into one another, just as would motion of the eye along the upward, downward, leftward, and rightward axes. But, whereas motion of the eye along the four axes would produce a series of sensations of a single quality of proportionally varying intensity, motion of the eye in the region between these axes would produce a series of sensations of one quality that would proportionally shade off into other qualities, as yellow shades off through green into blue. Steinbuch supposed that, already in the womb, before the foetus ever experiences light, random motions of the eye lead it to experience all of these muscle sensations. The foetus is supposed to compare these sensations with one another and so discover that they make up a two-dimensional order. Here, note, the muscle sensations are experienced first, in no particular order, then compared with one another, their degrees of qualitative intensity and similarity, and the manner in which they shade off into one another, noted, and an order then constructed on that basis. Coming into the world with this order already in mind, the infant then has visual experiences. Each visual experience has three components: a muscle sensation, determined by the orientation of the eye; a collection of colour sensations, determined by the nature of the light rays focused upon different parts of the eye; and a collection of nerve signatures. The nerve signatures are themselves sensations. Each retinal nerve (or small circle of adjacent retinal nerves) was supposed to produce its own particular sensation upon stimulation, quite independently of the nature of the light stimulating it or the nature of the colour sensation that nerve delivers. This would allow the infant, by moving its eyes, to cause what is really a static source of colour stimulation to 'track' over different nerve signatures. For example, a contraction of the upper rectus muscle, causing the eye to move up, would cause a colour patch to move from one circle of optic nerves to one higher up on the retina, and thus the nerve signature accompanying that sensation would change. Over time, the infant would learn to associate particular muscle sensations with the tracking of colours from the focus of the visual field to particular nerve signatures. The nerve signatures, once associated with muscle sensations, would come to be thought of as possessing the order of the muscle sensations, and hence function as signs, designating a location in the order of muscle sensations. In this way colour sensations

The First Exposition 181 would come to be seen as having location in an order, through the mediation of the nerve signatures (local signs) that accompany them. Steinbuch's sophisticated theory supplied the detail Reid's and Feder's accounts lacked - so much so that it became the paradigm for all the empiristic theories of space-cognition that followed it. But neither it nor its successors has been immune to criticism, and the criticisms that have been raised are interesting variations on Kant's First Exposition. Hatfield mentions two problems with Steinbuch's theory and, by implication, with empiristic accounts of space-cognition in general. The first is really a pseudo-problem, but examining it will help to introduce the second. In explaining the development of 'inner space/ [Steinbuch] applies different laws to apparently equivalent phenomena without further explanation. Simultaneously appearing [muscle sensations] of a single muscle are organized into a line according to the law of similarity, whereas the simultaneously appearing ideas of two muscles are first fused according to the law of simultaneity and then associated with yet other ideas on the basis of their character after fusion. In the first case, simultaneously appearing ideas are associated next to one another, while in the second, they become amalgamated. Steinbuch supplies no additional details. We are left to conclude that he simply assumed what he needed in order to get the result he wanted.53

This is a pseudo-problem because the phenomena simply cannot be equivalent, as Hatfield claims. It is physiologically impossible for a single muscle to contract to two different degrees at the same time, and hence impossible for there simultaneously to be two different ideas of muscular contraction coming from the same muscle. Hence, there can be no question of muscle sensations from the same muscle being amalgamated in the way that muscle sensations from different muscles are. Hatfield's point would be more appropriately levelled against Steinbuch's supposition that simultaneously occurring colour sensations are each associated with the specific nerve signature from which they come, so that eye motions lead us to experience colour sensations as tracking over nerve signatures. For this tracking to be possible, it must be supposed that individual colour sensations are somehow correlated with the signatures from the specific nerves delivering them. If all that is present to consciousness at any given moment is an arbitrarily large collection of colour sensations, and an arbitrarily large collection of nerve-signature sensations, but no one colour sensation is correlated with any particular nerve sensation, then a motion of the eyes would merely cause the set of

182 The Expositions colour sensations to change (the nerve-signature sensations would stay constant unless some form of blinding occurs) and this would no more be experienced as a tracking of colour sensations over nerve signatures than as the tracking of the colours over smells, pressures, or any other set of relatively enduring sensations. However, the coordination of colour with nerve sensations cannot take the form of fusion (as the coordination of different, simultaneously occurring muscle sensations with one another does). If the colour is to be seen to track over nerve signatures, it must preserve its identity through the process. So colour sensations and nerve signatures must remain qualitatively distinct from one another, yet be coordinated with one another somehow. How this could be possible without presupposing spatial coincidence is obscure. Just as Steinbuch's theory thus appears to tacitly invoke an intuitive awareness of coincidence in space, so it appears to tacitly invoke intuitive awareness of adjacency in space. If muscle sensations from the same muscle are never present to the mind simultaneously, but only successively, then why should the order of muscle sensations from a single muscle have the phenomenal character of a line in space? Why should they be represented as next to one another rather than after one another or, indeed, in some purely logical successor relation with no implications for manner of presentation to consciousness? We hear different sounds successively in time, and by comparing them in memory with one another we may form the idea of a graded sound series: the pitch scale. But the pitch scale does not appear to us with the phenomenal character of a line in space. Why, therefore, should our muscle sensations do this? This is Hatfield's second objection to Steinbuch.54 In asserting that the associative law of similarity orders elemental representations next to one another, [Steinbuch's] account begins already provided with a law for generating spatial representations. Without this associative principle so formulated, there would be no explanation why sensory elements representing various motions ever develop beyond a one-to-one correspondence between external spatial locations [i.e., physical turnings of the eye] and discriminably different nonspatial [muscle sensations]. The law of association that is responsible for the intuiting of these [muscle sensations] as next to one another does the real work in Steinbuch's derivation of space as a form of representation. But this law itself receives no further explanation.55

This objection, with its italicized reference to the little word 'next' recalls a point made by Kant about another little word, 'after.' In Hat-

The First Exposition 183 field's case, the point is more than the ad hominem observation that Steinbuch, despite his best intentions to the contrary, still ended up presupposing what he was trying to prove. Occurring as it does in the context of a reflection on the limitations of Steinbuch's theory, it emerges as a general problem: how could it be possible, from a collection of aspatial sensations, to derive, not just the idea that these sensations are related to one another in two or three dimensions of quality, but that they actually occur in an order with the phenomenal character of spatial adjacency? In other words, how do we come to represent them as given simultaneously and alongside one another, rather than as given between one another in the merely comparative sense of having remembered intermediate shades of quality? A similar point can be made in response to the empirist account of time-cognition. The temporal order, like the spatial, has certain phenomenal qualities. Objects in the temporal order do not merely occur between one another; they occur after one another. Were the temporal order based merely on the perceived Vivacity' relations between my current sensations and memories this phenomenal quality would be difficult to account for. Why should an ordered collection of present sensations and memories not have the character of a line in space rather than of a series of elements successively flowing out of existence? Why should it have any phenomenal character at all and not rather be presented as a collection of abstract between-ness relations? I hesitate to read these points back into Kant, if only because it seems erroneous to represent a philosopher as propounding an objection to a theory that had not yet been invented. But what does emerge is that Kant's position on space-cognition was not groundless. There were problems with the empirist account of space-cognition, both as it was formulated in his day and as it appeared for the century after - problems that appear to lead directly to Kant's own theory that spatial order must be originally present among sensations as we first experience them. Kant's First Exposition may not decisively refute the alternative, empirist account of space- and time-cognition, but it does present an alternative view and a challenge to the empirist account that no empirist theoretician of Kant's day, or of the period immediately after, was able to adequately answer. Appendix: Meditations on the Epistemology of Order The concept of order is one that has so far been analysed only mathemat-

184 The Expositions ically. But mathematics just specifies the formal features of the ordering relation and the ordered set (for example, in distinguishing among discrete, dense, and continuous partial orders). The concept of order can be considered from another angle: from the perspective, not of the formal features of the order, but of what it is that determines the locations of the ordered elements. This is a question that mathematics does not discuss. The mathematician will simply say, 'Suppose that x is the third element in the set' or 'Suppose that y is between x and z/ without ever considering what it is that would make x be the third element, or y be between x and z. But this is a question worth considering. There seem to be four basic grounds determining the locations of elements in an order,56 and it is possible to characterize orders, depending on which of these grounds is operative. I call these four basic types of order 'stipulative orders/ 'deductive orders/ 'comparative orders/ and 'presentational orders.' In a stipulative order, the locations of the ordered elements are determined by convention or definition. The order of letters in the alphabet is an example of a stipulative order. There is no reason why B is set between A and C other than that convention makes it so. In a deductive order, a first element or set of elements is stipulated together with a rule or set of rules. Subsequent elements are then recursively derived by application of the rule(s). Some deductive orders, however, may have their first elements given by experience rather than stipulation, and their rules determined by empirical investigation, so that subsequent elements have the status of deductions from the phenomena in accord with natural laws. The paradigm example of such an order is the causal order. In a comparative order, the locations of the ordered elements are determined by some scalable quality in the elements themselves. The order of colours in terms of their brightness, saturation, and hue, or of sounds in terms of pitch and volume is an example of a comparative order. Comparative orders are tied to experience in a way in which deductive and stipulative orders are not. The elements must be experienced and inspected first, before a determination of where they occur in the order can be made. Presentational orders fall between stipulative and deductive /comparative orders. As in stipulative orders, the location of elements in presentational orders has nothing to do with any discernible features of the elements themselves. But, unlike in stipulative orders, in presentational orders the elements are not located in a simply arbitrary way. Location

The First Exposition 185 is determined by the manner in which the elements are presented to a detector or, alternatively, by the manner in which the elements occur in the experience of a subject. There is some question whether presentational orders really exist, or whether all non-stipulative orders are really comparative or causal orders. Kant, however, thought that presentational orders are distinct. He thought, moreover, that there are exactly two of them: space and time. For Kant, the way we determine the location of a sensation in space or time is not by deducing it from causal or other natural laws - certainly not originally.57 Nor is it by inspecting the qualitative features of the matters of appearance. The matters of appearance are indifferent to their locations and could occur anywhere in the spatiotemporal order, so that in determining the location of a matter in space or time, inspecting the matter is useless. To determine the location of a matter it is necessary to consult, not the matter, but the manner in which that matter is presented. Appearance contains more than matter for Kant. In appearance, matters occur successively in time, and at any given moment many of them are presented as disposed alongside one another in space. In appearance, we are not just aware of matters, we are aware of one matter as occurring after another, and of one matter as being disposed next to another. It is by consulting these manners in which matters are presented and disposed in the appearance that we define locations of matters in space and time. Unless this point is grasped, and it is recognized that, for Kant, space and time, as forms of appearance, are presentational orders, his account of space and time cannot be correctly understood.

6 The Second Exposition

Whether space and time empty of sensation, and likewise infinite space and time, are phenomena. For they are not noumena. (R432O; Ak, XVII 505) 2. Space is a necessary a priori representation that lies as a ground of all outer intuitions. One can never make a representation of there being no space, though one can well think that no object is found in it. It is therefore to be seen as a condition of the possibility of appearances and not as a determination dependent upon them, and is an a priori representation, that necessarily lies as a ground of outer appearances. (A24/B38-9) 2. Time is a necessary representation that lies as a ground of all intuitions. With respect to appearances in general one cannot remove time itself, although one can certainly take appearances out of time. Time is therefore given a priori. In it alone is all actuality of appearances possible. These could all be omitted, but time itself (as the general condition of their possibility)1 cannot be eliminated. (A31/B46) i.

Analysis of the Argument a. Premises

The Second Exposition contains an argument drawn from the claim that there is an imbalance in the dependence relations between space and time, on the one hand, and 'objects' or 'appearances/ on the other. While it is impossible to 'make a representation' of the absence of space, or to remove time from any appearance, it is purportedly possible to

The Second Exposition 187 'think' that space does not contain 'objects' and to remove all appearances from time. As thus stated, the space argument does not come off well, because the point of contrast is not drawn in the same terms in the two opposed circumstances. Whereas Kant's claim is that we cannot 'make a representation' of the absence of space, his supposedly contrasting claim is not that we can 'make a representation' of space that contains no objects, but just that we can think that there are no objects in this space. One way we might try to patch up Kant's argument is by supposing that, when he writes 'make a representation of,' he really means nothing more than just 'think of.' If so, then the contrast he is trying to draw would be formally valid because it is drawn in the same terms on both sides, but it is hard to see how it could be sound. Thinking, for Kant, is a cognitive activity that operates under very loose constraints. I can think anything, Kant maintains, as long as I do not contradict myself (Bxxvi n). But, in that case, it is hard to see why I should not be just as able to 'make a representation' (i.e., think) of a world of objects where there is no space, as I am able to think of a space where there are no objects. There is no obvious contradiction in the thought of an object that exists without being located or extended in space, or of a world of such objects. Indeed, whole systems of philosophy, such as Leibniz's monadology, have been written around this thought, and even Kant is committed to holding that aspatial objects such as freely acting souls and God may be thought to exist in some noumenal realm, if only as postulates of practical reason (Bxxvi-xxix). If Kant's premise in the space argument is to be read as both pointing to a valid contrast and being at least plausible, the equation of making a representation with thinking needs to be taken the other way around. It must be 'think of that really means the same thing as 'make a representation of/ and 'make a representation of must mean something more than just 'conceive without contradiction.' But what more? At Bxxvi n, where Kant remarks that I can 'think' anything as long as I do not contradict myself, he contrasts thinking with cognizing, remarking that not every possible object of thought is a possible object of cognition. This point is further clarified in the sections of the Critique on the highest principles of all analytic and all synthetic judgments (Ai 50-87 6189-97), and the explication of the postulate of possibility (A22O-1/ 6267-8). Not all objects that can be thought can be cognized, Kant claims, because cognition is based on experience, and just because there is no contradiction in the thought of an object, it does not automatically

i88 The Expositions follow that that object could be given in any possible experience. Experience presupposes the satisfaction of certain further conditions in addition to bare logical consistency, Kant claims, and not all logically consistent concepts do satisfy these conditions. To prove that a concept is not only thinkable but cognizable, one must therefore demonstrate that its object either is actually or at least could possibly be experienced. This means proving one or the other of the following: (i) that it is, in fact, experienced (giving an a posteriori argument), (ii) that it is a necessary component that all experience can be known in advance to have to contain (giving a 'deduction'), or (iii) that an object corresponding to the concept can at least be imagined in conformity with all of the conditions of the possibility of experience (this amounts to 'constructing' the concept in accord with these conditions). In light of this position, it is at least in conformity with general tenets of the Critical Philosophy to take 'make a representation' to mean something like 'prove to be a possible object of experience' or 'construct in accordance with the conditions of the possibility of experience/ Kant's claim in the Second Exposition would then be that, while I am able to think without contradiction that there are aspatial objects such as monads or souls, I could not ever experience such objects or even imaginatively constitute (i.e., 'make') such objects without violating what I know to be conditions of the possibility of my experience. To preserve the terms of the comparison, Kant's position would also have to be that empty space is not merely something I can think without contradiction, but something that I could actually experience, or at least prove to be in accord with the principles of the possibility of experience. Of course, Kant does not say 'experience,' or even 'possibly experience/ but 'think/ But perhaps what he means by 'think that no object is to be found in space' is 'think that a space that I am now experiencing or could possibly experience might well not contain any object/ This position on the meaning of Kant's premise in the space argument of the Second Exposition is speculative. Kant's own pronouncements in the Second Exposition do not make it clear how he intended the phrase 'make a representation' or the term 'think' to be understood. He certainly says nothing to endorse the reading I have just proposed. He may well have simply never thought the matter through clearly. But the reading I have proposed does grow out of his own distinction between what can be thought and what can be cognized, and since his premise would be indefensible if it turned on claims about what can be thought without contradiction, I propose in what follows to take his claims to be about

The Second Exposition 189 what is experienced - or 'thought' about what could possibly be experienced. Whether this is ultimately any more palatable a reading of the Second Exposition, given what Kant has to say elsewhere about empty space, is a question that is examined more closely in §iv, below. Paralleling the reading I have just proposed for the space passage, I will take Kant's point in the time passage to be that we cannot construct, in conformity with the conditions of the possibility of experience, a representation that is not in time, though we can suppose that a time empty of objects could be given in a possible experience. This is again something more than what Kant actually says. All that he says is that, whereas appearances cannot be abstracted from the temporal manifold and represented on their own, the form of time can be abstracted from appearances and represented on its own. This leaves it ambiguous what the various possible or impossible abstract representations are to consist in: whether to abstract appearances from the temporal manifold means to be able to 'think' time without appearances, or whether it, rather, means that we can take empty time to be a possible object of experience. Since opting for the former alternative creates the same problems that were discussed in connection with the space argument, I will pursue the latter option. It may not be exactly what Kant meant, but since what Kant said is unworkably ambiguous, there is little alternative but to disambiguate his pronouncements in a way that seems most consistent with his overall position, and proceed from there. b. Conclusions Kant draws a number of conclusions from these premises, all of which are already contained in the passages cited at the outset of this chapter. He infers: (i) that space and time are necessary representations, (ii) that they are given a priori, (iii) that they are grounds of intuitions (all outer intuitions, in the case of space; all intuitions whatsoever, in the case of time).

Whether as a further consequence of these conclusions, or because he considers the formulations to be equivalent, he goes on to conclude: (iv) that space is a ground or condition of the possibility of appearances, and time of their actuality.

190 The Expositions Of these conclusions, the first follows from the claims that it is impossible to represent the absence of space or remove time from any appearance, whereas the second is a consequence of the remaining claim, that an experience of empty space and time is possible. (It might be thought that the second conclusion would follow from the first conclusion, since whatever is a necessary component of experience can be anticipated in advance of experience. But, in that case, Kant would open himself to the objection that, just as space and time are necessary for the representation of objects and appearances, so objects and appearances are necessary for the representation of space. Appealing to the possibility of experiencing empty space and time obviates this objection and establishes that the representation of space and time is independent of the representation of objects.) The third conclusion is just a combination of the first two, because to be a condition or a ground just means to have to be given (necessity) as a first or antecedent element, upon which all others can only subsequently be established (priority). But the relation between (iii), the claim that space and time are grounds of intuitions, and (iv), the claim that they are conditions of the possibility of appearance, is problematic. c. Appearance or Intuition? A Problem of Representation Terminology Kant's use of the terms 'intuition' and 'appearance' is fluid enough at both ends that the two claims could mean the same thing. As noted at the conclusion of chapter i, above, Kant occasionally uses the term 'intuition' to designate, not what is given to the cognitive system prior to all processing, but our (necessarily intellectual) representation of particulars. And, as noted in chapter 2, above, 'appearance' is also a very broad term for Kant. It can designate anything that could be called 'an object of consciousness,' whether within the mind, as mental representation, or without it, as independently existing external object - everything, that is, from raw, intuited data given prior to all intellectual synthesis (A9O/ 6122) to objects of perception consisting of an array of qualitative matters barely thought under the categories of quantity and quality (as at 6207), to objects that are 'distinct from the representations of apprehension' (Ai9i/B236), and hence from the objects of perception (6207). But this fluidity of reference creates problems here. Does Kant mean to use 'intuition' to refer to immediate representation or to the representation of particulars? If the former, does he intend 'appearance' in the

The Second Exposition 191 same way, or does 'appearance' refer instead to representations resulting from intellectual processing - or even to the objects of those representations? The premises of Kant's argument leave us in a similar quandary. There the operative expressions are 'representation/ 'object/ and 'appearance/ and it is not clear whether these terms designate immediate or mediate representations or whether they designate the same or different representations. Kant uses 'representation' as a generic term to refer to all types of experience and their objects ^320/6376), and he admits that he sometimes uses the term 'object' to refer to any type of representation (Ai89-90/B234-5).2 This much is clear: Kant's ultimate position will be that space and time are not just forms of our experience of objects, but forms of immediate, sensory intuition. As such, they are grounds or conditions both of our cognition of particulars, objects or 'appearances/ and of our intuitive (i.e., immediate, original) representations. But this is a thesis that Kant has not established yet, and before he can establish it he has to come to terms with a problem he has not yet faced: the problem of blindness.3 Given that intuitions (understood as immediate representations) without concepts are 'blind/ how can Kant make any claims about what intuitions exhibit prior to or independently of all intellectual synthesis? How, in particular, can he be sure that the spatial order is originally given in intuition and not subsequently constructed by the intellect as part of the processes of bringing the intuited manifold to unity under concepts? If Kant is not to beg these questions, his argument cannot be premised on the supposition that space and time are already to be found in our intuitions prior to all cognitive processing. He might perhaps be able to conclude that this the case (if his argument, in fact, leads that far), but his argument must start with claims about representations to which we are not blind. Kant's premises ought, therefore, to assert just that it is not possible for us to experience or construct (through intellectual processing) an object or appearance that is not in space or time, but that it is possible to experience (through intellectual processing) empty space or time - or, at least, that it is possible to have an (intellectually processed) experience that we can think could be an experience of an empty space or time.4 Below, I argue that the claim about empty space and time, in particular, is such that it allows Kant to go on to draw a conclusion about what our experiences must be like prior to intellectual synthesis - or at least,

192 The Expositions prior to that intellectual synthesis that brings the matters of intuition together under concepts of objects and 'appearances' (here understood as whatever we come to be conscious of through intellectual processing, at however primitive a level). To this extent, the argument of the Second Exposition does address the blindness issue, and at least approaches a conclusion about the constitution of our original intuitions. However, I do not see how the first of Kant's claims - that objects and appearances cannot be represented apart from space or time - could license a conclusion about intuition as opposed to one just about intelligible experience. d. The Two-Part Structure of the Exposition There are thus two central conclusions to the Second Exposition, the conclusion that space and time are necessary conditions of the possibility of appearance and the conclusion that they are prior conditions of the possibility of appearance - 'prior' in the sense of being present, if not originally in intuition, then at least in some more primitive kind of consciousness occurring prior to our intellectual representation of objects. As noted above, each of the two main claims premised in the Exposition leads to a different one of these component conclusions, so that the Exposition falls naturally into two separate parts. In what follows, I refer to the first part as the inextricability argument. It proceeds from the premise that it is impossible to represent the absence of space or remove time from an (intelligible) experience without also removing the possibility of representing any of the remaining content that is given in the space or time. From this it infers that space and time are necessary conditions for the possibility of that content. But this is not all that Kant aims to establish in the Second Exposition. While it might indeed be impossible to remove space or time from the matter of appearance, it could equally be impossible to remove the matter of appearance from our representations of space or time. 'Matter' and 'form' might be mutually necessary and might mutually condition each other. This would be the case, for instance, were all space the extension of some object, as Descartes maintained,5 or all time the succession of some set of ideas, as Locke maintained; or were both space and time relations of objects, as Leibniz maintained. This is a possibility Kant is unwilling to accept. In the Second Exposition, he claims that, while spatiotemporal order is a necessary ingredient in all our experiences of objects and events, objects and events are not necessary for the possibility of space or time. From this further claim he infers, naturally enough,

The Second Exposition 193 that both space and time must be present in our experience prior to any recognition of objects, or, as he puts it, that they are 'a priori' (how exactly it is that this follows is something that will have to be discussed in more detail below, as it depends on the invocation of missing premises I have so far not mentioned).6 This is a different sense of 'a priori' from the negative sense that figured in the First Exposition. There 'a priori' meant 'not abstracted from comparison of sensations or the matters of appearance.' Here it means 'present prior to any constitution of the objects that appear through intellectual processing.'7 In what follows, I refer to this second part of the Exposition as 'the independence argument.' ii.

The Inextricability Argument

In both editions of the Introduction to the Critique, at Ai and 63, Kant claims that, while experience can tell us that something is so, it can never tell us that it could not be otherwise. Kant's premises in the inextricability argument appear to present us with a claim about what could not be otherwise: they tell us that we can 'never' make a representation of the absence of space and that we 'cannot' remove time from appearances and still be able to represent the appearances. Yet this is not the case. As noted above, Kant's premises are ambiguous. They could be read as affirming either (a) that it is impossible for us to cognize objects or appearances that are not in space or time, or (b) that it is impossible for us even to think of objects that are not in space or time. But on neither of these interpretations do the premises affirm anything that strictly 'could not be otherwise.' Not only could (b) be otherwise, but, as far as Kant is concerned, it is otherwise. Kant believes that we can 'think' anything that does not involve a contradiction (Bxxvi n) and there is no contradiction in the thought of an aspatiotemporal object. This is what a monad or a thing in itself would be, and Kant took it to be possible for us to at least think of monads and things in themselves, (a) could be otherwise as well. Kant does not consider space or time to be in general necessary for the representation of objects or appearances. We cannot judge, he claims, whether the intuitions of other thinking beings are bound to the same forms to which ours are bound (A27/B43; Fortschritte [Ak, XX 267!). They may experience objects and appearances under quite other forms than we do, or under no forms at all (6138). But, if Kant is willing to grant that other thinking beings may experience objects and appearances without space or time, then he must accept that our own

194 The Expositions experience could alter over time (were we, say, to evolve into these hypothetical other beings). For all we know, our forms of intuition could change tomorrow.8 Given these facts, Kant's premises in the inextricability argument can only be based on two things: introspective observation of the brute fact that, as I am now constituted, I cannot have aspatiotemporal representations, and observation of other human beings, who generally demonstrate or report that, as they are now constituted, their representative capacities operate under the same restriction. None the less, there has been a great deal of opposition in the literature to what is referred to as this 'merely psychological' assertion and the 'adolescent thought experiment' (of trying to imagine aspatiotemporal objects and finding that one cannot do so) upon which it is based.9 It is claimed either that Kant did not really intend to make such an assertion or that, in so far as he did, the argument of the Second Exposition fails.10 The opposition stems from two sources. On the one hand, it is charged that, as stated, Kant's premise is hopelessly vague and that it presupposes nothing less than a complete theory of mental representation - a theory that Kant nowhere supplies in the terms necessary for his claim here to be made out.11 On the other hand, it is charged that a merely psychological inability to represent the absence of space and time (in whatever sense of 'represent') is completely inadequate to establish the conclusions Kant wants to draw.12 But neither of these objections poses an insuperable problem. a. The Sense of 'Represent' As noted at the outset of this chapter, the sense in which Kant must be taken to claim that it is impossible to 'represent' is the sense of being unable to have a sensory experience. To claim that the absence of space cannot be represented is to claim that there is nothing I could do to remove the spatial component from any experience that contains it, and thereby give myself a new experience of the remaining content of the original experience without the space. And to claim that time cannot be removed from any appearance is likewise to claim that there is no act I can possibly perform whereby I could give myself the content of any appearance without experiencing that content as extended or at least located in time. This is not to say that I cannot 'think' this content apart from space or time, in the sense of being able to conceive it without contradiction. I can think of colours just with regard to their qualities of hue, saturation, and brightness, for example, without having to think of them as located

The Second Exposition 195 anywhere in space or time. But it seems to be impossible to experience a colour without experiencing it as extended or located in space, and as existing at or over a certain time. The difference here is that, when I think of something, I merely consider the content of its concept. But, when I experience, I believe that an object actually exists corresponding to the concept. Whatever this object may be, Kant is claiming, it is inextricably temporal, and sometimes also inextricably spatial as well. When taken in this sense, Kant's claim about the inextricability of space and time does appear to be warranted. I can change my position or manipulate the objects in the world around me in such a way as to ensure that there is no occurrence of the colour red in my visual field. I can do the same with any other colour. I can give myself visual experiences in which there are no colours whatsoever present, but only grey scales, or no grey scales but only colours. But while any given colour can be removed from my field of view, I cannot give myself a visual experience that is not extended and located. Moreover, I cannot give myself a visual experience that is not extended in a certain way - my visual experiences must exhibit certain topological and affine features. Geodesies in my visual field do not turn back on themselves; any two points on my visual field may always be connected by a line, with there being only one such line that will be a geodesic, and so on. The same is true of those tactile representations that arise from stimulation of parts of the skin. I experience these representations as localized somewhere on my body (though often the locations are not very precise) and as spatially related to one another in virtue of these locations (though, again, often only vaguely so). But, while I can (under happy circumstances) remove any given representation (of heat or cold, rough or smooth, sharp or flat) from my tactile experiences (usually by simply moving my body), I cannot remove this spatial component - whatever representation I give myself will be experienced as extended and located somewhere on my body and as spatially related somehow to whatever other tactile representations I am experiencing. This is a feature of my personal psychology that may not extend to all other human beings, much less to all other forms of life. Thus, I can well conceive that there may be types of brain damage that result in an inability to perceive location or extension. None the less, I discover that, for me, space is inextricable from visual and haptic experience, and that those who are unable to perceive location or extension have seriously and extensively impaired cognitive abilities, so that rather than have an alternative way of perceiving the truth, they seem rather to have

196 The Expositions improverished abilities to perceive the truth. Since virtually all other human beings report the same experiences with the inextricability of space and time, I affirm that, in general, space is a necessary feature of our visual and haptic experiences. For time, inextricability is even more universally true. It applies, not just to some sensory modalities, but to all, and indeed to all representations whatsoever. Whatever experiences, memories, fantasies, or thoughts I have always occur at a certain time and always have a certain duration, and while I can (again, under happy circumstances) manage somehow to remove any given sensation, memory, image, or thought from my consciousness, in so far as I am conscious of anything at all, it must be at and over a time. Thus, at least as far as introspection and generalization from introspection are concerned, temporal order and temporal duration do appear to be ineliminable from all experiences, and spatial order and spatial extension from a broad class of our experiences: visual and haptic experiences (and perhaps others as well). b. The Adequacy of the Argument As Patricia Kitcher has forcefully pointed out, Kant had a dim view of the ability of appeals to introspection to establish significant results.13 Yet, if I am correct, the inextricability argument rests on little more than a generalization from introspection. Of course, both of us could be right. That Kant took a dim view of appeals to introspection does not mean that he did not find it necessary to rely upon them occasionally - especially in contexts where the job to be done is not so much to demonstrate a conclusion as to exposit it, or in contexts where the thesis to be established is so fundamental that it cannot be derived from more fundamental presuppositions but only indicated or shown to be plausible by appeal to various kinds of clue or evidence. In the end, the fact that I cannot extricate space or time from my sensory experiences, brute fact though it may be, does supply evidence for the conclusion that space and time are necessary features of all my sensory experience. It may not supply absolutely conclusive evidence, but it does not supply woefully inadequate evidence either. And the evidence gets better the older and the more widely experienced I get, and the greater the number of people I survey. Given that Kant himself insists that it is merely a contingent fact that space and time are our forms of intuition, it is hard to see what other evidence could be provided.14

The Second Exposition 197 A good deal of the opposition to Kant's 'merely psychological' argument results from commentators' looking to the inextricability argument for demonstrations of a far stronger conclusion than the one Kant actually intends to establish. It is important to keep in mind just how modest the conclusion of the inextricability argument is. All that Kant wants to prove is that space and time are necessary features of our sensory experiences. There is not a word said in the Exposition to explain what makes them necessary. In particular, there is not a word said in the Exposition about the constitution of the subject. Kant does not say that space and time are necessary because they are automatically injected into sensory experience by some antecedent feature of the subject's cognitive constitution. He may well believe this, but it is not demonstrated by the Second Exposition. None the less, this is how he has been read.15 When the Exposition is taken to be directed towards this stronger thesis, it is naturally found wanting. Thus, Kemp Smith remarks that in a second respect Kant's proof is open to criticism. He takes the impossibility of imagining space as absent as proof that it originates from within. The argument is valid only if no other psychological explanation can be given of this necessity, as for instance through indissoluble association or through its being an invariable element in the given sensations.16

But nowhere in the Second Exposition does Kant make any claims, either by way of premise or by way of conclusion, that space (or time) is subjective (or 'originates from within/ as Kemp Smith puts it). Kant concludes that the representation of space and time is necessary, but whether its necessity is grounded on the constitution of the subject's cognitive system, on its physiology, or on the world in which the subject is located is not determined. The conclusion Kemp Smith sees Kant drawing from the premise is simply not one that he draws. Another critic of the inextricability argument, Guyer, stresses Kemp Smith's alternative explanation: Even if space and time were empirical representations acquired only through acquaintance with more particular objects, one could imagine them becoming so well entrenched that they could not be imagined away, even if any particular object could be.17

But the inextricability argument is not supposed to prove that space and

198 The Expositions time are a priori representations (representations originating in us independently of experience). The conclusion of the inextricability argument is rather that space and time are necessary features of all our sensory representations. While Guyer is quite right that the non-empirical nature of our representations of space and time does not follow from their inextricability, their inextricability does at least constitute good evidence for their necessity. Walker makes yet another mistake: It is difficult to see [the claim that we cannot represent to ourselves the absence of space] as more than a psychological remark, though Kant draws from it the conclusion that space and time are necessary a priori representations underlying all our experience ... If it were true it could only be a contingent truth about us, and would no more prove that space and time were a priori than my inability to imagine a chiliagon shows the impossibility of any such figure.18 The example of the chiliagon is inept. If Kant's claim is just that it is impossible to have a sensory experience of the absence of space, then by contrast it is not impossible to have a sensory experience of a chiliagon. Admittedly, I might not know immediately (without first discriminating and then counting them up) that the figure has exactly 1,000 sides. But that does not change the fact that the figure I am experiencing could possibly be a chiliagon. The grossness of our senses does not in any way decide the form of a possible experience in general/ Kant says at A226/ 6273. It is possible to construct a chiliagon. Therefore, even though I may not be able to tell whether any given figure is a chiliagon, a myriagon, or a circle, I can still think that it might be a chiliagon. The experience is not, therefore, impossible; it is just indistinct. (By parallel argument, Kant does not claim that we can know that a given representation is of an absolutely empty space or time - as opposed to one filled with an infinitesimally small degree of reality - but just that we can think that some of our representations might be.)19 Further, the necessity Kant is trying to establish for space and time is not some sort of absolute necessity that space and time are supposed to have in themselves, as objects or as features of the world.20 It is necessity for our possible representations. Thus, in the Second Exposition, Kant nowhere says that space and time are simply necessary. He always qualifies this by saying that space and time are necessary as grounds of our representations. And while the 'contingently true psychological remark' that I cannot represent the absence of space or time may be quite irrele-

The Second Exposition 199 vant to establishing that space or time are necessary objects or necessary features of the world, it is far from irrelevant for establishing that space and time are necessary features of all my representations. On the contrary, my inability to extricate space or time from my representations, contingent truth about my psychology that it may be, is powerful evidence for the thesis that I must necessarily represent in space and time. There may be another worry behind Walker's objection, however one that lurks behind his contrast between a 'contingent truth' about our psychology and the claim that space and time are at least necessary (if not a priori) representations. How can any contingent claim be taken to establish the necessity of a representation? There are two answers to this question. The first is that, while a contingent claim cannot deductively entail a necessary truth, it can be taken to provide evidence for a conclusion about the existence of a general rule that applies necessarily to all the cases that fall under it. To deny this is tantamount to denying the possibility of induction (which Walker certainly has the right to do, but then it will not just be Kant's argument in the Second Exposition that has to be rejected). The second, and more serious answer is that Walker's lurking question mistakes the scope of the necessity operator in Kant's conclusion. While Kant does indeed conclude that space, for instance, 'necessarily serves as a ground of outer appearances,' he also believes that it is 'necessarily' a ground of outer appearances only for us: Since we cannot take the particular conditions of sensibility to be conditions of the possibility of things, but only of their appearances, it follows that while we can indeed say that space comprehends all things that can appear outwardly to us, we cannot say that it comprehends all things in themselves, be they intuited or not, or be they intuited by this subject or that one. ^27/643)

It is thus a contingent truth that, for us, space is a necessary ground of outer appearances. In other words, the scope of the necessity operator extends only over the representations had by us or other beings like us. It does not extent outwards to bracket the thesis that we ourselves and other beings like us necessarily represent in this way. Of the following two assertions - A: In fact (x [necessarily represents p]); B: Necessarily (x represents p) - it is A that Kant seeks to establish, not B. Ultimately, therefore, we are dealing with a conclusion that affirms that a certain type of being is as a matter of fact constrained to represent in a certain way. For this being, it is in effect necessary that its representations have

2OO The Expositions the identified structure.21 But the fact that this is necessary is a brute fact and nothing more. Admittedly, as anyone familiar with Kant's philosophy of mathematics will attest, there are a great many assertions about space and time to which Kant wants to ascribe the special status of 'synthetic a priori' truth - assertions that he wants to claim are absolutely necessary and strictly universal. Even these assertions, however, are ultimately limited in their scope to just the experiences of a certain kind of being: We simply cannot judge of the intuitions of other thinking beings, whether they are bound to the stated conditions that bind our intuition and are universally valid for us. If we add the limitation (under which a judgment is made) to the concept of [its] subject, then the judgment holds unconditionally. The proposition: All things are next to one another in space, holds under the condition, 'if these things are taken to be objects of our sensory intuition.' ^27/643)

The claim that space and time are necessary features of all our sensory representations is a fundamental presupposition upon which the whole of Kant's account of synthetic a priori knowledge is based. But it is none the less itself a contingent presupposition. The premise that space and time are inextricable from our experience offers some empirical justification for it, but the most this premise can do is render it likely (indeed, very likely, given the degree to which everyone's experience confirms it). The conclusion could still be consistently denied (like any contingent presupposition). Were it denied, the book could be closed on Kant's account of synthetic a priori knowledge in the Critique of Pure Reason. iii.

The Third Exposition in A and the Validity of Geometry

Whereas the First Exposition claims that our concepts of space and time are not drawn from anything to be found in the matter of appearance, the Second Exposition's inextricability argument goes on to assert that all matters of appearance are none the less in space and time.22 In so far as this assertion is accepted, it entails that anything we know about space and time can be taken in advance of any actual experience to hold of the objects of that experience. Since space and time must be presupposed for a representation of objects to be possible, the features of space and time must necessarily be reflected in those representations. For example, if space is three-dimensional and Euclidean, then no five objects can be equidistant from one another.

The Second Exposition 201 ID, §14 ^6, contains an especially explicit statement of this point: [Time] is a condition, extending to infinity, of intuitive representation for all possible objects of the senses ... Hence, it is clear that all observable events in the world, all motions and all internal changes necessarily accord with the axioms which can be known about time and which, in part, I have already expounded. For it is only under these conditions that they can be objects of the senses and can be coordinated with each other. (Ak, II 401-2)

This is a point for which Kant is well known. But the perspective from which it is seen here is one from which it is seldom viewed. Everyone knows that Kant supposed that particular axioms of geometry and mathematics are synthetic a priori truths and that, from this, he inferred that space and time must therefore be forms or formal characteristics of the subject whereby it is affected in intuition. This is the Transcendental Exposition. But here the synthetic a priori status of the axioms of geometry and mathematics is not presupposed; the very possibility of there being such things as synthetic a priori principles of geometry and mathematics (quite apart from any reference to what such principles might be) is explained. Space and time precede our representations of objects and events as necessary conditions of the possibility of those representations, the inextricability argument tells us. And this is why the characteristic features of space and time (described by the axioms of geometry and mechanics) end up being valid for all our experience of objects and events. Commenting on the different methods of demonstration in the Prolegomena and the Critique, Kant remarked that, whereas the Critique follows a synthetic method, the Prolegomena's method is analytic (Ak, IV 263). What he meant by this, he later explained, was that, in the Critique, he had sought to isolate the elements and principles of 'pure reason' and then describe how these elements and principles together account for the generation of certain synthetic a priori items of knowledge; in the Prolegomena, in contrast, he had presupposed that certain synthetic a priori items of knowledge exist and then tried to argue that their existence presupposes certain general conditions in the human cognitive system (Ak, IV 274-5). Among the presupposed items of synthetic a priori knowledge were the axioms of geometry and mathematics (Ak, IV 279), and the Prolegomena's discussion of the grounds of these axioms parallels the Critique's Transcendental Exposition. But Kant's comments in the Prolegomena imply that, over and above the analytic demonstration

2O2 The Expositions of the Transcendental Exposition, the Critique ought to contain a synthetic demonstration of the validity of the axioms of geometry and mathematics. In so far as the Critique does contain such a demonstration, it is to be found in the inextricability argument. It is there that the argument to geometry occurs. The immediately following sentences of the A edition's Third Exposition (later incorporated into the B Transcendental Exposition) substantiate this relationship: 3. The apodictic certainty of all geometrical principles, and the possibility of their a priori constructions, is grounded on this a priori necessity [of the representation of space]. (A24) 3. The possibility of apodictic principles of the relations of time, or axioms of time in general, is also grounded on this a priori necessity. ^31/647)

Here, Kant refers back to the demonstration of necessity offered by the Second Exposition's inextricability argument and claims that it is what grounds (and, by implication, frames) the certainty of the axioms of temporal relation and geometry. In B, this relation between the inextricability argument and the status of the principles of geometry and temporal relation is obscured. In line with Kant's methodological pronouncements in the Prolegomena, the overall impression given by the B edition is that there are two independent arguments for the necessity of space and time - one synthetic, given by the inextricability argument and proceeding from grounds to consequents, from the available empirical evidence to a conclusion about the necessary constraints on our representative capacities; the other analytic, given by the Transcendental Expositions and proceeding from consequents to their grounds, from the presupposition that geometry, mathematics, and mechanics contain synthetic a priori propositions to what it is that makes this possible. Kant's B-edition decision to separate the Transcendental Exposition from the Metaphysical disconnects the premise of the Transcendental Exposition, the thesis that there are synthetic a priori principles of geometry, mathematics, and mechanics, from any apparent grounding in the Second Exposition's inextricability argument. Instead, it gives the impression that Kant has a prior, unquestioned commitment to the absolute necessity of the principles of Euclidean geometry and Newtonian mechanics. But Kant's retention of A27 at 643 indicates that this is not

The Second Exposition 203 the case. The necessity of the principles of geometry, mathematics, and mechanics is not absolute necessity but necessity that is taken to apply only to beings 'like us' - beings who, as a matter of fact, are constrained to represent in space and time. All of Kant's synthetic a priori principles are therefore only hypothetically necessary. // it is true that space and time are, in fact, necessary features of all our sensory representations, then the axioms describing space and time are necessarily and universally valid for all our experience. But the antecedent must be granted (or made likely by appeal to empirical evidence) before any claims about necessity or universality can be unlocked. iv.

The Independence Argument

Kant's premise in the independence argument - that we can have experiences that we can plausibly think to be of an empty space or time might at first appear to be contradicted not only by his considered position on what can possibly be perceived, but even by his position on what we can think without contradiction.23 In what follows, I argue that the texts are not as antithetical to the independence argument as they may at first seem. a. The Conceivability of Empty Space and Time Throughout his career, Kant frequently reiterated the claim that space and time cannot possibly exist on their own, referring to the contrary opinion as 'a most absurd fabrication' and a 'fable/ and referring to independently existing space and time as 'Undinge.'24 The reasons for this position are frequently reiterated in his work, though they are seldom all stated in one place. Kant accepted that space and time are infinitely divisible - this is something that, from the time of his earliest writings, he took to be indubitably established by mathematics.25 Furthermore, he took infinite divisibility to entail that space and time cannot be supposed to consist of simple parts26 - not without committing the fallacy of treating the infinitesimal as the determinably last member of an infinite series (or, as Kant occasionally put it, of supposing that 'an infinite regress has been completed' and has identified a last member).27 For Kant, the result that space and time are not compounded of simple parts is potentially absurd (because it violates a 'demand of reason' that all composites be made up of something simple).28 But, even were it

2O4 The Expositions accepted, it would imply that space and time consist of nothing more than relations, so that, were one to remove all composition from them, there would be nothing left that had been compounded.29 But, for Kant, this is tantamount to a demonstration that space and time cannot subsist on their own, because it would be a contradiction (a 'most absurd fabrication') to suppose that there are 'mere relations' existing where there are no relata whatsoever.30 Accordingly, Kant drew the conclusion that 'space, considered as something that subsists by itself, is in itself nothing actual' (A43i 76459). What can be called substantival (independently subsisting) space and time are impossible.31 But though Kant may have taken space and time to be mere relations, that cannot exist apart from relata, it does not follow that these relata have to be objects. They could instead be sensations, or some other sort of matter that exists only in our subjective experience.32 Of course, it would need to be proven that there is a valid distinction to be drawn between sensations, or other purely subjective matters of apprehension, and objects, and that not all of our sensations refer to objects. But this is an issue that has to do with real possibility and the facts of how our experiences are to be interpreted, not with mere conceivability. It does seem at least conceivable that there might be certain sensations or matters given in subjective experience that do not refer to any object. Examples are our sensations of black, cold, and perfect permeability, all of which seem to refer to the absence rather than the presence of any object. A space filled with such sensations could be thought to be empty of objects even though the space does not exist on its own, but is only given as the order in which certain sensations are presented. Admittedly, such 'subjectively full but objectively empty' spaces are not truly empty. But Kant's claim in the Second Exposition is not that space can be thought apart from any sensation, but just that it can be thought apart from any object. And since his conclusion in the Second Exposition is just that space is not a determination of objects, and may be given in our experience prior to that synthesis through which objects first come to be recognized, the claim that space can be thought apart from objects is all he needs to make for his purposes. With time the issue is more difficult. A time within the world when there are no objects would be a time before which the world was annihilated and after which it was re-created. But the notion of a re-creation of the world after an interval of empty time involves the same causal paradoxes as does that of its original creation at an arbitrary moment in absolute time. In the Antinomies, Kant rejected the latter as a violation of the

The Second Exposition 205 conditions on the possible form of the sensible world (as at A433/B46i). It is hard to see how he could have found the former to be any more acceptable. At R4756 (Duisburg 21 [Ak, XVII 699]) Kant tried to come up with an alternative sense in which time could be 'empty/ remarking that a temporal interval could be technically 'empty' even if things exist over that interval, as long as there is no continuous series of alterations occurring. But this solution is no better. A jump in the continuous series of alterations is ruled out by the causal principle ^207-9/6253-4). And just as there is no ground in an empty time for why the universe should begin at one moment rather than another, so there is no ground in a completely static interval for why change should resume at one moment rather than another. Thus, the one is as much a violation of the causal axiom as the other, and involves the same illegitimate notion of absolute beginning (or absolute resumption). However, if we consider the time over which an (objectively) empty space endures to be a locally empty time (in that part of the universe), then the resumption of activity could be explained by causal signals originating from without the region. Admittedly, Kant's claim in the time argument is not that all objects may be removed from time, but all appearances may be. But, if 'appearances' does not just mean intersubjectively reidentifiable objects, as they emerge through synthesis in accord with the Analogies, then I can see no way to defend Kant's position on time in the Second Analogy. In so far as his position is sound, it must be interpreted in the more restrictive way I have proposed. To sum up, Kant's rejection of the possibility that space and time subsist on their own does not entail that he accepted that they can exist only through reference to objects. A space consisting of sensations will do just as well, and if the sensations can be taken to refer to the lack or absence of any object, then the space can be conceived to be (objectively) empty. Derivatively, the time over which such a space endures can be conceived to be a (locally) empty time. b. Arguments for the Conceivability of Empty Space and Time Of course, simply because Kant does not reject the conceivability of empty space and time in those texts that have tended to be taken to carry this implication, it does not follow that he accepted this result. But the matter permits of positive, as well as purely negative proof. To see why, let us digress for a moment and consider how Kant's position contrasts

2o6 The Expositions with that of someone who really did believe that empty space is inconceivable: Descartes. In a passage that has since become notorious, Descartes claimed that the void between the walls of a jar could not exist because, if there were really nothing between the walls of a jar, then they would have to be together.33 However, Descartes was greatly assisted in giving this demonstration by the assumption that extension and body are one and the same thing. Once this assumption is granted, a contradiction can immediately be drawn from the concept of empty space. But this assumption is not one that Kant shares. For Kant, extension by itself is not body. The extension must also contain something real. When the 'real' in our experience is translated into physical theory and given an analogue in the external world of bodies, it emerges as repulsive force. It is through exercising a repulsive force that objects impact on our sense organs, and so lead us to have sensations. And sensations, for their part, vary in intensity, corresponding to the degree of repulsive force in the affecting object,34 so that repulsion is the ground of all degrees of reality in experience, and the diminution of the 'real' in experience down to zero corresponds to the fading of the repulsive force in a body down to zero. As Kant explains in the Anfangsgrunde (compare also R4756 (Duisburg 21 (Ak, XVII 699) and 1*5431 [Ak, XVIII 156]), not all space need necessarily contain repulsive force and, as a consequence, not all space need necessarily be supposed to contain body. Let me conclude [this chapter] with [a discussion of] the well-known question of the possibility of empty spaces in the world. The possibility of these spaces cannot be contested. For space is required for all the forces of matter and, since space contains the conditions of the laws of the expansion of force, it must necessarily be presupposed before all matter. Thus, matter is attributed a force of attraction in so far as it takes up a space around itself by pulling [at whatever may be in this space]. It does this without, however, filling the space, which can be thought to be empty even there where matter is exercising an effect. This is because matter is not there exercising an effect through repulsive force, and therefore does not fill the space. (Ak, IV 534-5)

Empty space is possible because there is a difference between taking up space (by exercising an attractive force in it) and occupying space (by exercising a repulsive force that would prevent any other matter from entering it). On the supposition that the degree to which a body will tend to expand under the influence of its own repulsive force is already

The Second Exposition 207 limited by its own attractive force, working to counterbalance the repulsive and cause the parts of the body to collapse, a body will not expand to infinity, even if the surrounding space is empty.35 Thus, space is one thing, body another; space is what is taken up by the expansion of a body's attractive force (and this space, Kant stresses, is not first created by the attractive force of the body but is, rather, a prior condition determining the nature of that force), body is what is taken up just by the expansion of the repulsive force. Void (beyond the limit of the repulsive force) is therefore, in principle, possible. c. The Real Possibility of Empty Space and Time Granting, then, that empty space and time are at least conceivable for Kant, are they such that they could be represented in an actual experience, or at least thought to be represented by an actual experience? Once again, a range of texts appears to advocate the contrary view. Most notable among these are a large number of passages from the Analytic of Principles, where Kant bluntly, clearly, and repeatedly insisted that empty space and time cannot possibly be perceived (Ai72/B2i4, 6219, 6225, Ai83/B226, Ai88/B23i, 6233, Ai92/B237, 8257), and a range of passages where Kant claims that empty space or time could not be possible objects of experience: Empty space is ... even less an empirical condition that would make up a part of possible experience [than it is an independently subsisting correlate of things]. (For who can have an experience of the absolutely empty?) ^487/6515) An experience [of absolutely empty time or empty space], being completely empty of content, is impossible. (A$2i76549)

It would be a mistake to set too much store by these passages, however. We have to ask what sort of empty space and time they are intended to deny. Is it objectively empty space and time (a space and time in which there are no objects) or absolutely empty space and time (a space and time in which there are not even sensations)? It is only of the latter that the claim can be asserted without argument (and Kant does not provide any argument in any of the passages I have cited). Perception is by definition a consciousness that contains sensation (6207, Bi6o), and experience by definition cognition that determines an object through perception (6218), so it follows merely by definition that a space or time

208 The Expositions in which there is no sensation cannot be given in a 'perception' or 'experience/ But this analytic consequence poses no problems for Kant's position in the independence argument, since that argument is just concerned to claim that space and time may be empty of objects, not that they may be absolutely empty. Whereas the claim that space and time cannot be perceived to be absolutely empty may be true by definition, the claim that they cannot be perceived to be empty of objects stands in need of argument. When Kant does address this issue (as he does in the Anticipations and the Anfangsgrtinde), it leads to a rather more cautions conclusion: not that empty space or time could not be possible objects of experience, but just that no experience could be adequate to prove that an absolutely empty space or time are, in fact, present: There is no perception, and consequently no experience possible that could prove a total absence of everything real in appearance... that is, a proof of empty space or empty time can never be drawn from experience. For the total absence of the real in sensory intuition can ... itself not be perceived. ^172/6214) No experience, or inference from experience, or necessary hypothesis needed to explain experience can justify our supposing empty space as actual. (Ak, IV 535)

To claim that no experience can be known to be of an absolutely empty space or time does not rule out the possibility that an empty space or time could be experienced (in some wider sense of 'experience,' not limited just to knowledge of empirically given objects). The case is similar to that of a chiliagon. Given the limited discriminative powers of our eyes, no visual experience could be adequate to prove that a roughly circular object is a chiliagon rather than a circle. But we do not think that chiliagons (or, for that matter, circles) are not possible objects of experience. We take it that such figures could exist, but that they are simply very hard for our senses to tell apart. Similarly, an absolutely empty space or time might exist, even though our senses may not be adequate to tell them apart from a space or time filled with some infinitesimally small quantity of sensation or the 'real' of experience. In this regard, it is worth repeating that Kant's claim in the Second Exposition is very careful. He does not say that we can experience absolutely empty space or time, but that we can think that certain of our experiences could possibly be of an empty space or time. It is this impossibility of proving that any given experience is, in fact,

The Second Exposition 209 of an absolutely empty space or time that provides the sole support for the principle of non datur hiatus (A228~9/B28i-2) - the principle that 'nothing that proves a vacuum, or even admits it as a part of empirical synthesis, can enter into experience' - and not any supposed impossibility of having an experience that might be of an empty space or time. Kant tries to infer the principle as a consequence of the principle of continuity, but the Anticipations of Perception deny the validity of the principle of continuity ^171-2/6212-13), and when the principle is resurrected in the Second Analogy ^207-9/6253-4), it is applied only to alterations effected by a cause, not to the pattern in which the real may be extended in space. Admittedly, some effort at establishing that a hiatus would violate the conditions of the possibility of experience is made in the Third Analogy, in the following passage: I certainly do not mean to deny empty space with what I have said, for it could always be in those places that perception cannot reach and so where no empirical cognition of simultaneity [between reciprocally interacting bodies in accord with the Third Analogy] takes place. But then it is, for all our possible experience, no Object whatsoever. (A2i4/B26i)

But the most that this argument claims is that a knowledge of recriprocally interacting objects is required in order to determine objective spatial relations, and even that is a claim that Kant is only partially able to cash out. Nothing in his account of the principles of cause or reciprocity requires contact of cause and effect, so reciprocally interacting bodies can be conceived to be separated from one another, with points of an intervening, empty space defined relatively to these bodies by triangulation. So empty space can be objectively given, and the argument of the Third Analogy can effectively deny the perception of an empty space only in those circumstances where there are no surrounding landmark bodies to be perceived. Moreover, prior to the determination of objective spatial and temporal relations through synthesis in accord with the analogies, there is a subjectively given manifold of apprehension, and it remains a question whether this subjective manifold may not contain empty spaces, or an array of matters that can be taken to refer to the lack of anything real in space. There is therefore no clear proof of the impossibility of an experience of empty space to be drawn from anything Kant says about the conditions of the possibility of experience in the Analytic of Principles. And in the Antinomies, he explicitly admits as much:

2io The Expositions Thus, there could well be a space (be it full or empty)36 bounded by appearances, but appearances could not be bounded by an empty space outside of themselves. And this holds as well for time. (A^i, 33/3459, 461) One easily notes that by this would be said: empty space so far as it is bounded by appearances, consequently empty space within the world at least does not contradict transcendental principles and could therefore be admitted in light of these (although its possibility would not immediately be affirmed thereby). (A43in/ 6459,46in)

Even here, however, Kant closes by remarking parenthetically that the possibility of an empty space is not being 'immediately affirmed.' What may be giving him pause is the question of whether a fully worked-out physics would permit the possibility that the forces of attraction, rigidity or cohesion might overcome a body's repulsive force and prevent it from always extending into any adjacent, unoccupied space. This issue is examined in greater detail in the Appendix to this chapter. For now, however, the main point is that the 'possibility' Kant has in mind at A433n/B459, 46in may be physical possibility as determined by empirically discerned laws of forces, and not anything that could be derived from a consideration just of the conditions of the possibility of experience in general. d. Arguments for the Real Possibility of Empty Space and Time Of course, simply because Kant might occasionally affirm the real possibility of empty space or time, or not say anything to rule out this possibility explicitly, it does not follow that this possibility is well grounded in his general account of human cognition. It might be that his conclusions exceed (or underestimate) his proofs. Let us turn, therefore, to consider this latter issue. Once again, I want to approach the topic by, first, considering how Kant's position differs from that of a philosopher who clearly denied the possibility of having representations of empty space or time: Berkeley. In his famous attack on abstract ideas in the Introduction to the Principles and in his subsequent use of this point in his attacks on primaryquality realism (Principles, 9-15, and Dialogues, I 187-94), Berkeley appealed to the apparent fact that it is impossible to cognize space without representing some colour that is extended in space or some tactile sensation that is located in space, or to cognize time without representing

The Second Exposition 211 some series of ideas that are successive in time.37 In this sense, the representation of 'empty' space or time is impossible for Berkeley. But Kant can grant Berkeley's argument without having to deny that empty space or time is really impossible, because what Kant means by empty space and time and what Berkeley means are not the same thing. For Berkeley, a space or time is not truly empty unless it is empty of all sensible content (of all 'ideas'). But, Kant's claim in the Second Exposition is not that space and time can be empty of sensible qualities, but just that they can be empty of objects or appearances. And, for Kant, it is a real question whether the content that is present in space and time must always be taken to constitute or refer to an object or, as he puts it, to something 'real.' In the Second Exposition, Kant seems to have taken this premise to be so obvious as not to stand in need of any further justification. But some indication of his grounds for holding the view can be gleaned from the Reflexionen and the Anticipations: The possibility of thinking an empty space and empty time is nothing other than the diminution of the reality in both (in the first case of impenetrable extension) which, since it can be diminished without end, passes over into nothing... A completely empty space is a mere idea of decomposition [of, say, the force of impenetrability] down to nothing, but not of complete removal [of the extension the force formerly occupied]. (R5341 [Ak, XVIII156]) In addition to (the form of) intuition, [appearances, as objects of perception] contain the matters of some object in general (whereby something existing in space or time is represented); that is, appearances contain in themselves the real of sensation, hence a merely subjective representation from which one can only be aware that the subject is affected and that one relates to an Object in general. Now a continual alteration is possible between empirical awareness [perception] and pure awareness, where the real of perception completely disappears and a merely formal awareness (a priori) of the manifold in space and time remains. (6207-8)

Sensible qualities can designate varying degrees of presence of the 'real' (i.e., of an object, ultimately expressing its presence through exercising a repulsive force), and these degrees can diminish, at least in principle, to zero (no presence of any reality in the space or time). Accordingly, to conceive of the real possibility of an empty space or time is to do nothing more mysterious than conceive the ideal limit (equal to zero) of the process of gradual diminution of the 'real' in intelligible

212 The Expositions experience. It is to conceive, for example, total blackness (the absence of all colour, i.e., all reality in visual experience), absolute cold (the absence of all heat, i.e., all reality in haptic experience), perfect permeability (the absence of all resistance to motion, i.e., all reality in kinaesthetic experience), silence, odourlessness, and tastelessness. Note that, in conceiving these things, we are not straining at the limits our imaginative or cognitive powers are commonly supposed to possess and conceiving some pure manifold, or even nothing at all. Black, cold, silence, permeability, and the like are matters of intelligible experience - indeed, matters that we regularly encounter in our everyday experience - they are just matters that are not taken to refer to the presence of any object, or, as Kant puts it, to any 'real' in experience. A space or time that is thought to exhibit these characteristics, even to perfection, has sensible content; it just might not contain any real objects or appearances. Berkeley himself supposed that we have (or, at least, can imagine) such experiences as those of black, cold, perfectly permeable regions, and that these are what we mean when we refer to 'absolute' space and time.38 But, immaterialist and sensible quality realist that he was, he thought it a misnomer to refer to such spaces or times as 'empty.' Since there is no 'real' material substrate underlying any of our ideas, as far as Berkeley is concerned, and since all our ideas are equally real, black, cold, penetrable regions are as 'full' as any other. But Kant did not follow Berkeley on this point. All that this means, however, is that Kant's disagreement with Berkeley does not have to do with what exists or can exist in space (both are agreed on the facts of that matter) but over whether the sensible qualities with which space and time are filled should always be considered to be (or, in Kant's case, to refer to) objects. Again, it needs to be stressed that Kant's claim is not that we actually experience empty space or time as so described but that we are able to conceive the real possibility of such an experience. It may be that there is no such thing given to us as a total absence of any object in space or time, and that even the darkest consciousness (as Kant puts it in Prolegomena, §24) contains some infinitesimally small quantity of the 'real.' But since we regularly experience the fading of colour, the cooling of heat, the loss of resistance, and so on, we can readily extrapolate from this experience to form the conception of the ideal limit (equal to zero) of the continued progress of this process and form some conception of a completely empty space or time.39 Nor is this conception a mere idea of reason. For all we know, some of our experiences of black, cold, silent, permeable, etc., regions may, in fact, be actual experiences of this result. It is in this sense that we can 'think' that there may be no objects in

The Second Exposition 213 space, or remove all appearances from time. To 'think' there are no objects in space or time is not simply to conceive the concept of empty space or time without involving ourselves in a contradiction; but neither is it to do so much as experience a sensible representation that we know to be of an absolutely empty space or time. It is rather to experience a representation that looks no different from an empty space or time, so that we can think that it could well be of an empty space or time, just as the experience of a roughly circular representation could be thought to possibly be of a chiliagon. This may also explain Kant's odd remark at A43in/B459n, 46in, that intramundane void 'does not contradict transcendental principles although its possibility would not therefore be affirmed thereby.' Seen from the perspective of Kant's account of possibility in the Postulates, this is an absurd claim. Something is possible just if it satisfies the conditions of the possibility of experience, so, if intramundane void does not contradict any transcendental principles, how can Kant say that its possibility is not affirmed? The answer is that, while intramundane void may not violate the principles of the possibility of experience, there is one other thing required to establish real possibility, and that is the possibility of having an experience that could demonstrate the actuality of the object, or at least provide the basis for a plausible inference to its actuality. And, in the case of void, Kant takes all the possible experiences to be systematically ambiguous. They might arise from the presence of void, but there is no way to know for sure. Appendix: Empty Space and Time in Kantian Physics It might be objected that, even if void cannot be directly perceived in our experiences, it might still be inferred from causes (say, a vacuum-pump experiment) or from postulating its necessary existence as a condition required to bring about certain effects (e.g., variations in density [Ai72-375214] or the inertial or gravitational mass of matter [Ai73/B2i5l, or the apparently unretarded motion of the planets [Ak, IV 563]). But Kant denies that such inferences could ever be legitimate. the total absence of the real in sensory intuition can firstly not itself be perceived; secondly it cannot be inferred from any particular appearance or the difference of the degrees of reality of any appearance, nor may it even be presupposed in order to give an explanation of those degrees of reality. ^172/6214) all experience gives us only comparatively empty spaces to know, that can be completely explicated, in all outstanding degrees, by the characteristic of matter

214 The Expositions to fill space with a greater or smaller (diminishing to infinity) power of extension [i.e., repulsive force], without needing empty space. (Ak, IV 535)

Kant's reasons for making this claim are more fully explicated in the Dynamics Chapter and at the close (Ak, IV 563-4) of the Anfangsgrunde. In the Dynamics Chapter, Kant insists that we do not need to postulate the existence of void space to account for differences in the density of various kinds of matter. We can, instead, postulate that each part of matter exercises a repulsive force, by which it resists the entry of any body into its space, its degree of resistance increasing to infinity as it is compressed to a point. On this postulate, identical quantities of different kinds of matter could be taken to exercise different amounts of repulsive force at the same volume, thus accounting for differences in density without having to postulate void space. However, the most telling consideration in determining whether the postulation of empty space is either required to account for observed effects or indicated by observed causes is, as far as Kant is concerned, the nature of the forces determining the cohesion and rigidity of bodies. He raises two possibilities: cohesion and rigidity could be original forces in bodies (like gravitation and repulsion) or they could be merely derivative effects of the original forces of gravitation and repulsion. The latter could be the case, Kant speculates, if there were an ether (a kind of material with abitrarily large repulsive force in comparison to its attractive force). Under the force of gravitation (near the sun or in the atmosphere of the planets), the ether would be compressed, and its parts would exert a strong repulsive force against all other bodies, thereby creating the effects of rigidity and cohesion we see in the materials around us. But, at a distance from massive, strongly gravitating bodies, the ether would expand and become less dense (hence, allowing unretarded motion of the planets around the sun). If this were the case, then vacua would be physically impossible. Any empty spaces would be immediately fillled by the ether (Ak, IV 563-4). But, if the cohesion and rigidity of the parts of bodies are attributable to an original force within each body acting, along with its original attractive force, to cancel the effects of its natural tendency to expand into any insufficiently resisting space, then the possibility of vacua within the universe could not be denied. The evacuation of a space would not necessarily lead the surrounding bodies to expand to fill that space. Kant takes it that we have no way of determining which of these alternatives is the correct one. Everything we might think we need vacuum for (to account for differences in density or the motion of the planets)

The Second Exposition 215 can be done by postulating spaces completely filled with a minimally resistant matter, such as an expanded ether (Ak, IV 535, 564). And inferring the existence of empty space as an effect of physical causes presupposes an account of those causes that we are not (at least not now) in a position to supply: No one has a right to be put off by the fact that these reasons for rejecting empty space are purely hypothetical; anyone who wants to assert its existence is no better off. Those who propose to decide this controversial issue dogmatically, whether on the one side or the other, run into mere metaphysical presuppositions ... and ... these can decide absolutely nothing concerning the question... One sees readily that the possibility or impossibility of empty space must be referred, not to metaphysical grounds, but to the difficultly disclosed secrets of nature, having to do with the manner in which matter sets limits to its own force of extension. (Ak, IV 564)

This passage appears to hold out the possibility that a more sophisticated science, able to determine the manner of operation of the forces limiting the extension of matter, might be able to demonstrate the impossibility (or the actuality) of void space. However, this possibility should not be taken to undermine Kant's premise in the independence argument. Here, at least,40 he is explicit that the question of void is not a metaphysical matter, but one for empirical investigation (of the "difficultly disclosed secrets of nature') to determine. Even should it turn out, therefore, that, as a matter of fact, there are no truly empty spaces, this would be merely a consequence of certain higher-order empirical (and hence, contingent) facts about the world, and the real possibility of the existence of void spaces could still be affirmed. e. Summary and Conclusions Kant's goal in the independence argument is to overcome blindness, at least in part, and demonstrate, if not that space and time are originally present in our intuitions as forms, at least that they are already given prior to any of the acts of intellectual processing that result in the cognition of intersubjectively reidentifiable objects. To establish this point he makes the claim that space and time may be conceived to exist independently of any recognition of the objects that appear through intellectual synthesis. Though this claim might at first appear to be in conflict with claims Kant repeatedly makes about the objects and limits of both possible thought and possible experience, a careful reading of the texts at

216 The Expositions issue shows that Kant never explicitly rules out the real possibility of empty space and time. What is more, positive arguments for both the conceivability of empty space and time and the possibility of experiencing them can be gleaned from Kant's position on the nature of body as a space filled with repulsive force, and his position on the possibility of continual remission in any real, positive quality. There is nothing contrary to the Critical Philosophy in the assertion that an experience of black, cold, perfectly permeable regions of space might at least be thought to be experiences of empty space, and that the duration of such experiences might be thought to be experiences of empty time. However, while empty space and time are 'possible' in the sense that they do not violate the first principles of the possibility of experience, the evidence for their actual existence is systematically ambiguous. Fortunately, possibility is all that Kant needs to establish for his purposes in the independence argument. As long as it is even possible that we might have experiences of a space or time that do not contain any objects, it follows that there can be no necessary connection between space- and timecognition and object recognition. The intellectual synthesis through which objects or appearances are first given to us should not, therefore, be supposed to be what first gives us spatiotemporal relations. Those relations can be present among the matters of our experience quite independently of any such synthesis. If what I have said is correct, then the blindness problem is attacked by the independence argument of the Second Exposition. This is what one might have expected, given that the blindness problem is new to the Critique and that the Second Exposition is the one part of the Expositions that has no precedent or ancestor in ID, where blindness was not a problem. But the Second Exposition's victory over blindness is only partial. It establishes that space and time must be supposed to be present in our experience prior to or independently of those forms of intellectual processing that first yield a consciousness of objects or appearances, but it does not establish that space and time are entirely independent of all intellectual processing whatsoever. There might be some sort of intermediate intellectual synthesis (the figurative synthesis of imagination, for example) that generates an array of matters in space and time prior to any perception of objects but subsequently to the intuition of sensory impressions. This final, loose end is addressed by the Later Expositions.

7 The Later Expositions

What I call the 'Later Expositions' are the last two of the numbered paragraphs of the A and B Expositions. (The numbers are different in A and B, and in the B space and time sections.) These paragraphs can be treated together because they all argue for the same conclusion: that our original representations of space and time are not 'concepts/ but are given in intuition. To justify this conclusion, they appeal variously to the singularity, whole/part priority, and infinite or unbounded magnitude of space and time. i.

The Singularity Argument

3. [A: 4.] Space is no discursive or, as it is called, universal concept of relations of things in general, but a pure intuition. For firstly, we can only represent one space, and if we speak of many spaces, we understand them to be only parts of one and the same unique space. These parts can also not precede the one, allinclusive space as its components (out of which its composition might be possible), but can only be thought in it. It is essentially one. The multiplicity in it, and consequently also the universal concept of spaces in general, is based merely on delimitations. From this it follows that an a priori intuition (one that is not empirical) lies [A: would lie] as a ground of all concepts of space [A: of spaces]. (A24-5/B39)

In this passage, which I refer to as 'the singularity argument/ Kant concludes that space must have been originally given in intuition because it is represented as one thing. The connection between singularity and an origin in intuition is not directly explained, but it appears to turn on the notion that the singularity of its referent rules out the possibility that a representation might be a 'discursive or universal' concept, and this is

218 The Expositions taken to leave no other alternative but to suppose that it originated in intuition. Thus, with all the enthemematic premises supplied, Kant's argument would appear to be the following: 1 Either a representation is a discursive or universal concept or it must have been originally given in intuition. 2 All our representations of space are such that, in principle, they can signify just one object (or delimited parts of this one object). 3 A representation that is such that, in principle, it can signify just one object cannot be a discursive or universal concept. Therefore, our representations of space cannot be discursive or universal concepts, but must have been originally given in intuition. a. Justification for the Third Premise The third premise of this reconstructed argument can be taken to be true by definition. As Kant explicates it in his Logic, §§5 and 6 (Ak, IX 93-5), a discursive or universal concept just is a representation that emerges through abstraction from experience. We are supposed to collect various experiences together, compare them, note that they resemble one another in certain respects, and 'abstract' these resembling features (or abstract from the other features in our consideration of the concept).1 In so far as 'discursive or universal concepts' are composed in this way, they are inherently general in their reference. They refer to something common to a number of experiences. For this reason, discursive or universal concepts, as collections of features common to a number of experiences, may be used to designate all those experiences exhibiting the features contained in the concept - indeed, to refer, not just to all such past experiences, but to all possible experiences as well. By this means many different representations are brought 'under' one representation, as Kant likes to put it (A77/BiO3); indeed, a potentially infinite number of different experiences may be brought 'under' the concept. But because they represent what is common to a number of different experiences, discursive or universal concepts represent only a portion of the content of any one representation. Consequently, there can be no guarantee that they will capture all the features that differentiate any one particular experience from any other. Though Kant claims that we can use discursive or universal concepts to refer to just one object (Logic, §1 [Ak, IX 91]), it is always possible, at least in principle, that an arbitrarily

The Later Expositions 219 large number of other (at least possible) objects might also satisfy the concept but differ from the one actual or intended referent in ways we have not thought in the concept.2 As a result, the fact that a representation can, in principle, signify only one object (regardless of how many objects it actually or intentionally refers to) is a proof that it could not be a discursive or universal concept. b. Justification for the Second Premise The second premise is more controversial, but it is one that Kant at least attempts to analyse and further explicate. He admits that, even though we experience many distinct, determinate spaces (e.g., my office, the inside of my car, my yard), we hold that each of them exists at a location somewhere within a single, all-embracing space. We hold, that is, that each of them is only a part of a larger space, that extends indeterminately beyond them. Moreover, Kant maintains, the unity of the parts of space in the whole is prior or essential to the parts themselves, not accidental. The many spaces are not thought to be a collection of previously given components out of which a single whole just happens to have been subsequently assembled, so that they might be supposed to exist independently of the whole and merely accidentally possess the locations they have in it. Rather, in so far as they are represented, it is only through delimiting or introducing boundaries within a previously given whole, so that they are always thought as existing in the whole and as each defined and individuated through its location within it.3 Thus, nothing about space is universal or general. Particular spaces are particular parts of one space, each individuated by its location in the one space, and the wholes in which they are located are singular objects, in which all particular parts are determined by delimitation. A few years ago a spate of articles appeared on the question of whether Kant was right to insist that all particular spaces can be represented only as contained within a single, all-encompassing space.4 But, while this question may be interesting in itself, its bearing on Kant's singularity argument in the Later Expositions is negligible. Despite Kant's references to essential oneness and the all-embracing character of the containing space, the point that the singularity argument really turns on is that, in representing space, we are representing, not a universal feature common to a number of particular experiences (like red, which is common to the experiences of a stoplight and an apple), but a particular itself (or a part of a particular). Kant puts this point by calling space

22O The Expositions 'one' and 'essentially united/ but the context of the argument makes it clear that it is not oneness or unity that is at issue, but particularity: the point is that spaces, and the wholes in which they are determined, are all particulars (each a singular object or a particular part of a singular object), not that there is necessarily only one of them. The oneness of space could be given up, but the argument would still work as long as any discrete spaces are taken to have the status of so many unique particulars (or parts of particulars), rather than of a single common feature or difference abstracted from a number of different particulars. This is an important point, that should perhaps be dwelt upon in more detail. There is a difference, Kant is telling us, between the way the particular or specific spaces are related to space in general and the way particular objects are related to generic concepts. A representation of a particular contains all the features found in any generic concept that it satisfies. It does this even though it is supposed to be a separate representation in its own right, distinct both from the generic concept and from other particulars that satisfy this same concept. The representation of the particular is differentiated from the generic concept by the fact that there are other features in it, in addition to the features it shares with its generic concept. Another way to put this is to note that a particular representation is related to a generic concept as a superset is related to a subset (the particular representation as superset repeats the elements of the generic concept along with certain additional elements). The particular representation/concept and subset/superset relations beg the classic problem of the one and the many. The features or elements making up the abstract concept or subset are supposed to be in all the various particular representations that instantiate the concept, or all the various supersets that contain the subset, yet each specific feature or element, as it exists in all these instances or supersets, is supposed to be identically the same element.5 But a particular space stands in an entirely different relation to space in general. The features that are thought in the representation of a particular space do not constitute a superset containing the features that are thought in the representation of space in general; they are merely a delimited portion of the features thought in the representation of space in general. Thus, with our representations of space, the set-theoretic relations of the previous paragraph are reversed - that is, the particular space is a subset of the generic space as superset. What is more, the generic space is thought to be an ordered superset, and it is thought that its parts cannot be just any subset of elements in the superset but only a

The Later Expositions 221 delimited portion of this order. That is, the elements of the subset (the particular spaces) must preserve the order of the elements of the superset (space in general), and they cannot skip any superset elements in doing so. For example, if the superset is the ordered set A = , then B = can be a part and C = can be a part, but D = and E = cannot be parts. (However, to speak of the part/ whole relation in any set-theoretic terms whatsoever, even those of ordered sets, is to introduce a distortion. The parts of a whole do not in any sense exist apart from the whole, whereas, in the above examples, the sets B and C are represented separately. Strictly, B should be understood as the portion 12-41 of A, and C as the portion 11-3 I of A, where the elements between the ' I ' are taken to be end-points located in A. As Kant puts it, particular spaces exist only in space in general, as delimited portions of the content of the more generic representation.) The parts of space, in so far as they exhibit the characteristic relations to the whole just described, can be said to exhibit mereological6 relations of membership in the whole. I will describe the instances of a generic concept, in contrast, as exhibiting taxonomical relations of membership to the generic concept. Kant's basic claim in the singularity argument is that, because we represent particular spaces as mereologically rather than taxonomically related to space in general, our representations of specific spaces must be representations of parts of particulars (which would make our representations of the wholes to which these spaces belong representations of particulars) rather than representations of universal or common features that a number of particulars are thought to share in common (which would make our representations of space in general into merely a more abstract or generic concept of what is given in the parts).7 This all means that those who have criticized Kant's position on the unity of space have not really attacked the singularity argument in the Later Expositions. The singularity argument turns on the claim that space is a particular and that spaces are particular parts of particulars, so that we have representations of space and spaces that are not merely representations of some feature or set of features abstracted from a collection of different experiences. In so far as Kant's critics have themselves spoken of discrete spaces as so many distinct individuals, they have given up any pretense of criticizing the exposition.8 Kant's position in the singularity argument would be undermined only if space were taken to be a common feature of discrete worlds, the way red is taken to be a common feature of a stoplight and an apple.

222 The Expositions This is not to say that Kant would have accepted that there could be more than one space. He clearly rejected this view. But his reasons for doing so need not be invoked to defend his position in the singularity argument.9 However, there are other, more serious problems with the singularity argument, to which we should now turn. c. Justification for the First Premise The first premise of the reconstructed argument is both highly controversial and completely unexplicated and undefended (indeed, since the premise is enthemematic in Kant's formulation of the singularity argument, he does not even acknowledge its existence). Granting that space is a particular and that our representations of space and spaces are representations of singular objects rather than of abstracted, common features, why should we suppose that these representations must have been originally given in intuition rather than only subsequently constructed through intellectual synthesis? If discursive or universal concepts are supposed to emerge through intellectual acts of reflection, comparison, and abstraction from previously given experiences (cf. Logic, §6 [Ak, IX 94]), then why not suppose that singular representations emerge through intellectual acts of combination of previously given experiences?10 One very common and very short way of dealing with this question is to suppose that Kantian intuitions just are singular representations.11 In this case the conclusion that space is an intuition follows immediately from the claim that it is singular.12 But, while this was the sort of trick Kant could get away with in ID, where singularity could possibly be taken to be a defining characteristic of intuitions, in the Critique such a supposition is no longer open to him. The Critique holds that intuitions that have not been processed into intellectual representations cannot be known by us. Thus, in so far as particular representations are known, it is only through intellectual processing. Of course, as admitted in chapter i, above, Kant continues to use the old terminology from ID in the Critique, so that the term 'intuition' sometimes just means 'singular representation' rather than 'immediately given representation.' This might seem to open the possibility that Kant's goal in the Later Expositions might just be to prove that space and time are 'intuitions' in this older sense. But, if this is how intuitions are defined, then the singularity argument is trivial. Since the question still remains of how it is that singular representations come to be

The Later Expositions 223 cognized - whether they must be originally given in raw, sensory experience or might originate through intellectual acts of combination or figurative synthesis, the question of whether 'intuitions,' so called (i.e., singular representations), are given only through or already prior to intellectual synthesis remains completely undecided, and the argument proves nothing of interest either way. Kirk Wilson, who has done more than anyone else to explain the underpinnings of Kant's singularity argument, is none the less one who fails to appreciate this.13 Though he admits that, for Kant, knowledge is possible only through a synthesis that expresses what is given in the manifold in a concept, and so recognizes that Kant's claims about the blindness of intuitions are problematic,14 his solution to the problem fails to come to grips with the issue: To be sure, Kant defines synthesis as the generation of experience. But here Kant is not using 'experience' to mean sensible perception of, say, my desk as a spatiotemporal object characterized by sensible qualities. (Perception is merely intuition accompanied by consciousness.) For Kant, experience is empirical knowledge (Ai76/B2i8), and Kant identifies experience with 'the sum of all knowledge wherein objects can be given to us.' (A237/B296)15

According to Wilson, there is a distinction that needs to be drawn between two kinds of cognition for Kant. There is a primitive level of cognition that consists just in perception ('intuition with consciousness') of singular objects with mereologically related parts given in space and time (for example, my experience of my desk). But, in a stricter sense, nothing can be said to be 'experienced' unless it is unified with everything else that has been 'perceived' in a scientific theory of the workings of the universe. This allows Wilson to give what he thinks is an innocuous explanation of how Kant could say that intuitions are blind without concepts. An intuition is objective insofar as it presents the mereological structure of an appearance, but it is 'blind' without further synthesis relating it to other appearances in one knowledge. Kant is quite clear that 'appearances can certainly be given in intuition independently of functions of the understanding' (Ago/Biaa); though such appearances 'would be for us as good as nothing' (Am). Intuition contains logically and temporally prior to all experience principles which determine the relations of objects (A26/B42), but without synthesis these relations remain unconnected with any knowledge, and therefore, 'blind.'16

224 The Expositions While Wilson is certainly correct to observe that for Kant, all the different objects of our experience must be connected in 'one knowledge/ his conclusions about what this implies for the nature and scope of our blindness to intuitions are forced, and his picture of the role played by synthesis in eliminating our blindness is incomplete and misleading. On Wilson's reading, we are not really blind to our intuitions at all. They are not, as his own citation from Am puts it, 'for us as good as nothing/ On the contrary, they are, he feels constrained to note, 'objective.' For Wilson, in intuition an appearance consisting of a mereological sum of parts is given. What we are blind to, according to Wilson, is just its relations to other appearances. Apparently, therefore, we are not blind to the appearance itself. Far from being, for us, as good as nothing, this appearance is known, already through its mere intuition, to have mereological structural characteristics. This is a very technical and restrictive sense of what it means to be 'blind' and it is in no way justified by Kant's text. The role played by synthesis in eliminating blindness is also underrepresented on Wilson's account. For Kant, synthesis does not just figure in relating appearances such as 'my desk' to one another in 'one knowledge.' It is required in order to recognize appearances in the first place. Indeed, it is even required for the perception of the qualia and figures constituting an appearance. Wilson opines that, for Kant, perception is just 'intuition with consciousness/ but for Kant the words 'with consciousness' add something more to the word 'intuition' than just the thought that the intuition is accompanied by some sort of awareness. An intuition 'with consciousness' is not just an intuition, or even an intuition that has somehow (without being in any way processed or transformed) been brought to our awareness. For Kant, consciousness requires a unity of apperception (An6-i7, 6135), and that in turn requires synthesis (Aio8, 8133). For an intuition to be had 'with consciousness' requires not just that the intuition be given but that it be synthesized or combined (6136-7). And 'combination does not lie in the objects, and cannot somehow be obtained from them through perception and thereby first taken up in the intellect; rather it is solely a performance of the intellect, which itself is nothing more than the capacity... to bring the manifold of a given representation under a unity of apperception' (6134-5). One nas only to consider the examples of the house, the ship, and the stove-heated room from the Second Analogy (Aigo-i/ 6235-6, A192/6237, A202/6247-8) to appreciate that, for Kant, the recognition of singular objects like 'my desk' requires a determination of the manifold in time that is governed by the categories of substance,

The Later Expositions 225 causality, and reciprocity.17 And the Critique's Axioms of Intuition describe other acts of synthesis that must be performed before even otherwise uninterpreted patches of colour or other sensible qualities can be picked out of the manifold.18 Therefore, at least two levels of blindness (blindness to individual objects and blindness to perceptions, such as colour patches) figure in Kant's account of cognition prior to the level that Wilson is concerned with. Acts of synthesis are involved in removing blindness at all of them. But, if the output of the process of synthesis is a concept (and Wilson concedes this)/9 then there can be no justification for distinguishing between a unified knowledge of the world and the 'sensible experience of my desk as a spatiotemporal object characterized by sensible qualities/20 on the ground that only the former is conceptual, the latter properly an intuition. Kant's singularity argument therefore goes awry. The features that it appeals to as evidence that space and time are originally present in our intuitions could not, in fact, be features that could be possessed only by intuitions and not by intellectual or mediate representations as well. There can, in fact, be no features that could be possessed only by intuitions and not by intellectual representations - none that could be known by us, at any rate. Where Kant's argument goes wrong is in its tacit invocation of the supposition that all our mediate representations or concepts emerge from comparison of intuitions and abstraction of common features and that none are generated in any other way. Kant certainly believed this in Logic, §1, where he claims all our 'concepts' are representations of common features abstracted from experience. But his logic of concepts is simply out of line with the theory of knowledge of the Critique. The Critique recognizes that abstraction is not the only process performed by the mind to generate mediate representations; even the cognition of mereologically structured particulars requires a process of running through and synthesizing the array given in intuition. Perception itself is not immediate but presupposes processes of combination or association, and consequently percepts are mediate representations, not intuitions.21 Kant never patched up this infelicity in his account of concepts. As a consequence, he may never have realized that the singularity argument simply misses the mark. If 'concept' is a word used to refer to any mediate representation, not just to attributive or sortal universals abstracted from experience, then percepts of mereological wholes are 'concepts.' But, even if the term 'concept' is restricted to designating sortal or attrib-

226 The Expositions utive universals, percepts of mereological wholes are still mediate representations and not intuitions. In neither case has Kant succeeded in demonstrating that our original representations of space and time are intuitions. d. The Argument of the Time Section Unfortunately, the singularity argument as it appears in the time section casts little light on these problems and questions. The time singularity argument is oddly disanalogous to that for space, being both inexplicably abbreviated in certain respects, and strangely amplified in others. 4. Time is no discursive or, as it is called, universal concept, but a pure form of sensory intuition. Different times are only parts of one and the same time. But that representation that can only be given by a singular object is intuition. (A3I-2/B47)

Like the space passage, this text appeals to singularity or particularity to draw a conclusion about origin in intuition, apparently by means of the same tacit, disjunctive syllogism that is between the lines in the space section. But, whereas in the space passage Kant appends a number of elucidatory theses to illustrate in precisely what sense space is singular (i.e., that it is to be understood as a particular), only the first and most general of these three theses figures in the time text. We are told that different times are, in fact, all parts of one time, but not that the single whole precedes the parts, or that the parts emerge only through delimiting it. As if to make up for this lack, the time passage contains something not found in the space passage: an attempt to explain exactly what singularity has to do with origin in intuition. We are told that when there is (in principle) only one particular object that can 'give' a certain representation to us, that representation must be an intuition.22 Oddly, what the explanation appeals to is the singularity of the object that causes or, as Kant puts it, 'gives' the representation, not the singularity of the object that is signified by the representation. But it is the latter claim, and not the former, that Kant makes in the space passage and that is implicit in the time passage's argument that different times are only parts of one and the same time. I speculate, but what might lie behind this less than rigorous argument is a careless or confused mode of expression. Kant might have intended to say that a representation that can only be satisfied (not given) by a singular object is an intuition.

The Later Expositions 227 In this case, the time argument would be no different from the space argument, and open to the same objection. Alternatively, Kant might have really meant to say that intuition is 'given' by a singular object. In this case, the argument would appear to rest on the tacit notion that each distinct object that acts on our representative capacity brings about an effect that differs from that brought about by any other object (and hence is, in this sense, a 'singular representation/ that is, a representation that refers to just one object). In contrast, all our 'concepts' are what Kant calls 'general or reflected' representations (Logic, §1 [Ak, IX 91]) - reflected, because they arise from reflection upon a number of previously given effects (which makes them repraesentationes discursivae, according to Logic, §1); general, because they represent something or some set of things common to this number of different representations (which makes them repraesentationes per notas communes, according to Logic, §1). As such, concepts are inherently abstract. Because they represent what is common to a number of different representations they represent only a portion of the content of any one representation, and abstract from the rest. Consequently, there can be no guarantee that any given concept will capture all the features that differentiate the effect brought about by one object from that brought about by another. As a result, the fact that a representation can only arise as a result of our being affected by one, particular 'object'23 is an indication that it is not a concept but, as Kant puts it, an 'intuition.' But this version of the argument only multiplies the problems already noted with the singularity argument as it appears in the space section. If Kant's claim is that 'intuitions' are by definition representations that can only be given by singular objects, then the argument is trivial, since it does nothing to prove that what it calls 'intuitions' are immediately given prior to any intellectual processing. If, on the contrary, Kant is intending to make the non-trivial claim that those representations that can only be given through singular objects are known independently of intellectual processing, then it is not obvious why the claim should be accepted as true. Why should we suppose that the effect of a singular object on us should not require intellectual processing (in the form of combination of the manifold or of a figurative synthesis of the imagination) in order to be cognized, just as much as the cognition of a discursive or universal concept requires intellectual processing (in the form of reflection, comparison, and abstraction)? Worse, rather than simply appeal to the singularity of our representa-

228 The Expositions tion, as the argument in the space section does, the argument of the time section shifts the emphasis and makes the conclusion turn on a claim about the singularity of the object causing the representation. In doing so, it makes the surprising supposition that we can know what the objects that cause or 'give' our representations are like. It may well be charged that, if this is indeed Kant's supposition, then it invokes some sort of cognitive access to the way the objects that affect us are in themselves, independently of how they appear to us in our representations something that Kant denied that we do, in fact, have. It would appear, therefore, that the singularity argument is little more than an argument from ID (the singularity argument originally occurred in ID, §14 \2., and §15, IB [Ak, II 399 and 402]) that has been incongruously transplanted into the Critique despite the fact that the background presuppositions that alone made it valid have changed.24 The Critical account of representation takes intuitions to be immediate representations, and knowledge of singular objects to result from intellectual synthesis. Thus, for the Critical account, singularity is by itself no reason for automatically inferring an origin in intuition, unless 'intuition' is (uncritically) defined to consist, not of the representations immediately delivered by the sensory faculty, but of representations of singular 'objects,' however they might be supposed to originate. e. Conclusions The most that the singularity argument establishes within the context of the Critical account is that our representations of space and time could not be a certain kind of intellectual representation: discursive or universal concepts arising from intellectual acts of reflection, comparison, and abstraction. Considered as such, the singularity argument works by pointing out that, unlike our discursive or universal concepts, which represent some respect that a number of objects may have in common, our representations of space and time are either of one, unique thing or of the particular and individually distinct parts of this one thing. So understood, the argument may have a certain value - it could be used, for instance, to bolster the independence argument of the Second Exposition by demonstrating that our representations of empty space and time could not arise through abstracting some general or common feature from our experiences of particular objects or experiences (such as their extension). But beyond this limited use it is of no worth.

The Later Expositions 229 ii.

The Whole/Part Priority Argument

Though the time singularity argument abbreviates many of the points found in the space section, the time section does eventually invoke the observations that the parts of time are given as already located in the whole and emerge only through delimitation of this whole. However, in the time section, these observations are made in the last numbered paragraph and apparently figure as premises of a distinct argument, not as merely elucidatory remarks on the claim that time is singular.25 There is a small, but significant variation in the statement of this argument in A and B, so I refer to it as either the A whole/part priority argument or the B whole/part priority argument in contexts where this distinction is important, or simply as the whole/part priority argument in those where it is not. 5. ... All determinate temporal magnitudes are only possible through delimitations of a single time that lies as a ground ... But where the parts themselves and every magnitude of an object can only be determinately represented through delimitation, there the whole representation cannot be given through concepts (for they contain only partial representations [A: for there the partial representations go first]). Rather, an immediate intuition must lie as their ground. (Aj2/ B47-8)

The argument is hinted at in the space section as well: [The parts of space] can also not precede the one, all-inclusive space as components (out of which its composition might be possible), but can only be thought in it. It is essentially one. The multiplicity in it, and consequently also the universal concept of spaces in general, is based merely on delimitations. From this it follows that an a priori intuition (one that is not empirical) lies [A: would lie] as a ground of all concepts of space [A: of spaces]. (A25/B39)

However, since the time section contains the more complete and explicit argument (it explains why the priority of the whole to the parts should entail an origin in intuition whereas the space argument merely claims that it does), and since in the space section it is a question whether the point is not being made merely in the service of buttressing a claim about the singularity of space rather than as a part of an independent proof, I will confine my comments to the argument as it is given in the time section.

230 The Expositions The argument appears once again to be a disjunctive syllogism, that proceeds from the tacit premise that our representations must either be 'concepts' or intuitions. Only here, the reason offered for denying that our representations of time belong in the first category is not that time is singular, or even that specific times are mereologically rather than taxonomically related to time in general, but rather the fact that the parts of time are only represented by describing boundaries around a region located within a larger time. Just why this whole/part priority is supposed to rule out 'conceptual' status for the representation is differently explained in A and B. In A, the thesis is that, with all our concepts, that is, with all representations not immediately given in intuition, it is the parts that are given before the whole, whereas, in B, it is that our concepts can never be more than representations of parts. Thus, in its two variants, the argument looks like this: 1 A representation either originates as a 'concept' or as an intuition. 2 The parts of time are not given prior to the whole, but emerge only through delimiting a previously given whole. 33 If a representation is a concept, then its parts are given prior to the whole. 3b If a representation is a concept, then the whole is never completely given. Therefore, our representations of time must have been originally given in intuition and could not have first arisen as 'concepts.' a. Premise 2 All of the premises of this argument are problematic. The second premise has drawn the fire of many of Kant's commentators and critics. It has been charged that the thesis that the whole of time is given to us prior to any of its parts is absurd and impossible to accept26 and that, even if acceptable, the premise is internally inconsistent as it contradicts Kant's own position in the Axioms of Intuition, where it is claimed that space and time are extensive magnitudes, and that all extensive magnitudes are such that 'the representation of the parts makes possible (and so necessarily precedes) the representation of the whole' (Ai62/B2O3).27 However, the second objection has been conclusively answered in a number of recent works,28 and the first loses much of its force if one considers that Kanf s position may have been that each of us only ever has one intuition, that takes time to occur (time being one of its 'forms'), so

The Later Expositions 231 that up to any given moment only a portion of it has been received. In this case, any merely momentary experience is properly just a part of an intuition, and not the whole, and there is no obvious absurdity in supposing that the whole of time is given in intuition - or, more properly, would be given in a finished intuition - and that any particular, determinate time is cognized through introducing delimitations into as much of this one, ongoing and ever-growing intuition as we have received up to any given moment. However, even if this (admittedly radical) interpretation of Kant's account of intuition were not accepted, Kant's second premise in the whole/part priority argument would not necessarily have to be rejected as absurd. All that the premise strictly requires is that any determinate time be given through introducing delimitations into a previously given, indeterminately larger whole. From this, it does not necessarily follow that an infinitely large expanse of time must first be given before any part of time can be cognized, though a time that is unbounded in the sense of having no clearly determined end-points may have to be given. This is, in fact, what Kant appears to think, since at A$2 7847-8, where he states the whole/part priority argument, he claims that the premise entails that our original representation of time be considered to be 'infinite' only in the sense of being unbounded. Granting, then, that there is no obvious absurdity or inconsistency in the second premise of the whole/part priority argument, let us turn to consider how that premise might be justified. Though Kant does not go into details here, the justification is obvious to anyone familiar with the history of Kant's struggles with the paradoxes of the continuum from the Physical Monadology on up to the Second Antinomy and the Anfangsgrunde. From the beginning, Kant took it to be unquestionably established by geometry that space and time are infinitely divisible.29 And he took this in turn to entail that space and time cannot have simple component parts. Every part of space and time is itself a space or time that may be divided into yet further parts, so that there are no ultimate parts out of which the whole could possibly have been constructed. Such parts as there are, are themselves always composites within which further parts may be defined by the introduction of divisions and boundaries, and in this sense are 'wholes' that have been given prior to these parts. There are no parts that are not themselves already 'wholes' of further parts. This position is explicitly stated in the Anticipations: The property of magnitudes according to which no part of them is the smallest

232 The Expositions possible (no part is simple) is called their continuity. Space and time are quanta continua because no part of them can be given without it being contained between boundaries (points and moments), and consequently only in such a way that this part is itself in turn a space or a time. Space therefore consists only of spaces, time only of times. Points and moments are only boundaries, that is, mere locations of the limitation of spaces and times. But locations always presuppose an intuition that can confine or determine them, and neither space nor time can be composed out of mere locations, considered as components that could be given even before space or time. (Ai69~7O/B2ii)

Kant took the point in the other direction as well. Not only, on his view, are all the parts of space and time themselves always composites of further parts, and so (if they are supposed to be originally given) wholes that are given prior to their parts, but any whole of space or time is itself merely a portion of a larger whole. His argument for this latter point does not rest on infinite divisibility, however, but on a complex set of considerations that he advances in the Observation to the Antithesis of the First Antinomy (A431, 433/6459, 461). In brief, his point is that there could be no such thing as an experience of a boundary of the world in space or time. All parts of the world, in so far as they are objects of experience for us, must be given as surrounded either by other objects or by an indeterminately extended expanse of empty space or time (the latter alternative is one that Kant rejects for reasons that need not be repeated here,30 so that the argument ends up being a demonstration of the indeterminate extent of the world in space and time). Either way, any given space or time, whether occupied by objects or not, would have to be given as contained within a larger space or time. In somewhat more detail, the argument Kant has to offer for this claim appears to rest on the following considerations: to claim that an object (be it a part of space or time or an actual physical thing occupying this part of space or time) is bounded is, in effect, to claim that there is at least a possible experience that consists of a sensible representation of the boundary of the object. But, if a sensible object is to be represented as bounded in space, there must be a point in the sensory field where it stops and is succeeded by something else. And if it is bounded in time, there must be a moment in time where it stops and is preceeded or succeeded by something else. An object that simply fills the sensory 'field of view/ or all of time up to a given moment (i.e., the present moment or the moment of birth), cannot be represented as bounded because the evidence is inadequate to determine that result (just because we experience

The Later Expositions 233 the object to only reach out - or back or forward in time - so far does not mean that it does not, in fact, extend farther out beyond the current bounds of our senses). Similarly, were we in the progress of our experience to run into a 'wall' we could not cross, the data would again be inadequate to determine that the object is bounded (just because we cannot get beyond the wall does not mean there is nothing out there, and in particular it does not rule out the possibility that the object may continue on the other side of the wall). Rather, if the object is to be actually represented as finite, there must be some perspective from which it appears as terminating within the sensory field or within an expanse of time - that is, as stopping and being succeeded or preceded or followed by something else. This something else must be either another physical object, occupying a further expanse of space or time, or an empty space or time, but, in either case, there must be a larger space or time, extending indeterminately far out beyond the given, bounded region. This result cannot be evaded by claiming that the given, bounded object might be bounded by nothing. If this 'nothing' were literally nothing (no sensory experience), then the object would not, in fact, be represented as bounded, any more than an object is represented as bounded when it fills the sensory field and there is no place in the field where it is represented as terminating and being succeeded by something else. Consequently, the object, if it is to be represented as finite in space or time, must be represented as terminating somewhere within the sensory field or over time and, beyond this point, being succeeded by something else. The only way to evade the implication that all determinate spaces and times (or objects occupying space or time) must be given as located within an indeterminately larger space or time is to take the 'something else' that bounds the object to not itself be an object in space or time. But, in that case, we are no longer conceiving a possible experience (which, as the Second Exposition has already claimed, is necessarily spatiotemporal). Kant remarks on this at the conclusion of the Observation on the Antithesis of the First Antinomy, noting that the Antithesis argument cannot be avoided by the Leibnizian stratagem of maintaining that there might be an absolutely first event in time or an absolutely outer limit in space with nothing beyond it, not even absolute space or time. For what is involved in the [proposed] way out [of the Antithesis argument] consists tacitly only in this: that instead of a sensory world we think of some (God knows what) intelligible world and, instead of a first beginning (a being before

234 The Expositions which there was a time of non-being) a being that presupposes no other condition in the world; instead of a boundary of extension, walls of the world whole, and thereby space and time go out of the way. - But the talk here is only of the mundus phaenomenon, of its magnitude, with respect to which the aforementioned conditions of sensitivity [space and time] can in no way be abstracted without overthrowing the thing itself. The sensory world, if it is bounded, lies necessarily in an infinite void. ^433/6461)

b. Premise 33 The two versions of the third premise represent Kant's attempt to explain why the infinite divisibility of time, understood as entailing whole/part priority, should be supposed to entail that our representations of time must have originated in intuition rather than first been constructed as concepts. The version of the third premise in A appears to be a more or less unreflective attempt to do this job by simply invoking the standard problem with infinite divisibility, as represented by the composition paradox (see chapter i, above). As traditionally stated, the composition paradox appeals to the traditional definition of a substance as that which is able to exist on its own, independently of 'support' from anything else. On this definition, a composite thing is not a 'substance' in the strictest sense of the term, since it depends, first, on its parts, and, second, on those parts having been assembled in a certain way. The parts, however, can quite well exist in separation from the substance, as their manner of arrangement in the substance has to do merely with relations of position and so with locations, and these are taken to be merely accidental (substances are taken to preserve their identity across transport to different locations). Consequently, the parts of a composite are what is most properly called 'substance/ so that a composite is actually a collection of substances set in certain relations to one another.31 (This understanding of the notion of a substance leads to the conclusion that every composite thing must have certain ultimate, simple component parts of which it is composed, and this conclusion is set in opposition to the infinite divisibility of space in the composition paradox. But these further consequences need not concern us here.) The traditional understanding of a substance, therefore, leads up to the notion that all composite things are built up out of component substances. The composite depends on its parts being set in certain relations to one another, whereas these parts do not depend on it. In this sense, the parts of a composite are prior to the whole. This is what Kant

The Later Expositions 235 appears to be appealing to in the third premise in A, when he says that 'there the partial representations go first/ The case of time, which is an infinitely divisible continuum where the parts are defined only through delimitation of a larger whole, is being contrasted with the case of substances and composites of substances, where the whole arises through aggregation of parts. c. Premise 3b If this was in fact Kant's line of thinking, then the fallacy in it, and the reason for the change in B, is obvious: what the premise entails is not the transcendental conclusion that time must be originally given in intuition rather than being a 'concept,' but the metaphysical thesis that time must be a totum rather than a substantival composite (i.e., the conclusion of the observation on the thesis of the Second Antinomy, A438 76466). Before Kant could generate the conclusion that time does not originally arise in our concepts, he would have to assume that our concepts represent all and only substances and substantial composites - an evidently false supposition. Accordingly, Kant changes his line in B and premises, not that, with 'concepts,' the parts precede the whole, but that concepts just are partial representations. But here he is undone by his own ambiguous and insufficiently critical terminology. If a 'concept' just is an intellectual representation resulting from the abstraction of general, common differentiae from a number of previously given experiences, then of course it follows that all concepts are partial representations. For, given the manner in which such 'concepts' arise, they represent only a part of what was originally presented in the experiences they were abstracted from. But if this is how Kant is understanding 'concept' in the whole/part priority argument, then the argument proves nothing of any value.32 For, even if it should follow that time is not a 'concept' as so understood, it would not follow that it is not still an intellectual representation of some other sort (a percept or experience), emerging through some other process than abstraction (for instance, combination) and hence it would not follow that the representation of time must have originated in intuition. After all, according to the Critical account of the relations between the faculties, intellectual synthesis is required for all cognition, not merely that of 'discursive or universal concepts.' So, from the fact that time is not originally given in a discursive or universal concept, it does not follow that it might not be given through some other intellectual operation, such as,

236 The Expositions for instance, the composition of many previously given matters in the representation of particulars. d. Premise i In so far as there is a good case to be made in the whole/part priority argument, it may not be the one Kant intended to give (if, indeed, his thoughts on this matter were clearly enough worked out for us to be able to ascribe an intention to him). The best way to take the argument is as premising that our representations either arise through intellectual combination of previously given matters or are originally given in intuition, and as then proceeding to claim that, since time is not a compositum but a totum (that is, because it is not composed of parts but originally given as a whole in which parts may only subsequently be defined by delimitation), the representation of time cannot originally arise through combination. In this case, 'Concept/ as Kant is using it in the first premise, would not mean the same thing it did in the singularity argument, where the term was explicitly qualified with the adjectives 'discursive' and 'universal.' Rather than representations arising through intellectual acts of abstraction, Kant's concern here would be to oppose our representations of time with a different kind of intellectual representation: those arising through combination of parts. This is admittedly a purely speculative reconstruction that may not reflect Kant's intended meaning. But it at least has the virtue of making sense of all the premises. It is very difficult to see why the conclusion ought to follow from the premises were Kant supposed to be out to use the point about whole/part priority to prove that our representations of time are not discursive or universal representations. The most useful reading of the whole/part priority argument, then, takes the first premise to assert that all our representations must be such that they either arise from intellectual combination of more primitive, previously given matters or are originally given in intuition. The argument then proceeds to observe that time is a totum rather than a compositum and thus reaches the conclusion that the representation of time could not have originated through intellectual combination of more primitive, given matters. Strictly, the first premise is false, since there are other alternatives, notably the one considered by the singularity argument, that some of our representations may arise from abstraction, or the one considered by the independence argument of the Second Exposition, that some of our representations may arise from synthesis of the manifold

The Later Expositions 237 under concepts of objects or other 'appearances.' Of course, these last two alternatives are ones that have already been considered and rejected. And if the argument is read negatively, as directed just to reject the first disjunct of the first premise, rather than affirm its second disjunct, then it still makes a valid contribution. Perhaps, when everything Kant has to say in the later arguments has been examined, we will discover something approaching a complete enumeration of alternatives. iii.

The Infinity Argument

The first half of the first sentence of the passage in which the whole/part priority argument is given - The infinity of time means nothing more than that' and the second sentence - 'For this reason the original representation time must be given as unbounded' - were omitted when the whole/part priority argument was cited above. This was done because they are gratuitous. Kant may have inserted them only to give an appearance of parallelism with the final argument of the space section, where 'infinity' is premised of space as a further reason for concluding that our representation must originate in intuition. In the last time exposition, infinity appears, not as a premise for concluding anything about the nature of our representation of time, but as a consequence of the whole/part priority of time. Whole/part priority entails that any determinate time must be represented as contained within a larger time. This larger time either must be represented as indeterminately extended (unbounded) or, if it is to be thought as determined, must be thought as a bounded portion of a yet larger time. Time is therefore 'infinite' though not in the sense that it contains an infinite number of parts, but just in the sense that it has no end-points. However, in the section on space infinity makes more than just a passing appearance as the object of an elucidatory remark. It figures as the source of an independent exposition. I call this exposition the 'infinity argument.' It occurs in two very different forms in A and B: 5. Space is represented as given as an infinite magnitude. A universal concept of space (which is as common to the foot as to an ell) can determine nothing with respect to magnitude. Were there no unboundedness in the progress of intuition, no concept of relations could bring with it a principle of the infinity of those relations. (A25) 4. Space is represented as an infinite given magnitude. Now any concept must

238 The Expositions indeed be thought as a representation that is contained in an infinite multitude of different possible representations (as their common specific difference), and so contains these different possible representations under itself. But no concept can be thought to contain an infinite multitude of representations in itself. Yet this is how space is thought (since all the parts of space to infinity are simultaneous). Thus the original representation of space is an a priori intuition and not a concept. (639-40) These arguments fit the by now familiar pattern of an expanded disjunctive syllogism. Kant supposes that our representations either must be 'concepts' or must have originated in intuition. The fact that space is infinite is somehow taken to rule out the first alternative, thus leaving the option that space must have been originally present in intuition. a. The A Infinity Argument In A, the idea appears to be that an adequate intellectual representation of space could not arise by abstraction from experience. To represent all spaces or the totality of space, the representation would have to be drawn from the broadest range of experiences possible, but a universal concept obtained by abstracting just what is common to all the relevant experiences would have to abstract from all particular determinations of size and shape, and so would represent a space that is not only not infinite but has no particular magnitude whatsoever. But, Kant supposes in A, if the infinity of an object cannot be cognized by abstraction, then the only way it could come to be known is by drawing it out of a 'progress of intuition' that is recognized to be 'unbounded.' In so far as we know space to be infinite, we can therefore conclude that it must have been originally represented in intuition. But it is hard to follow Kant in seeing this argument as premised on anything like a complete enumeration of all the possible alternatives. Were space to first originate through a synthetic intellectual process, whereby one aspatial matter originally given in intuition is set next to another to generate a spatially arrayed matrix, and were this process of combination conceived to be such that it could be indeterminately extended, without any obvious end-point ever being reached, then, too, there would be a sense in which our representation would arise through 'unboundedness in the progress of intuition' - an unbounded series of matters of intuition would have to be successively given as material for the construction of a representation of space thought to be infinite (or at

The Later Expositions 239 least indefinitely extended). But, from this, it would not follow that the space is originally given in intuition rather than constructed through the intellectual process of combination of matters. Its infinity would be a mere inference, drawn from the fact that the process of combination is apparently unending. The most that might follow from Kant's argument is that the intuition would have to be already articulated in time, since the argument premises that a successive series of matters of intuition (a 'progress' of intuition) is required for the cognition of the infinity of space. b. The B Infinity Argument If 'unboundedness in the progress of intuition' just involves reference to an unbounded temporal series of successively given matters of intuition, then it is not hard to see why Kant jettisoned the A version of the infinity argument in B and replaced it with an alternative argument that insists that the infinity of space is given (adding special stress to the word 'given') and including a parenthetical remark to clarify that all the infinitely many parts of space are thought to be present simultaneously. In B, the claim is that a universal concept, that arises through abstracting some feature common to a number of different experiences, can in principle be supposed to refer to an infinite number of experiences (i.e., it can have an infinite number of instances and, in this sense, contain an infinity under itself)- But space, Kant observes, is not supposed to have an infinite number of instances, but an infinite number of parts. And no 'concept/ he claims, could be thought to contain an infinite number of parts (i.e., connotative features) in itself. The claim is simply asserted and not justified or explained, but I speculate that what lies behind it is the tacit notion that the 'concepts' Kant is talking about are intellectual representations that arise through, first, abstracting and, then, combining a number of features or respects in which a number of objects are observed to resemble one another. If this is the case, then no 'concept' could be infinitely rich in content unless an infinite process has been completed. Each of the features or respects combined in such a concept is the product of a distinct operation (of abstraction and combination), so for the concept to contain or mention or refer to infinitely many differentiae or respects, an infinite number of operations would have to have been performed, and since each operation takes some time, the generation of such a concept would not be possible for beings like ourselves.

240 The Expositions If this is indeed Kant's argument, then it might be thought to leave him open to an objection: if intuitions without concepts are blind, so that no cognition can be had without conceptualizing what has been given in intuition, but no concept can represent its object as infinitely rich in content, then how can we know that space is in fact infinite? There is a ready answer to this objection, however. It rests with pointing to the ambiguity in Kant's use of the term 'concept.' Sometimes, the term 'concept' is used to refer to any representation formed by the intellect. This is how it figures in the claims that intuitions without concepts are blind. But, in the B infinity argument, 'concept' is not used in this way. It does not refer to any intellectual representation, but just to a certain kind of intellectual representation: a discursive or universal representation arising from, first, abstracting and, then, combining with one another the features that a number of objects are observed to share in common. It is only this type of intellectual representation that cannot be infinitely rich in content, according to the argument. And all that the B infinity argument really claims is that we could not come to intellectually represent infinite space by means of this kind of 'concept.' It does not rule out the possibility of coming to conceptualize the infinity of space in some other way. Since we do know that space is divisible into infinitely many parts,33 and since nothing can be known without intellectual processing, we can be sure that there must, in fact, be such an alternative means of forming an intellectual representation of infinite space. Kant's whole/part priority argument already indicates what such an alternative means of conceptualization must be. Since the parts of time and space are supposed to arise only through delimitation of a previously given whole, it has to involve a whole of space being, first, given to the intellect34 and, then, subjected to a process of division. The concept of the infinity of the space arises through the realization that there could be in principle no end to the continual division of the space into smaller and smaller parts. An infinity of parts is not thereby given as actually existing in the space (that would presuppose that an infinite process of division had been completed), but it can at least be inferred that the process of division would go on forever, so that the space can at least be deduced to be infinitely divisible, if not actually perceived as composed of an infinite number of parts. This is just the position on the infinite divisibility of space that Kant presents in the Solution to the Second Antinomy ^523-4/6551-2; cf. Anfangsgrunde [Ak, IV 506-7]). We can see this mode of argument instantiated in the demonstrations

The Later Expositions 241 Kant actually gives of the infinite divisibility of space, paradigmatically in Physical Monadology, Prop. 3 (Ak, I 478-9). That argument involves an appeal, not to an immediate intuition of all the infinitely many parts of space, but to a geometrical construction.35 The construction demonstrates that a given line (in Kant's example, the line ab) can be divided into four increasingly smaller segments, and then goes on to show that the procedure for generating these ever-smaller segments could be iterated any number of times, so that there would be no end to the division of the segment into smaller and smaller parts. (The construction presupposes that any given space is contained within an indeterminately larger whole, so that any given line - in Kant's example, the line df - can be extended some way farther out into this larger, containing space.) The infinitely many parts are not all explicitly given through the demonstration. It is just shown that they could be, as it were, brought up out of the space in which they are at first only confusedly presented. As a result of the demonstration, we think that the space is divisible into infinitely many parts, even though there is no actual, explicit representation of these parts (all that is represented is the possibility of continuing the division). The concept is thus arrived at by way of reasoned inference rather than through composition of or abstraction from what is given in intuition. iv.

The Completeness of the Later Expositions

In chapter 2, above, I showed that, whether he is able to prove it or not, Kant is committed to the view that our intuitions are presented over time and articulated in space. The independence argument of the Second Exposition and the singularity, whole/part priority, and infinity arguments of the Later Expositions have attempted a negative proof of this thesis by demonstrating that our representations of space and time could not first have arisen through one or another intellectual process. The independence argument claimed that space- and time-cognition are independent of object recognition, and hence that those intellectual procedures that serve to generate concepts of objects (and specifically, of extended and enduring objects) cannot be supposed to be what first gives rise to our concepts of space and time. The singularity argument complemented this result by claiming that our representations of space and time could not have first arisen by abstraction from matters previously given through intellectual synthesis. And the whole/part priority and infinity arguments demonstrated that our representations of space

242 The Expositions and time could not have first arisen through a combination of matters that, as originally given, are in no way spatial. At no point, however, has Kant presented an argument that could demonstrate that space and time could not have first originated from any sort of intellectual process whatsoever. All his arguments so far have been directed just to demonstrating that certain intellectual processes are inadequate to do this job The question that must be asked now is whether the job Kant has done so far might not be adequate - whether, that is, the list of intellectual functions he has so far considered is complete. If it is, then Kant might be entitled to the conclusion that, in so far as space and time are intellectually represented, this representation cannot have first originated through any intellectual operation, but must have been transmitted to the intellect from sense, where space and time are originally present as intuitions. The success of Kant's argument in the Later Expositions, therefore, depends on nothing less than his being able to demonstrate that he has given a complete inventory of all the synthetic procedures of the mind. This may seem like a tall order to fill. But, for Kant, the situation is no hopeless. While we may be blind to our intuitions, we are not blind to our intellectual representations, nor, as far as he is concerned, are we blind to the fundamental procedures of the mind whereby intellectual representations are formed. We have a capacity to reflect on these procedures and conceptualize them, too, generating in the process the only pure intellectual concepts it is possible for us to have (6128, A93~4/ 6126). Moreover, the magnitude of the task is greatly mitigated by a certain factor: Kant's architectonic. He believed that he had given an exhaustive inventory of all the fundamental synthetic procedures of the human mind, under the guidance of the table of categories (and quite independently of anything said in the Aesthetic about the intuited or constructed nature of our original representations of space and time). For him, a summation and examination of the fundamental synthetic procedures of the mind was quite possible (A64-5/B89, A8o-i76106-7). It was, in fact, achieved by the Transcendental Analytic. According to the picture Kant develops in the Analytic, the mind synthesizes the manifold in four basic ways, generating representations on three increasingly sophisticated levels, called 'perception' (of appearances), 'experience' (of objects), and 'empirically guided thought' (about the world).36 The four types of synthesis are guided by the categories of quantity, quality, relation, and modality, respectively, and the types of representations they generate are, most basically, representations of the

The Later Expositions 243 shape of similarly qualified regions (what Kant calls 'the homogeneous') within the sensory fields; perceptions of a multiplicity of contrasting sensible qualities or matters of appearance (colour patches, sounds, etc.); experiences of enduring, mind-independent, intersubjectively reidentifiable objects; and postulations of the existence of unobserved or unobservable (remote in space or time, or exceedingly small or momentary) entities within the framework of a scientific theory. Today we would refer to these processes as pattern recognition, quality differentiation, object recognition, and theoretical inference. In the Kantian texts that have been examined so far, they have manifested themselves as combination (of many given matters into a shape), comparison (of different qualities to generate a quality space), experience of objects or appearances, and the postulation of the existence of void space. (A fifth intellectual function arising in connection with the singularity argument, abstraction, can be considered to be the fundamental 'logical' function of the intellect [cf. Logic, §§5-6 (Ak, IX 93-4)!, as opposed to the four previ ously listed functions, which are cognitive.) Kant claimed to have gone so far as to have identified the fundamental principles governing each type of process, which he referred to as the Axioms of Intuition (i.e., axioms applied to intuition to govern the process of pattern recognition), Anticipations of Perception, Analogies of Experience, and Postulates of Empirical Thought. A demonstration that space and time are originally given in intuition could therefore be provided by exhibiting that none of these four (or five, if we include abstraction) types of synthesis could plausibly be supposed to originally generate a representation of space or time out of intuitions that are originally aspatiotemporal. As a matter of fact, this task has already been performed. The latter three types of synthesis have been considered and rejected in the first two Expositions. The First Exposition demonstrated that spatiotemporal localization could not emerge from the process whereby we differentiate sensory qualities from one another or order them in terms of their intensive magnitude. The Second Exposition demonstrated that space- and time- cognition could not plausibly be supposed to be dependent upon the process of object recognition.37 And, as noted in connection with the Second Exposition, at least as far as Kant's own conception of natural science is concerned, a spatiotemporal order of pre-objective matters of appearance is already present in perception and everyday experience and it is, if anything, the non-existence or problematic existence of space and time (considered as void, absolute, or substantival) that theories of nature tend to

244 The Expositions establish.38 But, if Kant is right, then there is only one other process that the mind performs in generating representations of objects: the process of combination of various homogeneous matters in a determinate space or time. This is the process outlined in the Axioms of Intuition. And the possibility that space or time might be constructed by such a process is refuted by the whole/part priority and the infinity arguments. Kant's Metaphysical Expositions can therefore be considered to be an exhaustive inventory of the human cognitive functions, designed to prove that, unless space and time were originally given in intuition, no intellectual function could generate our representations of them. v.

The Composition of Intelligible Spaces and Times

The conclusions of the previous section may appear to pose a problem for Kant. As noted in connection with Kirk Wilson's reading of the Later Expositions in §i.c, above, for Kant there can be no simple or direct transmission of the content of an intuition into the intellect. All understanding, even that involved in the perception of singular objects, includes a synthesis of apprehension, that proceeds from the parts arrayed in the manifold to a combination under the thought of an object or appearance. This might appear to imply that, far from being originally given in intuition, our representations of space and time could only first arise through intellectual acts of some sort, most notably combination, so that a proof that our representations of space and time could not result from combination or, worse, from any intellectual act whatsoever would be tantamount to a demonstration that we can have no such representations. The objection rests on a misapprehension, however. Kant's claim is not that our representations of space and time do not result from intellectual acts, but that they are not originated by them. Intuitions without 'concepts' are blind, so that a manifold of intuition that has not been combined in some way and so brought to a unity of apperception is as good as nothing to us. Before our representations of space and time can be cognized by us, the array of parts they contain must be combined. The question, however, is whether combination is what first generates a representation of space and time, or whether it merely renders intelligible a space and time that are already present in the intuition. This topic deserves to be considered in more detail. There are two kinds of combination that can be conceived. To build a jigsaw puzzle is to combine in one of these ways. First, various pieces

The Later Expositions 245 are given, and these pieces are subsequently assembled or put together to generate an object that did not exist prior to the act of combination. Let us refer to this type of combination as 'assembly/ The other kind of combination can be illustrated by the discovery of a previously hidden image in a complex visual presentation. The object is already given in the visual field, and the task is just to discriminate correctly between those adjacent colour patches that belong within its outline and those that belong outside of it. Let us refer to this latter type of combination as 'recognition.' Now note that only assembly originates a new representation. Recognition presupposes that the matters to be combined are given in a spatiotemporal array to begin with, so that, while it renders this array intelligible, it does not first create it. Demonstrating that the sort of combination involved in our cognition of space and time is recognition rather than assembly would therefore serve as an alternative method for establishing the conclusion of the Later Expositions. Such a demonstration can, in fact, be given, drawing on the way Kant describes the process of composition or successive synthesis in, of all places, the very text that has been taken by many to be most hostile to the intuitionist conclusions of the Later Expositions, the Axioms of Intuition. In providing this demonstration, I will be supplying what is in effect an alternative, 'transcendental argument' for the existence of original intuitions of space and time - one that proceeds by showing that, unless a prior intuition of wholes of space and time is presupposed, a basic cognitive achievement we are all able to make - counting and measuring in space and time - would be impossible. Set at the basis of the B edition 'proof of the Axioms of Intuition is the notion that the mind must perform a certain process upon the manifold that is given to it in intuition before this manifold can be perceived as an appearance of any sort, even as a 'patch' characterized by some sensory quality. Kant refers to this process at 6203 as 'thinking the unity of the combination of the manifold of resembling matters [Gleichartigen] in a concept.' This is a typically convoluted and obscure Kantian description, that can be understood in any of a number of different ways, supposing that it can be understood at all. But Kant at least gives an example. I cannot represent a line, however short it may be, without drawing it in thought, that is, without producing all its parts one after another from a point and thereby first recording this intuition. And this is just the way it is with even the shortest time. In that case, I think only the successive progression from one

246 The Expositions moment to another where, through all the parts of time and their additive placement, a determinate magnitude of time is finally produced. (Ai62~3/B2O3)

This example deals just with space and time - indeed, just with the production of geometrical figures and determinate temporal intervals in imagination. It makes no reference to perception as opposed to imagination, or the perception of a manifold of empirical intuition that would contain sensations or 'matters of appearance' of various kinds. Accordingly, it makes no reference to what Kant calls the 'homogeneous' - to a manifold of resembling matters. Perhaps the segments of a line could be supposed to be homogeneous with one another and heterogeneous with any point or space not on the line, and the parts of the represented time homogeneous with one another and heterogeneous with all times before or after it. This is certainly the case when a line is drawn in black ink on white paper, either to represent a geometrical line or to model an interval of time. Then the parts of the line are all homogeneous (black) and contrasting or heterogeneous with their surroundings (white). Though Kant's example does not mention homogeneous matters, it does mention the two other components of the 6203 description: unity under a concept and combination of various, given matters. The concept is a line or a determinate time interval. The thesis is, broadly, that the various matters that are given, the parts of a line or the parts of a time, cannot be 'thought' (brought to consciousness) unless these parts are all depicted at once in a single representation. By itself, this broad thesis is nothing new. The whole point of the Deduction was that consciousness requires bringing many different representations together into one representation (An6-i7, 6136-7). Imagine a solid black triangle drawn on a sheet of white paper. Imagine that all the points on the sheet are named by the triplet , where x and y refer to the Cartesian co-ordinates of the point on the sheet of paper, and b is selected if the point is black, w if it is white. Then imagine that each point of the sheet of paper is made the object of a distinct thought. The result would be an infinite list of thoughts, '(o, o, b),' '(3/ 7/ w)/ and so on. As long as each point on the sheet is the subjectmatter for a distinct thought, there is nowhere a thought of the appearance of the sheet as a single whole, and there is therefore a sense in which the sheet has not been perceived. To be represented, this infinite multiplicity of information has to be somehow brought together into a single thought, the 'sum' of what all the listed thoughts 'add up to/ as it were. The thought 'triangle' does this. It captures an infinity of different

The Later Expositions 247 representations in a single representation, and thereby brings many thoughts together in a single consciousness able to perceive the 'sum' of what has been presented. But, for this to happen, some process of 'summation' has to occur. All the different thoughts of points on the sheet have to be put together or compounded. However, the example from the Axioms does not just make this broad point. It goes on to describe a specific way in which this composition is supposed to occur: we pick a starting-point and then we successively add parts to it. Thus, we draw a line, by starting at a point and successively adding part to part, or we think an interval of time by picking a starting-point and thinking of the successive progression from one moment to the next. In Kant's example, the 'drawing' appears to be something I do. But it is important to be clear about what I do and what I am constrained to do. When I draw a triangle on paper, there is a sense in which the 'space' for my activity already exists. The paper is there; all its points are ordered in two dimensions, and all I do is mark off certain of these points (by colouring them black) one after another. While I have a certain freedom over how to carry out this procedure - I can mark any point I wish, and as I mark off one adjacent point after another I can change direction as I wish - the paper itself constrains me in other very important ways. The order of points is originally fixed by the paper, not by my own decisions about how to mark. Unless I cut and paste, I cannot mark (o, o) immediately after (-3, o) - not without leaving a gap in the line. (With paper I can at least cut and paste, but I cannot cut and paste parts of my visual field.) All I can do, in other words, is choose how to run through an order of points that is already given. I cannot create or define the order itself or, to put the point more technically, I cannot change its topology, or even its metric, as I please. These are aspects that are simply given and outside of my control.39 This is what drawing is - outlining what is already there, not assembling, constructing, or creating it. Though Kant does not use the same example as I have, his presentation in the Axioms makes clear, using other examples, that there are certain constraints on the spontaneous activity of drawing: This successive synthesis of productive imagination in the production of figures is the basis for the mathematics of extension (geometry) with its axioms. [The axioms of geometry] are a priori expressions of the conditions of sensory intuition, under which alone the schema of a pure concept of outer appearance can

248 The Expositions arise, for example, that between two points only one straight line is possible, that two straight lines cannot enclose a space, and so on. (Ai63 76204) Though in this passage Kant speaks of 'productive imagination' as the ground or basis for geometry, he must mean just that it is the ground or basis for the recognition of the axioms of geometry, not that it in any way determines the content of these axioms. As the second sentence cited indicates, these axioms reflect constraints on the possible acts of 'productive imagination' that ultimately arise from 'the conditions of sensory intuition/ conditions that determine the possible shapes and patterns (the schema) that concepts of figures in space (pure concepts of outer appearances) can take. Where the question is one of empirical intuition rather than pure intuition, the constraints are even more rigorous. In pure intuition all that is given is a spatiotemporal 'field' within which figures can imaginatively be generated by actively marking off points. But, in empirical intuition, the field is already given as filled with sensations or matters of appearance. Some of these matters are qualitatively identical or similar, others contrasting. Sharply contrasting matters define lines or, more properly, edges. Whereas, in pure intuition the lines can at least be drawn, in empirical intuition they are already given and can only be recognized. None the less (and this is the whole point of the argument of the Axioms), an analogous procedure to that of drawing is required for the perception of appearances in the empirically intuited field. Just as, in pure intuition, we begin from a point and successively add parts to it, so too, in empirical intuition, we begin from a point and successively add parts to it. Only here the addition of parts does not proceed in any direction fancy dictates but is determined by the quality of sensation already given at those parts. Adjacent parts may be added to one another only if they are homogeneous - literally of the same kind, so qualitatively identical or similar. More formally put, the 'combination' of the empirical manifold can be captured by the following recursive definition: i) identify a single matter of appearance, m; ii) identify all those matters that a) resemble or are identical to m, and b) are either adjacent to m or adjacent to some other matter previously identified as adjacent to m.

The Later Expositions 249 The output of this recursive procedure is the delineation of a 'patch' of qualitatively identical or resembling matters, or (an aspect of the same thing) of an edge between qualitatively contrasting matters. Kant therefore takes it that this procedure is identical with the procedure for describing a determinate space or time in pure intuition. Thus, the output of the procedure is also a shape of a certain determinate magnitude or a line of a certain length (hence the principle of the Axioms that we cannot perceive an 'appearance' - i.e., a sensory patch - in empirical intuition without perceiving it as an extensive magnitude). The most significant point to note about this procedure is the way the little word 'adjacent' figures in clause ii(b). I am interpreting here, but it seems evident that the Axioms are written over the tacit supposition that the matters presented in intuition are already given adjacently to one another in space and time.40 Successive synthesis or 'combination' does not determine these adjacency relations; it merely identifies them and combines them in a single thought adequate to represent them in all their multiplicity, the way the single thought 'triangle' represents at once an infinity of coloured points at various locations. The opening two sentences of the B 'proof of the Axioms testify to this interpretation. There, Kant remarks that an intuition in space and time is already present a priori as a formal condition of all appearances: 'All appearances contain, with reference to their form, an intuition in space and time, that is present a priori as their ground.' But, he goes on to observe, before the multiplicity of matters articulated in space and time can be perceived or 'taken up into empirical consciousness' by us, we have to 'combine' them into a single concept adequate to represent them in all their multiplicity (or at least adequate to represent a few of their salient features). Clearly, there is a reference being made here to the way intuition is before combination, and to what combination is supposed to do. And equally clearly, intuition before all combination is described as already containing a manifold in space and time. The function of combination is not to assemble or produce this manifold but to enable the mind to think it in all its multiplicity in a single thought. Briefly, it is to turn a spatiotemporal array of representations into a representation of a spatiotemporal array. Any hint there might be that the spatiotemporal order of the manifold is generated by productive imagination or some other higher cognitive faculty is simply an artefact of Kant's manner of describing the procedure of thinking a spatiotemporal array of representations as a representation of a spatiotemporal array. The higher cognitive faculties are

250 The Expositions responsible for determining the spatiotemporal features that are thought in our representation of a spatiotemporal array. But, in generating this representation, they take as data an originally intuited spatiotemporal array of representations. Though Kant uses a vocabulary of active production, the adjacency relations are not created by the higher faculties; they are simply 'run through' and brought together in a single consciousness by them. Though this is not by itself a reason for assuming that it is correct, I cannot forbear observing that the intuitionist reading of the Axioms obviates a classic problem of Kant scholarship: the problem of localization.41 Were the manifold not already articulated in space and time were its spatiotemporal articulation instead produced by 'productive imagination' - then it is hard to see how the procedure Kant describes could ever yield a cognition of two qualitatively identical but separate sensory patches. If my imagination identifies qualitatively similar matters and adds them to one another to generate a figure, then it should take all the qualitatively identical matters, from wherever they may occur in my sensory field, and put them all together in one place. I should not see stars when looking up at the sky at night but rather some single shape created by setting all the qualitatively identical luminescent points next to one another against a black background. This may seem arbitrary, but that is how the procedure is described: composition of the homogeneous matters is taking all the qualitatively similar matters and setting them together. If the way the matters are originally given (as in space and time to begin with) does not place any constraints on this procedure, then they should all end up being set next to one another. Of course, we could go on to ask why they should be set together in one way rather than another - why I should see one sensory patch as round rather than square, or oval rather than triangular. If the reason for our perception of the particular shapes and locations of sensory patches is that the matters of appearance are originally given to us in that array, then there is no problem. But if spatial and temporal order are supposed to be constructed by some combinative procedure of productive imagination out of matters that, as originally given, are entirely nonspatiotemporal, then Kant has a localization problem of monumental proportions. Why, ultimately, are sensations placed here rather than there, now rather than then? And, if the homogeneous matters are supposed to be combined, then how could it be the case that I can simultaneously perceive two separate but qualitatively identical sensory patches?

The Later Expositions 251 An intuitionist interpretation of the Axioms can obviate these problems and make sense of the text. But, if the intuitionist interpretation is correct, then the central premise of the whole/part priority and B infinity arguments are substantiated: there must be a pre-given whole of space and time within which particular spaces and times are determined by drawing boundaries or identifying edges. The Axioms present only one passage that poses any sort of problem for the intuitionist interpretation: the opening sentence of the Ai62/ 6203 paragraph, T call an extensive magnitude that in which the representation of the parts makes possible the representation of the whole (and therefore necessarily precedes it).' While some commentators have raised the possibility that Kant might be talking about two kinds of space and time, determinate spaces and times in the Axioms, and space and time in general in the Aesthetic,42 or that the Axioms might just be about the conditions for the measurement of spaces and times, not about the conditions of their perception,43 an alternative way around the problem should be evident from what has been said so far: Kant should be taken at his word. With space and time, the representation of the parts makes possible the representation of the whole. It does not make the whole itself possible, but it does make a representation of the whole possible. What is originally given is an array of representations in space and time. In order for this spatiotemporal array of representations to be converted into a representation of a spatiotemporal array, the parts of the array must be run through and summed up and recognized as constituting an instance of some spatiotemporal concept: round, oblong, filament-like, intermittent, enduring, and so on. This is the story of the Axioms. But it is an intuitionist story. The running through, summing up, and recognition do not create the spatiotemporal array; they describe it and so bring it together in a single representation. The composition of the parts makes possible the representation of the whole in a single concept, but the parts are themselves originally given in an array. Indeed, because this originally given array is continuous, not discrete, the parts can themselves first be defined only by outlining the edges between qualitatively contrasting, extended 'matters of appearance' or by actually drawing lines where there are no qualitatively contrasting matters already given. To sum up: what is originally given is a spatiotemporal array of representations. To be cognized, the multiplicity in this array must be brought to unity - the array of representations converted into the representation of an array. For this to happen, the various individual representations

252 The Expositions must be run through, summed up, and recognized to constitute an instance of a single concept. But, since the array is continuous, before the various individual representations can be run through and summed up, they have to be distinguished from one another. This requires the recognition of boundaries within the originally given array of representations, marking one representation off from another. Some of these boundaries are given in empirical intuition, as edges between qualitatively contrasting, extended matters of appearance. Others may be arbitrarily designated in imagination or introduced by physical operations such as drawing. As a consequence, the parts of space and time are originally given as each at its own special location in it; they are not so many different, independently given components that need to be put together; they come out of the box, as the toy manufacturers like to say, 'with no assembly required/

8 The Transcendental Expositions

The remarks that Kant placed under the title Transcendental Exposition of the Concept of Space' are repeated, in whole or in part, three times in the Aesthetic. They occurred originally over four separate locations in the A Expositions, where they were not distinguished from the other 'metaphysical' Expositions. These are: A24 (the third numbered paragraph for space in A), A25 (the close of the fourth numbered paragraph for space in A, retained in the third numbered paragraph in B), AJI (the third numbered paragraph for time in A, retained in B), and A$2 (which is part of the fourth numbered paragraph for time, also retained in B). The Transcendental Expositions occur a second time under separate title in the sections of B entitled Transcendental Exposition of the Concept of Space,' (640-1) and Transcendental Exposition of the Concept of Time' (648-9). And they occur finally in §8 of the Aesthetic ^46-9/663-6). In all of these passages, Kant makes one or other of the same two points: that our knowledge of certain features of space and time cannot be supposed to arise either a posteriori from experience or a priori from analysis of concepts. These points are not always made together, and they are not always directed towards the same conclusion. In the A space and time Expositions, they serve to buttress the claims that our representations of space and time are neither drawn from the matter of appearance nor constructed by intellectual processes. But, in the Transcendental Exposition of the Concept of Space' and at A46-9/ 663-6, they serve two further purposes: Kant takes them to establish that our representations of space and time are grounded on the constitution of the subject not on the features of the objects that affect the subject, and he takes them to provide an explanation for how the sciences of geometry and mechanics are possible.

254 The Expositions Accordingly, the Transcendental Expositions need to be considered under three headings, depending on which purpose is uppermost in Kant's mind: buttressing the anti-sensationist and anti-constructivist conclusions of the Metaphysical Expositions, establishing that our representations of space and time are grounded in the constitution of the subject, and accounting for our knowledge of geometrical and mechanical truths. Let us consider how the texts are directed towards each of these three purposes. i.

The Buttressing Argument

The argument under the first of the three headings, which I call 'the buttressing argument' (since it serves to buttress the conclusions already established by the Metaphysical Expositions), occurs in two separate passages of the A space section, at A24 and A25 (the first of which was excised from B, but the second of which was retained), and in two separate passages of the time section, A3i and A32 (both of which were retained in B). The passages are scattered because the points they make are directed towards distinct, subsidiary conclusions. The first passage in each pair provides evidence for the thesis that our representations of space and time are not drawn from sensation, and so buttresses the attempt of the first two Expositions to establish that our concepts of space and time are not empirical concepts that have been drawn from the matter of appearance. I refer to it as 'the priority argument.' The second attempts (I argue, unsuccessfully) to provide further evidence for the thesis that our original representations of space and time are immediately given in intuition and so is aimed at buttressing the conclusion of the Later Expositions. I refer to it as 'the immediacy argument.' a. The Priority Argument The priority argument occurs in the third numbered paragraph of the A Expositions: 3. The apodictic certainty of all geometrical principles, and the possibility of their construction a priori, is grounded on [the] a priori necessity [of the representation of space]. For were [the] representation of space a concept arrived at a posteriori (by being worked up out of general outer experience), the first principles of the mathematical determination [of space] would be nothing but perceptions. They would have, therefore, all the contingency of perception, and

The Transcendental Expositions 255 rather than it being necessary that between two points there should be only one straight line, it would just be that experience always teaches that it is so. Also, what is obtained from experience has only comparative universality through induction. We could therefore only say that, so far as has up to this time been observed, no space has been found that has more than three dimensions. (A24) 3. The possibility of apodictic principles concerning the relations of time, or axioms concerning time in general is grounded on [the] a priori necessity [of the representation of time]. Time has only one dimension: different times are not simultaneous, but successive (just as different spaces are not successive, but simultaneous). These principles cannot be drawn out of experience, since this would give them neither strict universality nor apodictic certainty. We would only be able to say: this is what common sense teaches; but not: it must be so. These principles hold as rules under which in general experiences are possible and inform us prior to experience and not through it. ^31/647)

The point of these passages is straightforward. Kant assumes that there are certain things that we know to be necessarily true of space and time. These are the principles of geometry and the axioms of time. Given that this is the case, it follows that space and time could not be known by experience (at least, those features of space and time described by the principles and axioms in question could not be known by experience). For, as Kant observes at Ai and 63, experience can teach us only that something is or has in the past regularly been the case, not that it must be the case or could not possibly be otherwise. Were the principles of geometry or axioms of time known through experience, they would have only 'comparative universality through induction' and would not be known with apodictic certainty. Since experience is inadequate to deliver this kind of certainty, our knowledge of space and time must arise from some other source. Kant expresses this argument infelicitously, however. Though the term 'sensation' does not occur in either version of the priority argument, what the argument really proves is not that space and time are not known by experience but just that our knowledge of them is not drawn from what is given in sensation. In so far as what is given in experience is known a posteriori, through waiting for objects to impress our senses and then inspecting the resulting effects, it cannot provide apodictically certain knowledge. But, for Kant, it is at least possible that our experience might contain more than just the subsequently knowable effects of particular objects on our senses. It may, in addition, exhibit certain fea-

256 The Expositions tures that are standardly present, regardless of what objects affect us, features that can therefore be anticipated in advance of any particular experience (and, in this sense, be knowable a priori), and that can therefore serve as the basis for necessarily true and universally valid judgments. Thus, at Bi, Kant remarks that 'It could well be that even our experiential cognition is a composite of that which we sense through impressions and that which our own cognitive capacity (merely occasioned by sensory impressions) brings out of itself/1 and, at A2, he remarks that 'even among our experiences there may be assembled cognitive elements that must have their origin a priori ... For when one removes everything that belongs to the senses from [experience], there still remain certain original concepts, and certain judgments drawn from them that must arise completely a priori, independently of experience/ Despite what Kant says in the priority argument, therefore, there may be elements given in experience that could provide a foundation for apodictically certain principles - these elements would just not be part of the a posteriori component of experience. The priority argument holds true only for those elements that are properly a posteriori and can be known only subsequent to affection. They alone are inadequate to ground our knowledge of the principles of geometry and axioms of time. They, however, are sensations. Sensation, as Kant defines it at Ai9-2o/B34, is that in the effect of an object on our representative capacity that results uniquely from the fact that it is that object, and not some other, which affects us. It is to be distinguished from that in the effect that would be there regardless of what object happened to be acting on us.2 As such, it is sensation alone that can only be known after being affected by the object, and this makes it alone the properly a posteriori element in experience (A42/B6o).3 This argument not only buttresses the conclusions of the First and Second Expositions, but takes them a step farther. The First and Second Expositions establish only a very restricted sense of priority for our concepts of space and time. The Second Exposition establishes that these concepts are a priori just in the sense of being given prior to objects and independently of the process of object recognition,4 whereas the First establishes just that they are not abstracted or derived from anything given in the matters that are arrayed in space and time. Neither text, however, establishes that our concepts of space and time are given independently of any reference whatsoever to the specific sorts of effects that objects may have on our representative capacity. Establishing that our concepts of space and time are not dependent on any universal intellec-

The Transcendental Expositions 257 tual procedures for synthesizing the intuited manifold under concepts of objects does not prove that these concepts are not determined by the way in which we are affected by objects, since these concepts could be drawn from the way objects act on our senses to first bring about intuitions. And, if affecting objects could determine the order in which matters are disposed in experience as well as the quality of the matters so disposed, then even establishing that our concepts of space and time are not drawn from the matter of intuition would not suffice to prove that they are not determined by affecting objects. It is only the priority argument that rules out the possibility that our concepts of space and time might be determined by the specific ways in which we are affected by objects.5 Aside from this point about the proper focus of Kant's argument and its consequences, one further topic needs to be addressed. It is commonly charged that it is false that our knowledge of the principles of geometry and axioms of time is apodictically certain. There are various, internally consistent but mutually incompatible geometries, and there are even various ways of conceiving the topology of time. Which of these alternative descriptions of space and time describe the actual world is, so it is charged, something that can be known only a posteriori, by empirical investigation. This objection goes back at least as far as Helmholtz, and has been frequently reiterated ever since.6 While recent work has shown it to be less viable than it was previously taken to be, it is still so popular outside of the circle of Kant specialists that the recent responses to it are briefly summarized here. It has been argued that Kant never denied that alternative kinds of physical space or time are thinkable.7 His point was merely that there are certain geometrical and chronometrical propositions that are necessarily true of the phenomenal space and time we picture to ourselves when doing, say, geometrical constructions on paper.8 A variant on this defence, recently propounded by William Harper, establishes that, for Kant, the perception of solid, medium-sized physical objects requires that we extrapolate from the observed, momentary facets they present to us to draw inferences about the aspects these same objects would present were they rotated,9 and that in order to do this we must take certain geometrical propositions to be axiomatic in advance of experience (i.e., before actually seeing the object rotate).10 On this view, there are certain geometrical propositions that must be supposed to be necessarily true not just of a phenomenal or imaginary space in which geometrical constructions occur, but of the local space of the world around us in

258 The Expositions which medium-sized objects are embedded.11 Both views allow, however, that we may as a matter of theory infer that the large-scale structure of the universe, or the very small-scale structure of the submicroscopic world may be appropriately described by other geometrical principles that are discovered by experience, and to which we have no a priori commitment. While this psychological defence goes well beyond anything Kant can be supposed to have intended (eighteenth-century views of the nature of space did not incorporate such sophisticated distinctions, and eighteenth-century discussions of the factors involved in object recognition were in a similarly primitive state), it is in line with the approach Kant himself took. Though the separation of Metaphysical from Transcendental Expositions in B makes it appear so, Kant did not just assume the apodictic certainty of the principles of geometry and axioms of time. He inferred it as a (likely) conclusion from the inextricability argument of the Second Exposition (see chapter 6, §iii, above). The inextricability argument appeals to a fact of our psychology: that we seem unable to have sensory experiences that are not extended and located in Euclidean space and classical time. Thus, when Kant begins the priority argument, he does not merely remark that the apodictic certainty of the principles of geometry and the relations of time 'is grounded on the necessity of space and time'; he refers back to the argument of the Second Exposition and remarks that it is grounded on 'this necessity.'12 (This is a point of translation that I skipped over above, merely in order to avoid inserting a demonstrative pronoun that refers back to an argument that was not supplied. But now that the proper occasion has arisen, the omission has been rectified.) b. The Immediacy Argument Let us turn to Kant's immediacy argument, which occurs at the end of the space and time singularity arguments. (The relevant portions were omitted when these passages were cited in chapter 7.) All geometrical principles, for example, that in a triangle two sides added together are greater than the third, are never derived from universal concepts of line and triangle, but from intuition, and moreover with apodictic certainty. [A25/B391 The proposition that different times cannot be simultaneous cannot be derived

The Transcendental Expositions 259 from a universal concept. The proposition is synthetic, and cannot arise from concepts alone. It is therefore immediately contained in the intuition and representation of time. (A32/B47)

In these passages, Kant sets up an opposition between two different ways of coming to know the truth of a proposition. He refers to these two different ways of knowing as 'derivation from universal concepts' and 'containment in intuition/ but these are cryptic descriptions that presuppose acquaintance with a system of logic and an epistemology that Kant no more than hints at here. The outlines of this logic and epistemology are as follows: Kant supposes that all judgments, of which those encoded in the principles of geometry and the axioms of time are just examples, consist of two elements: a collection of concepts referring to objects (the matter of the judgment) and a collection of concepts referring to relations (the form of the judgment).13 The judgment asserts that the relations hold or do not hold between the objects.14 It does this by using the concepts to stand proxy for the objects and relations they name, so that in the judgment itself the relational concepts appear as connectors linking the objective concepts.15 Thus, the principle that any two sides of a triangle added together are greater than the third invokes the concept of the sum of any two sides of a triangle (itself a complex concept naming a relation between more primitive concepts) and the concept of the remaining side of the triangle, and the relation of being greater than. The objects of the former concept are affirmed to be greater than the objects of the latter, and this is represented in the principle by the use of the concept of the 'greater than' relation as a connector linking the former object concept to the latter. Similarly, the axiom that different times cannot be simultaneous invokes the concept of one time and the concept of a different time, and the relation of simultaneity, and in the axiom it is denied that the simultaneity relation connects the two concepts. The concepts that figure as matter in judgments are obtained in all the ways we have seen Kant propose - by abstraction from experience, by synthesizing the manifold given in intuition to generate perceptions of sensible qualities, intersubjectively reidentifiable objects, and theoretical entities, or even just by arbitrary stipulation. But it is the ground of our knowledge of the relations between the objects of concepts that Kant is particularly concerned with here. It is these relations that our propositions affirm: they are what is true or false in our propositions. And the two different ways of coming to know the truth of a proposition that

260 The Expositions Kant mentions in the passages cited above are, at bottom, two different ways of coming to know of the existence of relations. One of these ways is derivation from the concepts themselves. Here we are supposed to discover the relation simply by examining the related concepts and deriving the relation by analysis and deduction. (For this reason, Kant refers to judgments of this type as 'analytic.')16 This is to be contrasted with the second way of knowing, containment in 'intuition/ To derive a proposition from what is contained in intuition is not simply to intuit it. Intuitions that have not been conceptualized are, after all, blind. Kant's point is still that 'intuited' propositions are known by compounding or in some other way 'synthesizing' our intuitions. It is just that when we synthesize our intuitions into a single perception or image17 we are supposed to discover an instance of the relation affirmed in the proposition.18 This is why Kant calls propositions derived in this way 'synthetic' propositions.19 There is a contrast intended here between this way of knowing (synthesizing an intuition into a single perception or image that instances the relation between objects described in the proposition), and knowing by taking a number of concepts (be they abstracted from or constructed out of intuitions, or be they simply stipulated arbitrarily) and then deriving the relation between the concepts named in the proposition by analysis and deduction. Thus, Kant's instanced propositions about the measures of the sides of triangles and the simultaneity of different times are not supposed to be learned analytically, by derivation from concepts that we have previously obtained from experience or imagination, but only synthetically by actually experiencing or constructing a triangle or a pair of different times and witnessing the inevitability of the relation among the lines or times thus constructed.20 In Prolegomena, §7, Kant contrasts these two different ways of knowing by saying that knowledge obtained by, first, forming a number of concepts and, then, deriving relations between them by analysis and deduction is knowledge based on 'discursive judgment,' whereas knowledge obtained by synthesizing an intuition into a single perception that instances the truth of a proposition is knowledge obtained by 'intuitive judgment.'21 This usage, where the terms 'discursive' and 'intuitive' are applied to judgments, is paralleled in the passages cited above from the Critique, where Kant also speaks of deriving propositions from 'intuition' (Kant's name for the faculty for connecting concepts into judgments is 'judgment'; see Ai3O-i/Bi69). But care needs to be taken to distinguish cases such as these from the more usual case, where the

The Transcendental Expositions 261 terms 'discursive' and 'intuitive' are applied, not to judgments, but to representations. Judgments are not representations; they are descriptions of the relations between a certain kind of representation: concepts.22 All concepts are discursive and, in this respect, they are contrasted with intuitive representations. What makes a representation intuitive is that it is given immediately. What makes a representation discursive (conceptual) is that it is the product of some process performed upon immediately given representations. 'Intuitive' judgments, on the other hand, are those that report on the relations exhibited concretely in perception, whereas 'discursive' judgments report on what follows from analysis and by deduction from concepts, apart from any reference to whether the relations thus uncovered are actually instanced in perception or not. Considered in this way, what the immediacy arguments actually establish is not something about where our representations of space and time originate (in intuition or through some process performed upon intuitions), but merely something about whether our knowledge of the features of space and time can be supposed to be analytic (true by definition of the concepts involved) or synthetic (true in so far as the world actually exhibits itself in the appropriate way to us in experience). However, Kant obviously wanted to draw a conclusion of the former type from the arguments. The passages where the arguments are stated are both devoted to proving that our representations of space and time originate in intuition and do not first arise as discursive or universal concepts. The arguments at the end of both passages are clearly intended as further reasons for accepting this overall conclusion. It is tempting to infer that Kant was misled by his own ambiguous terminology here. He mistook an argument that establishes that our judgments about space and time are 'intuitive' (that is, synthetic as opposed to analytic) for one that establishes that our original representations of space and time are intuitive (that is, immediately as opposed to mediately given). If so, then this would continue a tradition of confusion over the intuition/concept distinction that we have seen established in the singularity argument (discussed in chapter 7, §i, above). This should not detract, however, from the fact that the 'intuition' argument does draw attention to an important fact about the nature of our knowledge of space and time, and one that will prove significant for Kant's later subjectivity argument. There are two other objections that need to be considered in connection with this argument. One concerns how its results can be made consistent with the results of the previous, priority argument. If there are

262 The Expositions propositions about the nature of space and time that can be known only synthetically, that is, by perceiving or imagining that spaces and times or the objects embedded in space and time are, in fact, related to one another in the ways described by the proposition, then how can these propositions be, as Kant claims in the priority argument and reaffirms at A25/B39, 'known with apodictic certainty'? The answer to this question requires reiterating something said in connection with the priority argument: For Kant, it is not legitimate to assume that everything given in experience must be given a posteriori. It could be that our experiences exhibit certain necessary and universal features that can be anticipated in advance of the actual experience. Even if our propositions are drawn from what is given in experience, therefore, we cannot infer that they must be a posteriori. They could be based on an a priori element of experience and not on mere sensation. The second objection to Kant's argument is that its central premise is false. As Hilbert's development of a complete set of axioms for geometry conclusively illustrates, the propositions of geometry and the axioms of time can be derived purely analytically.23 In Kant's defence, it has been observed that, prior to the development of polyadic logic, some seventy years after Kant's death, Hilbert's axioms could not be formulated. At the time Kant wrote, recourse to straight-edge and compass construction was necessary to demonstrate the existence of the points, lines, and figures mentioned in geometrical propositions.24 But it may be possible to say even more than this on Kant's behalf. There is more than one way of axiomatizing geometry, and different axiomatizations describe different spaces. Which of these alternative geometries describes the space of our actual experience remains a question that can be decided only 'synthetically/ by observing how objects are, in fact, related to one another. It cannot be determined merely by analysis of and deduction from concepts. Some might want to say that this makes the question of which geometry applies to physical space an 'empirical' question. But again, for Kant, not everything that is decided by experience is determined by the properly empirical element in experience, sensation. We may grant that the question of which geometry is the correct one must be determined by experience but deny that this means that the question may be empirical (i.e., determined by reference to sensation as matter of appearance). What decides the question may be some a priori element of experience. That, at any rate, is what the priority argument would have us conclude.

The Transcendental Expositions 263 ii.

The Subjectivity Argument

In the Critique of Pure Reason, Kant's argument for the subjectivity of space and time occurs only in the 'Transcendental Exposition of the Concept of Space' (not at all in the time section)25 and at A46-9/ B63-6.261 draw on the former, more succinct version. The 'Transcendental Exposition of the Concept of Space' is divided into four paragraphs. The first and fourth can be ignored as they do not contribute to the argument. The remainder of the text presents two arguments, one given in the second paragraph, the other in the third. The first recapitulates the conclusion of the buttressing argument, that the propositions of geometry must be cognized by means of an a priori intuition: Geometry is a science that determines the properties of space synthetically and yet a priori. What must the representation of space be then, for such a cognition of it to be possible? It must originally be intuition, for no propositions that go beyond what is contained in a concept may be drawn from a mere concept, though this is what happens in geometry. But this intuition must be a priori, that is, found in us prior to all perception of an object, and consequently must be pure, not empirical, intuition. For the propositions of geometry are all apodictic, that is, bound up with a consciousness of their necessity, for example, the proposition that space has only three dimensions. Such propositions cannot be empirical or experiential judgments, nor inferred from such judgments. (640-1)

Beyond the fact that the major points are presented in reverse order (here the observation on the synthetic status of the propositions of geometry comes before the observation on their apodictic certainty) there is nothing in this portion of the argument that differs from what was said in the A-edition buttressing arguments. One of the two major premises of the argument is contained in the second-last sentence: the propositions of geometry are necessarily true. Kant proceeds to ask how to account for this: not by analysis, because these propositions describe a relation that cannot be discovered either by analysis of the concepts involved or by deduction from what analysis reveals (this is the second major premise of the argument); so, he concludes, they must be known by 'intuition.' (I put 'intuition' in quotes because, as already noted when discussing the immediacy argument, which this passage merely repeats, what is established here is not that the propositions of mathematics must be

264 The Expositions based on 'intuitions/ understood to be immediately given representations, but rather that our knowledge of these propositions must be obtained through 'intuitive/ that is, synthetic or experiential, judgments. From the mere fact that our knowledge of the propositions of mathematics is not obtained by analysis of concepts but is based on judgments of experience, it in no way follows that the experience in question must be already given in an intuition rather than worked into a perception through intellectual processing. That mathematical propositions might be based on some a priori intuition is indeed a possibility, but it is also a possibility that they might be based on something the intellect contributes to experience. This is a question that should not be begged at the outset, though Kant encourages precisely this by using the loaded term 'intuition'- a choice that might be legitimate enough if used as a synonym for 'judgment of experience' or 'synthetic judgment/ but that is patented to induce us into making an unnoticed slide to 'immediately given representation/) But, granting that our knowledge of the propositions of geometry is obtained through 'intuitive' judgments, that is, judgments of experience rather than analytic judgments, how is it possible for this knowledge to be apodictically certain? If these propositions were known only through 'after the fact' (a posteriori) inspection of the content of our experience, they would have only 'comparative universality through induction' (as the priority argument at A24 puts it). Since we ascribe necessary validity to the propositions of geometry, they must be 'found in us prior to all perception' (641). Consequently, there must be such a thing in us as an a priori experience, however paradoxical it may at first sound to propound the notion (since it amounts to claiming that there is a nonempirical experience).27 And this experience must be a priori in the strong sense of being given independently of any reference to the specific effects different objects have on the representative capacity, not just a priori in the weaker senses of the First and Second Expositions.28 It is only with the second argument (the third paragraph in the 'Transcendental Exposition of the Concept of Space') that Kant makes an advance beyond what was said in the A-edition buttressing arguments and beyond what was established by the Metaphysical Expositions in general. The advance is initiated by a reflection on the result that has just been established: that the propositions of geometry are known through reference to an a priori experience. This result is problematic. How, Kant asks, could it be possible for there to be such a thing as an experience (or 'intuition' as he question-beggingly puts it) knowable prior to being

The Transcendental Expositions 265 affected by any particular object? How could the content of any experience be apodictically given, so that it can be anticipated without having, first, to obtain the intuition and, then, to inspect the representations given through intellectual synthesis of that intuition? Now how can an outer intuition, that precedes the objects themselves, and in which the concepts of these objects can be determined a priori, attend the mind? (B4i)

The answer that Kant immediately proceeds to give is that this sort of knowledge can be accounted for only by supposing that we are so constituted that we can receive intuitions only in a certain way - a way that determines that all our intuitions must end up exhibiting certain formal features, these formal features being the ones described by our a priori knowledge.29 Obviously, [an a priori outer intuition can be accounted for] in no other way than in so far as it has its place merely in the subject as this subject's formal character, whereby it comes to be affected by Objects and thereby acquires immediate representation (that is, intuition) of them; hence, [in no other way than in so far as the intuition has its place in the subject] only as form of outer sense in general. (B4i)

Kant does not here explain why this is the only possible account that could be given. He simply claims that this is 'obvious/ However, an explanation of why the propositions of geometry must be grounded in an a priori intuition (as opposed to an a priori form of intellectual synthesis of intuitions) can readily be thought of, and Kant does supply an explanation of why this a priori intuition must be grounded in the subject towards the close of the third version (A^6-g 7863-6) of the Transcendental Exposition. Let us consider each of these points in turn. a. An Intuitivity Argument A reason why the propositions of geometry must be supposed to be grounded in an a priori intuition can be readily obtained if we consider that the propositions of geometry are descriptions of space. Consequently, the a priori experience that teaches us these propositions must be an experience of space. But the Metaphysical Expositions have already established that space is originally given in intuition and not

266 The Expositions merely an artefact of intellectual synthesis. Accordingly, it can be concluded that the a priori experience that serves as the ground of our knowledge of the propositions of geometry must be an a priori intuition (of space) and not something that only first emerges through intellectual processing. (By similar argument, the axioms of time, some mathematical principles - especially those involving counting - and mechanical principles - in so far as they involve reference to motion over time - are all descriptions of time. And, as the Metaphysical Expositions have already established that time is originally given in intuition, the same conclusion follows for time.) In this respect, interestingly, the Transcendental Expositions are not independent arguments but turn crucially on an appeal to the Metaphysical. Without the Metaphysical Expositions, the most that the Transcendental could establish is that our knowledge of the propositions of mathematics rests on an a priori experience, that for all we know could be dictated by intellectual, rather than intuitive form. b. The Argument for Grounding in the Subject Kant's clearest argument for why these a priori intuitions must be supposed to be grounded in the subject comes from A48-9/B65-6: Now were it not the case that there lay in you a capacity to intuit a priori, were this subjective condition on the form [of your intuition] not at the same time the a priori universal condition under which alone the object of this (outer) intuition itself was possible, were the object (the triangle) something in itself without relation to your subject, then how could you say that something that lay necessarily in your subjective requirements for constructing a triangle, would also have to necessarily pertain to the to the triangle in itself? For you could not add anything new (the figure) to your concepts (of three lines) that would consequently have to be necessarily found in the object, since this object [would be] given apart from your cognition [of it] and not through this cognition. Were it not therefore the case that space (and so also time) is a mere form of your intuition that contains a priori conditions under which alone things could be outer objects for you and that they [are] nothing apart from these subjective conditions, then you could make out a priori absolutely nothing synthetic about outer objects. It is therefore indubitably certain, and not merely possible or likely, that space and time, as the necessary conditions of all (outer and inner) experience, are merely subjective conditions of all our intuition, in relation to which all objects are mere appearances.30

The Transcendental Expositions 267 If our intuition were totally contingent, in the sense that there were no constraints whatsoever on it and in principle anything could appear in it, then there could be no a priori knowledge grounded on intuition, that is, no knowledge of the content of an intuition prior to having the intuition. But if, on the contrary, we insist that there is a priori knowledge grounded on intuition, then there must be constraints on the kinds of intuitions that are possible. There are two possible grounds from which such constraints could be drawn: the constraints may be constraints on the possibility of the existence of things, or they may be constraints on the possibility of their experience. In the former case, we still could not know anything a priori about objects (even though there might be certain conditions on the possibility of their existence). For, our knowledge of the constraints on the possibility of the existence of objects would have to be inferred from experience of objects, and such experience, depending as it would on our having to, first, encounter the objects, could supply us with only 'comparative universality through induction' and would not be truly a priori. There is no alternative, therefore, but to allow that, if there are certain constraints on the possibility of intuitive experience, then these constraints have the effect of determining that all our intuitions must exhibit certain general features (that is, conform to a certain form or pattern), regardless of what object happens to be affecting us. This alone can assure us in advance of any particular intuition that the experience would have to exhibit those features. In so far, however, as these constraints are taken to apply regardless of what object might affect us, they must be taken to be grounded in the cognitive constitution of the subject. Remark: Subjective Grounding and Conditionally A Priori Truth It might be objected that the subjective option is really no better than the objective one. After all, there seems to be no a priori reason for ruling out the possibility that the subject may develop or change over time, and, if that is the case, then could it not also be possible that the subject might change in such a way that its receptive constitution would be altered and it would come to intuit the world under a different set of constraints? Would we not then still be left having to base the truth of Euclidean principles on a merely empirical generalization from experience, the supposition that the future will be like the past and that our intuitions will continue to occur under the same constraints? However, where the constitution of the subject is taken to determine, in part, its intuitions, we can at least draw the hypothetical conclusion,

268 The Expositions S: In so far as the subject remains as it is, its intuitions will exhibit certain characteristic features. This is quite different from the objective case, where the hypothetical conclusion we would have to draw would be: O: In so far as the objects remain as they are, and the subject continues to perceive just the same set of them, its intuitions will exhibit certain characteristic features. S is able to do something O cannot: permit us to extend the rule to hitherto unperceived objects and so make a claim that can be taken, albeit only under the hypothesis, to hold a priori, in advance of experience of objects.31 While Kant was not willing to attribute type-O hypothetical necessity to the principles of geometry, there are indications that he was satisfied to give them merely type-S hypothetical necessity.32 We simply cannot judge whether the intuitions of other thinking beings are bound to the same conditions that determine our intuition and are universally valid for us. Now, if we add the limitation under which a judgment is made to the concept of the subject of that judgment, then the judgment holds unconditionally. The proposition, 'all things are next to one another in space/ holds [A adds: only] under the restriction that these things are taken as objects of our sensory intuition. So were I to add this condition to the concept and say, 'all things, as outer intuitions, are next to one another in space/ then this rule holds universally and without restriction. ^27/643. See also 672; A254/B31O; A286/B342-3; Prolegomena §57 [Ak, IV 350-1]; Fortschritte [Ak, XX 267].)

c. An Argument for Grounding in the Receptive Constitution of the Subject There is one final point made by Kant at 641 that remains to be demonstrated. This is that the 'subjective constitution' that serves as a ground for our a priori intuitions is a manner in which the subject is constituted so as to be able originally to receive intuitions rather than a manner in which it is constituted so as to think of or otherwise intelligibly represent its experiences. This final point follows directly from what has been established in §ii.a, above. Since space and time are forms of intuition, and intuition just is the receptive capacity, it follows that, in so far as our

The Transcendental Expositions 269 intuitions of space and time are grounded in the constitution of the subject, it must be the subject's receptive constitution in which they are grounded. As a priori forms of intuition, space and time are acquired by the subject (albeit originally acquired from the manner in which the subject is constituted so as to be able to receive sensations), not produced by it. Everything that Kant says at 841 can be justified, therefore. Not only is the a priori experience on which the propositions of geometry are grounded an a priori intuition, it is an intuition grounded in the constitution of the subject, and, as an intuition, it is grouded in the way the subject is constituted so as to be able to originally receive matters in sensory experience. iii.

The Explanation of the Possibility of Geometry and Mechanics

In the buttressing argument and the subjectivity argument, Kant appeals to the fact that there is synthetic a priori knowledge of space and time in order to justify other claims: that space and time are given independently of sensation in intuition, and that they are grounded on the manner in which the subject is constituted so as to be able to receive an intuition. But neither of these conclusions are what Kant took the Transcendental Exposition to be primarily directed to establish.33 For Kant, the primary task of the Transcendental Expositions is not to assume the synthetic a priori status of our knowledge of space and time in order to demonstrate its origin in subjectively determined, a priori intuitions, but just the reverse: to postulate its origin in subjectively determined, a priori intuitions in order to explain why it is synthetic yet a priori. Seen in this light, the Transcendental Expositions are not arguments at all; they are not intended to prove anything. Their purpose is rather to explain something the existence of which is already taken for granted. I understand by 'exposition' (expositio) the distinct (if also not complete) representation of that which belongs to a concept. The exposition is metaphysical when it contains that which presents the concept as given a priori. (638) I understand by 'transcendental exposition' the explication of a concept as a principle from which we can see the possibility of other synthetic a priori items of knowledge. For this purpose it is required (i) that such items of knowledge actually do follow from the given concept, (2) that these items of knowledge are

270 The Expositions only possible under the presupposition of a given mode of explicating this concept. (640)

These definitions of 'metaphysical' and 'transcendental' expositions only loosely correspond to Kant's actual division of the text (the later Metaphysical Expositions are not 'metaphysical/ as Kant defines it, since they establish the intuitive rather than the a priori origin of our concepts of space and time, whereas the priority part of the buttressing argument in the Transcendental Exposition is a 'metaphysical' exposition, as Kant defines it). But Kant does make the point that a Transcendental Exposition is principally supposed to explain how we come to be in possession of certain items of synthetic a priori knowledge. The explanation presupposes certain things, however, and it is here that arguments or demonstrations must be given as underpinnings. We must, first, identify a particular concept that lies at the root of the synthetic a priori judgments and from which they 'follow/ Kant does not amplify but, given the concrete instances he goes on to discuss (the concept of space for the science of geometry, that of time for mechanics), what he seems to have in mind is either that the concept represents some 'object' that all the synthetic a priori judgments are about, or that it is for some reason a prerequisite of their intelligibility. A root concept having been identified, it must then be established that only when this concept is taken to originate in a certain way can the synthetic a priori status of the related judgments be accounted for. In the case Kant is concerned with, this mode of origination is, of course, abstraction of the form of intuition from the remaining content, or abstraction of the necessary features of objects in so far as they are constructed in accord with this form. The first of these tasks, identifying a root concept, is easily done for geometry. Geometry just is, by definition, a body of synthetic a priori propositions describing the properties of space. So geometry obviously 'follows' from what the concept of space contains, though, as has already been remarked, geometry does not proceed from the concept of space by way of analysis (how it does 'follow from the concept' is the second task to be undertaken, and will be more closely examined in a moment). But Kant also wants to take time to be a concept from which a body of synthetic a priori knowledge 'follows.' Here he runs into a problem. There is no science of time analogous to geometry, so it is much less obvious what body of synthetic a priori propositions is supposed to follow from this concept. Kant has so much trouble deciding this question

The Transcendental Expositions 271 that he devotes the whole Transcendental Exposition of the Concept of Time' to this one topic and refers us to the time priority argument (given in the Third Exposition of the time section) for the rest. The concept of alteration and with it the concept of motion (as alteration of place) is possible only through and in the representation of time. Were this representation not an (inner) a priori intuition, no concept whatsoever could make intelligible the possibility of an alteration, that is, a conjunction of contradictory predicates in one and the same subject (for example, the being of a thing in a particular place and the not-being of that very thing in that very place). Only in time can both contradictory determinations be found in one thing, namely, after one another. Thus our concept of time explains the possibility of as many synthetic a priori items of knowledge as are presented by the general doctrine of mechanics, and this is not a meagre contribution. (648-9)

There seems to be an unstated presupposition here that mechanics, like geometry, is a science containing synthetic a priori propositions (though perhaps not exhaustively so, as is the case with geometry). But, whereas geometry describes space directly, the synthetic a priori propositions of mechanics do not describe time, but motion. The whole burden of Kant's argument is to show that the concept of motion, understood as the location of an object at different positions, would be absurd, because contradictory, were a representation of time not presupposed. Motion has to be understood as the successive location of an object at different positions. In this sense, the concept of time makes possible the concept of motion, and so the whole of mechanics, including whatever synthetic a priori principles it may contain. So, synthetic a priori knowledge of mechanics is ultimately grounded on the concept of time, as geometry is on the concept of space.34 The second task of the Transcendental Expositions, properly so called, is to show that the items of synthetic a priori knowledge in question follow only from a certain mode of explicating the root concepts. More specifically, it is to show that the synthetic a priori status of the propositions of geometry and mechanics can only be accounted for if we suppose that our concepts of space and time are grounded in the way the subject is constituted so as to be able to receive matters in intuition, so that these concepts can be supposed to be representations of the form of intuition. Though one might take this to be the major task of the Transcendental Expositions, Kant omits entirely to do it in the time section. There he makes a passing claim to the effect that the representation of time needs

272 The Expositions to be an a priori inner intuition in order to account for the possibility of alteration, but this claim is neither explained nor justified, and the whole of Kant's attention in the text is focused instead just on establishing that the representation of time, however it may be supposed to originate, is indeed foundational for mechanics. The space section is somewhat better. It concludes with the remark: Thus only our explication makes the possibility of geometry as a synthetic mode of a priori cognition evident' (641), and if one reads the Transcendental Exposition of the Concept of Space' in reverse, one can draw the following explication from the subjectivity argument: if we suppose that the subject is so constituted that it can only receive intuitions successively in (classical) time and part-ordered in (Euclidean, threedimensional) space,35 then we can deduce that our representations of space and time must originate as formal features of all our intuitions, that may be anticipated to characterize all our intuitive experience, even in advance of any actual experience, and hence a priori. Consequently, propositions describing space, such as the propositions of geometry, must be describing what are in effect a set of constraints on all possible sensory experiences, regardless of their contingent content. This means that these propositions could not be falsified by any possible experience (so long as the subject's constitution remains unaltered), and hence (under this condition) can be affirmed in advance of experience. This explication still leaves two things to be desired. First, it is necessary to justify the uniqueness claim Kant makes. Appealing to subjectively grounded constraints on the possibility of receiving intuitions is supposed to be the only way in which the synthetic a priori status of the propositions of geometry could be explicated. To resolve this question Kant, brings in the buttressing arguments. They establish that, in so far as the propositions of geometry are synthetic and a priori, they must be supposed to be grounded on a form of intuition. This does not quite get Kant all the way (we still have no argument for why the form must be subjective), but he seems to have simply taken it to be obvious that the only way to account for the necessity of knowledge of the form of intuition is to suppose that the form is grounded on the way the subject is constituted so as to be able to receive an intuition.36 Objective constraints on the form our intuition can take would be too unstable, since different objects could well determine different forms. The second gap in Kant's explication of the possibility of geometry concerns the nature of the link between our a priori intuition of space and our knowledge of geometrical propositions. While the Transcenden-

The Transcendental Expositions 273 tal Expositions do, indeed, try to demonstrate that it is possible for geometrical propositions to have synthetic a priori status so long as they are taken to be descriptions of an a priori form of intuition, they remain silent on how exactly this sort of description is possible. How do we manage to isolate successfully the spatial form from the rest of what is given in intuition so that we can be sure that what we are describing pertains just to the form and is not in any way polluted by some tacit, contingent, a posteriori element? Unless Kant can explain how we can do this with at least some degree of success, he will not really have shown how geometrical propositions are possible. Kant does have an explanation of how we might distinguish a priori from empirical elements in our experience, and get assurance that a synthetic proposition is, indeed, based on the a priori elements, but this explanation occurs only late in the Critique, in the Doctrine of Method ^712-24/6740-52). There he introduces the notion that, besides analysing or expositing our concepts, we can construct them. To construct a concept is to create an object (or give ourselves an image or a perception of an object) that satisfies all the features thought in the concept. Kant believes that when we do this we can discover certain things to follow from the 'definition' of the concept that are simply not contained in it analytically and that cannot be derived from it by any deductive procedure.37 Some concepts turn out to be impossible to construct, even though they are intelligible in the sense that they involve no obvious contradiction (e.g., the concept of five equidistant points or of two straight lines enclosing a space). Others turn out to specify two or more distinct objects, even though it is very difficult to give a further specification of the nature of this difference (e.g., two incongruent kinds of 30-6090 triangle with a shortest side of 5 centimetres can be drawn on a piece of paper).38 And, most significantly, yet others turn out to exhibit properties that had not been thought in, or perhaps could not otherwise be demonstrated of, the concept, even though there is no way to do the construction without superadding these features (e.g., two circles centred on the opposite ends of a common radius are found always to intersect at two points).39 Kant takes it that the reason this further information can be discovered through constructing objects or images for concepts is that the a priori elements in our experience place independent constraints on what can be represented, and so, as a consequence, add certain necessary determinations to whatever objects are actually imaged or experienced, thus specifying objects in ways that go beyond what is or

274 The Expositions sometimes (as in the case of incongruent counterparts) even can be thought in our bare concepts of objects themselves.40 Thus, by constructing an object in accord with a concept and attending to whatever further properties or relations are necessarily revealed by this process, we can isolate those elements of our experience that are attributable to and descriptive of the forms of our intuition.

Summary and Conclusions to Part II

In Part I, I argued that Kant conceives the human cognitive system to be divided into two primary faculties, a lower, sensory-intuitive faculty and a higher, intellectual-discursive faculty. I also argued that he conceives the representations delivered by the lower cognitive faculty tc consist of collections of intensity values disposed alongside one anothei in space and presented after one another in time, and I noted that he takes the intensity values to result from our being affected by objects and their spatio-temporal order to result from the nature of the subject The Expositions contain his arguments for these latter two views. Since intuitions that have not been brought under concepts are blind, these arguments cannot be given by isolating and dissecting our intuitionj to reveal what they contain or what their various components are grounded on (A22/B36 not withstanding). Instead, the Expositions pro ceed as follows: 1 The Metaphysical Expositions establish that there are no known intel lectual operations that could generate concepts of space and time either innately or by drawing on what is given in sensation. 2 The Transcendental Expositions claim that there is no way of account ing for the peculiar, synthetic a priori status of our judgments abou the nature of space and time other than by supposing that these judg ments are determined by our own constitutions. Both of these arguments are instances of what in the literature an called 'transcendental arguments/ that is, arguments that a certaii result must obtain because it is required for something else - which al are agreed is, in fact, the case - to obtain. It is just that the Metaphysica

276 The Expositions Expositions are directed to expositing the conditions of the possibility of our concepts of space and time, whereas the Transcendental Expositions are directed towards expositing the possibility of our synthetic a priori knowledge of certain propositions describing space and time.1 The Metaphysical and Transcendental Expositions may be briefly summarized as follows.2 i.

The Metaphysical Expositions

The Metaphysical Expositions point to certain salient features of our concepts of space and time and ask how concepts exhibiting such features could originate. They argue that this could not happen by abstraction from anything given in the matters that we observe to be arrayed in space and time in our intelligible experience, nor as a result of the operation of some intellectual principle governing the manner in which originally given aspatiotemporal matters are sorted or arranged by the higher cognitive faculties. Our concepts of space and time must be drawn from something originally given in intuition, but not by way of construction or inference from matters that, as originally given, are aspatiotemporal. Rather, space and time must be already present in the intuition as manners of disposition or forms of presentation in which the matters of intuition occur, and our concepts must be drawn from them considered as such. 1 To prove these points, the first thing that is necessary is to observe that our concepts of space and time are concepts of orders in which a number of objects can be arranged, not concepts of some property that a number of objects can share in common, or concepts of a kind to which a number of objects may be supposed to belong.3 There is therefore a distinction that can be drawn between space and time as orders and the things that are ordered in space and time. The former can be called 'form/ and the latter 'matter/ 2 Observe next that, where space and time are concerned, the 'form' is not fixed by the 'matter/4 This is not the case with all orders. Certain kinds of orders (comparative orders) are determined by the features of the ordered elements. Colour space is an example of this kind of order. It is because the ordered elements, visible colours, have the three intensive qualities of brightness, hue, and saturation that colour space is three- dimensional. It is because the hues all shade into one another, whereas saturation and brightness have extremes of darkness

Summary and Conclusions 277 and light, that colour space is finite but unbounded in the hue dimension (so that all paths through the hues circle back on themselves), but both finite and bounded in the saturation and brightness dimensions. In contrast, the matters that are found by experience to be ordered in space and time do not possess any qualities that fix their spatiotemporal locations. By vision, we experience various colour patches to be arrayed in visual space; by touch, we experience various pressures and temperatures to be arrayed in tangible space. But there is nothing we can discover upon inspection of these ordered matters that determines their location in the visual or tangible spatial order. By isolating a particular red colour patch and examining it, we can determine where it must be located in colour space but not where it must occur on the visual field. By isolating a particular feeling of heat and inspecting it, we can determine (roughly) where it occurs on the temperature scale but not on which part of the body it must be felt. Visual and tangible sensible qualities are indifferent to their locations in 'position space' in a way in which they are not indifferent to their locations in 'colour space' or 'temperature space/ so that it is only through 'the progress of experience'- through experiencing the order in which matters, in fact, occur as our experience extends outwards and onwards - and not through inspection of the properties of individually isolated matters, that we can determine their locations in 'position space.' The point is even more obvious for time. There is no matter of experience that may not be supposed to occur indifferently at any time whatsoever; furthermore, any matter of experience may be conceived to persist over an interval of time. If, however, the temporal order were drawn from the properties of the matters experienced in time, then the matters in time could not be supposed to persist over an interval without undergoing some noticeable alteration. It is evident, therefore, that our cognition of the spatiotemporal relations of the matters of experience is not drawn from anything exhibited by those matters themselves.5 Two alternatives remain: the order could be spontaneously constructed by the mind, or it could be originally given in experience. In the former case, the ordered matters would be merely the matter of the objects of appearance or of our perceptions; in the latter, they would be the matter of intuition. 3 Observe next that, though our concepts of space and time represent orders in accord with which a number of matters can be arranged, the matters experienced as so arranged need not be full-fledged physical objects (solid, extended, movable, intersubjectively reidentifiable

278 The Expositions bodies, thought as occupying a single space and reciprocally interacting with one another in accord with laws describing the operation of universal forces). Space and time can be experienced to be filled with matters that are ambiguous or unintelligible to common-sense perception, and so do not designate any object that we can identify, and they can also be experienced to be filled with matters that, according the most advanced science of Kant's day, could possibly be taken to designate the absence of anything 'real' in space or time (e.g., matters such as black, cold, and permeability). These suppositions do not violate any of the conditions of the possibility of experience (though they might fall short of satisfying certain canons of scientific theorizing).6 Evidently, therefore, original space- and time-cognition could not be supposed to depend upon object recognition, much less upon the formation of theories about the operation of forces. 4 Observe, finally, that space and time are thought to be infinitely divisible. This one feature has a two distinct implications. It implies, first, that space and time themselves could not be independently existing entities and, second, that our representations of them could not have arisen from an intellectual synthesis of parts that are themselves in no way spatial. The first of these implications follows from the fact that, if a thing is taken to exist on its own, independently of anything else, then all the conditions for its existence must have been satisfied (this is not the case where we are talking about things that exist only as objects of our representations - such objects can be given to us in experience without all the conditions for their existence also being given in experience). In particular, if the object that exists is a composite, then it is supposed that all of its components exist. But an 'object' that is infinitely divisible has no components. When all relations between parts are removed from it, nothing remains - which is tantamount to saying that it is composed of nothing, and so is itself nothing - or, rather, is nothing but a system of relations, that cannot be supposed to exist independently of relata. From this it follows that our concepts of space and time could not be concepts of objects able to exist in their own right, however these concepts might be supposed to be given. In so far as space and time are known by us, it is only through reference to some further content that is given in space and time - if not objects (as [3] has already shown), then something more primitive than objects, such as the matters for our cognition of objects.7 The second of these implications follows from the fact that we are

Summary and Conclusions 279 finite beings, and as such are not capable of performing infinite tasks. Since space and time are infinitely divisible, constructing a representation of space and time by assembling previously given parts would be an infinite task, which is impossible for us. More to the point, since space and time, as infinitely divisible, have no ultimate parts, any 'parts' out of which space and time were assembled would themselves have to be supposed to be composites of further parts. There is no alternative, therefore, to accepting that any intellectual acts of combination of spaces and times are carried out on materials that are already extended in space and time. To this extent, space and time must be already given to the combinative capacities of the intellect.8 Taken together, these four observations on the nature of our (necessarily intellectual) representations of space, time, and the matters given in space and time indicate that our concepts of space and time are drawn from a form already present in intuition. For space and time are concepts of an order in which matters are given, and moreover they are concepts of an order that is not derived from the content of the ordered elements; from synthesis of the ordered elements under concepts of objects; from scientific reasoning; or from spontaneously setting any, conceivable, previously given parts alongside one another to generate a spatiotemporal matrix. If this is an exhaustive list of the possible forms of 'synthesis' the mind can perform (and Kant's architectonic implies that it is), then it indicates that the spatiotemporal order is not the product of any mental process performed upon the matters that appear as arrayed in space and time or, indeed, upon any conceivable parts of space or time. Were these parts not originally given in a spatiotemporal order in our first experience of them, there would be no way to explain how we come to perceive them as standing in spatiotemporal relations to one another. But Kant's name for that which is given in an experience that is original and prior to all processing is 'intuition/ and his name for the order in which various matters are given in intuition is 'form of intuition/ Hence, space and time must be intuited, and they must be intuited as the manner in which various matters occur in intuition; that is, they must be forms of intuition. ii.

The Transcendental Expositions

Nominally, the Transcendental Expositions establish the same conclusion as the Metaphysical: that space and time must be a priori forms. But

280 The Expositions they begin, not from the supposition that we are in possession of certain concepts, but that we are in possession of certain items of synthetic a priori knowledge: the propositions of geometry and certain axioms describing the possible temporal relations of objects. And, from this beginning, they go on to establish both a quite different kind of priority from that which follows from the Metaphysical Expositions and a further conclusion about the subjectivity of the forms of intuition. The Transcendental Expositions do not, however, establish anything about the intuitive status of space and time. Though they claim that the propositions of mathematics are 'intuitive' judgments, they do not show that the objects these judgments describe, space and time, are originally given in intuition. (An 'intuitive' judgment is a judgment merely drawn directly from experience rather than from analysis of concepts. It implies nothing about whether the the salient features of the experience are given in intuition or generated through intellectual processing.) i From the a priori status of our knowledge of the principles of geometry and the axioms concerning time, the Transcendental Expositions infer that the objects these principles and axioms describe, space and time, could not be known through sensation. According to Ai9~2O/ 634, sensation is by definition that in the effect of an object on the representative capacity that is attributable to the object (as opposed to that in the effect that would be there regardless of how or by what we are affected). As such, sensation is precisely that in our experience that cannot be anticipated in advance and hence is the truly a posteriori element in experience (Ai67/B2o8~9). In so far as the propositions of geometry and axioms of time can be known in advance of any particular experience, they cannot be descriptive of anything given in sensation, and hence it follows that our representations of space and time cannot be drawn from sensation. This is a slightly different claim from that the Metaphysical Expositions were able to establish. The Metaphysical Expositions led to the conclusion that our representations of space and time are not drawn from the matters that appear in space and time in our experience, leaving it ambiguous whether these matters are sensations, considered as effects of an object on the representative capacity so far as we are affected by it, or just the matters that emerge at spatiotemporal locations when the originally given manifold of intuition is processed in perception. Though the Metaphysical Expositions established that our concepts of space and time are given independently of at least these lat-

Summary and Conclusions 281 ter matters (and are, in this sense, a priori with respect to them), they did not warrant any conclusion about whether spatiotemporal form is independent of our being affected by objects or whether it might, along with the matter of appearance, be equally an effect of objects upon us. The Transcendental Expositions clearly rule this latter option out. 2 From the synthetic status of our knowledge of the principles of geometry and axioms concerning time, the Transcendental Expositions infer that these principles and axioms could not be known by analysis of their component concepts (not, at any rate, in so far as these concepts are taken to refer to an object of a possible experience). They must, rather, be discovered through the exhibition of an instance of the principle or axiom in experience. Since, however, the principles and axioms in question are a priori, the experience cannot verify them in virtue of its a posteriori content but only in virtue of certain components in it that are present regardless of what object may be affecting us. The only way to explain the existence of such extraneous, invariant components, however, is to suppose that they arise from the way the subject's cognitive system is constituted, and so are grounded in something that will be present regardless of what object happens to be affecting it. Since the principles and axioms in question are all about space and time, we can conclude that the subjective constitution in question must be the constitution of the subject's sensory capacities. This follows from the fact, already established by the Metaphysical Expositions, that space and time are the forms of sense intuition. But, since the subject's sensory capacities are purely receptive or intuitive, it also follows that this constitution must be a receptive or an intuitive constitution. Rather than being constituted in such a way as to order sensations in space and time, the subject must be constituted in such a way as to receive sensations in a spatiotemporal order. The subject's constitution must determine, not how it processes sensations, but how it is able to first acquire them. Thus, the conclusions originally drawn in chapter 2, above, about what it means for space and time to be forms of intuition, are justified by an argument that draws on the combined resources of the Metaphysical and Transcendental Expositions, as well as on an understanding of Kant's representation terminology. iii.

Conclusions

In the Transcendental Expositions Kant invokes a premise that many

282 The Expositions will not be willing to grant, even in the mitigated form in which it has recently been defended (namely, as the claim that we must presuppose the truth of approximately Euclidean axioms if we are to identify solid, enduring objects).9 This is not the case with the Metaphysical Expositions, which seek to establish just that space and time are orders in accord with which the raw data of intuition are first presented to us. There the argument supposes just that we are in possession of concepts of space and time (which is obvious), and that through these concepts we think of space and time in certain ways: as orders in which various elements can be disposed; as homogeneous fields that can contain matters indifferently at any location, regardless of what qualitative characteristics these matters may happen to exhibit; as characteristics even of unintelligible experiences where no objects can be recognized; and as wholes, every part of which is again a space or time, so that points and moments are not parts of space and time, but merely limits that can first be recognized only as locations within a previously given, larger space and time. These suppositions of the Metaphysical Expositions are, like the supposition about the synthetic a priori status of our judgments about space and time, fundamental premises of Kant's argument. We may choose to contest them, and if we do then Kant has nothing to say to us. But the suppositions at the base of the Metaphysical Expositions are so evident from our ordinary experience that it is more difficult to deny them. The Metaphysical Expositions pay a price for this increased certainty. At the same time that their premises are stronger and more difficult to deny, their conclusions are weaker. They establish just that our representations of space and time are distinct from the matters that are represented in space and time and are given independently of these matters. The Transcendental Expositions are able to establish this conclusion as well, but they are able to establish something more: not just that space and time are given independently of the matters in space and time, but that they are given independently of empirical experience, and so are 'a priori' in the stronger sense of being anticipable in advance of being affected. Thus, those who claim that Kant's transcendental idealism can be based exclusively on the argument of the Metaphysical Expositions10 are wrong. The Metaphysical Expositions do not lead to the strong conclusions about a priori origination and subjective grounding that are characteristic of transcendental idealism and that are provided by of the Transcendental Expositions. At the same time, however, the Transcendental Expositions are able to

Summary and Conclusions 283 establish their strong conclusion only through a reliance on the Metaphysical. It is the inextricability argument of the Metaphysical Expositions that legitimates the fundamental premise of the Transcendental, and the Metaphysical Expositions alone which are able to overcome blindness and establish that spatiotemporal order must be originally present among the matters of intuition. Without relying on that proof, the Transcendental Expositions can do no more than establish that there exists in us an a priori, subjectively grounded experience of space and time, but not that the a priori components of this experience are originally given in intuition. Thus, those who dismiss the Metaphysical Expositions as a collection of bad arguments that can be passed over in favour of the more provocative (if equally bad) Transcendental Expositions11 are just as wrong as those who seek to make Kant's entire argument rest on the Metaphysical Expositions. Indeed, they are doubly wrong, because the even weaker conclusion that the Metaphysical Expositions are able to draw about priority ought not to be disparaged. The Metaphysical Expositions may not establish Kant's transcendental idealism, but they do present what is (for the eighteenth century) a powerful set of arguments for a formal intuitionist account of space- and time-cognition - an account that postulates that neither space- nor time-perception should be taken to arise from intellectual synthesis of matters that are in no way spatial or temporal, but that space and time are, instead, originally given as orders or manners of disposition in which the raw materials of intuition are first presented. The implications of this position are significant and far-reaching. Indeed, they are in their own way as provocative as anything that falls under the rubric of Kant's transcendental idealism. (One such implication is that, since space is a manner in which the matters that make up our intuitions occur, our intuitions must be physiological states.) Altogether too much attention has been focused on Kant's strong conclusion about the subjectivity of the forms of intuition and the subsequent controversy over transcendental idealism, and far too little (in fact, none) has been focused on his weaker, but still important conclusion that, subjective or not, space and time are forms of intuition and as such orders in which sensations are originally received by us. This conclusion was in its own right a novel contribution to the history of theories of space- and time-cognition.12 It is time it was recognized and attended to as such.

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PART III

Conclusions from the Above

Concepts

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Introduction

Our expositions teach, therefore, the reality (that is, the objective validity) of space with respect to all that can be outwardly presented to us, but at the same time the ideality of space with respect to things in so far as they are considered in themselves through reason, that is, without reference to the constitution of our sensibility. We affirm therefore the empirical reality of space (with reference to all possible outer experience), but [at the same time]1 its transcendental ideality, that is, that it would be nothing were we to set aside the conditions of the possibility of all experience and consider it as something that underlies things in themselves. (A27-87643-4) Our claims teach, therefore, empirical reality of time, that is, objective validity with respect to all objects that might ever be given to our senses. And since our intuition is always sensory, there can never be an object given to us in experience that does not satisfy the condition of time. However, we contest any claim of time to absolute reality, according to which it would belong unconditionally to things as a condition or property without taking account of the form of our sensory intuition. Properties that pertain to things in themselves can never be given to us through the senses. In this consists the transcendental ideality of time, according to which, when one abstracts from the subjective conditions of sensory intuition, time is absolutely nothing and cannot be attributed to things in themselves ([that is,] apart from their relation to our intuition), as either something subsisting [in its own right] or inhering [in things]. ^36-7/652)

These texts express the central tenets of what is called Kant's transcendental idealism.2 As the title of the sections in which they are stated ('Conclusions from the Above Concepts') implies, transcendental ideal-

288 Conclusions from the Above Concepts ism is supposed to follow as a conclusion from the Metaphysical and Transcendental Expositions. In this part, I examine just how far that is the case. As described in the passages cited above, transcendental idealism consists of two principal assertions. One is the claim that space and time are 'absolutely nothing/ as Kant puts it, apart from reference to our intuition, and so do not pertain to things as they are in themselves or independently of how they appear to us through sensory intuition. In what follows, I refer to this as the 'non-spatiotemporality thesis.' The second is the claim that space and time do and, in fact, must qualify all the objects of our sensory experience. This claim is an obvious consequence of a more basic conclusion that Kant has already drawn from the Expositions: the conclusion that the spatiotemporal form of our intuitions is not an effect of objects on us but is determined by the constitution of our sensory faculty, and so comes to characterize all of our experiences, regardless of what object may be affecting us (A26/B42). In what follows, I refer to the more basic conclusion as 'the subjectivity thesis.' Chapters 9 and 10, below, examine the non-spatiotemporality thesis, and chapter 11 the subjectivity thesis. The non-spatiotemporality thesis is notoriously problematic, and its grounds are notoriously obscure. My examination of it is devoted almost exclusively to a consideration of whether and how it might be conceived to follow from the Expositions, and whether it can be consistently affirmed without undermining or contradicting other Kantian claims. In contrast, the subjectivity thesis is both characteristically Kantian and well founded, being an obvious consequence of the Transcendental Expositions, as laid out in chapters, above. However, it is imprecisely formulated and precarious. It is not clear what Kant means by claiming that spatiotemporal form must be grounded on the constitution of the subject, and it is not clear how this thesis serves to found an 'empirical realism' that is distinct, on the one hand, from a transcendental realism about the subject (which affirms that, considered as things in themselves, we have sense organs constituted so as to determine the spatiotemporality of all our intuitions), or, on the other, from garden-variety (or, as Kant would call it, 'empirical') idealism (which affirms that the existence of an external world beyond our representations is either uncertain or impossible). My examination of the subjectivity thesis is accordingly devoted to these latter issues.

9 Kant's Argument for the

Non-spatiotemporality of Things in Themselves

(a) Space does not represent any property whatsoever of things either in themselves or in their relations to one another; that is, it does not represent any determination that attaches to the objects themselves and that would remain even were one to abstract from all subjective conditions of intuition. For neither absolute nor relative determinations can be intuited prior to the presence of the things to which they pertain, and consequently neither can be intuited a priori. (a) Time is not something that would persist on its own, or would attach to things as an objective determination that would remain when one abstracts from all subjective conditions of their intuition. For, in the first case, time would be something that would still be actual apart from any actual object. As for what concerns the second case, time, as a determination or order pertaining to things themselves, could not precede objects as their condition, and be cognized and intuited a priori through synthetic propositions. But the latter could certainly take place were time nothing but the subjective condition on which all intuitions can take place in us. For then this form of inner intuition can be represented prior to objects and consequently a priori. These two passages occur immediately under the title 'Conclusions from the Above Concepts' at A26/B42 and A32-3/B49, just after the close of the space and time Expositions. They affirm that space and time are neither properties nor relations of things as they are in themselves, and that time is not an independently subsisting thing in its own right. Kant most likely intended to make the latter claim about space as well (he did make it elsewhere)1 and simply neglected to do so as a result of

290 Conclusions from the Above Concepts the carelessness and lack of attention to detail that was so typical of him. As 'conclusions from the above concepts' these non-spatiotemporality theses ought to follow from what has been said in the Expositions, but it is hard to see how. Kant does supply two further reasons, but they are not helpful. He tells us that time could not be an independently subsisting entity because it would be absurd were it to exist apart from any objects. But one has to stretch to see how this claim could be justified by anything said in the Expositions. The First Exposition assumes that our concepts of space and time are concepts of an order in which various matters may be disposed, and one might want to claim that it would be absurd for there to be an order where there are no ordered elements. But a conclusion drawn from a shared presupposition is not the same thing as a conclusion from what is uncovered by the Expositions, and hardly deserves to be called a conclusion 'from the above concepts/ Worse, the First Exposition establishes that the spatiotemporal orders are original, not derived from the ordered matters, and this (epistemological) independence of order from ordered elements sits unhappily with the (ontological) dependence of order on ordered elements, that Kant affirms when he says time could not exist apart from there being things in time. The two are not contradictory, but it is very hard to see how the latter could be in any sense a consequence of the former. Kant also tells us that space and time could not be properties or relations of things in themselves because, were that the case, space and time could not be known a priori. This is a cryptic remark, but it does seem to invoke the following variation on the priority argument of the Transcendental Expositions: Suppose (i) that space and time were features or relations of things in themselves and (2) that we had direct knowledge of the spatiotemporal features of things as they are in themselves through sensory intuition. Then, (3) it would only be through observing things and discovering what their properties and relations in fact are like that we would learn about space and time, and all descriptions of space and time would accordingly be generalizations from past experience that possess 'merely comparative universality through induction.' But, (4) this last consequence cannot be accepted since the propositions of geometry and axioms of time are necessarily true.2 Accordingly, we must reject either (i) or (2), or both. Regardless of which we choose to reject, however, we are left having to confront the consequence that our knowledge of space and time could not be in any way determined by things in themselves. For, even if we were to accept (i), we would have to reject (2) and, with it, the notion that the spatiotemporal features we experience are in any way

The Non-spatiotemporality of Things in Themselves 291 related to any spatiotemporal features that might be possessed by things in themselves.3 The spatiotemporal features of our experience must therefore be determined purely by the constitution of the subject and be completely independent of any spatiotemporal features that might be supposed to inhere in things in themselves. (A qualification is in order. By 'the spatiotemporal features of our experience/ I mean to refer just to those features that are, in fact, the subject-matter for the propositions of geometry and axioms of time, that is, the metric, the affine features, and the topology of space and time. I do not mean to include the locations of sensations or matters of appearance among these features. The fact that a certain sensation or matter of appearance is located where it is in the spatiotemporal manifold may, for all Kant's argument is able to prove, be attributable to some feature of the affecting object. But the fact that this manifold has the metrical, affine, and topological features it does is not.) If this is indeed Kant's argument, then it really says nothing more than that our concepts of space and time cannot be supposed to be drawn from sensation, considered as 'effect of an object on the representative capacity,' and, in this sense, it is indeed a 'conclusion' from the priority argument. Indeed, it is a corollary of the general conclusion established by those passages, since they prove that our concepts of space and time could not be drawn from any sort of effect on the representative capacity, resembling or not, whereas the non-spatiotemporality thesis is concerned just with the specific case where the effect is a direct perception of the properties of the affecting object. But we really do not have a 'conclusion from the above concepts' here either, because, even if the argument Kant offers is drawn from the Expositions, the conclusion that he wants to establish is not the conclusion that this argument establishes but a far stronger one. The argument laid out here does not establish that things in themselves could not have any spatiotemporal properties or relations whatsoever. What it establishes is just that any spatiotemporal properties or relations things in themselves might happen to have could not be what fix the spatiotemporal features of our intuitions. The latter, as known a priori, could not be determined by the former, so that, even were there a correspondence between the two, it would be purely accidental, the forms of our intuition being determined by the constitution of 'our subjects' and not by anything in affecting objects, and being such, therefore, that they would in principle remain the same, even were any supposed correspondence with things in themselves to cease to hold. This is already a very strong conclusion. The first thing it does is place

292 Conclusions from the Above Concepts a roadblock in the way of using an argument from effects to causes to infer the nature of things in themselves from the nature of our representations. Since things in themselves are not what determine the forms of our intuition, we cannot infer anything about what things in themselves are like from the fact that they appear to us as arrayed in space and time.4 But the conclusion does more than this. It claims not only that we cannot know whether or not things in themselves are in space or time, but also that we can know that, even if they were, their spatiotemporal features would not be what determines the form of our intuition and so would be nothing to us. We might be tempted to think that this is, in fact, Kant's conclusion. Perhaps all he means to say is that the space and time we experience are not determined by any properties or relations of things in themselves (though, for all we know, they might 'correspond' to such properties or relations).5 But, as strong as this conclusion is, Kant has a much bolder one in mind. His point is not just that the spatiotemporal form of our experience is not determined by any properties or relations things in themselves might have, but that things in themselves do not have any properties or relations that could be legitimately termed spatiotemporal. It is not just that any spatiotemporal properties or relations that things in themselves might have would be nothing to us, but that they would be nothing. Thus, at A33/B49, Kant speaks of time being 'nothing but' the subjective condition under which all intuitions can take place in us. In the passages cited at the outset of Part III, above, A28/B44 and A36/B52, as well as at A26 7642-3, he describes space and time as 'nothing' when we consider things as they might be in themselves. At A37/B54, he describes his previous argument as having established that 'absolute reality' cannot be attributed to space and time, since they are 'nothing but' the form of our intuition. And, at A42/B59, he says that space and time would 'disappear' if we were to take away the subjective constitution of our senses. While the weaker conclusion, that any spatiotemporal properties or relations that might pertain to things in themselves could not be what determine the forms of our intuition, is just a consequence of the Transcendental Exposition, it is not obvious how Kant could derive the stronger conclusion, that things in themselves could not have any sort of spatiotemporal properties or relations, from anything said in the Expositions.6 Thus this, too, is a conclusion that does not, in fact, seem to follow 'from the above concepts.' In what follows, I consider whether Kant has some other, or perhaps

The Non-spatiotemporality of Things in Themselves 293 some deeper argument to offer for the non-spatiotemporality thesis. Since Kant himself considers the thesis under two heads, the question whether time (and space) are themselves independently subsisting entities, and the question whether they are properties of independently subsisting entities or relations of (otherwise)7 independently subsisting entities, I treat these questions separately in what follows. As it turns out, there are further arguments to be offered, but the arguments under the two headings are distinct. i.

Substantival Space and Time

I refer to the view that space and time are independently subsisting entities as the view that they are 'substantival.' This expression is motivated by a commonly accepted usage of the term 'substance/ according to which a substance is something that can exist on its own, independently of anything else. Despite the fact that it does not appear explicitly in the Aesthetic, Kant has an argument for rejecting the possibility of substantival space and time. It goes as follows: Space and time are infinitely divisible. Consequently, they cannot be composed of simple parts. Consequently, were we to abstract from all relations of composition in our concepts of them, nothing would remain to be thought. There would be no simple component parts of space or time left over to be identified as the items originally set in spatiotemporal relations to one another. But this is the same as to say that space and time consist entirely of relations, and a relation is not a substance; it cannot exist on its own, any more than a property can. Were there no other things given as standing in spatiotemporal relations to one another, there would be no spatiotemporal relations, and space and time would not exist. Hence, space and time could not be substantival entities, existing as things in themselves in their own right. In what follows, I refer to this as 'the decomposition argument/ since it turns on the claim that space and time, as infinitely divisible, cannot have simple component parts, and so could be decomposed into nothing (or into nothing but relations of composition). One indication of Kant's acceptance of the decomposition argument comes from ID, §1414: by means of time it is nothing but relations which are thought, granted that there are no beings which stand in relation to each other. Thus, in time as a magnitude

294 Conclusions from the Above Concepts there is composition; and should this composition be conceived as wholly cancelled, it would leave nothing at all behind it. (Ak, II 399)

The wider context in which these claims are made is not very appropriate, however. In ID, §1414, Kant's project is not to assume infinite divisibility to prove that time consists of nothing but relations, but the reverse: to claim that time consists of nothing but relations in order to prove that it does not consist of simple parts and so must be continuous.8 None the less, the passage is instructive in showing that Kant thinks that were all relations between composite parts removed from time 'it would leave nothing at all behind it.' Consequently, were time considered as a thing existing in its own right, apart from any other 'beings which stand in relation to each other,' it would be a composite thing that is not composed of anything. That Kant recognizes that his claims have this implication and rejects the implication as absurd (a contradiction, in fact) is indicated by his remarks on substantival space and time later in ID, where he asserts that the conception of time as 'some continuous flux within existence, and yet independently of any existent thing' is 'a most absurd fabrication' (ID, §14 15), and that the conception of space as 'an absolute and boundless receptacle of possible things' is an 'empty fabrication of reason: since it invents an infinite number of true relations without there being any beings which are related to one another, it belongs to the world of fable' (ID, §15 ID). These remarks are the ancestors of the Critique's statement of the non-spatiotemporality thesis for time, where Kant claims that time could not be substantival because then 'it would be something that would still be actual apart from any actual object.' This, Kant takes it, is absurd - a fact that is underwritten by his later claim that the (Newtonian) mathematical natural scientists, who assert that space and time subsist as things in themselves 'must be in conflict with the principles of experience themselves,' because they 'postulate two eternal and infinite, self-subsisting non-entities (space and time) that are there (without, however, there being anything actual) only in order to contain everything actual' (A39/B56).9 The decomposition argument identifies just what 'principles of experience' the Newtonians are in conflict with. The principle in question is that of the infinite divisibility of space and time, which entails that it is absurd that they should exist apart from anything else real. While Kant's remarks on decomposition and his conclusion that there

The Non-spatiotemporality of Things in Themselves 295 is a contradiction in the notion of substantival space or time are not made together in ID, they do occur together in the Entdeckung. There, Kant chastises Eberhard for failing to comprehend simple mathematical demonstrations of the infinite divisibility of space and time, such as those given by Keill in his introductio ad veram physicam. He goes on to note that it will not do to try to evade this result by postulating a distinction between abstract or mathematical and concrete or physical space and time, first, because this would bring all the laws of physics into question in so far as they invoke mathematical principles (especially those involving infinitesimals such as the laws of the fall of bodies), but also because it can be apodictically demonstrated that any particular thing in space, any particular alteration in time, in so far as they take up a part of space or time, are divided into as many things and into as many alterations as the space or time that they take up can be divided into.10 To overcome the paradox that one feels here (in so far as reason, which requires that the simple ultimately be given as a ground of all composites, contradicts that which mathematics proves of sensory intuition), we can and must admit that space and time are mere thought-entities and creatures of imagination. (Ak, VIII 202-3)

The infinite divisibility of space and time, Kant tells us, leads to a 'paradox.' The 'paradox' is generated by the principle that, where there is a composite thing, there must be something that this composite thing is composed of, whereas space and time, since they are infinitely divisible, can have no simple parts and so are not composed of anything - which is so much as to say that they do not exist. The decomposition argument is thus encapsulated in Entdeckung (Ak, VIII 202-3). But it is easy to miss, because Kant does not stop at this point, but goes on to draw other conclusions. What makes the result of the decomposition argument 'paradoxical/ according to Kant, is that it is valid, not only of space and time, but of whatever objects they might contain, thus engendering a total nihilism about the empirically given world. To evade the paradox we must reject the supposition that space and time are substantival. Kant proposes, instead, that we consider them to be mere appearances. However, for our purposes here we need not follow Kant either in his claim that the conclusion of the decomposition argument applies to objects in space and time as well as to space and time themselves, or in his claim that the only solution to the ensuing 'paradox' is to take space and time to be subjective. What is important is

296 Conclusions from the Above Concepts just to note that Kant does employ the decomposition argument to prove that space and time could not be substantival. A slightly different version of the decomposition argument occurs in Anfangsgrunde, 2 (Ak, IV 505-8), in connection with Kant's demonstration of the infinite divisibility of matter.11 Kant there opens his discussion by observing that, while in general mathematicians can carry on their practice without having to worry about the cavils against infinite divisibility that have been raised by philosophers since Zeno of Elea, when the infinite divisibility of space is taken (with the aid of certain further, conceptual considerations) to entail the infinite divisibility of matter, a problem is created that the mathematician must stand aside and allow the philosopher to address. The problem arises because, as Kant succinctly puts it towards the end of the section, 'that which has been composed of things in themselves must admittedly consist of simples, for here the parts must be given prior to all composition' (Ak, IV 507).12 If there is to be a composite thing, supposed to exist in itself rather than as appearance, there has to be something from which it has been compounded. But infinite divisibility rules that out where space and time are concerned, and we are left having to wrestle with the apparent implication that space, time, and all the things they contain are nothing at all. Kant's explanation of just why infinite divisibility rules out the possibility of composition is slightly different from that given in ID, but, superficial differences aside, the argument turns on the same basic points: If, namely, matter is infinitely divisible then (concludes the dogmatic metaphysician) it must consist of an infinite number of parts, for a whole must from the outset contain the totality of parts into which it can be divided. This last proposition is also undoubtedly certain of any whole as thing in itself. Consequently, since one cannot admit that matter, indeed not even space, consists of infinitely many parts (since it is a contradiction to think an infinite number, the concept of which already contains the notion that it can never be represented as completed, as wholly completed), one must decide either to say that, the Geometer notwithstanding, space is not infinitely divisible, or, to aggravate the Metaphysician, by saying that space is not a property of a thing in itself and also that matter is no thing in itself. (Ak, IV 506)

Here the claim is not that an infinitely divisible whole would not be made up of anything but that, if it were conceived to be made up of anything, these parts would have to be conceived, absurdly, as both finite

The Non-spatiotemporality of Things in Themselves

297

and infinite in number, the latter in so far as the magnitude is thought as infinitely divisible, the former insofar as its division is thought to run down to simples at which all further division and, with it, all counting of parts stops. The reasoning behind this last claim is most obscure, but I speculate that Kant's thought may have run along the following lines: when considering an infinitely divisible magnitude, we can conceive it in two ways, only one of which is actually legitimate: we can conceive it as a magnitude that can be divided forever, or we can suppose that the division of the magnitude would stop after a certain number of iterations.13 In the former case (the legitimate one), the magnitude is thought to have no simple parts - indeed, not to have any parts at all - and so not to be composed of anything (this is the argument of ID). In the latter case, where the division is thought to run down to something simple, the parts could not be infinite in number. (For each step in the division of the whole [into halves or thirds or whatever] generates only a finite number of parts and if the division stops after a finite number of iterations, etc.) Trying to evade this consequence by simply stipulating that the division could be carried on forever to generate, at the end, an infinite number of parts is mere chicanery since it asks us to imagine that there could be an end to the division of the magnitude (a last step in the iterated process of division at which simple parts are uncovered) and yet that the division of the magnitude would go on forever. Of course, Kant is wrong about this. There can be a last step (or endpoint) to an infinite regress without there having to be a next-to-last step, so that though the series terminates, the trip to the terminus (so to speak) does not. But Kant cannot be expected to have appreciated this. For him, as for everyone else in his day, the concepts of infinity and unboundedness were not clearly differentiated,14 so that to say that a series is infinite just meant that it has no end-points, and to say that it has end-points ruled out the possibility of its being infinite. Kant's argument was a good one in his day. It just cannot be expected to convince us today. But to return to the topic, if this is indeed Kant's argument, then the Anfangsgrunde is not a revision to or a change of heart about the argument of ID, but merely a different approach to making the point. In the Anfangsgrunde, like the Entdeckung, Kant is out to do more than just prove that space and time could not be substantival. In the Entdeckung, Kant draws the conclusion that space and time must be products of imaginative synthesis of the subjectively grounded forms of intuition; in the Anfangsgrunde, he draws the conclusion that neither space nor things

298 Conclusions from the Above Concepts in space could be things in themselves. It is important to note that these further conclusions do not follow from the decomposition argument alone but presuppose certain additional premises. Strictly, all that the decomposition argument in the Entdeckung leads to is the conclusion that space and time are not substantival. Before he could transform this negative conclusion into the positive one that space is just a form of intuition, Kant would have to rule out any alternatives, notably the alternative that, while not a thing in itself in its own right, space is a property or relation of things in themselves. This omission is rectified in the Anfangsgrtinde, in so far as it is argued that anything that occupies space must also be an appearance, but here again the argument depends on a further claim: the thesis that the infinite divisibility of space entails the infinite divisibility of the objects in space. This claim is by no means obvious (indeed, Kant's attempt to prove it in Anfangsgriinde 2 [Ak, IV 504-5], makes no sense).15 The point of this remark is simply to stress that we should not allow any qualms we may have about these add-on arguments to distract us from appreciating the force of the core, decomposition argument. That argument establishes only that space and time could not be substantival, not that they could not be properties or relations of things in themselves or that they, together with extended matter in general, must be mere appearances. Kant recognizes this in the Antinomies, which contain one of the clearest statements of the decomposition argument - the proof of the thesis of the Second Antinomy: Were composite substances not composed of simple parts then, were all composition removed in thought/6 no composite part and (since there are no simple parts) also no simple part, and so nothing at all, would remain and consequently no substance would have been given.

It should be stressed that Kant fully accepts this argument. What makes the Second Antinomy an antinomy, and so an instance of dogmatic metaphysics that leads to absurdity and needs to be resolved somehow, is that its thesis and antithesis arguments are taken to apply to things in themselves. Were they taken to apply to appearances, there would be nothing antinomical about the thesis argument (just given), and its antithesis (the claim that space and time, together with everything in space and time, are infinitely divisible). They could both be rejected as resting on the false supposition that, for a representation to

The Non-spatiotemporality of Things in Themselves 299 be given in experience, the entire series of its conditions must first have been given. But when the arguments are asserted of things in themselves, they are entirely legitimate, and lead to a genuine antinomy. The case under consideration now, however, is one having to do with things in themselves - with whether space and time could be considered things in themselves. In this context, the argument of the thesis of the Second Antinomy cannot be set aside as erroneous. It quite legitimately establishes that any composite substance must be composed of simple parts. Since space and time are infinitely divisible (this is the ground of the antithesis argument), we are forced to conclude that no composite substance can be in space or time - or, conversely, that space and time cannot be substances. Kant's observations on the proof of the thesis make it clear that he does not see the Antinomy arising except in cases where substances are the subject of investigation: Moreover, that which belongs only to the state of a substance does not consist of simples, even if it has a magnitude (for example, alteration), that is, a certain degree of alteration does not arise through an accumulation of many simple alterations. Our inference from composite to simple holds only for selfsubsistent things. Accidents of states, however, do not subsist on their own. (A440/B468)

Applying this remark to space and time, we can say that what Kant's argument in the thesis of the Second Antinomy proves is that space and time could not be substances. Instead, they must be acknowledged to be something other than substances, be it 'accidents of states' of substances or (Kant's preferred alternative) manners in which the appearances of substances are disposed in our intuitions. To sum up, there is ample evidence to indicate that Kant accepted (i) that it would be a contradiction for there to be a composite thing that is not composed of anything, (ii) that space and time are infinitely divisible, and (iii) that the infinite divisibility of a magnitude entails that it has no simple parts, and so that there is ultimately nothing that it is composed of. Taken together these three claims entail that space and time could not be things existing in their own right (though this does not rule out that they might still turn out to be properties or relations of other things). Unfortunately, Kant never stated this argument on its own, in a passage dedicated to proving just that space and time could not be substantival. Instead, it only ever occurs in the midst of other projects,

3OO Conclusions from the Above Concepts where it is mixed together with other arguments and concerns (some of a dubious nature), and where it is easily overlooked or, worse, rejected without due examination. But that Kant did accept the argument, and moreover took it to be so obvious as almost to be not worth mentioning, is indicated by the offhand way in which he introduces its conclusion at two places in the Aesthetic, A32/B49: Time is not something that subsists in itself... for in [that] case it would be something that would still be real apart from any real object/ and A39/B56: Those who assert the absolute reality of space and time ... as subsisting ... must assume two eternal and infinite, independently subsisting non-entities (space and time) that are there (without, however, there being anything real) only in order to contain everything real in themselves.' Obviously, Kant thought there was something patently absurd about space or time existing apart from any other objects. The passages cited above explain why. ii.

Relative Space and Time

Kant gives two arguments why space and time could not be supposed to be properties or relations of things in themselves. Both take the form of reductio ad absurdum. One is that, under this supposition, we could not account for our synthetic a priori knowledge of space and time. It occurs at A26/B42 and A33-4/B49. The other is that, under this supposition, things in themselves would have to be infinitely divisible, which by the decomposition argument would entail that they could not even exist. It occurs at Anfangsgriinde, 2 (Ak, IV 505-8), is hinted at by Entdeckung (Ak, VIII 202-3), and is between the lines of the Second Antinomy. Neither of these arguments is adequate. The first was shown at the outset of this chapter to be able to establish no more than just that any spatiotemporal features things in themselves might have could not be supposed to determine the spatiotemporal forms of our intuition, not that things in themselves could not have any spatiotemporal features. The second depends on Kant's being able to establish that whatever occupies a space must be divisible into as many parts as the space it occupies. However, in order to establish this thesis, Kant needs to come to terms with a powerful alternative conception of the nature of matter: that proposed by his own, earlier Physical Monadology. According to this view, matter is not composed of spatially extended parts but of extensionless physical monads, which fill space only by the exercise of a repulsive force, so that, while the sphere of the monad's activity may be divided to infinity, the monad itself may not be so divided.17 Kant never

The Non-spatiotemporality of Things in Themselves

301

came to terms with this earlier position. The attempt of Anfangsgrunde, 2 (Ak, IV 504-5), to refute it begs the question against it/8 and the Antithesis of the Second Antinomy does not even presume to offer an argument; it assumes that the only way for a part of a composite to fill space is by the plurality of its parts and simply ignores the possibility that it might do so by means of a repulsive force. But though Kant himself mounts no adequate argument to demonstrate that things in themselves could not have spatiotemporal determinations, we should not leave this topic without first considering whether the Aesthetic might none the less contain further resources for such an argument. The Transcendental Exposition has already been examined and found wanting, but the Aesthetic contains another set of arguments, the Metaphysical Expositions, from which it is possible to draw 'conclusions from the above concepts.' Let us consider whether they might contribute to Kant's non-spatiotemporality thesis, even though he may not realize it.19 Though Kant himself may not have explicitly intended to do so, his Metaphysical Expositions constitute a profound meditation on the question 'what is the ground of the location of the matters of appearance in space and time?' To this question they give the answer 'the progress of experience.' What determines that a matter is located earlier in time is that it is experienced earlier. What determines that it is located between certain others is that it occurs disposed between those others in experience. Experience does not just present various matters to us, it presents these matters successively in time and simultaneously in arrays in space, and it is this spatial and temporal manner of occurrence in experience that is the ultimate ground of all our knowledge of spatiotemporal relations. Kant's answer is backed up with a rejection of alternative answers that might be proposed. Perhaps the most natural response to the question 'what is the ground of the location of an element in an order?' is to say that it is determined by the element's causal history. According to this rival solution, as a result of certain causal circumstances, things emerge in a certain place at a certain time. Then, throughout the subsequent course of their history, they move from place to place either as a result of causal interactions with other bodies or through the action of inertial forces. The ground of the location of a thing in space and time is just the complete causal history that specifies the origin and development of the thing from some assumed initial state of the universe. The problem with this account, from Kant's perspective, is that it is circular. The only way we human beings can discover causal laws is by

302 Conclusions from the Above Concepts ascertaining through experience what tends to follow upon what,20 and as this experience presupposes an awareness of temporal order, it is a knowledge of temporal order that serves as the basis for a knowledge of causal relations and not the other way around. It might be the case that, for things as they are in themselves, location is determined by causal history, but, as far as we are concerned, spatiotemporal order is already to be discovered among the raw data of perceptual experience, before we get around to synthesizing our percepts under concepts of cause and effect. Localization in the space and time of our experience must therefore have some other ground. Another alternative to Kant's account is to suppose that the location of matters in space and time is determined by some set of properties in the matters themselves, in the way that the hue, saturation, and brightness of colours determine their location in colour space. But Kant rejects this on the grounds that, if it were the case, then we ought to be able to deduce where individual matters of appearance are located by isolating and inspecting them, whereas this is not, in fact, the case. By isolating and inspecting a colour, I can certainly discover its location in an ideal colour space but not where it is presented in the spatiotemporal orders in accord with which my experience progresses. Nor are there any peculiar qualities that designate location obvious in the matters of appearance. There is no matter of appearance that we may not imagine moved, yet completely identical with respect to all its qualities. A matter of appearance acquires spatiotemporal relations to other matters only through being presented before, behind, or between them. Considered on its own, it cannot be known to be presented anywhere in experience as opposed to anywhere else. Kant's conclusion from the Metaphysical Expositions, then, is that, as far as we are concerned, the spatiotemporal order of matters of appearance is a presentational order, not a causal-deductive or a comparative order.21 This conclusion has an interesting corollary that bears on the issue at hand: it could not be drawn about any spatial or temporal determinations that things in themselves might be supposed to possess. A presentational order is an order determined by the manner in which the ordered elements are presented to an observer or to a detecting device of some sort. But to consider the order in which things are presented to an observer or a detector is not to consider any determination that they can be supposed to possess in themselves, independently of this relation. Accordingly, were things in themselves extended or located in space or

The Non-spatiotemporality of Things in Themselves 303 time, their spatiotemporal determinations would have to be fixed by causal relations or internal properties. A spatiotemporal order of things in themselves would have to be a causal order or a comparative order, not a presentational order. Indeed, were we to anticipate the analysis Kant will give of causality later in the Critique, we would have to conclude that a spatiotemporal order of things in themselves could only be a comparative order. These reflections on presentational, causal, and comparative orders establish that, even if there were a sense in which things in themselves might be in space or time, it would have to be a very different sense from that in which, according to the Metaphysical Expositions, the matters of appearance are in space and time. Granting Kant's limitations on the scope of causal concepts, in so far as things in themselves can be meaningfully said to be located in space and time, it is only through reference to individual properties, supposed to grade off into one another in such a way as to determine a quality space, in the way that the colour qualities of hue, saturation, and brightness determine a threedimensional colour space. The spatiotemporal order of the matters of appearance, however, is not determined by their nature or their internal properties. Regardless of what properties a matter of appearance may have, it is still a question in what order that matter occurs in the experience of a perceiver, and this question is to be resolved only by the progress of experience, not by inspection of the isolated matter. A direct realist theory of spatial and temporal perception is therefore ruled out by the Metaphysical Expositions. We could not even imagine that, in perceiving the spatiotemporal order of the matters of appearance, we are directly perceiving the spatiotemporal relations that hold of things in themselves because the two spaces and times are radically different. The space and time of things in themselves, if there is one, would have to be an order of internal properties, whereas the space and time of our experience is an order of impressed effects. Consequently, our knowledge of the order in which objects are disposed before or presented to us is nothing more than that: knowledge of the order in which we are affected and not of the order of any internal properties that these objects may be supposed to express independently of all reference to their affecting us: the presentation of a body in intuition contains absolutely nothing that could belong to an object in itself. Instead (it contains) merely the appearance of something and the manner in which we are affected by this thing. (A44/B6i)

304 Conclusions from the Above Concepts Indeed, not only could we not suppose that the space and time of our experience constitute direct perceptions of the space and time in which things in themselves occur, we could not even be justified in thinking that the two correspond to each another. For, even if things in themselves act on us to cause our intuitions, why should we suppose that the order in which we are affected by them at all corresponds to any order defined by their internal properties? In the 'presentation space' of our experience, the matters of appearance are given without any regard to the order of their qualities. Reds occur immediately alongside greys without having to shade off through the spectrum of intermediately ordered shades, hues, and tones. Sounds of quite different pitch and volume occur one right after another without having to be separated by the sounds that intervene on the scale. Why should we suppose, therefore, that the order in which we are affected in any way corresponds to the order of qualitative differences among things in themselves? But even were it the case that we could say something synthetic about things in themselves by means of pure understanding (which, however, is impossible), this could still not be referred to appearances, which do not represent things in themselves. I am therefore, in this latter case, only ever able by transcendental reflection to compare my concepts under the conditions of sensibility, and then space and time will be, not determinations of things in themselves, but of appearances. What things in themselves may be I do not know and do not need to know, since for me a thing can never be otherwise presented than in appearance. (A2/6-7/ 6332-3)

To sum up, the notion that the space and time we experience is a presentational order (that is, an order where the locations of the ordered elements are determined by the manner in which those elements are presented to an observer) establishes two things: that the space and time we experience could not be the space and time in which things in themselves exist (so direct realism about spatiotemporal properties is false), and that we could not even legitimately suppose that the space and time we experience correspond to the space and time in which things in themselves are disposed. iii.

Limits of Kant's Result

More than this cannot be said, however. In particular, it cannot be said that there is no sense whatsoever in which things in themselves could be

The Non-spatiotemporality of Things in Themselves 305 in space or time. They could be, but it would have to be a quality space or (though Kant would never have allowed this on the basis of theses he establishes later in the Analytic) a causality space. We must conclude, therefore, that the Metaphysical Expositions are ultimately no more successful at establishing Kant's non-spatiotemporality thesis than are the Transcendental. They go a good way towards doing so, by establishing at least that things in themselves could not be in the sort of space and time we experience (presentation space and time), but they do not establish the strong thesis that space and time are 'nothing' outside of our experience.22 Someone desperate to prove Kant right at all costs might object to this conclusion by stating that perhaps by 'space' Kant just means 'presentation space,' so that, if things in themselves are in some other kind of 'space/ and this space is as radically different from presentation space as I have described, then Kant can be proven wrong only by legislating a wider sense for the term 'space' than he himself intended.23 Verbal legislation can cut both ways, however. The only proper approach to this issue is to set aside the matter of how to apply labels and consider just how far a 'space' or 'time' in which things in themselves might be supposed to exist might resemble the spatiotemporal forms of our intuition. If the answer is 'not at all,' then Kant's strong conclusion that space and time would have to be 'nothing' apart from our intuition is warranted. But, if there are respects in which an order, in which things in themselves might be supposed to exist, might resemble the spatiotemporal forms of our intuition, then to that extent Kant's conclusion must be mitigated. On this score, a great deal has to be conceded to anyone wishing to advance the view that things in themselves could be arrayed in a spacelike or time-like order. Such a space or time would (likely)24 have to be a quality space, where the locations of things in themselves are determined by internal properties that shade off into one another in various dimensions. Admittedly, a quality space can be very different from a presentation space. In quality space, position is determined by possessed properties, not by order of occurrence to an observer. In principle, many different things may have the same property, and the same thing may have many different properties or may change its properties in an abrupt or discontinuous fashion. Were the order of things in themselves just an order determined by variations in properties, then, given these facts, two or more different things could be in the same 'place' at the same 'time' or

306 Conclusions from the Above Concepts different states of the same thing could exist as the same 'time' (i.e., different things or different states of things could share some of the same properties), or the same thing could be in different, disconnected places at the same time (i.e., have different properties simultaneously), or things could abruptly disappear from one place or time and appear at another without passing over intervening locations (i.e., without shading through the intermediate stages of property variation). An order in which such relations are permitted could well be said to fall too wide of what we ordinarily think of as position in 'space' or 'time.' But a quality space need not necessarily exhibit these odd features. It can more closely resemble a presentation space if the postulated properties of things in themselves are supposed to obey certain laws: that no one 'spatial' property can be shared by two different things or parts of things, and no one 'temporal' property by any two different states of the same thing; that no one thing could have a discontinuous set of properties; that no thing or part of a thing or state of a thing could change its properties in a discontinuous fashion; that any change that leads one thing to acquire the properties of another must 'displace' the other to different local properties, and so on. The effects of these suppositions would be just the same as if we were to postulate that, in the realm of experience, no two things or parts of things have the same colour or have parts that possess a discontinuous collection of colours, and that everything changes its colour in a continuous fashion, displacing the colours of other things when it comes time to acquire theirs. Under such circumstances there would be a real sense in which appearances not merely have an order of colour properties but are actually positioned in that order. Then colour-space would, in effect, be experienced space, and colour properties would be experienced locations. Perceivers would know, when encountering an object of a certain colour, that motions initiated in particular directions would trace 'paths' to particular other colours. More important, if they understood the colour solid, they could know in advance - a priori, as it were - that certain colours would be experienced in certain regions, even if no one had ever been there before,25 and they could know in advance of any particular motion just what colour changes in the visual field would be brought about by that motion, just from deduction from the present experience and the nature of the planned motion, without any reference to memory or prior accounts of the destination. They could even make judgments of distance based on colour properties (though, admittedly, distances would only be well defined along certain axes).

The Non-spatiotemporality of Things in Themselves 307 Similarly, were things in themselves possessed of local properties, were the distribution and variation of these properties governed by the sort of principles just mentioned, and were the properties to vary in just two or three dimensions, then there would be a real sense in which things in themselves would have determinate location in a 'spatial' order. Nor could Kant legitimately deny that this could be the case. If things in themselves exist, then they may exist with certain properties, and if they exist with certain properties, then these properties may undergo continuous or law-like transformations or be distributed in a continuous or law-like fashion. The only difference between the sense in which things in themselves would be in space and time, and the sense in which objects of experience are in space and time, would be that the latter do not have their location in virtue of the possession of internal properties, but rather in virtue of their manner of presentation in the experience of a subject. Indeed, we could even go so far as to speculate that the way things in themselves are ordered in their quality space might correspond to the way matters of appearance are ordered in intuition, in the sense that the neighbourhood relations any given thing in itself has to its surroundings might turn out to correspond to the neighbourhood relations its appearance has to the appearances of its surroundings. But this could never be more than sheer speculation (speculation, moreover, that involves the supposition of a one-to-one correspondence between things in themselves and appearances). For all we know, things in themselves could have countless sets of n-dimensional scalable qualities (analogous to our colours, sounds, temperatures), each of which is law-like in the fashion described above, and each of which, therefore, could be used to locate the set of things in themselves in a different quality space, no one of which corresponds to any other (just as there is no correspondence between the colour of an object of appearance and its sound, or its sound and its temperature, even though colour, sound, and temperature are all scalable qualities that could be taken to define as many different kinds of 'space'). Why should we suppose that any one of them should correspond to the order in which we are affected? There is no reason, therefore, to deny that things in themselves could be in space or time. But there is every reason to claim that we do not, in fact, directly perceive this space or time (since in perceiving the locations of the matters of appearance we are not perceiving any discernible properties they might possess, and a direct perception of the locations of things in themselves would have to be a perception of some scalable

308 Conclusions from the Above Concepts quality), and that we can have no justification for claiming that the space or time we experience might correspond to them. iv.

Summary and Conclusions

Thus, while the Metaphysical Expositions are no more able to establish Kant's strong non-spatiotemporality thesis than are the Transcendental Expositions, they are able to establish a mitigated non-spatiotemporality thesis that complements, and in some ways strengthens, the mitigated thesis entailed by the Transcendental Expositions. The Transcendental Expositions establish that, even were things in themselves in space or time, they could not possibly determine the spatiotemporal features of our intuition; the Metaphysical Expositions establish that, even were things in themselves in space or time, their spatiotemporal features could not be the spatiotemporal forms of our intuition; both establish that, even were things in themselves in space or time, we could not have any warrant to suppose that their spatiotemporal features would correspond to the spatiotemporal features of our experience. The Transcendental Expositions are not able to rule out that experienced space and time may turn out (by accident) to be identical to a space and time in which things in themselves exist,26 but the Metaphysical Expositions make up for this lack by demonstrating that what it would have to mean for things in themselves to be in space or time could not be anything like what it means for the matters of experience to be in space or time. For things in themselves to be in space or time would have to be for them to possess a set of scalable properties, varying in accord with the laws described above. But our experience of space and time is not the experience of any property in the matters of appearance, and so could not possibly be taken to be a direct perception of any property of things in themselves. The order in which a matter occurs in intuition may perhaps correspond to the order in which some thing in itself occurs in a quality space, but it could not be a direct perception of it. The Metaphysical Expositions, for their part, are not able to rule out the possibility that the spatiotemporal forms of our intuition might be determined by these possibly corresponding features of things in themselves (though they can establish that we could never have any justification for making this assumption). But the Transcendental Expositions make up for this lack by demonstrating that, even if there were a correspondence, those general or global spatiotemporal features of our experience described by the propositions of geometry and axioms of time

The Non-spatiotemporality of Things in Themselves 309 could not be determined by any corresponding features there may be in things in themselves. Taken together, the Metaphysical and Transcendental Expositions establish that neither a causal-realist nor a direct-realist account of the perception of spatiotemporal properties of things in themselves can be affirmed. They establish that, if things in themselves are in space or time, it is in a radically different sense from that in which the matters of appearance are in space and time, and that, even then, the spatiotemporal features of things in themselves could not be supposed to determine the spatiotemporal features of our intuitions. But this is not all that Kant wanted to claim. He wanted to assert that things in themselves are just not in space or time in any sense. That is more than his arguments are able to support.27 Whether it is also more than he needs to say is a question that can be answered only after a more extensive survey of the argument of the Critique than I am able to undertake in this book.

10 The Unknowability Thesis and the Problem of Affection

We have therefore wanted to say that all our intuition is nothing but the representation of appearances, that the things that we intuit are not in themselves that which we intuit them as being, nor are their relations constituted in themselves as they appear to us, and that, if we abstract from our subject or just from the subjective constitution of the senses generally, all the constitution, all relations of objects in space and time, and even space and time themselves would disappear. As appearances they cannot exist in themselves, but only in us. What there may be concerning a relation with objects in themselves and apart from all this receptivity of our sensitivity remains completely unknown to us. We know nothing but our manner of perceiving them, which is peculiar to us, and which need not necessarily be attributed to every being, though certainly to every human being. With this alone do we have anything to do.... Could we bring this our intuition to the highest grade of clarity, we would not come any closer to the constitution of objects in themselves. For we would at best still completely cognize only our manner of intuition, that is, our sensitivity, and would do so only under the conditions of space and time that originally attach to the subject. What objects in themselves might be would never be known, even through the most clarified cognition of their appearances, which are alone what is given to us. (A42-37359-60) i.

Unknowability

Kant, following in a long line of 'secondary-quality idealists/ did not believe that our sensations are Aristotelian substantial forms or real qualities that are directly perceived in things as they are in themselves. This is something he took to be so obvious he never even bothered to

The Unknowability Thesis 311 argue for it.1 He simply asserted it in passages such as ID, §4; A28; 644; A29/B45; and Prolegomena, §9. Now that we have seen him complement this secondary-quality idealism with the assertion that the spatiotemporal form of our intuitions is not a direct perception of anything that can be supposed to inhere in things in themselves, it should not be surprising to see him close the Transcendental Aesthetic by concluding that our intuitions tell us nothing about things as they are in themselves but only about the manner in which they appear to us, as he does in the passage cited above. But, in drawing this conclusion, Kant seems to have completely cut the ground out from under himself. If we cannot know anything by means of intuition about things in themselves, how can we say that they could not be in space or time, or that space and time could not be things in themselves in their own right? It will not do to try to evade this conclusion by claiming that perhaps this knowledge may come directly from the higher cognitive faculties rather than through intuition - not, at any rate, if we accept Kant's major conclusion in the Transcendental Analytic, that all our knowledge is restricted to the objects of a possible sensory experience. And even if we do not accept this latter conclusion, Kant does, so is there not at least an inconsistency in his own argument here? This problem does not simply affect Kant's strong conclusion about the non-spatiotemporality of things in themselves, but the mitigated conclusion that I elucidated in chapter 9, above. The mitigated conclusion claims that things in themselves do not determine the forms of our intuition, and it claims that, even if things in themselves were ordered in space or time, it would have to be in a radically different sense. But, if things in themselves turn out to be unknowable, how could such claims be possible? The answer to this question is that Kant's claims, at least for the mitigated conclusion and for the thesis that space and time could not be things in themselves in their own right, are merely analytic consequences of his substantive claims about the nature of space and time as they appear to us. They do not presuppose any knowledge of things in themselves, but they do combine substantive claims about space and time as they appear with analyses of the concept of a thing in itself to demonstrate an incompatibility. In detail, the incompatibility arises as follows: i Kant's claim that space and time could not be things in themselves in their own right rests on his claims that space and time are infinitely

312 Conclusions from the Above Concepts divisible and that it is impossible for there to be a composite thing that is not composed of anything. The former is a principle of geometry that Kant assumes to be demonstrably true of the space and time of our experience, whereas the latter is an instance of a reflection on the priority relations of parts and wholes in intuited and created things: where a composite whole is given to a subject, the whole can precede the parts in the subject's awareness (since the parts need only be indistinctly given), but where a composite whole is created, its parts must be created along with the whole. The first half of this reflection follows from an observation on the limited discriminative powers of our sense organs, whereas the second is an instance of the principle of contradiction: if a composite thing were created without any distinct parts it would not be composite, but simple. Now, it follows by analysis of the concept of a thing in itself that, were the concept of the composite (problematically) applied to it, it would have to be in the second sense (of creation), not the first (of intuition), for a thing in itself just is a thing considered apart from all reference to how it might be given to a subject. If, in addition, the concept of being a space or a time were also (problematically) applied to that of a thing in itself, then the thing in itself would have to be thought as infinitely divisible. This would mean that any given part of the thing would have to be given as having yet further parts, so that there could be no simple parts. But this is tantamount to saying that the composite would not be composed of anything. Since applying our experientially given concepts of the composite and of space and time to the concept of a thing in itself generates a contradiction, one or the other must be removed. But the first concept cannot be removed without removing the second pair as well (since space and time are composite). Accordingly, space and time cannot be things in themselves. But this claim follows, not because of anything we know about things in themselves (beyond their mere definition), but rather from an inconsistency that emerges when our experientially given concepts are thought together with the concept of a thing in itself. 2 The mitigated conclusion can be broken down into three subsidiary theses: (i) We cannot know whether things in themselves might exist in a 'quality' space or time corresponding to the 'presentation' space and time of our experience. This thesis makes no knowledge claims about the nature of things in themselves one way or the other. (ii) We can know that any properties or relations things in themselves may have do not determine the spatiotemporal form of our

The Unknowability Thesis 313 intuition, in so far as that form is described by the principles of geometry and axioms of time. This thesis follows from a claim about space and time as we know them: the claim, namely, that our knowledge of the principles of geometry and axioms of time is synthetic, yet a priori. This claim entails that our knowledge of space and time cannot be determined by anything about the objects that affect us. But if no object distinct from ourselves could determine the spatiotemporal features of our experience, then it follows as an analytic consequence that things as they are in themselves could not do this either. (iii) We can know that, if things in themselves exist in space or time, they do so in a radically different sense from that in which the matters of appearance exist in space and time. This thesis follows on the assumption that the space and time of our experience are a 'presentation' space and time, where the location of matters is determined by the order in which they are given to a subject. But things in themselves are by definition things considered as they are apart from all relation to anything else, and hence apart from all reference to how they appear to a subject. It is analytic, therefore, that things in themselves would have to be located in some other kind of space and time than a presentation space and time. Thus, Kant's claims about the non-spatiotemporality of things in themselves do not violate his unknowability thesis because no substantive claims about things in themselves are involved in establishing their non-spatiotemporality. Instead, their non-spatiotemporality follows from premises describing space and time as we experience them premises that establish that these concepts contain something incompatible with the notion that their objects might exist apart from all reference to a cognizing subject, and so as they are in themselves. Guyer has put this point well by observing that Kant never uses the term 'thing in itself in the earlier portions of the Aesthetic. When the term is introduced, it is to describe a distinction that has only been established through the preceding argument - an argument that in no way presupposes it. Kant does not begin by introducing the concept of a thing in itself as that of a thing about which nothing whatever can be known and then violate such a conception by going on to claim that he does know that things in themselves are not spatial and temporal even if he does not know anything else about them.

314 Conclusions from the Above Concepts Instead, what he does is offer a number of arguments that things - not initially designated by any special concept - cannot really be spatial and temporal and only then introduce a specific concept, that of a thing in itself, meaning thereby a thing about which nothing can be known by intuitions of space and time and by the application of pure and empirical concepts of the understanding to such intuitions. Since such a concept is introduced only as a result of the prior proof that things in themselves are not really spatial and temporal, it can hardly be intended to undermine that previous result.2

ii.

Affection

This would all be well and good if Kant did not make any other claims about things in themselves in the course of the Aesthetic. But this is not the case. There are, notoriously, at least two other places where Kant appears to be inextricably involved in making a knowledge claim about things in themselves: in his definition of sensation, and in his account of the form of intuition as grounded in the 'constitution of the subject.' In the remainder of this chapter, I consider just the first of these claims. The problems posed by the second claim are taken up in chapter 11, below. Kant defines sensation as that in our experience that results from our being affected by objects (Ai9-2O/B34). This definition makes no explicit reference to things in themselves. But how else is it to be understood? What could the 'affecting objects' responsible for our sensations be if they are not things in themselves? The only other candidate the Kantian ontology would seem to provide is appearance. But, regardless of whether one takes appearances to be mental representations, logical constructs on mental representations, or the intentional objects of certain acts of mind induced in us as a result of the cognitive process, this much is clear: appearances are objects as they come to be known by us through the process of cognition, and so as a result of our being affected. How could that which emerges only through the process of cognition be the very thing that does the affecting or determines the form of what is thought through being affected? If we remain in any doubt about whether things in themselves are what Kant takes affecting objects to be, he is occasionally willing to make it explicit for us. Thus, at Prolegomena, §i3n. 2 (Ak, IV 289), he declares: Things, considered as objects of our senses existing outside of us, are given to us, but it is just that we know nothing of what they may be in themselves; rather, we

The Unknowability Thesis 315 know only their appearances, that is, the representations that they bring about in us insofar as they affect our senses, (my italics)

This is seconded by Prolegomena, §32 (Ak, IV 314-15): And in fact when we rightly consider the objects of the senses as mere appearances, we admit thereby that a thing in itself underlies them, though we do not know this thing as it is in itself constituted, but know only its appearance, that is, the manner in which our senses are affected by this unknown something, (my italics)3

Here we really do seem to be in the predicament of not being able to enter the Kantian philosophy without the concept of thing in itself and unable to stay there with that concept. We are unable to enter without it because, even though that is not what affecting objects are called, that is in the end what they turn out to be. But then, when we trace through the argument of the Aesthetic to its ultimate conclusion in the unknowability thesis of A42-3 7659-60, we discover that we were never supposed to be able to make knowledge claims about things in themselves.4 It will not do to try to evade this result by claiming that, in the notion of an affecting object, things in themselves are thought merely problematically (as 'something = x' or noumena in the negative sense, as Kant likes to put it), and so are merely pointed to or designated without making any knowledge claims about what they are or how they may be described. In the notion of an affecting object, the thing in itself is not merely an empty concept about which no knowledge claim is made; something very specific is claimed about it: that it exists outside of the subject and causes the sensation that the mind experiences. And in this claim a great deal is said about things in themselves in apparent violation of the major conclusions of the Critique. If 'outside of the subject' means 'outside in space/ then things in themselves are ascribed a location in space - something that, even if it is not as inherently impossible as Kant would like to think, is still beyond anything we can claim to know. And even if 'outside of the subject' means simply 'independent of the subject/ then a claim is still being made about the absence of a certain kind of reciprocal causal influence between the subject and the affecting object (that the latter would continue to exist in the absence of the former), or at the very least about the inherence of the properties of the affecting object in a substance distinct from that of the subject. What is more, the very notion of an affecting object carries with it the thought that this object is causally related to sensations. But, according to Kant, the categories of

316 Conclusions from the Above Concepts reciprocity, substance, and causality can no more be known of things in themselves than can the forms of space and time ^238-44/6297-302). Faced with this result, it is natural to wonder whether Kant actually needed to refer to affection, or whether, despite what he says, the critical philosophy could have been quite well formulated without any reference to affecting objects.5 There are three main reasons why eliminating all reference to affecting objects might be thought to be untenable for Kant: 1 Objectivity of reference. It might be thought that some reference to affecting objects is necessary in order to preserve the objectivity of our knowledge. Were our talk of appearances not grounded on something outside of us, that acts upon us independently of our wills, the distinction between reality and fantasy would collapse, and Kant's transcendental idealism would be shown up as identical with the caricatured view of Berkeley's idealism that was current in Kant's day.6 2 Manifest idealism. Connected with the previous issue is the notion that Kant needs some reference to affecting objects in order to stave off the charge that the Critique of Pure Reason denies the existence of extramental objects corresponding to our representations and holds that the only objects that exist are appearances, that reduce either to collections of mental representations or to the imagined or intended referents of mental representations, neither of which has any existence except through the thought of the subject. Kant was himself quite concerned to deny that his transcendental 'or more properly critical' idealism did do this, though with what right has been a topic of ongoing controversy. 3 The notion of a priori knowledge. Kant's remarks on affection by things in themselves ground his claims that sensations are given only a posteriori, whereas spatiotemporal form is a priori (i.e., 'in us' independently of our being affected by objects). These remarks cannot simply be abandoned without threatening one of the most central tenets of his thought: his distinction between a priori and a posteriori knowledge. Let us consider each of these reasons for postulating affecting objects in turn. a. The Objectivity of Reference Kant seems to have thought that he had to invoke affection by things in

The Unknowability Thesis 317 themselves in order to distance himself from a pernicious idealism that 'reduces everything to illusion.' This is the case with the two blatant references to affection by things in themselves cited above. The first of these passages occurs in the context of a discussion of 'manifest idealism/ which consists in the thesis that none but thinking beings and their ideas exist, without there being any other objects corresponding to these ideas. The second occurs in the context of a discussion of the traditional view that knowledge that is given through the senses is merely illusory. In both passages, Kant is concerned to distinguish his own position from these views, and he does so, in part, by claiming that the Critique postulates the existence of things in themselves that affect us so as to cause our sensations. However, Kant did not need to go to this extreme. The Critique has the resources to provide for the objectivity of reference without having to invoke the causes of our sensations, whatever they might be.7 The a priori framework of spatiotemporal forms and categorical synthesis places constraints on the kinds of objects or appearances that can be cognized on the basis of the sensations that are given to us. In doing so, it provides a criterion for distinguishing between reality and illusion: the illusory is that in our experience that cannot be successfully or completely brought into conformity with this a priori framework. (Thus dreams and fantasies, for instance, can be identified as illusory on the ground that they do not cohere with the rest of our experiences, that is, because the transition between dreaming and waking, or fantasizing and perceiving, violates established causal laws or contradicts other experiences.) Indeed, in Kant's eyes, the a priori framework not only defines (empirical) reality within the sphere of any given person's experiences but can be applied intersubjectively as well. It allows me, for instance, to predict how a solid object I am perceiving would look to, and be described by, an observer viewing it from another perspective, so that the reports of others can be identified as true or false. In cases of disagreement between different perceivers, there will always be some fact of the matter to be determined (even if this fact may not always be determinable from the available evidence). Either one construction upon the available, empirically given data will accord better with the a priori forms of experience, or one interpretation in accord with the a priori forms of experience will more closely accommodate the sum of the available data, or at least the question will be shown to be undecidable, given the currently available data, and the disputants will be shown that they both must withhold assent on either side of the question.

318 Conclusions from the Above Concepts Despite the excessive claims of Ak, IV 289 and 314-15, Kant is explicit in articulating this view: The difference between truth and dreaming is not made out through reference to the characteristics of the representations that are referred to objects, for they are the same in both cases, but by their connection according to those rules that determine the connection of the representations in the concept of an object. (Ak, IV 290) When ... we connect our sense intuitions (whatever they may contain) in space and in time, according to rules of the coherence of all cognition in one experience, illusion or truth will arise according as we are negligent or careful. It has merely to do with the use of sensuous representations in the understanding and not of their origin. (Ak, IV 291)

See also Ak, IV 374-5, where Kant employs the observation that he has provided for a priori forms of thought that can determine truth, whereas Berkeley did not do so, and so reduced everything to illusion.8 Of course, it is a question whether the a priori framework Kant provides is strong enough to be able in principle to resolve all disputes about how the appearances are to be constituted from our sensations, or whether some issues might remain radically underdetermined, even after an exhaustive investigation of all the empirically obtainable data.9 Not having the space to prove it here, I will simply make the bold claim that Kant imagined himself to have good grounds for being able to provide for a fact of the matter, not only in cases of everyday perception of solid, medium-sized objects, but even in such comparatively sophisticated cases as whether the planets make retrograde motions as they revolve.10 As for the other cases: even here the outcome would not be that anyone is free to believe what they will, but that all parties to the dispute must withhold assent, and the issue must be relegated to the sphere of the unknowable.11 b. 'Manifest' Idealism Kant's rejections of any attempt to equate his position with Berkeleyan idealism are numerous and emphatic.12 But they are not always to the point. In so far as they claim that Berkeley reduced everything to illusion, they invoke a caricature of Berkeley's philosophy that, while very popular in Kant's day, is none the less completely unjustified. As Berkeley was

The Unknowability Thesis 319 at pains to point out (over, say, Principles, 26 and 28-33)tne ^act tnat socalled material things are merely collections of ideas in us in no way prevents us from still going on to draw a distinction between reality and illusion. It makes all the difference, for Berkeley, where the ideas come from: whether we create them at whim in imagination, or whether they are imposed on us in accord with certain laws. (The fact that God does the imposition and sets and follows the laws is a further, and quite irrelevant detail. However the laws are grounded, the distinction between reality and illusion is already established by the distinction between ideas that do, and those that do not, have their cause in us.) In so far as Kant claims that the Critique provides for a distinction between reality and illusion by taking space, time, and the categories to be a priori forms of thought, constraining the kinds of objects that may be cognized on the basis of what is given in the sensory manifold, he does indicate a real point of difference from Berkeley's idealism. For Berkeley, there are no a priori forms of thought. But, from this, it does not follow that Berkeley 'reduced everything to illusion': a conclusion like that requires examining Berkeley's own way of drawing the distinction between reality and illusion and demonstrating that it cannot succeed, not simply proposing an alternative. Kant sometimes takes Berkeley's idealism to consist in something other than just the caricature of reducing everything to illusion, however. At Prolegomena, §i3n. 2; 669-71; and 6274, it is at least implicit that Berkeley's idealism consists in affirming that there are none but thinking beings and their ideas, and that no external objects exist corresponding to these ideas. In so far, however, as Kant's answer to the charge of Berkeleyanism consists merely in pointing out that the Critique draws the distinction between reality and illusion by reference to a priori forms constraining the kinds of objects that can be cognized on the basis of what is given in sensory experience, he hardly distances himself from this sort of idealism. The only sorts of objects that are provided for on this account are the objects that come to be known through the cognitive process. A mere appeal to a priori forms does not entail anything about whether the objects thought in accord with these forms must correspond to anything that exists independently of the cognitive process. But Berkeley, too, supposes that objects come to be known through the cognitive process, and that everything does not reduce to illusion. It might be objected that Kant none the less does take his appearances to correspond to things in themselves, whereas Berkeley's objects reduce

320 Conclusions from the Above Concepts to collections of currently perceived ideas, filled out and further amplified by being associated with certain other ideas, with which the given ideas have been commonly observed to be conjoined in the past. But Berkeley's objects correspond to things in themselves, too. It is just that these things are not material objects, but spirits that act on us to produce our ideas of the objects we perceive. Thus, certain of our ideas refer to other minds like ourselves, of which they are taken to be 'effects or concomitant signs' (Principles, 145), and others refer to an order of nature, instituted in accord with inviolable laws, that constitute, in effect, a series of messages from a divine spirit intended to inform us about the future course of our ideas of reality (New Theory of Vision, 147). It could hardly be objected that the things in themselves to which Kant's appearances correspond are material rather than spiritual. To be material just means to be in space, and Kant denies that things in themselves are spatial. (In so far as there is any difference between Kant and Berkeley on this score, it comes, not from anything Kant himself intended to say, but rather from what I have observed in chapter 9: that Kant is, in fact, unable to establish a strong sense of the non-spatiotemporality of things in themselves, so that there remains some sense in which things in themselves may be spatial [they may have qualities that are so distributed that they serve to individuate positions and that are, moreover, such that the order of things in themselves in their position space corresponds to the order of corresponding appearances in the presentation space of our experience].) If there is a difference between Berkeley and Kant here, it is not one that has to do with the difference between realism and idealism (both Berkeley and Kant were realists to the extent that they supposed that something outside of us corresponds to the objects that appear to us through experience), but with the kind of real objects that are affirmed to exist. Berkeley takes the real objects to be the minds of other human beings and the mind of God - in a word, he takes all transcendentally real objects to be thinking beings. Kant is quite unwilling to affirm this. For Kant, thought and its modes have to do only with the appearance of ourselves through inner sense ^36-8/654-5) and can no more be dogmatically affirmed of things in themselves than can any other predicate. Indeed, according to the B refutation of idealism, the representation of a thinking being is possible only through the representation of objects in space, and, since the latter are mere appearances, the former cannot claim to be anything more. Thus, Kant is more sceptical than Berkeley about the ultimate status of things in themselves. Whereas for Berkeley

The Unknowability Thesis 321 these are all minds, for Kant it is by no means clear that they all think, or even what it might mean for any of them to think. In so far as a world of things in themselves could be speculatively modelled in any way at all (something that Kant would have resisted doing), a neo-Lebnizian picture of aspatial monads exercising physical forces is no less an option than a Berkeleyan one of minds apperceiving ideas. In this sense, Kant's transcendental idealism can be said to allow for the possibility of nonspiritual things in themselves, whereas Berkeley's idealism is also a spiritual realism. This point of contrast with Berkeley rests on the supposition that it is at least possible that things in themselves, be they spiritual or nonspiritual, might correspond to appearances (though it need not be claimed that they can be known to so correspond or that anything more can be known about them). As far as Kant is concerned, this is a thought that involves no contradiction ^254/6310) and cannot, therefore, be supposed to have been ruled out by the Critique, however much the Critique might deny any knowledge of objects satisfying this thought. Indeed, not only is the thought of a (possibly non-thinking) thing in itself logically possible, it is, as far as Kant is concerned, implied by the very concept of an appearance, which carries with it the thought of some thing of which it is the appearance.13 Moreover, the intellectual notion of a thing in itself, though it may have no other content beyond merely serving to designate that which lies beyond the bounds of sense, is none the less necessary in order to define those bounds.14 But for Kant thus to invoke the notion that our appearances correspond to things in themselves is not the same thing as for him to suppose that these things are the causes of our appearances. The former claim merely asserts that it is conceivable (perhaps even necessarily conceivable) that there should be things in themselves, but it does not say anything about what they are. The latter claim, however, dogmatically affirms not merely conceivability, but knowledge, and knowledge, moreover, of a specific fact about things in themselves: that they are causes of the a posteriori components of our experiences. Only the former claim is necessary for Kant to establish that his transcendental idealism, unlike Berkeley's idealism, does not rule out the possibility that there may be unthinking things corresponding to the objects of our experience and existing independently of all reference to us.15 Thus, Kant's opposition to Berkeleyan idealism no more requires a reference to affecting objects than does his claim to be able to distinguish between reality and illusion within the realm of appearance.

322 Conclusions from the Above Concepts c. The A Priori/A Posteriori Distinction It would be premature to dismiss Kant's references to affecting objects as a mere slip of the pen, however. Besides the issues of realism and idealism, there is another context in which affecting objects figure in Kant's work: the definition of sensation. The situation here is particularly delicate because, in addition to describing sensations as effects of objects on us, Kant describes them as the properly empirical element in our experience, and as that which marks the distinction between an experience that is a posteriori and one that is a priori (A42/B6o, Ai67/B2o8-9). And the two latter descriptions are not easily separable from the former. The a priori, Kant assures us, can be distinguished by the criteria of necessity and strict universality (63-4). But why should these be taken as criteria of a priori as opposed to a posteriori origin? Because, Kant tells us, the a posteriori just is that which results from the manner in which we are affected by an external, independently existing object.16 Since the object exists independently of us, it has its own nature, and its effects, in so far as they are due to this nature, are precisely that which cannot be anticipated in advance of experience. They cannot, therefore, be known with necessity or strict universality. But this all appears to make the notion of affection by mind-independent, external objects indispensable. The very concept of a sensation carries with it the thought of an external, mindindependent object of which it is the effect.17 Take away this notion of an affecting object, and the distinction between sensation and the a priori elements of experience is threatened. What is more, in so far as the a priori is the essential element figuring in Kant's claim to be able to avoid a pernicious idealism unable to distinguish between reality and illusion, that charge would have to be resurrected as well. This is the problem of affection in its most virulent form. Before the Kantian philosophy could be supposed to escape this virulent form of the problem of affection, it would have to be shown that Kant could reject or reinterpret his remarks on affection by things in themselves yet still ground his distinction between the a priori and a posteriori elements in experience in some other way. What is needed, in effect, is an 'empirical exposition' of our concepts of sensation - a proof that these concepts are grounded in experience in a very different way than are the categories or the forms of intuition. The perception that Kant never thought to provide such an exposition, preferring instead to define sensation as that in the effect of an object on the representative capacity that is due to the character of the object (Ai9/B34), has historically generated the problem of affection.

The Unknowability Thesis 323 However, as I noted in the Appendix to the Introduction to Part II, above, Kant did write an empirical exposition for our concepts of sensible qualities. This exposition is provided, fittingly enough, only at the end of the 'Conclusions from the Above Concepts/ in the passages where Kant remarks that there are no representations that could be called 'a priori objective/ other than those of space and time and inveighs against any 'subreption'18 of space or time with sensation (A28-9, 644, A29/B45, A36/B52-3). The reasons that he gives for drawing these conclusions are numerous, and many are familiar as traditional themes employed for centuries by sceptics to demonstrate that our senses do not supply us with objectively reliable data, but merely semblances. At A28-9, the reasons are: (i) sensible qualities can vary with changes in the state of the sensory organ, even though the object we are sensing remains the same;19 (ii) they can vary with changes in the surroundings, even though the object remains the same;20 (iii) they vary with changes in the organ used to sense the object, so that the object does not appear in the same way to different sensory organs, even of the same subject;21 (iv) they are linked to feelings of pleasure and pain, that are obviously merely feelings in us and not states of the object;22 and (v) they cannot be anticipated in advance of experience.23 644 adds: (vi) they cannot be the basis for synthetic a priori principles. And A29/B45 adds: (vii) the same object could, for all we know, cause different sensations in different people. Of these reasons, (i), (ii), (iii), and (vii) recapitulate some of the sceptical modes (the fourth, sixth, third, and second, respectively, as described by Sextus).24 The point of all these remarks is the same: that sensations vary with circumstances and are influenced by a range of factors, including who is being affected, what organ is being affected, what state the organ is in, and the time, place, and surrounding environment in which affection takes place. This is to be contrasted with the case of spatiotemporal form, which Kant takes to be a constant and invariant feature of our sensory experiences.25 Note that, for this contrast to be drawn, it is not necessary that any reference be made to affection or to the idea of it being the same object that continues to affect us when we have different sensations. It is enough simply to observe that sensations vary, whereas spatiotemporal form does not. Our intuitions always exhibit matters arrayed in the same sort of space and time, but the matters themselves vary in different intuitions. This by itself is enough to establish that, whereas the spatiotemporal form may be anticipated in advance of the experience, the matters may be known only after the experience has been obtained.26

324 Conclusions from the Above Concepts Most of the other remarks Kant makes are familiar from past philosophy as well. Reason (iv) is a corollary of the heat-pain identification argument employed by Berkeley in the First Dialogue. However it is suited to establish only that sensible qualities cannot have objective reference and not the more fundamental point that they are given a posteriori rather than a priori (though the former task, and not the latter, is Kant's primary purpose in the text). But (v) can be employed to both purposes. Both Locke and Hume employed (v) as their crucial reasons for claiming that sensible qualities are a posteriori. In Enquiry II, and Treatise, 1.1.1 (p. 5), Hume offered two reasons why our concepts of sensible qualities presuppose specific effects on specific sense organs: (i) people whose sense organs have never been affected in a specific way can form no concept of certain sensations (one who has not tasted pineapple, for example, cannot conceive of the pineapple gustatory quality), and (2) people who lack specific sense organs are unable to conceive of any of a whole circle of sensible qualities (the blind can form no concepts of colour, for example). Locke gave the same two arguments at Essay, 2.2.3 and 2.1.6 (cf. 3.4.11), right down to the example of the taste of pineapple, further embellishing the point about the inconceivability of colours for the blind with the story, noted earlier, of a blind man who, after long investigation of others' reports of colour phenomena, declared that the colour red was like the sound of a trumpet. The moral of both cases is that our concepts of sensible qualities presuppose, not just activity of the sensory faculty, but specific types of effects on specific sensory organs, in the absence of which the concepts simply cannot be formed. Even the most detailed verbal communication with others who have had the requisite experiences is inadequate to supply a concept to those who have not had the experience, so that, in its absence, they can only substitute other concepts from their own experience that they take to be analogous.27 Sensible-quality concepts could not, therefore, be anticipated in advance of experience (hence, a priori). But Kant claims (remark [vi]) that the case is very different with space and time. Since they feature in the same way in all of our experiences, even the blind may apply them a priori to the visual experiences of the sighted.28 Here again there is no reference to affection. It is the features of the elements of our experience, specifically whether they can be anticipated in advance of experience or known only through experience that establish the distinction between a priori and a posteriori. The 'empirical exposition' of our concepts of sensible qualities that is to be found in the Aesthetic offers a number of reasons for

The Unknowability Thesis 325 concluding that sensible qualities cannot be anticipated in advance of experience. I conclude, therefore, that Kant did not need to refer to affection. Not only can he provide for objective reference without it, he can even ground the distinction between the a priori and the a posteriori without it. Regardless of what it may actually be that brings the a posteriori items of experience about, they are obviously dependent on a set of specific circumstances or occasions. In this respect, they are to be distinguished from our concepts of space and time, which are the objects of knowledge claims that can be affirmed to hold of all possible experience, future as well as present and past. d. Summary Though Kant on occasion describes things in themselves as the objects that cause our sensations, there is nothing in the critical theory that forces him to do so. He can draw the distinction between the a priori and the a posteriori independently of reference to affection. Having drawn this distinction, he can provide for the possibility of distinguishing reality from illusion by reference to collections of thoughts that can or cannot be successfully or completely synthesized under the a priori forms of our experience. And, while this position makes no reference to things in themselves, Kant can point out that the very notion of an appearance carries with it the thought of something of which it appears, so that things in themselves can at least be thought (indeed, known to actually exist), though nothing more can be known of them. In particular, it cannot be known that they are exclusively spiritual in nature or that they are the causes of our sensations. Indeed, since all our concepts of thought refer only to ourselves as we appear to ourselves in inner sense, and since, moreover, these concepts involve an essential, if tacit reference to appearances in space, we can conclude that the concept of a thinking being has meaning and intelligibility only with reference to our experience, so that things in themselves can no more be described as spiritual than as extended in space or time. Thus, any system of thought that affirms the transcendent existence of minds or souls, and that reduces all other objects to mere collections of ideas had by minds or souls, can be said to be quite at variance with Kant's transcendental idealism. In saying all of this, however, we do no more than think the necessary existence of (not necessarily spiritual) things in themselves as correlates of appearances. We do not invoke the notion that they are the causes of

326 Conclusions from the Above Concepts appearances. Sensations can be taken to be brute-factually given data, the origin of which cannot be further explained without transcending the bounds of sense. Affection and affecting objects simply do not have to be mentioned. Though Kant initially defines sensation as 'the effect of an object on the representative capacity, so far as we are affected by it' (A19-20/B34), he can be taken to be speaking loosely, and even metaphorically, employing a common and readily understandable picture of relations of affection between external objects, a subject, and this subject's representations to convey the point that, whatever their exact causes may turn out to be, sensations arise relative to the specific circumstances of affection, whereas the forms of intuition are invariant with regard to circumstances, so that propositions describing these forms have universal validity. This initial picture is underwritten, first, by the priority arguments of the Transcendental Expositions, which place a roadblock in the way of inferring that anything specific to the particular circumstances of affection is responsible for our representations of space and time, and, second, by the 'empirical expositions' of A28-3O and 644-5, which remind us that sensible qualities are relative to specific circumstances. However, while transcendent affection (affection by things in themselves) may thus be shown to be an extravagant supposition in no way required by the Kantian theory, there is nothing to prevent Kant from formulating an empirical theory of affection. Faced with a collection of sensations of inner and outer sense that are synthesized into appearances of our inner, mental states, on the one hand, and representations of our own bodies and other bodies outside of them in space, on the other, and noting that there is a constant conjunction between the two, so that certain empirical objects, acting on the empirically given body when it is in a certain state, are regularly conjoined with the appearance of certain sensations in inner sense, we can infer that there is a real (empirical) causal relation between these objects, and that empirical objects, affecting the empirical subject, produce this subject's original experiences. Indeed, there is nothing to prevent us from going a step beyond these facts to postulate that empirical objects are really (though only still empirically) centres of force, and that the effects they bring about on the body of the subject are 'impressions' of a degree of intensity varying in proportion to the strength of the force acting on the surface of the organ, and that the sensations that are originally represented in the subject's cognitive experience correspond to these impressions. This remains, however, a purely empirical account of affection,

The Unknowability Thesis 327 restricted to claiming that objects, as they appear to us in space and time, affect the body, as it appears to us in space and time, and so bring about the physiological intensity values corresponding to the sensations or matters of intuition that figure at the origin of our cognition. Though these affecting objects are, one and all, mere appearances, that have been 'constituted' through the cognitive process, not things in themselves existing independently of it, there is no absurdity in this affection relation, because what empirical affecting objects are supposed to produce is itself merely an appearance - a physiological state in the body of the subject of varying intensity - and so something that is likewise constituted and not something that is paradoxically supposed to exist prior to the affecting object as the material out of which it was itself constituted. The prior given matters out of which both empirically affecting objects and the representation of physiological states of the body are constituted, namely, sensations, are primitive, given data that merely correspond to physiological states and so, derivatively, to the affecting objects taken to cause them, but they are not properly described as the effects of those objects. To inquire after the cause of sensations (as opposed to the physiological intensity values to which they correspond) is to engage in transcendent metaphysics. Unfortunately, transcendent metaphysics is precisely what Kant appears to be engaging in at Ai9-2O/B34, when he defines sensation as the effect of an object on the representative capacity, and in Prolegomena, §§13.2, 32 and 36, when he refers to things in themselves as affecting objects. The first of these passages can perhaps be dismissed as a preliminary definition, offered in common and readily understandable terms because, (a) there is a grain of truth to it (empirical objects do turn out to affect the physiological states of the empirical subject, and 'sensation' can be used loosely to refer to these latter states rather than to the original, a posteriori matters of intuition to which these states correspond, and (b) the theoretical apparatus to explain and justify a precisely correct definition had yet to be developed. But the latter three references cannot be so readily explained away. Even they, however, may not have to be dismissed as mere slips of the pen. Appendix: The Legitimacy of Speculation about Transcendent Affection29 Though Kant's occasional identification of affecting objects with things in themselves is commonly taken to involve an illegitimate application

328 Conclusions from the Above Concepts of the concept of causality to things in themselves, we should consider just why and how far this application is indeed illegitimate. This investigation is especially indicated in the light of the conclusions of chapter 9, above, which demonstrated that the sense in which things in themselves are not in space or time is not as absolute as Kant might have liked. The concept of causality, as it figured in philosophy up to Kant's day, can be considered to involve one or more of the following four elements: 1 Constant conjunction, the claim that the cause is constantly or regularly followed by the effect, and the effect constantly or regularly preceded by the cause. 2 Necessary connection, the claim that the effect could not possibly have occurred without having been preceded by the cause, and that the cause could not possibly occur without being followed by the effect. Whereas a claim of constant conjunction only involves the brute-factual assertion that one type of event has always been observed to be followed by the other, a claim of necessary connection goes beyond this to claim that contrary observations or 'discontinuing experiments' are in principle impossible. Why disconfirmation should be supposed to be impossible is a further question that was not always well or adequately answered. However, one popular answer invoked a third element: 3 Efficacy, the claim that the cause does not merely constantly or regularly or even necessarily precede its effect, but does something special to make its effect happen. Appeals to efficacy can provide an explanation of why the effect is necessitated by the cause, but only if it is also supposed that the efficacious cause (i) is omnipotent or overbearing (an efficacious cause might fail to bring about its effect in adverse circumstances), and (ii) willing (certain kinds of efficacious causes, those supposed to be endowed with an ability to 'deliberate,' might choose not to act even though they have the power to do so). For this reason, efficacy needs to be distinguished from constant conjunction and necessary connection. But even omnipotent, willing, efficacious causes are not the only way to provide for necessary connection, as will be discussed in a moment. Thus, a distinction between efficacy and necessary connection is doubly indicated. 4 Adequacy. The most common (but not the only) way of explicating the notion of efficacy was by appeal to what I will call the 'containment model.' According to this model, a cause is able to 'make' its effect happen because it already contains the effect inside itself, perhaps

The Unknowability Thesis 329 literally or 'formally/ perhaps in some non-literal or 'eminent' sense. The cause makes its effect happen, by, to put it crudely, spewing it out. The containment model underwrites the further notion that a cause must be adequate to produce its effect. 'Adequacy' is cashed out in terms of the notion that the cause must contain, literally or 'eminently/ at least as much 'reality' as its effect. The notion that a cause must be 'adequate' to produce its effect licenses causal reasoning that transcends the bounds of sense. For, once adequacy is granted, it is possible to infer what a cause must contain merely by inspecting its effect. The paradigm example of an appeal to adequacy to transcend the bounds of sense is to be found in the argument from design for the existence of God, where it is claimed, not only that every effect must have some cause (i.e., be preceded by some other event upon which it regularly follows), but that this cause must be adequate to produce everything that is contained in the effect. In the case of the design argument, this adequacy is taken to entail being powerful enough to assemble the chaotic mass of the universe into a system, and intelligent enough to make that system self-perpetuating and able to sustain life. A more notorious and literal appeal to adequacy and the containment model is to be found in Descartes, who supposed that the cause of an idea must actually contain, either formally or eminently, everything that is represented in the idea, and used this as a ground for concluding that everything that is contained in the idea of God must be contained in the cause of that idea. In contrast, a model of causality that consists only of constant conjunction licenses no such inferences. Since, on this model, the cause is simply what regularly goes first, and there are no a priori constraints on what can possibly precede what in our experience, there can be no inference made from the effect to the cause except through reference to past experience. The cause has to have actually been experienced before its existence can be inferred, so that effects that are experienced for the first time, or that are experienced to follow in a completely haphazard and arbitrary fashion, without being preceded by any particular type of event, cannot be said to have causes. The paradigm for this model of causality was provided by Hume. Efficacious and necessitating causes are like constantly conjoined causes in this respect. Except where the efficacious cause is supposed to also be adequate, there can be no telling, apart from experience, what it will produce. Indeed, since efficacious causes can fail of their effects,

330 Conclusions from the Above Concepts even experience can provide only a rough and imprecise guide to identifying them. And the mere thought that a cause is necessarily connected with its effect warrants no inferences about what it is like unless, again, adequacy is invoked by supposing that the cause must somehow 'contain' at least as much 'reality' as is to be found in the effect. Though he proposes to answer Hume, Kant's causes are no more efficacious or adequate than Hume's. As for Hume, so for Kant, the cause is simply that which regularly happens first, not that which makes the effect happen. It is just that Kant thinks he can give a technical reason for taking this succession to be necessary rather than a mere generalization from experience. Kant's 'answer' to Hume consists in doing no more than providing for this necessity in the succession of effect upon cause, not in going any further beyond Hume's critique to provide for any sense of efficacy or adequacy in the cause. The 'necessity' Kant claims to demonstrate of the concept of cause is merely necessity of the succession of the effect after the cause, not efficacy, which would imply that the effect succeeds upon the cause because the cause made it do so (Kant does not provide for anything that makes the effect happen, he just provides an argument that it must happen), and certainly not adequacy, which would allow us to infer the nature of the cause from what is given in the effect. Thus, for Kant, experience is still necessary to tell us what the cause is (because, in principle, anything can still precede anything else, there being no notion that the cause produces its effect or must be adequate to do so), even though we might be assured a priori that there must be some cause for any given occurrence (Ay66 76794). In this respect, far from answering Hume, Kant backs up Hume's major contention (that causal reasoning cannot be used to transcend the bounds of sense and infer the existence of causes that go beyond anything we have ever experienced). There is nothing that licenses an inference to the nature of the cause from the nature of the effect independently of experience, or at least independently of analogy with past experience. From this, it would appear that for Kant there can be no legitimate inference to things in themselves as causes of our experience. Indeed, it appears that there could not even be any thought of things in themselves as causes of our experience, even by way of illegitimate inference. For the concept of cause, as Kant presents it, involves a reference to time (the cause is an event that must be conceived to have preceded another event in time). If things in themselves are not in time, then they cannot even be thought as causes of our experience. Such a thought would make no sense.

The Unknowability Thesis 331 Or so Kant claims. But his assertions of the complete emptiness of causal concepts used with reference to things in themselves might look far less certain in light of the conclusions of chapter 9, above. Despite what he claims, Kant is not able to establish that things in themselves could not be in space or time, but simply that they could not be in the kind of space or time (a space or time where locations are determined by manner of presentation) that we experience. Might that mean that we could at least think of causal relations between things in themselves and appearances? I maintain that it does not. This much must be granted: despite what Kant says, it is thinkable that things in themselves could be ordered in a different kind of space and time (say, a space or time where locations are determined by intensively graded properties, as long as these properties are 'well-behaved' in the ways described in chapter 9). And it remains a possibility that these 'quasi-spatio-temporal' relations which a thing in itself might have to its surroundings in its comparison space or time would mirror the spatio-temporal relations which its corresponding sensation has in presentation space and time to the sensations that correspond to the thing's surroundings. In this sense, quasi-temporal relations, and with them quasi-causal relations among things in themselves, are not unthinkable (though they are certainly unknowable). Causal relations between things in themselves and sensations would cross the two times, however, and that would forbid any notion of temporal precedence (while one thing in itself or sensation can precede another thing in itself or sensation in its quasi-time or time, a thing in itself could not precede a sensation without presupposing a larger time in which both are contained, and, given the radical difference between a time defined by manner of presentation and a time defined by comparison of graded qualities, that could not even be thought). The most that could be thought is that certain events in the one time correspond to certain events in the other time, not that they precede them. However, there is another sense in which causal relations between things in themselves and appearances might be thought, in conformity with Kantian principles. In addition to the 'schematized' concept of causality that figures in the Second Analogy, according to which a cause is an event that must be taken to precede another event in time in accord with a rule, Kant recognizes that there is a purely logical employment of this concept, that can figure in any thinking whatsoever. This 'logical' employment of the concept, it turns, out, is identical with the bare concept of an efficacious but also necessitating ground, stripped of all refer-

332 Conclusions from the Above Concepts ence to temporal precedence or succession, as well as of any conditions (like containment) that might serve to model the manner in which the ground is related to its effect. Were I to leave out the time in which something follows upon something else in accord with a rule, then I would not find anything more in the pure category of cause than that there is something from which the existence of something else can be concluded, and thereby not only would it be the case that cause and effect could not be distinguished from one another, but, since the ability to draw the inference requires conditions of which I know nothing, there would be no way of determining how the concept is to be applied to any particular object. (A243/ 6301)

Though Kant is at pains, both in this passage and in its surrounding context, to argue that such a purely intelligible concept of causality is good for nothing but empty thinking, we should not take him too literally here. Kant's main concern is to argue against any employment of the causal principle to infer specific things about the nature of transcendent causes from empirical effects, the way the design argument tries to infer, not just that there is a transcendent cause of the universe, but that power and intelligence can be ascribed to this cause. To this end, Kant is concerned to claim that the thought of a transcendent cause would be completely empty. But to be an empty thought and to be unthinkable are not the same thing. There is nothing in Kant's position to rule out the possibility of at least thinking a pure, unschematized concept of causality, understood as pure efficacy without either temporal precedence (or succession) or any 'conditions determining how the concept is to be applied' (i.e., considered adequate to produce its effect). And there is nothing to rule out thinking that things in themselves are such 'causes' (really, corresponding or concomitant grounds) of appearances. Indeed, if we accept the conclusions of chapter 3, above, then there is nothing to rule out thinking that these things in themselves exercise a force corresponding in its intensity to the intensive magnitude of sensation, and if we accept the conclusions of chapter 9, above, then there is nothing to rule out thinking that they are ordered in a comparison space in a way that corresponds to the way the corresponding sensations are ordered in presentation space and time. It is just that these speculations can in no way be considered to be knowledge, and that they are virtually empty: The concept of a funda-

The Unknowability Thesis 333 mental force is one that Kant takes to be a mere name for something, the possibility of which we cannot comprehend, though we can describe its effects (Anfangsgriinde [Ak, IV 513, 524]), and the ground, likewise of any quasi-spatiotemporal relations of things in themselves is something of which we have no concept. So, in both cases, we are merely naming something of which we have no knowledge, and our concepts of things in themselves thus remain purely negative. They designate something that might (or even must) be out there, but that cannot be in any way further known as thinking or extended, possessed of one set of properties or another. Even transcendent affection, therefore, may not be as much of a problem for Kant as has sometimes been made out. It cannot be known to take place, but it can at least be thought to occur. Given the resources Kant has available in his empirical exposition of our concepts of sensible qualities, he has no need to claim knowledge that things in themselves affect us, and the mere fact that they can still be thought is all that he needs to undertake the negative task of drawing the bounds of sensory experience.

11 Kant, Mendelssohn, Lambert, and

the Subjectivity of Time

(b) Space is nothing other than just the form of all appearances of outer sense, that is the subjective condition of sensibility, under which alone outer intuition is possible for us. (A26/B42) If we depart from the subjective conditions under which we can alone have outer intuitions, then the representation of space has no meaning. This predicate is only ascribed to things in so far as they appear, that is, are objects of sensibility. The enduring form of this receptivity, that we call sensibility, is a necessary condition of all relations in which objects are intuited as outside of us and, when we abstract from these objects, a pure intuition, that we call space. ^26-7/642-3) (b) Time is nothing other than the form of inner sense, that is, of the intuition of ourselves and our inner state. (A33/B49) If we abstract from our manner of intuiting ourselves (and thereby of also including all outer intuitions within our representative capacity) and consequently consider objects as they are in themselves, then time is nothing. It has objective validity only with respect to appearances, because these are already things that we suppose to be objects of our senses, but is no longer objective, when one abstracts from the sensory nature of our intuition and so from that mode of representation that is characteristic of us, and speaks of things in themselves. Time is therefore just a subjective condition of our (human) intuition (which is always sensory, that is, dependent on our being affected by objects), and in itself nothing. (A34-5/B5I)

The Subjectivity of Time 335 i.

Kant's Subjectivity Thesis

Kant's thesis that space and time are merely subjective is presented as the second major conclusion from the Expositions. It has already been proven twice over: first, and positively, by the argument of the Transcendental Expositions; second, and negatively, by the thesis of the nonspatiotemporality of things in themselves. The first, positive proof demonstrates that the space and time we experience must be grounded in the manner in which we are constituted so as to be able to receive sensations in our original, intuitive sensory experiences. The second, negative proof eliminates the alternative that things in themselves might be in space or time. If things in themselves could not possibly be in space or time then (supposing that they exist at all) space and time can only pertain to appearances. But appearances, by contradistinction to things in themselves, are that which exists only through being somehow given to a subject. Accordingly, space and time must be subjective. Though it may at first seem paradoxical, neither of Kant's two arguments rules out a parallel 'objective' status for space and time. This is because that which only appears to the subject can be classed into two groups. Some appearances, despite their status as 'mere appearances,' have an order and coherence to their manner of presentation that allows them to be interpreted as facets or states of solid, enduring, intersubjectively identifiable and reidentifiable bodies. Though they are not things in themselves, they are 'analogously' subsisting, altering, and interacting. They are to be contrasted with other appearances that fail to exhibit this 'objective' order and coherence, and so have the status of dreams or illusions. Kant puts this point by saying that the distinction between reality and illusion, or objectivity and subjectivity, can be drawn in two different ways. Taken in one way (that he calls 'transcendental'), the real is what exists in itself and its opposite is what exists only insofar as it is given to a subject. But taken in a different way (that he calls 'empirical') the real is what posses 'objective' order and coherence, whereas the illusory is what cannot be brought to fit into the picture of a single world of enduring objects, located in space, and interacting and altering over time in accord with universal laws. The second distinction can be drawn entirely within the sphere of what is denominated as 'subjective' by the first distinction. We distinguish under appearances that which pertains essentially to the intuition itself, and is valid for any human sense in general, from that which attaches

336 Conclusions from the Above Concepts only accidently to the senses, since it does not have to do with a reference to sensibility in general, but is valid only with reference to a particular position or state of this or that sense organ. And so people call the first kind of cognition one that represents the object in itself, but the second only the appearance of this object. But this distinction is only empirical. If one were to hold to it (as is commonly the case), and not see every empirical intuition as being in turn a mere appearance (as ought to be the case), so that nothing is to be found in it that pertains to any sort of thing in itself, then our transcendental distinction is missed, and we believe ourselves to know things in themselves, even though we never have to do with anything but appearances (in the sensible world), even by means of the deepest investigation of its objects. (A45 7662-3) When I say, 'in space and time both outer Objects and the self-intuition of the mind are represented as they affect our senses, that is, as they appear,' I do not mean to imply that these objects are a mere illusion. For Objects, and even the characteristics that we attribute to them, are seen as something actually given in appearance. It is just that, in so far as these characteristics depend only on the manner of intuition of the subject in its relation to the given object, this object as appearance has to be distinguished from itself as Object in itself. Thus, I do not say, Hoodies merely seem to be outside of me, or my soul only seems to be given in my self consciousness/ when I maintain that the quality of space and time, in which, as condition of their existence, I set them both, lies in my manner of intuition and not in these Objects in themselves. It would be my own fault if I made a mere semblance out of that which I ought to ascribe to appearance. (669) In saying that space and time are 'subjective/ therefore, Kant does not mean to reduce them to illusion. 'Subjective' is little more than another way of saying 'not such that it exists in itself/ The subjective is not transcendentally real, as Kant puts it, but it may be empirically real. ii.

Mendelssohn's Objection1

When understood as outlined above, Kant's subjectivity thesis might appear to call for no further comment. The arguments supporting it have, after all, already been canvassed in chapters 8 and 9, above. But unfortunately, this is not the case. Kant's subjectivity thesis is the most problematic of all the facets of his transcendental idealism - more so even than the more notorious non-spatiotemporality thesis. The problem with it has to do, not with the arguments offered in its support, but with an apparent inconsistency that the thesis runs into. How can space

The Subjectivity of Time 337 and time be declared to be subjective, or grounded on the manner in which the subject is constituted so as to be able to receive sensations, if the subject in question is a thing in itself and so supposedly unknowable? If, alternatively, the subject in question is taken to be an appearance, then how can what is supposedly so constituted as to have the appearances in a certain way be itself merely one of the things that appears to itself? Kant was not unaware of this problem. It was first raised by Johann Heinrich Lambert and Moses Mendelssohn, in correspondence with Kant shortly after ID appeared, and by Johann (Court Chaplain) Schultz, in a review of that work.2 While ID did not assert the unknowability of things in themselves (quite the contrary), §14 did assert that 'time is not something objective and real, nor is it a substance, nor an accident, nor a relation/ but is merely a 'subjective condition which is necessary, in virtue of the nature of the human mind' (Ak, II400; a parallel claim is made for space at Ak, II 403). And it stressed (Ak, II 392-3) that the form of intuition in general is entirely the subject's own, and refers, as a consequence, only to the subject's representations, not to any state of objects as they may be in themselves. ID thus affirmed both the subjectivity of spatiotemporal form and the ideality of everything that exists in space and time. Within a few months of Kant's defence of ID, these theses were under attack. Kant received the same objection from Lambert, Mendelssohn, and Schultz. Though Lambert deserves the credit for being the first to raise the objection, it was perhaps not surprisingly the 'popular philosopher/ Mendelssohn, who put it forward with the greatest brevity, clarity, and elegance. That time should be something merely subjective is a point with which, for a number of reasons, I cannot concur. Succession is certainly at least a necessary determination of the representations of finite spirits. Now finite spirits are not only subjects, but also objects of the representations of their fellow spirits, as well as of God. Consequently, succession is also to be seen as something objective. Since we must admit a succession at least in representing subjects and their alterations, why not also in the sensible objects in the world, the exemplars and models of our representations? (Briefivechsel, 89-90; Ak, X 115)

Mendelssohn's objection, like Lambert's before and Schultz's after it, questions why Kant's claims about the subjectivity of at least temporal

338 Conclusions from the Above Concepts form should not be run up to the transcendental level and affirmed of the subject as it is in itself. Mendelssohn thinks they should. The basis of his position is an appeal to the thesis that the inner states of the subject actually succeed upon one another in time - that is, that they come into and pass out of existence. This is the point of saying that succession is a determination of the representations of finite spirits. It is the same point that Lambert made by claiming that even an idealist must grant the fact of change - in, for example, the beginning and ending of representations (Briefwechsel, 80; Ak, X 107) - and that Schultz made by claiming that time is a form of the alterations of souls in the immaterial world as well as of bodies in the external world.3 But granting that the subject's representations actually succeed upon one another in time, Mendelssohn points out, we must consider that in so far as, first, this representation and, then, that one exists in the mind, the mind itself undergoes a change. (Finite spirits may be viewed not only as subjects that have representations, but also as objects that undergo them, as Mendelssohn reminds Kant.) If the representations change over time, so does the subject. But then the subject itself must be determined in time, in so far as it has representations, and as a consequence time must be recognized to be not merely an ideal feature of the things the mind represents, but a real feature of the mind that does the representing. And if this mind is supposed to exist in time, why not other things outside of the sphere of appearance as well?4 Mendelssohn's objection shows up an especially serious facet of the problem confronting Kant's subjectivity thesis. The problem is not just that taking time to be the form of intuition of the 'subject in itself violates Kant's position on the unknowability of things in themselves (a position to which Kant was not committed at the time of ID). Worse, the claim that we are making would seem to be that this subject is so constituted as to receive sensations successively over time, and this would appear to entail that it must itself be determined in time. And then how could time be the 'merely subjective' form of what appears to the subject? It would appear to have to be the 'form' of the subject itself. Consequently, at least one thing in itself (the 'subject in itself) would appear to be in time, in violation of the non-spatiotemporality thesis. a. Kant's Initial Response Even though Kant did not believe in the unknowability of things in themselves at the time of ID, he did believe that things in themselves

The Subjectivity of Time 339 could not be in space or time, and he felt the force of the objection raised by Lambert, Mendelssohn, and Schultz. Writing to Herz on 21 February 1772 he called it 'the most basic [objection] that can be raised against the position' and he confided that it had forced him to think through everything again (Briefwechsel, 105; Ak, X 134). He did not forget about the objection, either. At the time of writing the Critique he was still worried about it, and devoted the first half of §7 of the Aesthetic to addressing it, opening that passage by writing, Against this theory, that attributes empirical reality to time, but denies it absolute and transcendental reality, I have received from insightful men an objection that has been so universally raised that I assume it must naturally occur to any reader to whom these considerations are unfamiliar. It proceeds as follows: Alterations are actual (this is proven by the change of our own representations, even should one chose to doubt [the existence of] all outer appearances together with their alterations). Now alterations are only possible in time; consequently, time is something actual. ^36-7/653)

What made the objection especially compelling was that Kant accepted the premise. Time, for Kant (and, indeed, space as well) is not merely a relation that is represented by the subject, it is the manner in which the subject's representations occur. As such it is a necessary consequence that the subject, in so far as it experiences time, does not merely represent time, but represents over time. Kant had no choice, therefore, but to grant the main point of the objection: that in so far as the subject receives representations successively in time, it must itself be temporally determined. None the less, he thought he could preserve his claims about the subjectivity of spatiotemporal form and the transcendental ideality of space and time even in the light of this point. The letter to Herz contains an initial attempt at an answer. This attempt is flawed and ultimately unsuccessful, but it will be instructive to consider it, anyway. The key to Kant's initial answer appears to have been his discovery of what he took to be an obliquity in the cases of space and time: Why (I said to myself) does one not draw this parallel conclusion: Bodies are real (according to the testimony of outer sense), but bodies are possible only under the condition of space; therefore, space is something objective and real that inheres in things themselves. The reason [for rejecting this conclusion] lies in this: that where outer things are concerned, the actuality of the objects cannot be

340 Conclusions from the Above Concepts concluded from the actuality of the representations, whereas with inner sense the thought or the existence of the thought and of myself are one and the same. (Briefwechsel, 105; Ak, X 134)

From our representations of inner sense changing, we infer that we ourselves must pass through a temporal series of states, and hence that time must be absolutely real. But space is equally a form of intuition along with time, so it seems we should be able to run Mendelssohn's argument with respect to it as well. Kant runs this parallel argument in an odd way, however. To begin with, he misrepresents the charge of Mendelssohn's actual argument. Rather than take this charge to consist in the claim that, since our representations of inner sense change, we ourselves must change in so far as we experience them; he takes it to affirm that since our representations of inner sense change, the object of these representations must change. This (mis)reading of the argument makes it possible for him to present a spatial parallel that consists, not in an inference to the absolute nature of the representing subject based on the nature of its representations of outer sense, but an inference to the true nature of the represented object of outer sense, other bodies. A true spatial parallel to Mendelssohn's argument should consist in the claim that, since our representations of outer sense occur alongside one another in space, we ourselves (or at least our organs of outer sense) must be extended in space, and hence space must be absolutely real. Kant twists Mendelssohn's argument so that he can offer the parallel as instead affirming that other bodies must exist in space outside of us. This makes it artificially easy for him to offer what he takes to be an answer. Admittedly, in the case of inner sense, the distinction between represented object and representing subject is one that can be overlooked (though Kant, of all people, ought not to have done so for reasons that will become clear in a moment), since the object that is represented in inner sense is supposed to just be the representing subject. (The thought or the existence of the thought and myself are [supposed to be] one and the same,' as Kant puts it.) But the distinction between representing subject and object of representation is significant when Kant comes to run the 'parallel' argument for space - there we do not take for granted that the represented object and the actual object are one and the same, because the 'arguments of the idealists [and sceptics]/ as he puts it in §7 of the Aesthetic, have convinced us that this is not something that can be asserted without argument.

The Subjectivity of Time 341 This is where Kant makes his fast move: he applies the point about representation of objects in outer sense back to the case of representation of the self in inner sense. It is really incorrect, he points out, to suppose that inner sense gives us any more accurate a representation of its 'object' (i.e., the representing subject) than outer sense gives of external bodies in space. So, what follows about the subject in so far as it is represented through inner sense (namely, that it must be supposed to change over time) should no more be taken to imply that the subject really is in time than the fact that our representations of bodies are spatial should be taken to imply that things in themselves must be in space. The key to this difficulty lies in this: There is no doubt that I must think my own state under the form of time and that therefore the form of inner sensitivity must give me the appearance of alteration. That alterations are something actual is something that I deny as little as I deny that bodies are something actual, although by that I only mean that something actual corresponds to the appearance. I cannot even say: the inner appearance is altered, for how would I observe this alteration if it did not appear to my inner sense? (Briefwechsel, 105 [Ak, X 1341)

b. The Fallacy of Kant's Initial Response A moment ago, I said that Kant makes a fast move when he applies the point about the representation of objects in outer sense back to the representation of the subject through inner sense. What is fast is not Kant's assumption that inner sense is no less representational than outer and, like outer, gives us only a knowledge of ourselves as we appear to ourselves. That is a legitimate point that we may grant to him. But this is not all there is to the matter. Lambert, Schultz, and, above all, Mendelssohn did not commit the elementary error of assuming that the representations of ourselves through inner sense must adequately represent their object, and their objection cannot be dismissed so easily. Kant's fast move consists in his doing just this: in his taking the point about the representational nature of inner sense to be at all relevant to the argument. This original misconstrual of the form of the argument was what allowed Kant to think that the point about the representational character of outer sense is at all relevant to the case.5 But the point Lambert, Schultz, and Mendelssohn had to make was not simply that the object of the subject's inner sense experiences (which, in the case of inner sense experience, purports to be a reflection of the representing subject itself)

342 Conclusions from the Above Concepts undergoes alterations over time; it was that the subject that has the inner sense experiences (what I call the representing, as opposed to the represented subject) must itself undergo alterations over time in so far as its representations are successive in time. The linchpin of Mendelssohn's argument, recall, was his claim that for every item that is represented by a representing subject there is a corresponding state, which is the state of the representing subject in so far as it has that representation. Mendelssohn charges Kant with myopia, with looking at matters exclusively from a subjective or internal point of view - the point of view of the subject who has the representations and who sees only them and their temporal form of succession. Kant has failed to consider that the subject who has representations is itself an object namely, the representing subject - and he has failed to consider that for this representing subject to have a representation just is for it to be in a particular state. If the representations are successive, then so must be the states. If representation A exists now, then the representing subject must exist in representational state A*. If later, representation A is succeeded by representation B, then the representing subject must cease to be in representational state A* - that is, it must undergo a change. But if it changes then it, too, must be determined in time. Time, therefore, must be a 'real' determination of the representing subject itself, as well as of its representations. Now it might seem that Kant has a ready answer to this argument. He need merely observe that, when Mendelssohn claims that representation A is succeeded by representation B, he is not making a claim about how things are in themselves, but simply about how they are represented by the subject. Representation A does not actually precede representation B in the subject's mind, it may be claimed, it is merely represented as prior to B in time. The temporal precedence of A and B is itself merely the object of a representation, and not a manner in which representations actually occur. But this answer is hopeless. Not only can it be readily refuted, it violates the essential Critical insight into the nature of time as form of intuition. This can be shown by inquiring how it is that A can be represented as prior to B in time. If it is responded that representing A as prior to B in time consists in being in a complex representational state, that consists of representing A, and representing B, and representing A as standing in a relation of temporal precedence to B, then what is the ground of this relation? How can A be thought as prior to B if they are both simultaneously present in the representation? Not through thinking one as

The Subjectivity of Time 343 cause and the other as effect, since the Critique maintains that temporal relations must first be given in intuition as a ground for inferences about causal relations (A26ry-8/B^2^-4),6 so grounding temporal relations on a knowledge of causal relations would beg the question. And not anything in the content of A or B, since the First Exposition denies that our concepts of space and time are drawn from the empirical content of our representations. The fact is, as the Critique maintains, that our knowledge of temporal relations is ultimately grounded in the fact that certain representations actually occur and are presented in intuition before certain other representations. (This is just what it means for time to be a form of intuition.) This original succession can then be taken up in the unity of apperception and represented in a single, momentary, complex thought. But, were there no originally given succession in intuition to be run through, connected, and conceptualized by apperception, the original data for the thought that the temporal relation exists would be lacking, and the thought would be groundless. However, the supposition that temporal relations are merely thought in representations rather than being originally given as the manner in which representations are presented is unsustainable, even independently of the consideration that it violates the essential Critical insight about the nature of time as form of intuition. All we need do is note that the very claim that A is prior to B entails that there must have been a time when the subject was able to represent A but unable to represent B. (Otherwise, whatever the claim that A is related to B might mean, it does not mean that A was prior to B in time.) But, if the subject once had a representation just of A, and now has a representation both of A and of B and of the priority of A to B in time, then the subject must have undergone an alteration in its representational state. Thus, Mendelssohn's argument is vindicated. But it should be stressed that, when he is speaking to Kant, Mendelssohn does not need to vindicate his argument in this way, for Kant himself denies that temporal relations are merely thought as the objects of our representations. For Kant, as for Mendelssohn, time is unquestionably the order in which the subject's representations themselves occur. To sum up, the response - indeed, the entire approach Kant takes to Mendelssohn's problem based on his analysis in the letter to Herz - is totally inadequate. Kant takes the argument to turn on a tact appeal to the (illegitimate) notion that representations, especially representations gained through self-consciousness, must resemble their objects, so that it can be concluded that the representing subject must be in time because

344 Conclusions from the Above Concepts its representations of itself in inner sense are in time. But this is simply not how at least Mendelssohn's version of the argument actually works. For Mendelssohn, the inference is not from the temporality of the representations to the temporality of the object of those representations, but from the temporality of the representations to the temporality of the subject that has the representations. Mendelssohn can grant that the relation between the temporal order of a series of representations and the temporal order of the objects they represent is problematic. But he can insist that the relation between the temporal order of a series of representations and the temporal order of the states, that the representing subject is in in so far as it has these representations, is not. Representation B cannot appear to the representing subject after representation A without the representing subject itself undergoing a change from having representation A to having representation B. Despite what Kant thinks, this objection has nothing to do with any presumption that inner-sense is more certain than outer. The fact that the representations Mendelssohn has in mind may be inner-sense representations of states of the subject is irrelevant. A successive series of representations of objects of outer sense would do just as well to motivate the objection. A representation of an external object is as much a state of mind of the representing subject as any other, and if it is granted that representations of external objects succeed upon one another in the subject's consciousness, then it follows that that consciousness must itself be undergoing alterations in time. Indeed, though Mendelssohn himself seems not to realize it, there is nothing special about time. The argument could be run for space as well, the 'opposition of idealism' notwithstanding. Kant's question to Herz 'Why do I not argue that bodies are real according to the testimony of outer sense, and from this conclude that space must be absolutely real?' - is a red herring that does not parallel Mendelssohn's argument. Mendelssohn (unlike Lambert) does not simply say, 'Alterations are real according to the testimony of inner sense, hence time must be real'; he says, 'Representations are successive according to the Kantian theory that time is a form of intuition, therefore the subject that does the representing must itself undergo a temporal series of alterations.' The spatial parallel to this argument is: 'Representations occur alongside one another in space according to the Kantian theory that space is a form of intuition; therefore, the subject that does the representing must itself consist of a collection of representative states occurring at different locations in space.' Here it is not the existence of external objects that is affirmed on

The Subjectivity of Time 345 the testimony of outer sense, contrary to all the arguments of the idealists, but the extension of the sensory organs of the subject that is affirmed as a necessary condition of the possibility of space cognition, given the Kantian theory that space is a form of intuition.7 If, therefore, Kant's response turns on an attempt to saddle Mendelssohn with the view that objects as they are in themselves must resemble the representations we have of them, then he simply misses the point. This is not how Mendelssohn argues.8 If Kant is adequately to answer Mendelssohn, he has to come to terms with the fact that the objection goes from the temporality of the representation to the temporality of the subject that has it, not to the temporality of whatever object this subject might represent. Indeed, he has to come to terms with the fact that the objection goes from the spatiality of the order of representation to the spatiality of the representing subject. c. The Representing Subject as Appearance Faced with this result, we might wonder if Kant could not both grant Mendelssohn's argument and maintain his views on the transcendental ideality of space and time and the non-spatiotemporality of things in themselves by maintaining that even the representing subject is still only an appearance and not a thing in itself. In this case, Mendelssohn's argument would not go wrong in inferring that the subject that receives sensations successively over time in intuition must itself undergo a series of alterations over time, but in its tacit supposition that conclusions drawn about this representing subject are ipso facto conclusions about the subject as it is in itself. Could it be that these conclusions in fact never draw us outside of the sphere of appearance? This answer seems, however, to entail an absurdity. An appearance is by definition something that appears to a subject. And how could the subject that has the appearances itself be just one of the appearances that it has? Before the representing subject could have an appearance, it would have to exist. But if it is itself just an appearance, then for it to exist entails that it appear. But, how could it appear unless it already existed to have the appearance? In a word, the representing subject seems to be too big to be contained within the sphere of appearances. One way to try to get out of this circle (though not a successful way, as I show in a moment) is by claiming that appearances do not have to actually appear to a subject in order to exist. The notion of an appear-

346 Conclusions from the Above Concepts ance existing independently of appearing may seem paradoxical, but the Critique does go some way to removing this paradox. The 'Postulates of Empirical Thought in General' establish a distinction between objects as they initially appear through combination of the array of intuition what can be called raw appearances or percepts - and objects as they can be legitimately inferred or postulated to be on the basis of perceived data, even though these inferred or postulated objects may not themselves be actually given in intuition - these latter objects can be called 'phenomena.' Objects of the former kind, raw appearances or percepts, are exemplified by objects of everyday perception, like loadstone and iron filings; those of the latter kind, phenomena, are exemplified by theoretical entities of science, like the effluvia Kant (falsely) supposed to be responsible for magnetism (A226 76273). Phenomena are postulated as underlying, or lying between or beyond, the objects of everyday experience. Both classes of object, according to Kant, are only appearances and not things in themselves; it is just that the latter are not perceived through combination of the intuited array, but inferred with the aid of the principles - for example, by causal reasoning - from the things that are perceived. The representing subject would appear to be a phenomenon as opposed to a raw appearance or percept. It is not something that actually appears (that would lead to the absurd result that the subject that has the appearances is one of its own appearances), but it does seem to be something that is inferred to exist by reasoning from the data supplied by inner sensory experience. The distinction between postulated phenomena and perceived appearances might be thought to break the circle because Kant sometimes speaks as if phenomena or theoretical entities exist prior to being perceived. Thus, at A49376521, he remarks that 'everything is actual that stands in the context of a given perception in accord with laws of the empirical progress' of experience. This might be taken to imply that an object does not have to be actually constituted through intellectual synthesis in order to be legitimately supposed to exist as appearance or phenomenon. As long as this object is connected, in virtue of some natural law, with some other object that has been perceived, it can be supposed to exist, whether we think of it or not, and, indeed, even to have existed prior to the perception, if the law in question permits that kind of inference (as it would if it is a causal law describing the events antecedent in time to a perceived effect). Thus, it might be thought, by appeal to principles such as the causal principle, we might ascend beyond the

The Subjectivity of Time 347 sphere of our immediate representations and the appearances we constitute from them, and postulate an entire world of objects that exist unobserved and existed at past times to condition our present perceptions. Newton's law of universal gravitation, according to which everything in the universe can be causally connected to any given object of perception, and all the past states of the universe can be causally connected to its present state, would appear to offer a prime example of how this might be done. We might be tempted to say, then, that the representing subject, that is so constituted as to receive matters successively over time, is merely yet another postulate of empirical science (in this case, the science of transcendental psychology, established by the Critique). It is admittedly something that is taken to determine the temporal form of all of the rest of our experiences, but there is no circle because it is not taken to first arise or be created through experience, but is supposed to have existed all along, experience serving merely to deliver certain data to us adequate to allow us to discover that it had been there all along. Why, in the final analysis, should supposing that a portion of the experienced world (and only a portion, because the a priori elements have only to do with the form and not the content of what is known) is determined by the constitution of this theoretical entity be absurd? It is in the end no more radical than saying that a good portion of the content of the earth is determined by the constitution of the sun, or that a good portion of the form of the universe is determined by the law of gravitation. But, attractive though it may be, this answer to Mendelssohn's objection cannot be sustained. Though Kant remarks that 'everything is actual that stands in the context of a given perception in accord with laws of the empirical progress' (of experience), he also immediately adds that these things 'are not actual in themselves, that is, apart from this progress of experience' (A493 76521). In referring to unobservable and theoretical entities, we are not referring to things that exist in themselves. But to say that these things do not exist in themselves is to say that they exist only with reference to our cognition, so that, were we to remove the subject that does the cognizing, these things would be removed as well. Even though we may think of some of them as existing prior to the birth of the subject or beyond the reach of its senses, and determining its present experiences, all that we mean by this, as Kant himself explains, is that had it been the case that the subject had existed earlier, or had it been the case that its senses were more discriminating or more powerful, it would have had an experience of those objects. Our

348 Conclusions from the Above Concepts claims about the prior existence of phenomena are thus merely counterfactual claims about the kinds of experiences that would otherwise have been had. They do not imply that the objects actually exist on their own, independently of the perceiving subject. Nothing is actually given to us but perception and the empirical progression from this to other possible perceptions. For appearances, as mere representations are in themselves only actual in perception, which is in fact nothing other than the actuality of an empirical representation, that is, appearance. To call an appearance an actual thing prior to perception either means that we must meet with such a perception in the progress of experience, or it has absolutely no meaning. For, were the talk of a thing in itself, then it could certainly be said that it exists in itself, without reference to our senses and possible experience. But the talk here is only of an appearance in space and time. And neither space nor time is a determination of things in themselves, but only of our sensibility. Consequently, that which is in space and time (appearance) is not something in itself, but mere representations that, when they are not given in us (in perception), are nowhere to be found. ^493-4/13521-2)

While this fact poses no special problems where objective causes and principles, such as the sun or the law of gravitation, are concerned (since these are objects or principles within experience postulated as antecedent causes of other experienced objects), it does lead to a difficulty when the topic is the subjective grounds that are taken to condition experience itself. How can something that can only be supposed to exist in a phenomenal world postulated by a subject - something that is denied any independent existence in itself and supposed to exist only in the theories constructed by a subject - be identified with the subject that constructs the theories? Were it the case that our postulates merely discovered some antecedently existing thing in itself, then there would be no problem. But, if it is asserted that the objects we postulate do not exist in themselves, but only in our theories, then we end up confronting the absurd result that something that only exists in our theories is what makes our theories, thereby bootstrapping itself, and ourselves and the entire phenomenal world along with it, into existence. d. Kant's Critical Response to Mendelssohn Kant would appear to be caught on the horns of an insuperable dilemma here. The representing subject could not be an appearance, since that is

The Subjectivity of Time 349 absurd, but neither could it be a thing in itself, since then, by Mendelssohn's argument, it would have to be in space and time, violating the thesis of the non-spatiotemporality of things in themselves; moreover, it would, as thing in itself, be thought as so constituted as to receive representations successively over time, in clear contravention of the unknowability thesis. But in §7 of the Critique, Kant does try, a second time, to forge a way out of this very difficult problem. Kant opens his response by conceding Mendelssohn's point. 'I grant the entire argument/ he says.9 If the subject receives representations successively over time, then it must itself be temporally determined. By implication the same ought to hold for space: if the subject's representations are disposed in space, then it must itself be spatially extended. However, Kant does not remark on this implication and still appears to have in the back of his mind the same idea of the key to the solution to the problem that motivated his misdirected response in the letter to Herz: The reason, however, why this objection is so generally raised, even by those who know of no evident objection to the doctrine of the ideality of space is this: They do not hope to be able to apodictically demonstrate the absolute reality of space, because they are confronted by idealism, according to which the actuality of outer objects is not susceptible of any strong proof. However [they suppose that] the actuality of the objects of our inner sense (myself and my states) is immediately certain through consciousness. The former could be a mere illusion but the latter is, so they suppose, undeniably something actual. They fail to consider that both, without anyone contesting their reality as representations, only belong to appearance. (A38 7854-5)

Once again, Kant appears to imagine that the problem can be resolved simply by claiming that both inner and outer sense are merely representational, so that conclusions drawn about objects as they are represented in inner and outer sense cannot be supposed to be valid for these objects as they are in themselves. And, once again, he seems to miss the whole point. The argument does not turn on any claim about the objects that are represented by inner or outer sense; it turns on a claim about the subject that has the representations. But, immediately after writing this, Kant adds a further statement that casts the whole issue in an entirely new light: They did not consider, however, that both [the appearances of inner and outer

35O Conclusions from the Above Concepts sense?] only belong to appearance, even though one may not contest their actuality as representations. And appearance always has two sides: the one, where the Object in itself is considered (apart from any reference to the manner by which it is intuited - which means, as a consequence that its constitution always remains problematic), the other, that considers the form of the intuition of this object, which must be sought, not in the object in itself, but in the subject to which it appears, though it actually and necessarily pertains to the appearance of this object. ^38/855) What is significant in this text is Kant's proclamation that the object that appears to a subject has two sides or can be considered from two different perspectives: it can be considered as it is in so far as it appears to the subject through the subject's forms of experience, or as it is in itself, independently of any reference to how it appears. Kant's point seems to be, further, that this can be said of any object or representation. The subject's very intuitions can be considered in either of these two ways: either as things that appear to the subject successively over time and as disposed in space, or as states of a thing in itself. And, likewise, the subject that has the representations can be considered in so far as it can be postulated to be either in light of the representations as they appear to it, or as these representations are in themselves. This view is cemented by an amplification Kant provides in the previous paragraph: There is no difficulty in the answer. I grant the whole argument. Time is certainly something real, namely, the real form of inner intuition. It has, therefore, subjective reality with reference to inner experience. That is, I really have the representation of time and my determinations in it. It is therefore really to be seen not as object, but as the manner of representation of my self as object. If, however, I could intuit myself, or another being could intuit me, without this condition of sensitivity, then those very same determinations that we now represent as alterations would give a cognition in which the representation of time would simply not arise. There remains, then, its empirical reality, as condition of all our experience. Only absolute reality cannot be permitted, given what has been said above. It is nothing but the form of our inner intuition. If we remove the particular conditions of our sensitivity from it, then the concept of time also disappears and it attaches, not to the objects themselves, but merely to the subject who intuits it. (A37 7853-4) If we compare the answer Kant gives here to Mendelssohn to the answer he gave some ten years earlier in the letter to Herz, then we can

The Subjectivity of Time 351 say that the new answer is orthogonal to the old one. The old answer sought to evade the problem by drawing a line between the representing subject and its representations, and claiming that even the representations the representing subject makes of itself through inner sense are not necessarily accurate. The representing subject is taken to be thing in itself, the way it represents itself through inner sense is taken to be appearance, and the line between appearance and thing in itself is (erroneously) affirmed to be intraversable. The new answer draws a line between thing in itself and appearance, too, but it is a line that is perpendicular to the old line. Rather than identify the representing subject as thing in itself and its representations, including its representations of itself, as appearances, Kant takes the whole group to be such that they can be considered either as things in themselves or as appearances. The representing subject may be considered either as appearance or as thing in itself. And even this subject's representations may be considered either as things in themselves or as appearances. Thus, as Kant says, to another being, able to intuit the representing subject as it is in itself, those very things that for us occur successively over time (the representing subject's representations) would appear in some other way altogether, and neither the representing subject nor its representations would be thought, therefore, to be successive in time. For us, however, the representations appear as determined in time (and, indeed, in space), and thus we postulate the representing subject to be altering over time (and extended over space). However, this postulate is valid of the representing subject only as it is inferred to be through reference to what is given as appearance, and hence is valid only of the representing subject as appearance. This response circumvents Mendelssohn's objection by, as Kant says, granting the entire argument. If you take the representations had by a subject to be successive in time, then you must grant that this subject is itself determined in time. But this is a conclusion drawn from the way the subject's representations appear to you, and as such is itself a conclusion drawn about the subject only as a postulated appearance or phenomenon. You have to consider that, were those very representations, that appear to you as successive in time, considered as they are in themselves, then they could not have temporal determinations. Some other being, able to know these representations as they are in themselves, would know them in a way that involves no reference to time. Accordingly, even were such a being to conclude that these representations are all 'predicates' of some underlying 'subject/10 it would not conclude that

352 Conclusions from the Above Concepts this subject is in time. Thus, Mendelssohn's argument is entirely valid, but it leads to a conclusion only about the subject as it appears to us (or to itself insofar as it shares our forms of intuition), and not to a conclusion about the subject considered as thing in itself. iii.

Kant's Response to Mendelssohn and the Subjectivity Thesis

Kant's response to Mendelssohn's objection shows that it is possible to accept that our intuitions are constrained to exhibit spatiotemporal form without being compelled to accept that there are 'subjects in themselves' that are determined in space and time. The spatiotemporality of our intuitions is only apparent, and consequently the inference to the spatiotemporality of the subject that has the intuitions is an inference to the nature of the subject only as it appears. One problem remains outstanding, however. Kant does not want to assert just that our intuitions are constrained to exhibit spatiotemporal form. He wants to take a step further and claim that this constraint is grounded in the receptive constitution of the subject. This is a claim that has to be made about the subject considered as thing in itself. (As noted earlier, an appearance cannot be the very thing that is so constituted as to receive the appearances in a certain order.) But this poses a delicate question: how can Kant deny the legitimacy of Mendelssohn's inference, yet sustain the legitimacy of his own? If Mendelssohn cannot go from the (apparent) spatiotemporality of our intuitions to infer the spatiotemporality of the subject (as it is in itself), then what entitles Kant to affirm that the (apparent) spatiotemporality of our intuitions is grounded in the receptive constitution of the subject (as it is in itself)? a. Subjectivity and Non-spatiotemporality There is one potential objection to Kant's subjectivity thesis that can be quickly resolved in light of his response to Mendelssohn: the charge that the subjectivity thesis entails the spatiotemporality of the subject, considered as thing in itself. If we read the subjectivity thesis as the assertion that the subject is so constituted as to receive intuitions in space and over time, then this charge is inescapable, for the reasons that Mendelssohn articulated. But Kant's response to Mendelssohn makes it clear that both the subject and its representations may be considered in one or the other of two ways, which must be carefully distinguished. They may be considered as they are known by us (in space and time) or as they are

The Subjectivity of Time 353 in themselves. And this makes it possible for Kant to reformulate the subjectivity thesis. He can claim that the 'subject in itself is so constituted as to receive intuitions in a characteristic manner. But he can insist that this manner of receptivity only appears to us (and to this subject itself) as a constitution for receiving intuitions in space and over time. To paraphrase Kant's answer to Mendelssohn, in the knowledge of another thinking being, able to perceive things as they are in themselves, the subject's constitution would figure under some entirely different description - as would its intuitions. Thus, from the fact that the subject is so constituted as to appear to us to receive intuitions in space and time, it does not follow that there are 'intuitions in themselves' (or representative states of the 'subject in itself) existing in space or time, and hence it does not follow that the subject's receptive constitution entails anything about its being 'in itself determined in space or time. b. Subjectivity and Unknowability The issue remains, however, of what could possibly entitle Kant to make such a complex and detailed assertion about things in themselves as that there is a 'subject in itself that is so constituted as to determine what appears to us as the spatiotemporal form of our intuitions - especially in light of his otherwise firm commitment to the thesis of the unknowability of things in themselves. On this topic, there are three points that need to be made. First, quite aside from any consideration of whether it is knowable, Kant's claim is at least thinkable. As Kant admits at A242-3/6300-1, the categories of substance and cause exist in both purely logical and schematized forms. While the schematized versions of the categories are the only ones we can use to make knowledge claims (since for us knowledge is impossible unless something is given through sense intuition, and only the schematized categories can be applied to our forms of intuition), it is still possible to think the purely logical forms of these categories. Though the content of the thought is virtually empty, it is nonetheless possible to think of substance as that which exists only as subject and never as predicate (rather than as that which is permanent in time), and it is likewise possible to think of cause (or, indifferently, effect) as a ground from which something else can be concluded (rather than as an event that always precedes a certain other event in accord with a rule). It is possible, therefore, to think that there is an ultimate subject of which all representations are predicates, and it is possible to

354 Conclusions from the Above Concepts think that something in these representations could be the consequent of some ground in this subject. Neither of these thoughts involves an illegitimate application of the categories beyond the bounds of sense, since it is only the use of the schematized categories beyond those bounds that is illegitimate, and the categories are used here without reference to space or time and so without being schematized. Indeed - and this is the second point that needs to be made - the thoughts of the ultimate subject as ground of what appears as spatiotemporal order are not merely possible, but warranted. The first of the thoughts, the thought of the existence of an ultimate subject of which all representations are predicates, is not only a possible thought, but a necessary one. It is the thought of what Kant calls the necessary unity of apperception - the thought of the T to which all of my representations must be supposed to belong. And the second, the thought of this T as the ground of what appears as the spatiotemporal form of receptivity, is warranted by the argument of the Transcendental Expositions. None the less, these two thoughts do not constitute an exception to, or even entail a violation of, the unknowability thesis. They are mere thoughts and not knowledge. The reason why is stated by Kant at A2423/5300-1 and painstakingly demonstrated in the Paralogisms: there is no violation of the unknowability thesis because the thoughts of the ultimate subject and the ground of spatiotemporal order are completely empty. The thought of the T in which all representations inhere serves merely to point to the ultimate subject of thought, not to describe or identify it in any way, so that through this 1' nothing is thought. It is not thought that this 'I/ as a thing in itself, is in any way distinct from other things in themselves, or that what appear to us as our representations are the consequents of its interaction with other such distinct things (as Kant is at pains to prove in the Fourth Paralogism). Neither is it thought that the T that has an earlier representation is the same as the 1' that has a later one, or even that the T that thinks any one component of a representation is the same as the T that thinks the remainder (as Kant is at pains to prove in the Third and Second Paralogisms). The T is not even thought in enough detail for us to be able to identify whether its substance is material or immaterial. It is just that, because the thought of it is completely empty of all content, it looks as if it were distinct, simple, identical and ultimate. For what can appear more simple, identical, ultimate, than a thought with absolutely no content (A355)? And what can be more distinct from everything else than a thing that, because it is not thought to contain anything, cannot be thought to resemble anything else in any way?

The Subjectivity of Time 355 The thought that this T is the ground of what appears as the spatiotemporal form of intuition has even less to distinguish it. For, not only is the postulated ground completely unknown, even with regard to such basic questions as whether it is material or immaterial or whether it is the same from one representation or component of a representation to the next, but the manner in which it grounds its consequent is likewise unknown. From this it follows - and this is the third point - that Kant's subjectivity thesis must be an empty and virtually meaningless proclamation. To say that the 'subject in itself is so constituted as to appear to us to receive intuitions in space and over time is to say no more than that there is some unknown thing that constrains our intuitions to exhibit spatiotemporal form. This unknown thing can be called 'subject' or T/ but it cannot be known to be the same from one representation or component of a representation to the next; it cannot be known to be affected by other things distinct from itself; and it cannot be known to even be distinct from any other things. In effect, therefore, saying that there is some subject that is so constituted as to appear to us to receive intuitions in space and over time is to do no more than perform the grammatical trick of converting a fact that ought to be stated in the passive voice into the active voice. All that we can know is what appears to us: not the subject that has the representations, but just the representations themselves, and not the manner in which the subject is constituted so as to receive representations, but just the manner in which these representations appear to us as a result of this unknown constitution. All we can say, in other words, is that our intuitions are constrained to exhibit spatiotemporal form. Converting this fact into the active voice, and saying that there is something, we know not what, that is constituted in some way, we know not how, as to determine that all intuitions are received successively in time and alongside one another in space, adds nothing to this fact. But how this characteristic property of our sensibility itself should be possible, or how our understanding and the necessary apperception that lies as its ground and the ground of all thought should be possible, is a problem that may not be further answered or resolved, because these are the very things we require for all answers and all thought about objects. (Prolegomena, §36 [Ak, IV 318])

Summary and Conclusions to Part III

Kant draws two major conclusions from the Expositions: that space and time cannot figure in the world of things as they are in themselves (the non-spatiotemporality thesis) and that space and time are grounded in the manner in which the subject is constituted so as to be able to receive matters in intuition (the subjectivity thesis). When combined with the accepted view that our sensations do not represent properties of things as they are in themselves, the first of these conclusions grounds a further conclusion that sensory intuition cannot give us knowledge of things in themselves. When combined with the conclusion of the Transcendental Analytic, that intellect is also incapable of delivering knowledge of things in themselves, this further conclusion grounds the ultimate conclusion that things in themselves are unknowable. The preceding three chapters have shown that the non- spatiotemporality thesis does indeed follow from Kant's arguments in the Expositions - not in the radical form in which Kant states it, but none the less in a mitigated form that is adequate for his purposes. They have also shown that the (mitigated) non-spatiotemporality thesis is not inconsistent with the unknowability thesis. In its mitigated form, the nonspatiotemporality thesis does not make the dogmatic and synthetic claim that things in themselves could not be arranged in an order, or that any order in which things in themselves are arranged could not share the same topology as the order in which our sensations are presented in intuition. Instead, the non-spatiotemporality thesis makes the merely analytic claim that any order of things in themselves could not be a presentational order. However, the unknowability thesis is not challenged just by the non-spatiotemporality thesis. It is also challenged by Kant's attempts to

Summary and Conclusions 357 ground the matter of intuition in affection by objects (the affection thesis) and the form of intuition in the receptive constitution of the subject (the subjectivity thesis). On this score, I have drawn attention to two texts that are of vital importance if Kant's position is to be rightly and consistently understood: the 'empirical exposition' of A28-3O7644-5, and the remark on schematized and unschematized meanings of the categories in the section on phenomena and noumena ^242-3/5300-1). The first of these passages, when considered in tandem with the Metaphysical and Transcendental Expositions, is by itself adequate to establish a distinction between a priori and a posteriori components of our intuition and renders any appeal to affecting objects or the constitution of the subject unnecessary. The second opens the way for a use of the categories that would allow claims about affecting objects and the constitution of the subject to at least be made consistently (as claims utilizing the unschematized rather than the schematized categories), though they could never be asserted as knowledge. The first immunizes Kant from the very powerful objections of Jacobi and Mendelssohn, the former holding that a reference to things in themselves as affecting objects is ineliminable from the Critical Philosophy, in violation of the unknowability thesis, the lat^ ter holding that a reference to the temporal determination of the subject in itself is likewise ineliminable, in violation of both the unknowability and the non-spatiotemporality theses. The second immunizes Kant from the charge of being a dogmatic idealist, who would deny that anything exists but representations. For Kant, it remains possible to think that there are things in themselves that affect us and a subject in itself that is so constituted as to determine the form of our intuitions. Indeed, a reference to things in themselves is analytically contained in the very concept of an appearance, and a reference to a subject of all my thought is invoked by the thesis of the necessary unity of apperception, so that both things in themselves and a subject in itself can not merely be thought, but affirmed to exist, though nothing more can be known of them. While it can be thought that a subject in itself is the ground of the form of our intuitions and that other things in themselves are the grounds of our sensations, these subjectivity and affection theses are in fact empty claims (since we cannot know what the subject is in itself or what things are in themselves or whether the two are distinct) and the distinction between a priori and a posteriori components of intuition can be drawn without any reference to them. They serve merely to translate the proper idiom of Kant's Critical Idealism into a naieve realist paradigm, and are best set aside altogether as unnecessary and needlessly confusing.

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Afterword

The business of the senses is to intuit, that of the understanding to think. But thinking is uniting representations in one consciousness ... The unification of representations in one consciousness is judgment. Thus, thinking amounts to judgment, or referring representations to judgments in general... The logical functions of all judgment are so many possible ways of unifying representations in one consciousness. (Prolegomena, §22, [Ak, IV 304-5!)

The burden of this work has been to establish that what Kant refers to as 'sense intuition' is not a psychic, but rather a physiological phenomenon. I have argued that, for Kant, to intuit is not to have a thought of something, but to receive a piece of information - a piece of information that likely consists of the intensity value of a degree of stimulation, or, rather, in the intensity values of a number of different stimuli. Space and time, as forms of intuition, are not the properties or relations of the intentional objects of thought but the manners in which these stimulus values are disposed and presented. And, though we do attribute spatiotemporal properties and relations to the intended objects of our thoughts, Kant's claim is that the original datum for the cognition of spatiotemporal properties and relations is the reception of stimulus intensity values in space and over time in intuition. This position does not reduce to materialism, first, for the reason given in chapter 11, above (that all of these claims are made only about the subject as appearance and not as thing in itself), and, second, because, even where our concern is with appearances, intuition is only the first stage of a cognitive process - a process that may, for all we know, involve an immaterial agent at its higher levels. The precise

360 Afterword nature of these higher levels of cognition, and the manner in which they operate, is the topic of the Transcendental Logic. Though this work has been devoted to commentary just on the Transcendental Aesthetic, it is appropriate to close with a few, brief remarks on what is entailed for the interpretation of the later parts of the Critique. If what I have said is correct, then sense intuition is truly manifold. It consists of a multiplicity of matters splayed out over space and time, so that, at each discriminable point within the sensory field, there is a distinct sensory datum to be identified. Once this fact is appreciated, virtually the whole of the Transcendental Analytic can be seen as the working out of a single, basic project: explaining how, out of this physiological array of points of information, a unity of thought can arise. Unification is necessary because, were each data point the item of knowledge for a distinct consciousness, an apprehension of the totality of the information presented by the senses would be impossible. Consequently, if anything is to be known on the basis of the sort of sensory experience I have described, the first order of business must be to bring all the spatially and temporally disparate data together in the thought of a single consciousness. As far as Kant is concerned, this is something that involves an act of judgment, and this in turn involves apprehending all the data points in the array, connecting these points together in a certain way, and recognizing the connected data points as an instance of some one thing. There are four, increasingly broad levels at which this unification can occur. Unification is achieved, in the first instance, by judging that all the various data points are given as standing in certain spatial and temporal relations to one another. (The thought of a relation is a way of bringing the distinct thoughts of the two relata together in a single thought.) In the second instance, unification is achieved by judging that various data points are qualitatively similar or dissimilar, and noting that adjacent, qualitatively similar data points make up homogeneous patches of various shapes in space and time. (Just as the thought of a relation brings the distinct thoughts of the relata together in a single thought, so the thought of a figure brings a large number of spatially and temporally discrete items of information together in a single thought.) In the third instance, unification is achieved by judging that various, homogeneous patches refer to particular objects, of which they are aspects or appearances. (The thought of an object unifies the thoughts of all the different aspects this object can present when viewed from different perspectives in space or at different times in its history.) In the last instance, unifica-

Afterword

361

tion is achieved by judging that all the various objects of experience belong together in a single world governed by universal laws. Beyond this, no higher form of unification is possible. Unification at the first level presupposes an ability to think relations of position. At its most fundamental level, this requires an ability to note whether one intuited datum is coincident with another ('unity'), separate from another ('plurality'), or adjacent to another ('totality'). Unification at the second level presupposes an ability to identify relations of qualitative identity (of one matter with another), contrast (of a 'real' matter with a 'privative' or 'negative' one), or resemblance ('limited' identity). Unification at the third level presupposes the ability to apply a criterion for determining whether any given sensory patch refers to the same object or a different one and, if to the same, whether to a different part of this object or a later state of it. For reasons that Kant gives in the Analogies, and that are too involved to explain here, making these discriminations involves invoking concepts of substance and causality and connecting the subjectively given spatiotemporal array of sensory patches under these concepts to form thoughts of enduring, successive, or coexisting objects.1 Finally, at the last level, unification presupposes criteria for determining whether any given object is consistent with the sum of heretofore accepted knowledge (and so possible), is entailed by this sum (and so necessary), or is warranted in its own right independently of being entailed by anything else (and so actual). Broadly, anything that is constructible in space and time, and thinkable in accord with the conditions so far mentioned, is possible; anything that is given through intellectual synthesis of an actually obtained intuition or that follows by (legitimate) causal reasoning from actually given effects is actual; and anything that follows by (legitimate) causal reasoning from actually given causes is necessary. Now, these presuppositions of unification at the various levels are none other than the categories. Thus, once it is recognized that intuition is extended in space and enduring over time (so that each of us, perhaps, ever has only one intuition, that takes an entire lifetime to play itself out), it is possible both to see immediately why a transcendental unity of apperception is necessary and to provide a deduction for each of the categories. A transcendental unity of apperception is necessary because the information that is splayed out over space, and that has, up to any given moment, been presented at different times, needs to be unified in a single thought if knowledge is to arise. And the categories just are the different forms that unification can take, regardless of what empirical content the array may contain.

362 Afterword Much more would have to be said to provide anything like an adequate exposition of the transcendental unity of apperception or the transcendental deduction. All I want to do in this Afterword is indicate that, if intuition is taken to be extended in space and time, then it is possible to derive these traditionally difficult notions in a clear and succinct fashion simply by considering what is necessarily involved in unifying a collection of discrete bits of information presented at adjacent locations in space and time in a thought had by a single conscious being. Whether those who seek to treat intuition as a kind of intellectual or imaginative representation can hope to account for the necessity of a unity of apperception or the possibility of a deduction of the categories with equal ease is something that I will leave to the reader to consider. The main point of this book has not been to charge that those who treat Kantian intuitions as the products of intellectual or imaginative synthesis are condemned to give an awkward or intricate account of the Analytic; rather, it has been to show that, on any such account, our knowledge of the spatiotemporal properties and relations of the objects of experience would (at least, on Kantian terms) remain an impenetrable mystery. Were sensations not disposed in space and presented over time, and were the mind not somehow able to become conscious of each, individually located sensation, and then take them all and their relations up into a unity of apperception and think this manifold variety of data as some one thing (one relation, one figure, one object, one world), the question Herbart asked over a century ago2 would remain unanswered: why do I see one thing as round, another as square; one as being on the right, the other as being on the left? In this work, I have sought to give Kant's answer to this question, and I have argued that the answer I have attributed to him is the only one that could possibly be accepted. Not only is it the only answer that accords with Kant's texts and that follows from his arguments, it is the only answer that, as chapter 5, above, has shown, does not beg the entire question when viewed from the perspective of the background knowledge of matters of cognitive psychology in the eighteenth century. In addition, it is an answer that resolves the outstanding paradoxes and absurdities of transcendental idealism (the problems of the non-spatiotemporality and unknowability of things in themselves, the problem of affection, and the problem of the subjectivity of time), and it holds out the promise of being able to give a simple and straightforward explanation of the necessity of the unity of apperception and the possibility of a deduction of the categories.

Notes

Introduction 1 See Pastore, who has written around this distinction. Morgan, 79-83, 96, is very sympathetic to the nuances of the term 'nativist' but still exposits the views of Reid, Kant, and Lotze in terms of what is described as the 'modern mold' (106) for the notions of nativism and empirism. And, of course, there is Boring, 249 and throughout. 2 As stated in the Bibliographical Note, 'Object' translates Kant's 'Objekt,' and 'object' translates his 'Gegenstand.' 3 Treatise, 1.2.3. 4 I consider the views of some representatives of this position in chapter 2, below. 5 In taking this tack, I follow Gordon Nagel. For extreme advocates of the opposed view see Pippin, esp. ch. 2, and Waxman. 6 This is not to say that the specific locations of objects in space and time may not have to be constructed in accord with a priori concepts and principles but then the construction proceeds, in part, through reference to the already given locations of more primitive sensory data. 7 The qualification 'so far as is possible' is necessary because it is obviously the case that some abilities must be innate. If the processor has to learn how to learn, for example, it will never be able to get started. 8 AT, VIIIB 358-9. 9 Phaedo, 733-756. 10 Inquiry, 2.6; H, 1110-11. 11 De Anima, III viii, 43235-10. 12 Essay, 2.1.2. 13 Treatise, 1.1.1.

364 Notes to pages 7-12 14 AT, VI137-40. 15 AT, VI137. 16 The question of what constitutes a sensation and of how sensations differ - if they do - from innate ideas is a detail dealt with differently by the various sensationist theories. As my purpose here is classification, not exposition beyond the minimal amount necessary for classification, I pass over it here. In so far as it is an issue for Kant, it is dealt with in chapter 3, below. 17 Inquiry, 6.22; H, 1188-93. 18 For James, see ch. 20, esp. 270-82. 19 Though Kant rejects Locke's 'physiological' method at A86-7/Bn8-i9, he does not thereby reject all physiology. His complaint is really that Locke proceeds empirically, by observing how cognition, in fact, takes place in us following the 'historical, plain method.' Kant considers himself to be uncovering necessary conditions of the possibility of experience rather than merely empirically given factors. But nothing in his method rules out the possibility of physiological conclusions. These are the conclusions Kant arrives at in the Aesthetic. He may not always proceed by observing how cognition in fact takes place (though he does more of this than he would like to admit, as chapter 6 shows), but he does reach conclusions about the nature of spaceand time-cognition that entail that this knowledge must be based in the physiological constitution of the subject. 20 I will not pretend, however, that contemporary theorists of space- and timecognition have anything to learn from them - the arguments Kant directed against the primitive sensationism and constructivism of his day are equally primitive. 21 Aristotle and the school that grew out of his work on perception is perhaps best regarded as sensationist about spatial and temporal relations. 22 Kant fails to make any mention of the fact that his work in the Transcendental Aesthetic constitutes a contribution to the theory of perception. Perception (as opposed to knowledge) was not a question in which Kant had a great deal of interest. As evidenced by the framing question of the Transcendental Aesthetic, 'what, then, are space and time?' ^23/637), Kant saw himself to be out to address a fundamentally ontological question - one that had, in the details of its answer, profound epistemological implications (in so far as it provided an answer to the question of how synthetic a priori judgments are possible). But the implications that the detailed working-out of this answer, in terms of the formal intuitionist theory of space- and time-cognition, had for the theory of how it is that we come to know spatial and temporal relations were simply unnoticed by him. 23 Bennett, 4; see also Caird, 1281-2; Kemp Smith, 40-1 and 88-98; Garnett, 235;

Notes to pages 17-19

365

H.W. Cassirer, 23-4; and Robert Paul Wolff, 18, for examples of this view. The last work to do the Transcendental Aesthetic justice was the second volume of Vaihinger's Commentar of 1892. These days, when Kant's Aesthetic is read and discussed, it is for its incidentally articulated position on mathematical knowledge, or as perfunctory part of a treatment of the Critique as a whole. Introduction to Part I 1 Complaints about Kant's obscure terminology go right back to the very first review of his work, that by Christian Garve, re-edited by Feder and only subsequently published in its original form. See Garve, 839, who describes Kant's terminology as the thread of Ariadne winding through the labyrinth of his metaphysics. (I am indebted to Brigitte Sassen for drawing this passage to my attention.) Kant's piqued response was to charge that it was the business of his readers to figure out what he was trying to say through an appreciation of the whole of his work and not to plod through with the aid of a dictionary. (See, for instance, Entdeckung [Ak, VIII223].) But one has to start somewhere if one is to build up a picture of the whole, and for this reason dictionaries and indices of Kantian terminology have always had an important place in Kant scholarship. 2 Gram, The Sense of a Kantian Intuition/ makes this mistake. 3 See Stuckenberg, 90-1, who quotes from Kant's letter of early April 1778 to Herz (Briefwechsel, 170-3), giving his reasons for turning down Von Zedlitz's offer of an appointment at Halle: 'All change makes me fearful, even if it gives the greatest promise of an improvement in my condition; and I believe that I must heed this instinct of my nature if I want to extend to its full length the thread that the Fates have spun very thin and weak.' 4 The delightfully flirtatious letter from Maria Charlotta Jacobi of 12 June 1762 (Briefwechsel, 31) only goes to confirm this. She chastises Kant for leaving her and 'her female friend' to search for him through 'her garden' alone and wonders if he will come the next day to 'wind her clock' for her, mentioning that in the meantime she has been devoting herself to making a 'sword-belt' that will be dedicated to him. The only thing the letter proves is that he failed to show up for his earlier assignation. There is no indication that he managed to do otherwise later. But see George, 'Lives/ 490-1 and 49in. 17, for a somewhat less jaundiced view. 5 Stuckenberg, 360-4. 6 See Allison's introduction to his translation of the Entdeckung for observations on the relative merits of the objections raised by Maafi and Eberhard.

366 Notes to pages 20-8 7 See, for instance, his letter to Schultz of 26 August 1783 (Briefwechsel, 239-40), or that to Beck of i July 1794 (Briefwechsel, 677). 8 This is not to endorse the 'patchwork' thesis advocated by Kemp Smith, xix-xxv. According to that thesis, Kant changed his views over time and then patched a number of texts written at different times together into the Critique. What I am implying is the rather less flattering charge that he never got as far as definitely making up his mind, so that, rather than change his views over time, he changed his views depending on the direction from which he approached the problem. When one set of commitments was uppermost in his mind (as, for instance, when writing the fourth Paralogism in A), he would say one thing, and when another drew his attention (as, for instance, when responding to the Garve-Feder review), he would say another, and he would continue to hold both views simultaneously, simply hoping somewhere down the line to be able to work out a way of reconciling them. Since even the time before his death, that task of reconciliation has fallen increasingly on his commentators and expositors, who (with notable exceptions such as Adickes, Kemp Smith, and Vaihinger) have tended to be less historians of ideas than disciples and proselytes. 9 For a brilliant defence of the thesis that Kant was indeed engaged in a 'psychologistic' project see Kitcher, Kant's Transcendental Psychology, ch. i. Kitcher goes on to argue not only that Kant was engaged in such a project but also that it is not a bad thing to be so engaged - that Kant's 'transcendental psychology' is in fact an eighteenth-century ancestor of the sort of investigations of the 'task environments' of information-processing devices currently being undertaken in artificial-intelligence research and cognitive psychology. 10 See especially, chapter i, §vi, below. 11 For more on this see Hatfield, 12, and Kitcher, Kant's Transcendental Psychology, 12-13. Chapter i i Note the empiricism here. This sentence reads like a definition - as if 'sensibility, is just Kant's name for the manner in which we are capable of becoming aware of the effects objects have on us, whatever that manner may be. In fact, however, the term 'sensibility' standardly means cognition through the senses - the five external senses plus the inner sense of our own mental states gained through reflection or self-consciousness. Kant trades on this standard meaning. For him, affection through extrasensory sources, such as Platonic recollection, Augustinian mystical illumination, Cartesian pure intuition in the light of nature, Berkeleyan notional awareness, Reidian suggestion, or

Notes to pages 29-30 367 Swedenborgian spirit seeing, are never really taken to be serious options. He is, indeed, very concerned to argue against the possibility of intellectual intuition, but it is not clear that the alternative modes of knowledge just mentioned can all be legitimately described as forms of intellectual intuition. Empiricism is thus a fundamental presupposition for Kant, mitigated only by the remark that what is given through sensory experience may contain elements contributed by the mind itself as well as what comes from sensation. 2 There has been extensive discussion of whether these two views are identical and, if not, which ought to be taken as primary. See, most notably, Sellars, ch. i, §§3-78, 3-30; Hintikka; Parsons, 'Kant's Philosophy of Arithmetic'; Thompson; and Kirk Wilson. 3 Kant's terms Verstand and verstehen, are both equated by him with Latinate forms of intellect: intellectus and intellegere. However, I am reluctant to rely on the rare, English term 'intellection' to refer to the activity performed by the higher cognitive faculty. I have therefore adopted the practice of referring to the faculty (Verstand) as 'intellect' and the activity (verstehen, Verstand) as 'understanding.' Another, equally good, but also rare, word for understanding is 'discursion.' Kant occasionally employs it - for example, when saying that our intellects are discursive, which is just another way of saying that they understand, rather than intuit their objects. Using 'understanding' rather than 'intellection' has the further advantage of helping to make clear that the connection between the two is by no means as trivial as the terms 'intellect' and 'intellection' would imply. Kant thinks it is at least possible that some intellects may intuit rather than understand, so the identity of the faculty (sense, intellect) should be kept separate from that of the activity (intuition, understanding / discursion). 4 Kuksewicz and Mahoney. 5 Boler; Marenbon, 118-21. 6 Rules for the Direction of the Mind, xii (AT, X 415-16); Meditations on First Philosophy, VI (AT, VII 85-6); Passions of the Soul, I 47 (AT, XI 364-5); correspondence with Mersenne, 16 October 1639 (AT, II 598). The union is far from perfect in Descartes, however, since he frequently contrasts ideas gained by sense with those produced in imagination and with those clearly and distinctly perceived by the intellect. See, for instance, AT, VII 30-1 (Meditations, II) and 71-4 (Meditations, VI). His considered position appears to have been that sense and imagination are accidental modes of understanding, arising from the mind's union with the body. See AT, VII78-9. 7 Leibniz, 'Meditationes de Cognitione, Veritate, et Ideis' (Acta Eruditorium Leipzig, November 1684), G, IV 422-6; Christian Wolff, Philosophia Rationalis sive Logicae, §§77-89 of the main text; Baumgarten, §§504-33. Catherine

368 Notes to pages 30-1 Wilson, 73-103, has argued that the grounds for attributing a one-faculty theory to Leibniz are very slim (though the same does not hold for Wolff or Baumgarten). Still, her point is restricted to an explication of what can legitimately be inferred from Leibniz's texts. That the eighteenth century - and Wolff, Baumgarten, and Kant, in particular - read Leibniz as a one-faculty theorist is not open to question. 8 Baumgarten, §§521-2. 9 Hume, Enquiries, §2,17-18; Condillac, Part i, §2, esp. ^74; Helvetius, Essay i, ch. i. 10 The remark at Ai5/B29 that the two cognitive faculties 'possibly spring out of a common though to us unknown root.' Kant repudiates this remark in the Anthropology of 1798 (Ak, VII177), and even in the text in question he mentions that the common root is a mere 'possibility' (a sop to the dominant view?) and stresses that, even if there is such a thing, it is quite 'unknown.' 11 Tonelli; Hinske, esp. 68*-72*. 12 Hinske, 7O*~72*. 13 Ibid, 71*. 14 An amusing sidelight on this procedure of Kant's comes from the fact that, among the many translations of the Critique, four are into German (though one of these was also into verse, so perhaps it does not count) - a sufficiently clear indication of the degree to which Kant's 'undeutsche Ausdriicke' (Hinske, 68*n. i, citing Rosenkranz) were found unacceptable - and of the degree to which he ultimately succeeded at making himself intelligible. I am indebted to Rolf George for calling this surprising fact to my attention. See George, 'The Lives of Kant/ 485n. 6. 15 Hinske, 72*. The moral is one that has not hitherto made its way into Englishlanguage discussion of Kant's terminology. It is disappointing, for instance, to read Gram's 'The Sense of a Kantian Intuition' - certainly the most painstakingly thorough treatment of the issues surrounding Kant's use of the term Anschauung in the language - and see how Gram chases down every conceivable interpretative clue, including the etymology of Middle High German anscouuen, but fails totally to consider the Latin tradition. This, incidentally, is the main reason why I have chosen to translate 'Verstand' with the Latinate 'intellect.' Nothing is to be gained from translating 'Verstand' as anything other than 'intellect' - nothing other than a loss of sensitivity to the scholastic roots of Kant's thought. 16 Wundt, 117-20. 17 For this reason, the account of the sense/intellect distinction offered by Strawson, 47-8, following Prichard, 27-30, must be summarily rejected. An understanding of Kant's distinction must begin with Aristotelian cognitive

Notes to pages 32-5 369 theory, not with any 'austerely phrased necessities of thought' concerning the need to think all particulars under a certain description. 18 R5037 (AK, XVIII69). 19 See Kuehn, 'Kant's Conception of Hume's Problem/ and Kreimendahl, esp. ch. 2, in which extensive references to previous work on the question are provided. 20 What follows is loosely in accord with work on Kant's philosophical development and views on mathematics and physics that has been carried out by a number of scholars over the past decades. On Kant's philosophical development see Schmucker, esp. 421-33, though note that the position I go on to articulate differs from Schmucker's in some details. On the development of Kant's thought about mathematical and physical theory in particular see Friedman, Kant and the Exact Sciences, 1-34 and ch. i, and Brittan, ch. 2, 43-61, following work by E.W. Beth and Jaakko Hintikka. See also Humphrey, 485-90. 21 What Kant had in mind here may not have been just the simple matter of inspecting a diagram, though his views only come out fully later, in the Critique. For more on this see Friedman's Kant and the Exact Sciences, 96-127. 22 See esp. Brittan, 46-8,60. 23 For doubts about whether Kant ever inclined to the Newtonian position on substantival space see Reich, V-XVII, esp. XI-XII, and Friedman, Kant and the Exact Sciences, 5-9,28-9. For the opposite (more common) view see, among many others, de Vleeschauwer, Development of Kantian Thought, 47-51, and Stuckenberg, 418 and 4i8n. Even on Reich's and Friedman's position, however, Kant wanted to ascribe some reality to space - he just baulked at doing this by treating it as a substance. Consequently, arguments to the effect that space could have no kind of independent existence would have been troubling for him. 24 Kant seems to have found it impossible to conceive void space as anything other than an 'Unding.' See ID, §15 ID (Ak, IV 403-4); A26/B42; A39/B56; 670-1. In this he was in good company. Descartes's argument from the jar (Principles, II18) and Berkeley's stinging attack on the coherence of the notion of taking space to be a real substance when it can be conceived only through privative or negative qualities (De Motu, §§53-4) are just two indications of difficulties that many early modern thinkers experienced with this notion. 25 Kant's sensitivity to this problem is evident from 671-2. For more discussion of the nature of the problem and how it figured in the Leibniz-Clarke correspondence, where Kant likely encountered it, see Martin, 13-14. 26 In taking the tack I have followed here, and attributing the 'great light' of 1769 to a discovery of the importance of the sense/intellect distinction, I am

370 Notes to pages 35-6 setting aside a controversial, though by no means impossible, thesis advocated by Kreimendahl, to the effect that the 'great light' was occasioned by a reading of Hume. I am also repositioning the long-standing view that the content of the 'great light' consisted in a discovery of the subjectivity of space and time. If I am right, the fact that space and time are 'subjective/ whatever that might amount to, was merely incidental for Kant in 1770. He remarked upon it because it followed as a consequence from the real discovery: the existence of distinct sensible and intelligible worlds. While it would take me too far afield to go into them here, my reasons for setting aside Kreimendahl's hypothesis are given in The Great Light.' 27 Bayle, 'Zeno of Elea/ Remarks F-I. 28 Kant himself had already dealt with them in his Physical Monadology of 1756, where he had proposed a revised monadist conception of matter as the key to their resolution. For more on the intellectual climate surrounding the problem at Kant's time see Friedman, Kant and the Exact Sciences, 1-9, and de Vleeschauwer, 'Les Antinomies Kantiennes/ esp. 315-20, following Ernst Cassirer, II 497-505, 618-21. Cassirer's discussion is especially to be recommended for its treatment of the paradoxes in the context of the controversy over infinitesimals in mathematics. 29 See A438, 440/6466, 468. 30 See Allison, Transcendental Idealism, 39, following Al-Azm, Antinomies, 8, where the observation is made that, for Kant, the First and Second Antinomies are not concerned with space and time but with the world in space and time. 31 This is why, at A438, 440/6466, 468, Kant remarks that the paradoxes do not apply to space and time themselves, but only to entities that are supposed to be substantival, that is, such that they exist and are what they are independently of their relations to anything else, so that these relations are purely accidental to them, and so ought to be separable from them without destroying them. This is what the parts of substances are supposed to be like, whereas Kant takes it that the parts of space and time are defined through reference to their specific location in the whole, and so incapable of existence apart from reference to these relations. Since the parts of space and time are not self-subsisting entities, space and time are not supposed to be made up of parts that would remain even were all relations of composition removed. They are nothing more than those relations, and so would naturally be removed along with them. Of course, were space and time for some reason taken to be substantival (as Kant may have been tempted to suppose around 1768), then the paradoxes would end up applying to them as well. For more on this, see note 32, below.

Note to page 36 371 32 In the Physical Monadology, Kant answered the challenge posed by the paradoxes of composition and division by proposing that a substance can be extended in space but still simple because divisibility of a substance requires that the substance have parts, each of which can continue to exist on its own after separation (so that their composition in the substance would never have been more than 'accidental' to them to start with). Divisibility of a space, in contrast, requires only that one be able to demarcate its parts (say, by demonstrating the existence of a dividing line, point, or plane between halves of the space, as Kant does in Physical Monadology, Prop. Ill and Schol. [Ak, 1478-9]). And, Kant continued, from the fact that a space may be demarcated into two halves, it does not follow that the substance that occupies the space must similarly consist of two parts, such that one part occupies each half of the space and both could continue to exist on their own (Ak, 1480). Rather than fill space by 'a plurality of substantial parts' (Ak, I 480^), Kant maintained that a simple substance fills space "by the sphere of its activity' (Ak, 14813). Each simple substance, he claimed, has a repulsive force by which it excludes other substances from a certain region of space. But though this force defines a certain space as belonging to the substance, the substance itself is not to be imagined to be extended over this space (then it would be divisible). The space is simply quantitas extensiva praesentiae, the 'extensive quantity of the presence' (Ak, 148i27) of the substance, but not the substance itself. It is something that is created by the actione, 'action' (Ak, 1480^), of the substance, and though what gets created by this action, the space, may be divided (in the sense of having demarcation lines defined on it), the action that creates the space and the substance in which this action inheres are not thereby conceived to consist of parts that could actually be separated from one another and exist independently. As intriguing as this answer is, it was ultimately set aside by Kant. Though he officially explains why in the first observation to Proposition 4 of the Dynamics Chapter of the Anfangsgriinde (Ak, IV 504-5), the argument is so bad that it cannot supply his real reason. (For what it is worth, and here I follow a point already made by Adickes, 197-8, the argument begs the question against the physical monadist, who assumes that the monad at A exercises a repulsive force able to resist the approach of any other body within a sphere of radius Aa. To suppose, as Kant does, that A and a would approach each other unless a body at c intervenes and repels them both [the reader will here have to refer to Kant's 'proof and his diagram in Ak, IV 504-5] is in effect to deny what the monadist assumes: that the repulsive force of the monad at A extends out to a and is itself able to prevent a or anything at a from approaching A. Of course, it might be that Kant is supposing that the repulsive force acts only on contact,

372 Notes to pages 36-8 but that, too, is to beg the question.) An 'unofficial' but more likely reason for Kant's change of heart rests with the considerations advanced in the previous section: that his reflections on incongruent counterparts and construction in geometry were pushing him in the direction of treating space as an independently existing entity in its own right. This militated against the Physical Monadology's view of space as a derivative property or accident created by the action of substances, but, worse, it threatened to make space itself subject to the paradoxes of composition and division. As long as space is not considered to be an independently existing thing, but merely a determination or relation of substances, it can be affirmed to be infinitely divisible, and there is no problem because it is not conceived to be compounded from real things to begin with but to be nothing more than a network of relations, so that removing all relations of composition would naturally amount to removing the space itself. But were space supposed to be a self-subsisting entity in its own right, and so in effect a substance, this answer would not be available. The sense/intellect distinction of ID gave Kant a more profound and effective way of dealing with the paradoxes of composition and division - one that not merely solved the problem for bodies in space but allowed him to deal with the application of the paradoxes to space itself, which would be threatened were space taken to be substantival. Forging the notion of distinct sensible and intelligible worlds allowed Kant to attribute space and time to the way things appear in the sensible world, while maintaining that the substances that really exist are not in space or time at all, but are composites of simples given in a world discerned by reason (Ak, II 38913_14), and so to claim that he was not necessarily 'pleading a case' for the application of the concept of the continuous to objects in the intelligible world (Ak, II 38814_l6). (I am indebted to Allison Laywine for a number of critical comments that have helped me to improve as well as clarify the argument of this note.) 33 Compare Prolegomena, §13 Rem. Ill (Ak, IV 291-2), where almost the same wording is used to make the same point. 34 See in this regard Physical Monadology, Props. II and IV, where Kant argues that composite substances must have simple parts because were there no end to the decomposition of a substance - were division to go on forever without ever reaching any fundamental components - then this would mean that there are no fundamental components out of which the substance is built; that is, instead of being made up of something, the substance would be in effect made up of nothing - it would not exist. ID, §14 ^4, appeals to the same argument to establish the corollary point that time, since it is infinitely divisible, is not composed of simple parts and consequently consists merely of relations. (This, by the way, reveals Kant's major objection to the Newtonian

Notes to pages 40-3 373 notion of independently existing, or 'substantival/ as it is called, space and time. Space and time cannot be such entities, Kant thinks, because they are continua. As continua they are infinitely divisible, and as infinitely divisible they cannot be composed of parts. They are made up of nothing but are rather purely networks of possible relations. And, Kant concludes in ID, §15 ID, as well as A32/B49 and A39/B56, relations cannot exist on their own. They presuppose the presence of relata.) 35 I should stress that I am interpolating here. Whether accidentally or because of some purpose I am not able to discern, Kant drops space and the simplicity/continuity problem out of the discussion at this point (i.e., ID, §2iii [Ak, II 391-2]) and deals only with time and the totality/infinity problem. The application to the omitted cases is, however, quite straightforward. 36 This is hypothetical because Kant is at this stage proposing as a project to go on to demonstrate that space and time are indeed conditions just of intuitive cognition. 37 An awkward feature of Kant's resolution of the paradoxes is that he accepts that space and time are themselves continuous and infinite. (See, for instance, Ak, I 478-9, a demonstration of the infinite divisibility of space that he never abandoned.) But, according to what he has said in dealing with continuity and infinity, these latter concepts cannot possibly be represented in intuition, though they are not for that reason to be rejected as possibly valid discursive representations. Thus, Kant ends up being committed to the position that, as they are given in intuition, space and time are not represented as either continuous or infinite, but that these are features that are discovered only by the intellect, when it examines space and time as objects and 'discourses' (i.e., reasons demonstratively) concerning them. (See Anfangsgrunde [Ak, IV 5067], where Kant admits as much, stating that infinite divisibility can be thought by reason, even though it cannot be constructed and rendered intuitable.) There is, of course, no absurdity in this, since Kant only takes the intellect to demonstrate that substances are composed of simple parts (and he does not think that space and time are substances - cf. Ak, II 39922-yX and since he is willing to allow that there is a 'logical' use of the intellect (where it expands upon and analyses the objects of sense intuition) as well as a 'real' use (where it cognizes its own, proper objects). See ID, §5 (Ak, II 393-4), where this point is made with explicit reference to geometrical demonstrations (such as that of Ak, I 478-9). 38 For more detail on these points, see Marenbon, 119-21. 39 The so-called real use of intellect (ID, §5) is an exception to this. As Kant puts it in ID, §6, 'where the use of the intellect is real,... concepts whether of objects or relations are given by the very nature of the intellect and they have not

374 Notes to pages 43-9 been abstracted from any use of the senses nor do they contain any form of sensitive cognition as such.' However, ID, §8, quickly goes on to add that 'the concepts met with in metaphysics are not to be sought in the senses, but in the very nature of the pure intellect, and that not as concepts born with it, but as concepts abstracted out of the laws planted in the mind (by attending to its actions on the occasion of an experience), and so acquired concepts/ Even in its real use, therefore, intellect does not intuit its concepts immediately but deduces them discursively, by reflecting on its own operations in the process of cognition. 40 Perhaps because the infinite divisibility of space guarantees that any given concrete particular will have a richness of internal structure that cannot be apprehended in any finite time, but here I speculate. Kant seems to take the observation as being simply obvious. 41 See Entdeckung (Ak, VIII i99n), where Kant uses this chemical metaphor. This footnote is very helpful for illuminating the obscure and difficult point Kant is seeking to make in ID, §6. Though as author of the Entdeckung Kant no longer believed in a real use of intellect, uncovering concepts of things as they are in themselves, the point he is concerned to make in the Entdeckung about our concepts of space and time not being abstracted from experience is the same point that he earlier wanted to make in ID, §6, about ideas arising from the real use of intellect not being abstracted from experience. 42 The claim that Kant was significantly influenced by reading Leibniz's New Essays after they first appeared in 1765 has long been a standard point of scholarship on Kant's philosophical development. See, among many others, Tonelli, 234, and Beck, 'Lambert and Hume,' esp. 103-4. For reservations see de Vleeschauer against Windelband in de Vleeschauwer, Development of Kantian Thought, 45-6. 43 Marenbon, 121. 44 Meditations VI (AT, VII72-3). 45 Euler's paper 'Reflexions sur 1'espace et le temps/ was well known to Kant (Ak, II 378). 46 This is how Kant understood the Leibnizian position - witness ID, §7, and A43~5/B6o-2. 47 Why a 'pure intuition' rather than 'a form of the sensible world'? As I go on to show in the next paragraph, it is really the latter that follows. What we have here is a continuation of the terminological slippage already noted above in connection with ID, §1, where Kant runs 'intuitive cognition' and 'the sensitive faculty' into each other. This conflation occurs because Kant takes intellect to be an exclusively discursive cognitive faculty. As a result, he

Notes to pages 49-58 375 slips into thinking of sense as 'the intuitive faculty' so that 'forms of sensible experience' become, for him, ipso facto, 'forms of intuition.' 48 The title of the time paragraph (ID, §14 li) is potentially misleading. There Kant says that the idea of time does not arise from (non oritur) but is supposed (sed supponitur) by the senses (a sensibus)\ This should not be read as saying that time is not given in sensory experience at all. Kant really only means to say that the temporal order is not given in sensation. It is 'presupposed by the senses' only in that it is not inferred or derived subsequent to the act of sensing by comparing or abstracting sensations. But it is given, along with sensations, in sensory experience. The title of the corresponding space paragraph (ID, §15 !A) is clearer. There it is said that space is not abstracted (non abstrahitur) from external sensations (a sensationibus externis). 49 In ID, Kant postulates that this form is not simply received in the process of sensation but created by the sensitive faculty itself and imposed in accord with certain 'stable and innate laws' (ID, §4). 50 To the degree that the arguments recur in the Aesthetic they are examined in Part II, below. 51 Kant here opposes intuitive to symbolic, rather than discursive cognition. This distinction originated with Leibniz, G, IV 423, and it later found its way into the entry under' Anschauung' in Johann Christoph Adelung's Grammatisch-kritisches Worterbuch der hochdeutschen Mundart, where it played a crucial role in the definition (and unfortunately has continued to play a major role in contemporary discussions of what Kant meant by 'intuition'). As a matter of fact, Kant explicitly rejected the intuitive/symbolic distinction: 'It is a contrary and incorrect use of the word symbolic to contrast symbolic with intuitive modes of representation (as the new logicians have done). For the symbolic is properly a species of the intuitive' (Ak, V 351; I am indebted to Brigitte Sassen for drawing this remark to my attention). The remark is made only in the Critique of Judgment of 1790, but it is unlikely that this was a late modification to Kant's views. Already in the Prize Essay of 1764, for instance, Kant describes mathematical proofs - the things he is later to describe as constructions in 'pure intuition' - as proceeding through operations performed upon 'symbols in concrete' (§2). 52 The historical remarks that follow represent views that have long been standard among Kant scholars. For a representative exposition see Beck, 'Kant's Letter to Marcus Herz,' 57-60. 53 ID, §6, and Entdeckung (Ak, VIII iggn) hint at this motive. 54 Hintikka, 42-3; Kirk Dallas Wilson, 252-6. 55 Bennett, 4; see also Caird, 1281-2; Kemp Smith, 40-1 and 88-98; Garnett, 235; H.W. Cassirer, 23-4; and Robert Paul Wolff, 18, for examples of this view.

376 Notes to pages 58-67 56 See, for instance, Ernst Cassirer, II684-5; Robert Paul Wolff, 18; Walker, 12. 57 Our blindness to intuitions is not, therefore, so total that it allows us to doubt that there might even be intuitions, as some of Kant's commentators have worried. (See, for instance, Kolb.) Though intuitions are 'nothing to us' without concepts, they are not nothing. Their existence follows because intellect itself can only supply the form of unity, not any of the content of representations. The fact that we think objects rather than bare forms of unity is therefore already sufficient proof of the existence of intuitions. 58 This will prove to have implications when the time comes to consider Kant's position on space and time in the Critique. In ID, as noted above, Kant took spatiotemporal order to be the product of a law-governed synthesis of sensations. The new stress on the receptivity of sense will not permit this. 59 Vaihinger, II155-6; Kemp Smith, 99; Paton, I io8n. i; Wilkerson, 22. But see Parsons, Transcendental Aesthetic,' 65; Allison, Transcendental Idealism, 91-2; Pippin, 65; Walker 42-3; and Bennett, 62, for the contrary opinion. 60 And for Kant it would have been not only difficult but obscure, given that aside from Berkeley's New Theory of Vision - a work that does only a partial job of reducing visual space to a construction on more primitive data (see my 'Intuition and Construction,' where I have maintained this against Hatfield, 105-6, and Kitcher, Transcendental Psychology, 41) and with which Kant in any case demonstrates no clear acquaintance - no significant work had been done on constructivist accounts of space-cognition. It is for this reason that I maintain that Kant's critique of constructivism was unintended. Had he been aware of good constructivist theories of space-cognition, his own position would doubtless have been more sophisticated. 61 It may seem odd that Kant should thus be employing precisely the same premises to derive radically different conclusions, but, odd though it may be, it is by no means an unprecedented thing for him to do, especially where his thought about space and time is concerned. We can see the same thing happening with incongruent counterparts, where the same set of premises is used in the 1768 paper on quadrants in space to justify the conclusion that the relational theory of space must be rejected, in ID, §15C, and Prolegomena, §13 (Ak, IV 285-6) to justify the conclusion that space is given in intuition, and in both the Prolegomena and the Anfangsgrunde (Ak, IV 483-4) to justify the further conclusion that space is not a feature of things as they are in themselves. 62 Indeed, it follows that intuitions must be physiological states of the body of the perceiver, as I go on to argue in chapter 3, below. Thus, Kant still ends up with a physiological account of the lower cognitive faculty, just as Aristotle does. But this is a consequence of his proving that space is a form of intuition,

Notes to pages 67-77 377 not an empirical observation taken for granted from the outset. At the outset, intuition is defined in exclusively information theoretic terms. 63 Ironically, while we intuit in space and time, our knowledge that we do so is discursive (following from a demonstration). 64 Some of Kant's pronouncements on the topic are only apparently about singularity. This is most notably the case with ^4 of the 'Metaphysical Exposition of the Concept of Time.' There Kant writes that 'that representation that can only be given by a single object is an intuition.' The remark is really quite bizarre, because Kant is not saying that the intuition itself is singular or that it can only represent a singular object, but that it can only be caused by a single object. Prolegomena, §8, gives some clue what he might be after. There he writes: 'Intuition is a representation in so far as it would depend immediately on the presence of the object.' Here the contrast appears to be between the immediate effects of objects on the representative capacity and subsequent, higher-order representations of these effects, which could take place at any time, regardless of whether the affecting object is acting or not. Only the former are 'intuitions' because only they are immediate. But ^4 of the Metaphysical Exposition appears to be saying much the same thing as Prolegomena, §8: that intuition is that representation that depends immediately on the presence of an affecting object. It is just that the notion of immediate dependency is conveyed by saying that a particular object is what gives the intuition. Despite what might be concluded at first glance, therefore, ^4 of the Metaphysical Exposition is not saying that intuitions are singular representations; rather, it is saying that they are immediate effects of particular objects. Chapter 2 1 For a defence of a very strict reading of the implications of blindness see Kolb. Kitcher, Transcendental Psychology, 83-4, gives much the same answer to the problem as that which follows here. 2 A corollary of the position I am articulating here is that, in themselves, our intuitions in space and time are neither distinct nor unified. In other words, each of us only ever has one intuition. This intuition occurs over time (the length of our lifespan) and it is constantly growing. It also is spread out over space. Both the space and the time of the one intuition are unbounded (in the sense that they have no discernible outer rim). All plurality of intuitions arises from acts of mind, delimiting and bounding the space and time of the one intuition. And all unity of intuitions arises from acts of mind as well, bringing the manifold matters arrayed in different portions of the space and time of the one intuition to a unity under concepts. Though Kant never says

378 Notes to pages 77-81 that we only ever have one intuition (which is why this speculation deserves only a place in a footnote), the thesis does have a great deal of affinity with what he does have to say about the unboundedness and whole/part priority of space and time in the Metaphysical Expositions. 3 This point has been seconded, expanded, and worked into a profound and original account of Kant's theory of mind by Brook. I am indebted to him for allowing me to see a manuscript of his work, prior to its publication. While he and I disagree about some details, particularly concerning the manner in which Kant takes time to figure in cognition, what he has to say about the nature and role of 'global representations' constitutes a further substantiation and application of the views expressed here. 4 George, 'Kant's Sensationism,' 240, cites 6151; Hatfield, 103, cites Ai2i; Makkreel, 22, mentions Aioo and Ai43/Bi82; Waxman, 79-80, appeals to Bi6on. 5 Makkreel should be included in this group only with qualification as he recognizes that Kant takes space and time to be immediately given in the Aesthetic (see p. 22). Waxman is more radical; his whole book is devoted to proving that space and time are constructed by imagination, but see esp. p. 95 for a remark on imagination being guided by innately originating laws. In addition to the authors mentioned in the previous note, Patricia Kitcher, both in Kant's Transcendental Psychology, ch. 2, and in her earlier 'Discovering the Forms of Intuition,' has developed a detailed account of Kant's forms of intuition as 'process forms' generating spaces and times. 6 Few commentators have put the point quite this crudely. But see Waxman, 14 7 II 85, 94-8. Vaihinger was followed by Kemp Smith, 88-94. 8 Especially telling in this regard is the fact that Kant appears at some point to have considered the possibility that space and time might be pure intellectual concepts - either of the same type as the categories or special, 'intuitive' intellectual principles - and then to have moved away from this view. For the former view see R3927, 3930, and 3941 (Ak, XVII 349, 352, 356). For the latter see R3957 (Ak, XVII 364-5). (Contrast R3974 [Ak, XVII 371], where spatiotemporal form is clearly ascribed to sense in contrast to reason or intellect, and see Ernst Cassirer, II 621-8, for a discussion of the evolution of Kant's views on the matter and some speculations on when the non-Critical views were entertained [II 622n suggests sometime between 1768 and 1770, which corresponds to Adickes's dating of these reflections].) 9 That Kant did once mean exactly this is indicated by R3957 (Ak, XVII 374-5), dated by Adickes to 1769. However, since this reflection also goes on to identify space and time as intellectual concepts, it can hardly be looked upon as an expression of the Critical account.

Notes to pages 82-6 379 10 Kitcher, Transcendental Psychology, 23911. 35, passes over these passages. While the premises of Kant's arguments here may not have the most obvious relevance for questions of transcendental psychology, their intent of proving that space and time are originally given and not products of a synthesis is one that ought not be lightly dismissed. 11 Kitcher, Transcendental Psychology, 36 12 Allison's translation is irreproachable, and I have largely followed it here. 13 II80-8. 14 It is not, unless one takes each distinct moment of an intuition to be a distinct intuition. If, however, we go to the other extreme and take it that there is only one intuition, extended over an indefinitely long time, and that all distinct 'intuitions' arise from intellectual acts of delimiting portions of this originally given time, then it remains indeterminate exactly how far out, in both time and space, the intuition extends. 15 It may be objected that Kant also refers to pure spatiotemporal form (which, on the view I am advocating, must be seen as an intellectual abstraction from empirical intuition) as pure 'intuition.' But it is possible to take the expression 'pure intuition' to be elliptical for 'pure form already present in the empirical intuition,' whereas 'empirical intuition,' taken to refer to the spatiotemporal manifold of sensations, cannot be any sort of elliptical reference to a part or aspect of pure intuition. 16 Ai72/B2i4; 6219,225,257; A2i4/B26i; A487/B515; A521/B549. See also Ak, II 399, 401. 17 Vaihinger, II180-4, found the solution to this perceived problem of Kantianism in the theory of local signs, which he attributed to Lotze and Herbart. (In fact, the theory that position on the visual field is learned through experiencing certain sensory qualities that remain invariant with the location of retinal stimulation seems to have first been advanced by Johann Steinbuch in 1811. See Hatfield, 131-43.) Today one finds this view being attributed to Kant himself by Kitcher (Transcendental Psychology, 35-43), though with certain reservations about whether or not the principles linking our supposed local sensations with concepts of location in visual space are innate. For more on the history of the theory of local signs see Pastore, 153-91. 18 Vaihinger, II180. 19 1185,92-8. 20 A strained position given that the note occurs in Kant's remarks on the argument rather than in the argument for the Antithesis itself. 21 As if Kant's views on the two could be easily separated in his treatment of the antinomies! 22 II 85.

380 Notes to pages 86-8 23 1184. 24 Both of these views may seem to pose problems for Kant's transcendental idealism, which might be interpreted as ruling out the very possibility of speculation about what it is that causes the matter or the form of intuition. These problems, in so far as they arise for the view I am defending, are addressed in chapters 8-11, below. For now, however, just note that whether such claims are consistent with transcendental idealism or not, Kant does indeed say that the form of intuition 'lies ready a priori in the mind,' and that this claim, consistent or inconsistent, must be integrated into his account of space, time, and the forms of intuition. If the claim is inconsistent, then Kant's view that space and time are either distinct, a priori intuitions in their own right (as Vaihinger holds) or a priori elements of an empirical intuition (as I hold), will be fundamentally incoherent. But one or the other of these alternatives will still be Kant's view, incoherent though it may be, and the job of the historian of ideas will be to reflect it in all its incoherency. As a matter of fact, however, my job as a historian will not have to be quite so grim. In chapters 8-11, below, I argue that Kant's claims about the respective origin of the form and the matter of intuition do not presuppose any knowledge of things in themselves, as affecting objects, or the mind as it is in itself as transcendental subject generating experience out of impressed effects. They instead grow out of the Metaphysical and Transcendental Expositions of space and time, on the one hand, and a hitherto unremarked upon 'empirical exposition' of our concepts of sensible qualities that Kant includes, without appropriate fanfare, in the Aesthetic. In all cases, the Expositions proceed from the content of our concepts of space and time, on the one hand, and our concepts of sensible qualities, on the other, as these things appear to us. From this content the Expositions establish, first, a distinction between space and time, on the one hand, and sensible qualities, on the other, and, then, the special status of space and time as a priori, in contrast to sensible qualities as a posteriori, representations. Kant's claims about origin in the mind and through affection by objects are ultimately merely speculative hypotheses floated to account for the ground of this distinction. Rather than coming at the beginning of the Critical Philosophy, as its foundation, they are really only appropriate at the end, as a possible or likely account of the presence and characteristics of elements of which we are already, on quite independent grounds, certain. 25 Even the Analogies are concerned to account only for our cognition of the spatiotemporal relations of objects, and for this purpose they take the spatiotemporal order of subjective perceptions (e.g., that I see the top of the house before the bottom, or feel the warmth in the room before seeing the fire in the stove) as already given.

Notes to page 88 381 26 27 28 29

Kemp Smith, 86. Al-Azm, 39. Riehl, cited by Kemp Smith, 88. Kitcher, too, has argued that Kant can be defended against this objection, but on quite other grounds than those I give. Her position is that Kant does, indeed, simply assume that space and time are not given in sensation, but that, after Berkeley's revolutionary treatment of visual space perception in NTV and Leibniz's similar work on tactile space perception in his account of the Molyneux question in the New Essays, a rejection of sensibly based knowledge of space would be no more than an appeal to common background knowledge - and hence not an illegitimate assumption for Kant to make (Transcendental Psychology, 41-3). Philosophically this is an interesting and viable defence of Kant, but biographically it stands on very shaky ground. Berkeley and Leibniz may well have created an environment of scepticism about the ability of sense to convey information about spatial information (though, for some reservations on this score, see my 'Intuition and Construction') but the information Kitcher is able to muster for the thesis that Kant was at all in tune with these views is slim. There is little evidence of a preoccupation with the problems of visual perception in Kant's writing certainly none that can compare with the evidence for a preoccupation with the problem of mathematical method, the paradoxes of composition and division, the Leibniz-Newton debate over the ontology of space, or the significance of incongruent counterparts. This is so much the case that Kitcher ends up having to base her interpretation on an appeal to ignorance: Kant does not mention Berkeley on vision or Leibniz on the Molyneux question, but then he hardly ever mentions any other source of influence either (Transcendental Psychology, 35). A concern with the problems of space-cognition is none the less supposed to be demonstrated by certain lectures and by remarks in the Anthropology (itself a collection of Kant's lecture notes). Hatfield, 105, makes similar claims. But lecturers do not commonly confine themselves to expositing their own theories in their survey courses, and the fact that Kant knew of a theory or controversy is not by itself evidence that he was at all influenced by it. Indeed, if Kant's early remarks on the focus imaginarius (see Traume Ak, II 344-8; I am indebted to R.E. Butts, 'Methodological Structure,' igin.ig, for drawing these remarks to my attention) are any indication, his own views on the psychology of visual perception may have reflected the naive Keplerian position that we perceive depth by noting the convergence of light rays, not any appreciation of Berkeley's later concerns with this view. Kant did indeed have profound things to say about visual perception in general, and space-cognition in particular. But there is every

382 Note to page 89 indication that his contributions were an outgrowth of other methodological and ontological problems, not of any direct concern with the problems of space-cognition. 30 Besides the recalcitrant passages, there is one recent objection to the position I am advocating that should perhaps be mentioned: Waxman's claim (pp. 13-14) that ascribing 'real relations of juxtaposition, simultaneity, or succession' to sensations would either entail or at least 'make possible' the ascription of these same relations to things in themselves. It is this perceived problem that drives Waxman to construct the entire interpretation of Kant offered in his book. Yet, Waxman never explains why the spatiotemporality of sensations should make the spatiotemporality of things in themselves any more possible than it would be regardless. Waxman illustrates his claim with the example of seeing a pen roll down a desk while hearing a phone ring and being led, from the postulated simultaneity of the sensory experiences to infer that the pen and phone 'in themselves' are simultaneous. However, this is an inference that has no validity, even where the relation between sensory contents and objects considered as appearances are concerned. When I look up at the sky and see two stars simultaneously, I am not entitled to conclude from this that the two stars, considered even as appearance, let alone in themselves, exist simultaneously. And the reason for this has nothing to do with the idea that my sensory experiences are not simultaneous in time. Even granting that they are, the fact remains that the object of perception need not exist at the time of the percept. When extended to things in themselves, Waxman's claim becomes even more tenuous. Here an inference from the temporal location of my sensations to the temporal location of things in themselves is blocked, not because my sensations do not in fact occur successively over time in my experience of them, but because there are even stronger reasons (having to do with Kant's supposed subjectivity of space and time) to assume that the location of the 'effect' carries no implications about the nature of its 'cause' (if, indeed, any sort of causal reasoning can be supposed to be legitimate in this case - which is itself a highly dubious supposition in Kant's eyes). Aside from these considerations, Waxman's own suggestion, that all spatiotemporal order is constructed by the imagination, is no less liable to his objection than the view he disparages. If it is supposed that the spatiotemporal localization of an effect entails the spatiotemporal localization of its cause, considered as thing in itself (and this seems to be the tacit supposition that drives Waxman's examples), then why should I not be just as able to conclude that, insofar as my imagination assigns my sensations to various locations in space and time, it, considered as thing in itself, must be extended in space and acting over time? If it is illegitimate to assume that the 'imagina-

Notes to pages 91-3

383

tion in itself needs to be in space or time to cause an awareness of sensations in space or time, then why should it not be equally illegitimate to make this supposition of other things in themselves? And if the supposition is made of other things in themselves, then why should it not also be taken to license a conclusion about the imagination considered as thing in itself and so knowledge of the transcendental subject? 31 (Lest I be accused of blustering or offhandedly dismissing a serious piece of contrary evidence, I will here append a brief description of how Bi6on may be interpreted to suit the purposes of the position I advance in this book. I relegate this demonstration to a footnote because to accord Bi6on any more consideration would be to compromise the methodological precepts laid out in the Introduction to Part I, above. The reader is advised to consult subsection 'd/ immediately below, for relevant background to the account that follows.) Bi6on opens by drawing a distinction between space considered as form of intuition and space considered as formal intuition. The formal intuition is described as differing from the form of intuition in that it contains a combination of the manifold given in the form of intuition. Since, as 6129-30 points out, all combination is an intellectual act, it naturally follows that the formal 'intuition' of space will be a discursive, intellectual representation (and hence not an intuition, properly speaking, at all). But just because space considered as 'formal intuition' is determined by the intellect, it does not follow that space considered as 'form of intuition' is likewise dependent on intellectual determination. A manifold of matters could still be disposed alongside one another in space in our original sensory experiences prior to any intellectual combination under concepts. And moreover, since all combination presupposes the presentation of some material to be combined, this 'form of intuition' could well be described as an antecedent condition of the possibility of any intellectual determination of the 'formal intuition.' All that Bi6on can legitimately be taken to claim is that when the parts of the sensibly given manifold are collected together in the thought of a single or unified object (i.e., a formal 'intuition' of a space) an intellectual procedure is involved. Admittedly, Bi6on does not say that space is first given as a formal intuition by means of an intellectual synthesis, but just that it is given as an intuition by means of intellectual synthesis. But if anything comes out clearly in this tortured text, it is that intellectual synthesis is required just to effect a unification of the parts of the manifold in a single representation, and that this unity belongs to the formal intuition, not the form of intuition. 32 Waxman, 40, challenges his readers to 'adduce one or more instances of Kant's explicitly and unequivocally denying that imagination has a role to play in the advent of any representation of space or time whatsoever.' These pas-

384 Notes to pages 95-7 sages, where Kant ascribes space and time to receptivity, fit the bill. Waxman is not unaware of them. At one point (pp. 33-4) he remarks that they appear to conflict with his own thesis that space and time are originally produced by a synthesis of imagination, but he goes on to claim in his own defence that 'there are in fact two quite distinct senses of understanding [intellect] and spontaneity operative in Kant's philosophy: the discursive (conceptual, judgmental) sort and the nondiscursive.' Waxman takes discursive understanding and spontaneity to be involved just with 'concepts and the thought (in a judgment) of an object in general.' He holds that this leaves open the possibility that there may be a preconceptual, non-discursive variety of understanding and spontaneity (associated with imagination) that is originally responsible for space and time. But this position is unsustainable. As noted in chapter i, above, in the tradition in which Kant is working the discursive is not opposed to the non-discursive as the general to the particular, or as the conceptual to the imagined, but as the product of a process to that which is immediately given as raw datum. But even if Waxman were right and 'discursive' just meant 'general concept,' one stubborn fact would still not go away: the fact that Kant does not ascribe space and time to any kind of spontaneous activity of the soul but to our receptivity. Is Waxman's 'nondiscursive spontaneity' supposed to be identical to what Kant calls 'receptivity'? Then either his thesis is not as radical as he thinks (space and time are not the products of a synthetic process but are simply received - Waxman all but concedes this point in ch. 3) or he makes Kant say the very opposite of what he writes (space and time are products of a synthesis of imagination performed upon more primitive given elements, despite the fact that Kant writes of them as if they were raw data received prior to any synthesis). 33 I stress that I am speaking of the eye as a receptor system, not the visual cortex, much less the mind. 34 This same point has been made by Hatfield, 106-7, though against the background of a forms-as-mechanisms reading of Kant's position. 35 Kant's reflections from this period make numerous references to a distinction between an objective spatiotemporal order that results from combination in accord with principles and a haphazard, subjective order given in intuition. Among the most explicit of these references is the first page of 1^4675 (Ak, XVII 648-9), which was written on the back of a letter from Bertram dated 20 May 1775. For more on this see Guyer, 25-70, esp. 33-7. Guyer's exposition of the Duisburg Nachlafl and other Kantian texts of the period around 1774 makes clear that Kant is not merely filling in an unwelcome gap in the exposition here. On the contrary, he wants it to be the case that the formal temporal structure given in intuition should be inadequate to specify the real

Notes to pages 98-103 385

36

37

38 39

locations of objects in time. Kant hopes that, by supplying a set of rules for linking the subjective temporal form given in intuition with the real temporal relations of objects, he will forge a link between sense and intellect, explaining in the process why the categories must have objective validity as conditions for the possibility of experience. Kitcher, Transcendental Psychology, 74-7, presents an example of a case where combination does seem to generate spatial features: the Necker cube. This example really illustrates a higher-level process of space-cognition that is built on the data supplied by an original combination of the intuited array. (The Necker cube is, after all, a two- dimensional array in space that is ambiguous only when interpreted as a solid.) For more on this see the concluding paragraph of this section. It is also an aspect of cognition that was much discussed in the early modern period. For more on this see Mijuskovic, 54-6 and ch. 3. Kant's most likely source for this item of concern would have been Mendelssohn's Phaedon of 1767, though he would also have been able to run into it in Bayle (Dictionnaire, art. Leucippus, rem. E), or in Condillac's Essai sur I'origine des connaissances humaines, Part I, §1, ch. I, §6 - sources surprisingly not mentioned by Mijuskovic. See also A253/B2O9. It is also what is going on in Kitcher's example of the Necker cube. See note 36, above. Chapter 3

i For comments on the relation between Kant and Reid see Kuehn, Scottish Common Sense, ch. 9, and esp. 205-7, 242-4. While Kuehn sees many parallels and lines of influence between Kant and the Scottish school, Reid's account of perception is not one of them. On the contrary, Kuehn sees Kant as someone who walked in the way of ideas, who at the same time never 'offered any explicit arguments for rejecting the most fundamental tenet of Reid's critique of the theory of ideas/ and who, as a result (to paraphrase the critique Kant himself leveled at Reid in the Prolegomena), 'lost or misconstrued Reid's most valuable suggestions - and this in a fashion often painful to observe' (p. 242). Kuehn stipulates, however, that this assessment of Kant depends on accepting a phenomenalist account of Kantian appearances and holds that, were this account rejected, further research would be required on the question of whether Reid might have influenced Kant to reject the theory of ideas. On a related topic, Kuehn (pp. 176-7) sees Reid's account of sensations suggesting perceptual beliefs in virtue of original principles of the mind as possibly

386 Notes to pages 105-10 influencing the ID account of space and time as laws for the coordination of sensa. But any lines of influence there might be here must be slight, given that Reid's whole effort was to argue that spatial determinations are suggested of the external objects intended through acts of perception, and that our sensations, as acts of feeling of an immaterial mind, are in no way spatial. 2 It was passages such as this one that led George, 'Sensationism,' 229-41, to claim that Kant, like Reid and Condillac, took sensations to be mere feelings in the subject that have no representational function - they are not supposed to stand for anything other than themselves. 3 For germinal work on the act/object ambiguity in early modern philosophy see McRae, and Yolton, Ideas and Knowledge.' 4 This is the view of Kemp Smith's 'phenomenalist' Kant (pp. 270-84). 5 For a specimen of this approach see Aquila, Representational Mind, 33-146. 6 See Allison, Transcendental Idealism, 3-34,237-54. 7 There are various ways this might be done. The previous three notes give three possibilities. 8 The argument of this section borrows heavily from Aquila, 'Sensation.' 9 Among English commentators it has been held by the most recognized figures of the previous two generations, Kemp Smith (pp. 280-4), and Strawson (p. 91)10 See d. (iii), immediately below. 11 As remarked in the Bibliographical Note, I have attempted to preserve Kant's use of Gegenstand and Objekt in translation by translating the former with as 'object' and the latter as 'Object.' While it is not clear whether Kant intends this terminology to reflect a specific distinction, he does generally use Objekt to refer to a representation that emerges through synthesis of the intuited manifold in accord with the categories. Gegenstand tends more often to be used to designate the external, affecting object, independently of reference to whether it is represented by us or not. 12 The objects of perception that we postulate as influencing our sensory states still have a problematic status. They might be higher-order subjective states that we construct in accord with certain laws. They might be intentional objects considered in so far as they appear through our sensory experience and thus in conformity to certain epistemic conditions. Or they might be things as they really are in themselves, to which Kant mistakenly denies us epistemic access. For more on these possibilities see Bennett, Allison (Transcendental Idealism) and Aquila (Representational Mind), and Guyer, respectively. I will show below that the second of these three options represents Kant's considered view. 13 George, 'Sensationism,' 240-1.

Notes to pages 110-14 387 14 Kitcher, Transcendental Psychology, 174-80. Kitcher's claim that, for Kant, we determine temporal relations by applications of the causal principle is true of the temporal relations of objective states of affairs, but false of the temporal relations of intuitions. The latter serve as data enabling the application of the principle to generate the former, so that, while objective temporal relations may be determined by the causal principle, causal relations are determined, at least in part, by intuited temporal relations. The opposite view, that all temporal relations are determined by the causal principle, was roundly rejected by Kant in the Amphibolies ^275-6/6331-2, A267-876323-4), where he condemns Leibniz for taking precisely this intellectualist approach to time-cognition. Note, by the way, that the 'click experiment' that Kitcher (p. 179) cites cannot be taken as evidence that the temporal order is constructed by the mind. The most that it proves is that there is a certain threshold below which temporal relations cannot be discriminated and that, when required to make temporal discriminations below this threshold, the mind imports other criteria than experienced temporal order. In any case, the question is what Kant meant, and that is not a question that can be answered by appealing to the results of contemporary research on the issues Kant tried to address. 15 Kant does remark that time alone is the form of inner sense, and so of the mind's intuitions of itself and its inner states (A22/637), and this might be taken to substantiate George's claims - but only if we suppose that sensations belong, one and all, to inner sense, and this is a supposition that is rendered impossible by Kant's explicit recognition of the existence of 'outer' as well as 'inner' sensations ^23/638; KdU [Ak, V 189]; Anthropology [Ak ,VII 154]). Kant does take inner sense and, with it, time to be more inclusive than outer sense and space (A34/B5O, this is why he writes the Analytic of Principles around time rather than space, cf. A98-9, Ai38/Bi77>. But he says nothing to indicate that space is derived from time or any further features of the things given over time. The third analogy (which in any case mentions only the derivative objective order, and not the originally given subjective one) is no exception to this: it is concerned only with the determination of the simultaneity of objects in time, not with their localization in space. 16 Representational Mind, 68, my italics. Aquila's position has been further developed in Matter in Mind, esp. 6-12. 17 I am indebted to 6rigitte Sassen for drawing these passages from KdU to my attention. 18 This passage tells strongly against George's claim (in 'Sensationism') that Kant took sensations to be 'non-intentional' in the sense that they do not refer to anything other than themselves. Sensations, considered as 'determinations

388 Notes to pages 115-18 of the feeling of pleasure or displeasure/ are certainly non-intentional, but sensations considered as deliverances of the sensory faculty are not. This is one reason why we should not follow George's suggestion that Kant be numbered as a sensationist along with Condillac and Reid. 19 The following points borrow from Siegfried. 20 See A20-1/B35; 644; A29; Ai75/B2i7; Ak, IV 290, VII168, XX 268-9. 21 Prolegomena, §9, which states that the properties of a present thing cannot migrate into my representative capacity [Ak, IV 282] and thereby lead me to know it as it is in itself, does not contradict this. What is originally given to the representative capacity is the sensation (e.g., of strain in the muscles) which is quite different from the property (e.g., gravitational force) supposed to inhere in the appearance. It is just that the intensive magnitude of the sensation is taken to designate a corresponding degree to which the property is present in the object. 22 Kuehn (Scottish Common Sense, 206 and 242), has denied this thesis on the strength of Ak, IV 289. In this passage, Kant says that he considers all the properties of objects, primary as well as secondary, to belong, not to things as they are in themselves, but only to their appearances, and hence to have no proper existence outside of our representations. But he does not restrict the scope of the term 'representation' to sensations considered as felt effects on the sense organs or to mere aggregates of such sensations, though he certainly does include the secondary qualities (colours, for example) in the former class, calling them 'modifications of the sense of sight.' The possibility remains open that our representations of objects as appearances may not be representations of subjective states or aggregates of such states, but may rather be representations of the postulated causes of such states - considered, however, not as they are 'in themselves' but only as 'appearances.' 23 Consider the Cartesian claim that extension is the essence of body. While not everyone accepted this claim, those who disagreed with it tended to question just Descartes's assertion that extension is sufficient for body (both Locke and Leibniz, for instance, claimed that, in addition to extension, a body has to exhibit solidity or some other phenomena of force), not to question that extension is incompatible with the spirituality of a substance. Thus, when Locke (in Essay, 4.3.6) notoriously raised the question of whether God could have endowed solid extension with the ability to think, he was accused of materialism, not with countenancing a new kind of spiritual substance. 24 At Prolegomena, §60, (Ak, IV 363), he describes materialism as 'a psychological concept that is unfit for any explanation of nature and that moreover confines reason in practical respects.' At Prolegomena §57, (Ak, IV 351), he claims that the previous pages have led to the conviction that [the] appearances of

Notes to pages 119-20 389 [the subject] cannot be explicated materialistically.' At Bxxxiv, he presents the Critical Philosophy as the only true antidote to the intellectual perversions of fatalism, atheism, free thinking, fanaticism, superstition, idealism, scepticism - and materialism. (Materialism, in fact, heads off the list. Compare Ak, IV 36325_30.) At 6421, 'soulless materialism' and 'spiritualism' are presented as two equally objectionable doctrines of mind. And, at A 383, the Critique is presented as saving us from 'the danger of materialism.' 25 This definition of sensation is notorious for raising what in the literature is called the 'problem of affection.' (See Vaihinger, II 33-55, or Allison, Transcendental Idealism, 247-54, for more information.) By specifying that sensations are effects of objects on us, Kant obviously intends to distinguish them from other sorts of effects - presumably, effects that are attributable to the constitution of the subject. And, equally obviously, there is a background picture of affection being appealed to here, according to which we, as cognizing subjects, are located in a world of independently existing, external objects that act on our sense organs and so bring about representations in us. None the less, in order to determine that sensations are properly to be identified as effects of objects on us, it is not necessary for Kant to make any claims about external objects, considered as things in themselves that cause our sensations. The status of sensations as 'effects of objects' can be established on internal grounds, quite independently of identifying the objects that are their causes or making any claims about these objects. (For a discussion of how Kant does this, see chapter 9 and the Appendix to the Introduction to Part II, below.) However, none of these problems with Ai9-2O/B34 are my concern here. The significant point I want to draw from this passage is just that it specifies sensations as effects on us. Whether these effects are produced by external objects acting on the subject or are spontaneous deliverances of the subject's own cognitive system is irrelevant. (The latter question is considered in connection with the subject-matter of the following chapter, however.) The reason this more restrictive version of Kant's claim is significant is that it rules out an alternative: the view that the effects had on us are properly to be described as mental acts of thinking of, believing in, perceiving, or otherwise intending an object, and that sensations are not these acts, but the intentional objects thought of or referred to by them. 26 This is entailed by Ai9-2O/B34, 6207, and A32O/B37727 Why, then, does Kant bother to write a refutation of idealism, that is, of the view that the existence of objects in space outside us is doubtful (6274)? Or, more to the point, why does his refutation of idealism not appeal to these considerations, rather than invoke the strange and obscure claims about persistence through time that Kant, in fact, makes use of in the Refutation? It

39O Notes to pages 120-4 would seem to follow from what has been said that, if we accept the Kantian account of intuition and sensation, then there must be at least one object in space - namely, our own bodies. Surely, Kant would not have been bothered by the fact that our own bodies are not (technically) 'outside' us. It would seem that, if the existence of any body in space, even our own, can be demonstrated, idealism has been dealt a killing blow. One reason why a refutation of idealism is still necessary may be that the idealist is also an intellectualist, who rejects the thesis that there is a lower, sensory cognitive function that is necessary for perception, imagination, memory, or other cognitive functions. This is the implication of the dreaming argument, for instance (we are asleep, so our senses are not working, yet we are convinced that we really are perceiving and remembering events that are not happening and that never happened; so, the intellect can, for all we know, 'perceive' and 'remember' all on its own, without the need of the senses). If you think that the intellect can operate on its own, you will not be impressed by an analysis of the lower cognitive function that entails that it must be exercised by physical organs. That Kant did, in fact, appreciate this problem is indicated by his taking the supposition that we are capable of having intellectual intuitions (specifically, that self-knowledge is possible by means of an intellectual intuition) to be at the heart of the problem with idealism. 28 Though Kant's rejection of immaterialism is not as emphatic as his rejection of materialism, it is affirmed in most of the places cited in note 24, above. 29 Note also in this regard R4863: 'Organisches oder geistiges Anschauen, jenes durch den Korper.' 30 This point is also made in Part I, ch. 3, of Traume (Ak, II 344-8), though it is there supplemented by detailed physiological speculations about the manner in which the nerves function and the locations in the brain where awareness occurs, that Kant seems later to have eschewed (see below). The main point of Traume continues to be present in the Anthropology, however: that the physiological process responsible for perception can be affected by stimuli originating from elsewhere within the brain rather than from the sense organs. 31 This is a condition that could hardly be imagined were inner sense exclusively temporal in form, and it goes to show that the account of time as the exclusive form of inner sense (A23/B37, A33-4/B49~5o) is highly problematic in Kant. 32 Wilkerson, 26, provides a good example. Commenting on what he describes as Kant's slogan that some experiences - namely, sense impressions - are spatially related, Wilkerson writes: 'But something must have gone wrong, for it is downright nonsense to say that experiences are spatially related. My visual impressions of the concert are neither to the left nor to the right, nei-

Notes to pages 124-8 391

33

34

35 36 37

ther to the top nor the bottom, of my auditory impressions. They are simply not the sort of things that have spatial properties at all. Conductors, orchestras, and members of the audience are certainly in space and are spatially related to each other, but my perceptions of them are not.' See also Prichard, 75-6, where a similar complaint is made. This seems to be what motivates the positions of George, 'Sensationism,' and Aquila discussed earlier. Allison, Transcendental Idealism, 9, takes what is in effect the same line, claiming that spatiality pertains only to appearances, not sensations. Thus, Kant's response to Wilkerson (cited above, note) would be that my visual impressions of the concert are at least spatially related to one another (which by itself already invalidates Wilkerson's claim), and that they are even spatially related to my auditory impressions, since the former are felt in my eyes, the latter in my ears. We simply do not notice this ordinarily because we attend to the object referred to by the sensation rather than the sensation itself. But when the intensity of the sensations is increased to the point where they would become painful, then we become aware that we are feeling the visual sensations in our eyes and the auditory in our ears. Prolegomena, §13 Anm. 2 (Ak, IV 289). Just why Kant believes this is an interesting question that receives no clear answer in the Expositions. It is examined in the Appendix to this chapter. There is, however, at least one place, A29/B45, where Kant describes 'colour, taste and so forth' as 'mere alterations of the subject' (not, note, as the objects represented by such alterations, but just as the alterations themselves), thus implying that the subject itself does literally become red or wine-tasting when it has these sensations. Either Kant was speaking loosely here, or he was more confused than I am making him out to be. Colours and tastes simply cannot be literal alterations of the subject. Since colours are located and extended, they could not be effects on an unextended soul. As alterations of the subject, they would have to be alterations of the subject's body. But Kant himself denies that any body possesses secondary qualities such as colour at Prolegomena, §13 Anm. 2. An indication that Kant was speaking loosely is provided by the Anthropology's discussion of objective and subjective senses of sensation (154,156-7; see also KdU, §1, §3, Introduction VII [Ak, V 203, 205-6,189]). In these passages he remarks that sensations have two aspects. They can refer to an object or they can constitute feelings of the state of the affected organ. The 'objective' sense of sensation is explicitly intentional. In objective sensation what happens is that an effect on the organ somehow directs the mind, in virtue of its innate constitution to think of an object char-

392 Notes to pages 128-40 acterized by a certain sensible quality. The effect on the organ is not the sensible quality, but something else so mild that it goes unnoticed, and all our attention is focused on the intentional object. When the effect becomes more intense, we are distracted from attending to the object. What we then notice, however, is still not the effect itself, but rather an aesthetic feeling of pleasure or pain. (That this feeling is something we are led to represent as a result of being affected in a certain way is indicated by A29, where Kant says that the feeling of pleasure and displeasure arises as an effect of sensation, and so is not sensation itself.) 38 If this is correct, then Kant and Reid would stand on opposite sides of the divide between intentional object and inner state of the subject. For Reid, the raw, phenomenal experience of colours, smells, tastes, and so on, is a feeling had by the mind, of the same kind as the feeling of pain, and this feeling is to be distinguished from the thought of or the belief in some cause in external objects responsible for bringing the feeling about, as well as from any 'material impression' on the body of the perceiver serving as an intermediary in the causal process. The feeling is the inner state and the belief in the cause the intentional object. But, for Kant, this relation is more or less the reverse. It is sensible qualities that are the intentional objects of our beliefs, whereas the actual inner state is some spatio-temporally located 'effect' on the body of the perceiver, otherwise undescribed but for the fact that it has some intensive magnitude. 39 Thus Guyer, 202-3, notes that the premise of Kant's argument in the Anticipations is arbitrary in the extreme, and Bennett, 172, says it is at best an empirical fact, not an a priori one. 40 Thus Guyer, 201, notes that, if the Anfangsgriinde is relevant to Kant's views in the Anticipations, this would deprive his principle of a priori validity. Chapter 4 i See Vaihinger, II 35-55, and Allison, Transcendental Idealism, 247-54, f°r discussion of this objection. The classic statement of the objection (according to Vaihinger, 'probably the most valuable and most important thing that has ever been said about Kant') is to be found in Jacobi, 209-30, esp. 220-3. Summary and Conclusions to Part I i This conclusion emerges only from a consideration of the implications of the Analogies, passages that I have been able to remark upon only in passing. See chapters 2, §iv.c, and 3, §i.d(i).

Notes to pages 147-8

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Introduction to Part II 1 Martin, 11, reads Kant this way. 2 Vaihinger, II131-4, and Martin, 11-12, note that the positions Kant lists here appear to constitute a list of all the conceivable possibilities (space and time are considered as substance, accident, relation, and idea), not just a haphazardly gathered collection of historically popular alternatives. Vaihinger, II i3in, even notes that a similar list may be found in Gassendi - well in advance of the time when the champions of the substantivalist and relationist positions, Newton and Leibniz, came on the scene. Kant is not just setting his position forth in opposition to those of his two great predecessors, as one popular view has it (see, for instance, Paton, 1107, and Allison, Transcendental Idealism, 81). 3 Among the many who have made this observation are Vaihinger, II134-51; Kemp Smith, 113-14; and Buchdahl, 589-90. 4 'Space is no empirical concept, that has been drawn from outer experience' (A23/B38); Time is no empirical concept, that has been drawn out of any kind of experience' (A3O/B46). 5 'Space is to be seen not as one of the determinations dependent on appearances [but] as an a priori representation, that is necessarily present as a base of outer appearances' ^24/639); '[Time] itself (as the universal condition of the possibility [of appearances]) cannot be removed' (A31/B46). 6 'In respect of [space] an a priori intuition (one that is not empirical) is a base of all concepts' (A25/B39); 'the original representation of space is intuition a priori and not concept' (640); 'Time is no discursive or, as it is called, general concept, but a pure form of sensory intuition' ^31/647); 'the original representation time ... must not be given through concepts ... but rather an immediate intuition must be a base for them' ^32/648). 7 'Now how can an outer intuition, which precedes the Objects themselves and in which their concepts can be determined a priori, attend the mind? Obviously in no other way, than in so far as it has its place only in the subject, as the way it is formally constituted so as to be affected by Objects and thereby to acquire immediate representation of them, that is, intuition' (641). 8 A26/B42, A32-3/B49. Allison, 'Non-spatiality,' provides a good introduction for those who may be unfamiliar with the problem with Kant's claims in these passages (which has been called the problem of the neglected alternative). Vaihinger, II134-51,290-326, provides a typically exhaustive survey of the literature on the neglected alternative up to the 18905 - on which more recent work merely plays variations. 9 Everything about Kant's interests and sources of influence conspires to sec-

394 Notes to pages 150-1 ond this assessment. His sources were Newton, Wolff, and Leibniz, not Berkeley, Condillac, and Reid. And his formative pre-Critical work was focused on questions of physics, astronomy, chemistry, geology, and meteorology, not on medicine, psychology, epistemology, or the theory of perception. One has only to consider, for instance, the outmoded Keplerian theory of visual depth perception enunciated in Traume (Ak, II 344) to appreciate that, as late as 1766, Kant had no inkling of as central and important a piece of work as Berkeley's New Theory of Vision. It was the metaphysics of space and time, as debated by the Newtonians and Leibnizians, that was Kant's concern, and not the theory of space-cognition, even though it was to the latter field that Kant, quite possibly unwittingly, ended up making a contribution. These views have, however, recently been challenged by Kitcher, Transcendental Psychology, ch. 2, and Hatfield, 101-7, though on the basis of evidence which strikes me as weak: remarks in Kant's Anthropology and in student lecture notes. To be aware of a theory, and even to lecture on it in your classes on anthropology, is one thing; to appreciate its implications for your own work is quite another. 10 Many commentators (among others, Vaihinger, II155-6; Kemp Smith, 99; Pa ton, I io8n.i; Wilkerson, 22; and Aschenbrenner, 36) have maintained that Kant's references to 'concepts' of space and time in the Aesthetic are loose, and that what he really intends is to refer to something more general, such as 'representations' of space and time. This claim is based on the supposition that Kant's purpose in the Aesthetic is precisely to prove that space and time are not concepts but a priori intuitions. But this proposed revision addresses a spurious problem. Just because Kant thinks that space and time are forms of intuition does not mean that he does not also accept that intellect is able to conceptualize these forms. It is rather Kant's claims that space and time are intuitions and not concepts which are loose. As the citations in note 6 above show, Kant's exact point is that we do have concepts of space and time but that these concepts are grounded on an original intuition of space and time. To read Kant in any other way is to make nonsense of his position, given blindness. 11 See, classically, Arnauld and Nicole, Part I, ch. 9. Note also Meier, §§14, 115-16,124,132; and Kant's own Logic (Ak, IX 61-2). Cf. Leibniz, G, IV 422-3, and Baumgarten, §§510 and 528. 12 Metaphysical exposition is a species of what Kant calls 'transcendental deduction,' which he defines as 'the explication of the manner in which concepts are related a priori to objects' (A85 76117). It is easy to miss this point, because at one place (6159) Kant refers to the part of the Critique entitled The Clue to the Discovery of all Pure Intellectual Concepts' as a 'metaphysical deduction' of

Notes to pages 152-6 395 the pure intellectual concepts, and contrasts the metaphysical with the transcendental deduction of the categories. The metaphysical/transcendental parallelism is hard to ignore, but it would still be a mistake to identify the metaphysical exposition of the concepts of space and time with the metaphysical deduction of the categories, or the transcendental exposition with the transcendental deduction. The transcendental deduction of the concepts of space and time is completed by their metaphysical exposition. Transcendental exposition, which Kant defines as 'the explication of a concept as a principle from which the possibility of other synthetic cognitions a priori can be appreciated' (640), is not the same thing as transcendental deduction. If the transcendental exposition of the concepts of space and time corresponds to any part of the Analytic, it is to the Analytic of Principles, which is a sort of exposition of the schematized categories as bases for the a priori knowledge of certain principles. (Vaihinger, II151-4, makes a similar point.) 13 For instances of this picture see Parsons, Transcendental Aesthetic/ 67-8, 74-5; Hatfield, 88-95; Kitcher, Transcendental Psychology, 45; Allison, Transcendental Idealism, 81-99, esp. 82; Pippin, 59-60; Walker, 29,42,60; Broad, 27; Ewing, 33, 39; Paton, 1109,127; Prichard, 36; Caird, 1286; and Vaihinger, II 331-4 and references. There are, of course, minor variations in the way the picture is presented by different commentators. 14 For instances of this view see Prichard, 41,43; 24-5, 32; H.W. Cassirer, 24-5, 32; Strawson, 58; Bennett, 4; Wilkerson, 21; Walker, 29-30, 43-4; Buchdahl, 589; Parsons, Transcendental Aesthetic,' 72-3. 15 Indeed, Locke goes so far as to observe that for all we know different people could get different simple ideas when affected by the same object (Essay, 2.32.15, cf. 3.2.1-4). Since none of us could ever enter the mind of others to experience what they experience when their senses are affected in the way ours are by a certain object, we could never be sure that the simple ideas of others resemble our own. (The difference would be moot, however, since everyone would use the same name to refer to their individually different simple ideas, and thus all end up using the same word in naming the same stimulus source.) 16 It is interesting to note, in this regard, that appeals to the Molyneux question and experiments with newly sighted blind people were used by Kant's opponents to attack his claim that space is a priori. These considerations were taken to establish that the concept of space is different, depending upon which sensory organ, vision or touch, is operative, and hence that this concept is (or, more properly, these concepts are) specific products of specific sensory modalities, not a single form of intuition in general. See, for instance, Feder, 57-9.

396 Notes to pages 156-62 17 Hume's notorious example of the missing shade of blue (Treatise, 1.1.1; Enquiries, II) is an example of a case where some antecedently supplied sensory concepts might indeed permit us to deduce a sensible quality that we had never before experienced, though the circumstances required to make this possible are so special and artificial that for all practical purposes, the thesis that sensible qualities cannot be anticipated holds true. A Kantian observation is that Hume's case only demonstrates that, we can anticipate variations in the intensity of a given quality, not variations in quality. 18 See A41/B58 and compare Vaihinger, II 362-3, and Kemp Smith, 121, who miss the point by gratuitously reading Kant as attempting to establish a distinction between primary and secondary qualities at A28-9/B44-5. As A4i/ 658 makes clear, Kant is more sophisticated than his predecessors in distinguishing among at least four different kinds of concepts: concepts of sensible qualities, like red or the taste of a wine; concepts of objects, like motion, inertial mass, and impenetrability; concepts of space and time; like triangularity, succession, and duration; and schematized pure intellectual concepts, like substance and alteration. 19 Anthropology, §28 (Ak, VII167-9) exposits them very thoroughly, though in the context of a discussion of the limitations of the power of imagination rather than a generalized attempt to determine the source of sensory-quality concepts. 20 What Kant probably meant here is that, though sensible-quality concepts are subjective in that they depend on the constitution of the senses in the affected subject, they also depend for their character on the subject's senses being affected in a certain way by the object (e.g., though the taste sensation got from pineapple may be a sensation in the subject and no property of the affecting object, there will still be no pineapple sensation in the subject unless there are pineapples that have affected its taste organs). Space, however, since it depends on how the subject is constituted to as to be able to receive any sensation whatsoever, is not dependent on any specific effect on any specific organ, and is 'ideal' (i.e., a product of the subject's constitution) in a much purer sense. 21 See Entdeckung (Ak, VIII i99n) for an extended attempt on Kant's part to explain this difficult distinction. Chapter 5 1 Helmholtz, 'Recent Progress in the Theory of Vision,' 216. 2 This objection was already made by Kant's contemporaries. See Feder, §6, 21-5, and Maafi, esp. 124-5. Maafi's argument is summarized in Vaihinger,

Notes to pages 162-5

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II178, and Allison, Kant-Eberhard, 35-6. For a recent appeal to this objection see Walker, 29. In its most extreme form, the objection accuses Kant of doing no more than uttering 'the tautology that we could not become aware of objects as spatially related unless we had the capacity to do so' (Strawson, 58). 3 Allison, Transcendental Idealism, 85-6, and Guyer, 346-7, provide especially clear presentations of this view, but see also Allison's references to Dryer. 4 See especially Buroker, 76, as well as the authors mentioned in the previous note. 5 Dryer, 228-9; Guyer, 347. 6 Guyer, 347 but note that Dryer, 228-9, holds back from drawing this implication. 7 For Locke, however, our ideas of space do not come from all of the 'outer' senses, but only from sight and touch (Essay, 2.5,2.13.2), and even then the ideas of space obtained from sight are interestingly different from those obtained from touch (Essay, 2.9.8). 8 Though Kant here describes time as a form restricted to inner sense, he elsewhere notes that it is mediately applicable to all the sensations of outer sense as well in so far as these are also, as sensations, representative states of the soul, that the soul can discover in itself upon reflection ^34/650). 9 Compare also ID, §15 Cor.: 'of these concepts [space and time] the one properly concerns the intuition of an object, while the other concerns its state, especially its representative state.' 10 These clarifications of the meanings of 'outside me' and 'outside of and next to one another' were not included in the original version of the first space argument in ID, §15 1A. For what it is worth, however, the interpretation I am pressing here is still closer to the actual wording of that text. Kant does not there say that space is required to differentiate objects from myself or from one another but to locate them 'extra me' and 'extra se.' 11 Note that, in ID, §14 ^[5 and l5n (Ak, II 401 and 4Oin), Kant himself complains that his predecessors have neglected the concept of simultaneity, treating it as the mere absence of succession when, in fact, it is a special kind of connection between distinct things. 12 I am following a usage long established in work on the history of psychology in referring to this as the 'sensationist' view. In the Kantian context, it would be most accurate, though also most inelegant, to refer to it as the 'matter of appearance'-ist view. I hope the reader will excuse my use of what, in the light of page 160, above, is the potentially misleading former term, given that it allows me to avoid employing a circumlocution. 13 I focus on Locke's account of time perception to the exclusion of his remarks on space perception because the latter are even more liable to the Kantian

398 Notes to pages 167-9 response that will be presented below. I do not mean to imply, however, that Kant had either Locke's account of time or his account of space explicitly in mind in the First Exposition. I pick on Locke merely to illustrate the nature of Kant's opposition. For more on Kant's perceived opponents, see note 17, below. 14 This Vivacity' is a quite peculiar quality not to be identified with our ordinary understanding of the word - because, of course, we may have very vivid memories of childhood experiences and very faint ones of yesterday's experiences. I therefore put Vivacity' in quotes to indicate that I am using the word to designate some postulated temporal quale, not ordinary phenomenal vivacity. 15 One of the clearest statements of this account of time perception is to be found in Reid, Essays, 347 (see also Inquiry, II v and VI xxiv); however, Reid does not admit to holding it himself but attributes it to Hume instead - with what right I will not say here. 16 Note also Locke's discussion of the operation of memory, inserted in the second edition of the Essay, at 2.10.2. Here Locke does talk about memory reviving ideas 'some more lively, and others more obscurely.' But there is no implication that the liveliness or obscurity of ideas function as temporal indices. The most natural reading is rather that some of our ideas are recalled with more difficulty and more obscurely, some with less and more clearly, but that this has no necessary connection to how old they are. The age of ideas called up in memory is, for Locke, rather conveyed by a some further unspecified perception annexed to the recalled ideas. 17 The only immediately relevant difference between Locke's position and Leibniz's, however, has to do with the nature of the elements supposed to be in time. For Locke, they are ideas, for Leibniz objects. The Lockeian epistemological context is none the less more pertinent to Kant's actual project of explaining the basis from which our concepts of space and time are derived, and Kant loses by ignoring it. The Leibnizian position, which makes timecognition dependent upon the observed causal relations between things, is a straw man compared with the neo-Humeian development of Locke's position, which takes time-cognition to depend on the qualitative Vivacity' of our ideas. For causal relations to be perceived, objects must be cognized one after another, so Kant has an easy time accusing the Leibnizians of circularity. (See especially ID, §15, Corollary.) He would not have had such an easy time of it had he addressed Locke and Hume rather than this Leibnizian position - and doubtless his argument would have benefited from the challenge. 18 Kant's first space argument in ID (§151A) does not contain a similar appeal to circularity in the common definition of space. However, ID, §15 'JD, makes a passing reference to the point.

Notes to pages 171-3 399 19 Note also ID, §14 «j[i: 'Nor does succession generate the concept of time, but it makes appeal to it.' 20 For an example of such an experiment see Kitcher, Transcendental Psychology, 179-80. Of course, to assume that there is a neat distinction to be drawn between tautologous and empirical claims is to beg an important question, and the experiment cited by Kitcher can be faulted for having to invoke certain by no means obvious theoretical presuppositions (as I myself point out in the notes to chapter 3, §i.b, above). My point here is just that Kant's account of space- and time-cognition is not true simply by definition. It is as open to empirical confirmation or disconfirmation as any other scientific theory. 21 I now use this term in the nineteenth-century sense, to refer to the result of stimulation of the sensory organs of which we are immediately aware. 22 This is a point that Allison, Transcendental Idealism, 85, does not seem to appreciate in his own attempt to answer Maafi on Kant's behalf. Maafi found Kant's distinction between outer and inner sense to be unusual (it counted tastes and smells as 'inner' sensations, which Maafi considered to be unorthodox [Maafi, n8n]), but he accepted it for the sake of argument, defining 'outer' sense as the representation of objects distinct from our bodies, 'inner' as the representation of objects that are not distinct from us. Granting this, Maafi may well have accepted as non-trivial that space is necessary for the representation of objects 'outside' of us. His statement 'Dafi nun dasjenige, was bey alien Gegenstanden des aufieren Sinnes notwendigerweise zum Grunde liegt, der Raum sey,... ist eine Bemerkung, die einem aufmerksamen Beobachter nicht leicht entgehen kann' (pp. 118-19) could be ironic, but it could also be an indication that he considers the statement to be falsifiable, though not actually false. Maafi's problem was not that he found the necessity of space for 'outer' representation to be trivial, but that even granting its non-trivial necessity it would not follow that the representation of space is not abstracted from empirical experience like any other empirical concept. Feder, likewise (whom Allison does not consider), took the tautologous reading of Kant's argument to be a desperate last-ditch attempt to escape the objections he (Feder) had raised against Kant's position. 'Hoffentlich wird doch Niemand, um dem bisherigen auszuweichen, dem Kantischen Satz den Sinn beylegen wollen, dafi wir doch nicht Dinge im Raum wahrnehmen konnten, wenn nicht - Raum da ware' (Feder, 25). 23 Note the two alternatives Feder here recognizes to Kant's position that our concept of space is derived from a form of intuition. The first is that it is drawn out of sensation, the second that it is worked up by the power of thought (intellect).

4OO Notes to pages 173-5 24 Feder's objection shows up the inadequacy of a recent defence of Kant's first argument offered by Kitcher, Transcendental Psychology, 47. According to Kitcher, 'the argument has the form of an implicit reductio. Suppose that we acquire the concept of space from outer experience. We can acquire the concept of space from outer experience only if our outer senses can register spatial properties of distance, size, and shape. As we have seen, however, everyone acknowledges that these properties are not registered by vision.' One problem with this reconstruction (a second is pointed out in note 30, below) rests with the third sentence. As Feder's argument shows, the fact that our outer senses do not register spatial properties of distance, size, and shape, even if it were granted, does not suffice to show that our concept of space is not acquired from outer experience. It could still be acquired from outer experience of some other data registered by the senses, that, when suitably processed by understanding, can be worked up into a representation of spatial relations. Berkeley's impressive attempt to derive depth perception from association of visual and muscular sensations with experiences of the actual number of paces that needed to be trodden before reaching an object was based on the premise that depth is not immediately perceived. But it is, for all that, acquired from other data which are worked up by the senses andnot, for Berkeley, an a priori (non-empirical) concept. 25 He will, however, draw such a conclusion in the Transcendental Expositions. See chapter 8, below. 26 For the 'negative sense' of a priori, see the paragraph preceding the previous one. 27 Parsons, Transcendental Aesthetic,' 68, one of the few commentators who accepts that Kant's point in the first argument might be that 'the representation of space (as an individual...) must be presupposed in order to represent particular spatial relations,' fails to appreciate this point and as a result insinuates that Kant's argument would be stronger were it read along the lines of the standard defence referenced in note 3, above. 28 See the criticism of Vaihinger and Kemp Smith in chapter 2, above, for a fuller development of this point. 29 Beiser, 182-3, also makes this point. 30 This is a point that has been often made before. See especially Hatfield and Epstein, 380 and n. 67, and Falkenstein, 'Intuition and Construction,' but note also Armstrong, 55; Pitcher, 53-4; and Donagan, 318-20. For this reason I cannot accept Kitcher's (Transcendental Psychology, 47) attempt at defending Kant's position in the First Exposition. Her argument turns on the premise that everyone at Kant's time accepted that the spatial properties of distance, size, and shape are not registered by vision. This is false. Everyone (everyone

Notes to pages 175-7 401 working on the theory of vision, at any rate) did indeed accept that distance is not directly perceived by vision. But no one, so far as I have been able to determine, questioned that what were called apparent size and shape (i.e., size and shape as determined by the proportion of the visual field occupied by an appearance) were directly perceived by vision. Kitcher's (Transcendental Psychology, 40-1) attempt to argue that, if the third dimension is not immediately perceived by vision, no other spatial property can be, either, ignores the distinction between real and apparent magnitude. Our inability to immediately perceive depth entails only an inability to directly perceive real magnitude (size constancy), not an inability to perceive apparent magnitude. 31 §22, p. 93. Berkeley had made the same point at Principles, §116, and De Motu, §§54-5, though specifically in the context of an attack on Newtonian absolute space. 32 Feder, §6 24-5. 33 'Every Point of an Object appears and is seen without the Eye, nearly in a straight Line drawn perpendicularly to the Retina from that point of it where its Image falls': Porterfield, 5.1.10-16, 293-308. 34 Porterfield, 298. 35 Ibid., 5.1.12. 36 Ibid. 37 'The Connection betwixt these Ideas [of objects excited in the mind] and the Motions or Agitations excited in the Retina, optic Nerves and Sensorium, is unknown to us; neither need we ever expect to discover it: It is sufficient that we know, by Experience, that the Union of the Body and Mind is so strict, that some Motions in the Body do, as it were, cohere with certain Ideas in the Mind, so as they cannot be separated from each other, tho' we cannot find any thing common between them, nor so much as perceive that any Connection is possible; for there are a great many Things which do always follow others, without any proper Causality in that which goeth before, and which have no manner of connection with each other, but in the Will of God, who makes them accompany each other. And of this sort the Sensations of our Mind seem to be one; for it does not at all seem possible, that the Motions excited in the Sensorium, by Objects acting upon our Organs of Sense, can be the true physical or efficient Cause of the Sensations said to be excited by them; but only the occasional Cause which determines the Author of Nature, or some subordinate active Being acting under him, and by his Appointment, to produce these Sensations in the Mind, when that occasional Cause takes place': Porterfield, 3.7.2,214. 38 Inquiry, 1463,155b, 2iob. 39 Ibid., 1833.

4O2 Notes to pages 177-82 40 41 42 43 44 45 46 47

Ibid., 5.2, 5.4. Ibid., 6.4. Ibid., 6.8. Ibid., i56b, 1463. Ibid., 1573. Ibid., 1573. Hatfield, 131. What motivates my doubts about Hume's actual adherence to this theory are his references to time and space as manners of disposition of impressions and ideas in Treatise, 1.2 and 1.4.5. Hume's sensationist thesis that all our simple ideas are copied from antecedent impressions notwithstanding, there is very little difference between Kant's forms of intuition and Hume's manners of disposition. 48 See esp. Inquiry, 6.24, but also 2.5, and Essays, 3.7 347-50. 49 Ak, X 115.1 have used the translation of Zweig, 69. 50 Kant makes this point himself in ID, §15 (Ak, II406): The relation of cause to caused, at least in external objects, requires relations of space, but in all objects whether external or internal it is only with the assistance of the relation of time that the mind can be instructed as to what is earlier and what is later, that is what is cause and what is caused.' 51 The exposition which follows borrows heavily from Hatfield, 131-8, to which the reader is referred for more details. 52 Hatfield, 131-2 and n.6y. 53 Ibid., 140-1. 54 This is a classic objection. Besides being noted by Hatfield, it was especially well put by James, 270-1: 'Either because [Berkeley's disciples in Great Britain] were intoxicated with the principle of association, or because in the number of details they lost their general bearings, they have forgotten, as a rule, to state under what sensible form the primitive spatial experiences are found which later became associated with so many other sensible signs. Heedless of their master Locke's precept, that the mind can frame unto itself no one new simple idea, they seem for the most part to be trying to explain the extensive quality itself, account for it, and evolve it, by the mere association together of feelings which originally possessed it not. They first evaporate the nature of extension by making it tantamount to mere "coexistence," and then they explain coexistence as being the same thing as succession, provided it be an extremely rapid or a reversible succession. Space-perception thus emerges without being anywhere postulated. The only things postulated are unextended feelings and time.' 55 Hatfield, 141.

Notes to pages 184-91 403 56 I make no claims for completeness. There may be more and those that are listed may be further subdivided into relevant subclasses. 57 In the Amphibolies, Kant criticized Leibniz for making precisely this assumption. See A266-8/B322-4 and A275-6/B331-2. Chapter 6 1 Vaihinger, II370, claims that the parenthetical remark was added in B, and in this he has been followed by Kemp Smith and Allison. However, Schmidt, 74, asserts that only the parentheses were added in B, and the Akademie editions note no variants between the texts of A and B. The Schmidt version is the correct one. In A, there were commas where the parentheses stand in B, but the nested remark occurs in both editions. (I am indebted to Hiener Klemme for determining this. Klemme also remarks that it is unlikely that Kant was the one who gave the instructions to the printer to change the commas to parentheses.) 2 Kant's use of ambiguous terminology in the Second Exposition recalls something already encountered in the First. There Kant claimed that our concepts of space and time are not drawn out of the content of sensation. But 'sensation/ like 'intuition' and 'appearance,' is an ambiguous term. It can designate the matter of intuition, but also the matter of appearance. Taken in the former sense, it tacitly invokes the view that the 'matters' in question, the matters that are related to one another in space and time, are matters of intuition, and hence that space and time are originally present in intuition and not subsequently injected into the appearance by some process. But this is something Kant is far from having established. This is why I felt that the only way to preserve the valuable insight of the First Exposition was to alter the representation terminology Kant uses to communicate it, substituting 'matter of appearance' for 'sensation.' 3 In the First Exposition, Kant can sidestep the whole issue of blindness by starting with the evident fact that our intelligible experience exhibits various matters in a spatiotemporal array. He can then raise the question of what the spatiotemporal relations between these various matters could be based upon. Could the spatiotemporal order be a comparative order reflecting observed similarity relations between the various matters, or is it rather the case that the matters are indifferent to their location in the order and that the order is not, therefore, based on anything that could be observed in them? Though he refers to these matters as 'sensations,' nothing really hangs on that term: the matters could be the matter of intuition or they could be the material given through some sophisticated processing operation performed upon the intu-

404 Notes to pages 191-3 ited array. Kant's point is just that, whatever the individual matters observed to be in space and time are, matter of intuition or matter of understanding, their spatiotemporal order is not based on any observed similarity relations between them. Strictly, therefore, all that the First Exposition establishes is that the matters of appearance must be supposed to be already given in a spatiotemporal order if our concepts of their spatiotemporal relations are to be possible. It does not establish that these matters must be intuited in such an order (though it does not rule that possibility out either). 4 Of course, just because Kant ought to have said something does not entail that he, in fact, intended to say that thing. The alternative is to maintain that the Second Exposition makes a strong claim about our immediate intuitions that cannot be adequately supported, given blindness. I have not followed this route here only because the result it leads to (that the Second Exposition must be dismissed as a failure) is not interesting. It may none the less be the route Kant intended to take. Given Kant's slippery use of terms, it is very difficult to decide exactly what he intended to say. There is one consideration, however, though only a slight one, that tells in favour of the weaker interpretation of the premises that I advocate in the body of the text: in the space passage, Kant speaks of the impossibility of 'making' a representation of the absence of space and the possibility of 'thinking' a space that does not contain any object. But, aside from its technical use at Bxxvi n, 'thinking' is a term Kant reserves for use with reference to intellectually processed representations in general (see Ai9/B33). The term 'make' also carries connotations of activity. Note further the operative terms in the time passage: 'remove' and 'take out.' The overall impression one gets is that Kant intends to refer to representations that result from some amount of processing, not to representations immediately received in intuition. 5 For an indication that Kant may have had Descartes in mind here see R4756 (Duisburg 21; Ak, XVII 699). 6 The two parts of the argument that I have identified here should not be confused with the 'subjective or absolute' and 'objective or relative' arguments that Vaihinger, II193, and Kemp Smith, 104, claim to find in the text of the Second Exposition. According to them, the Second Exposition is primarily directed to establishing that space and time are subjectively necessary for all experience, but as a consequence are also shown to be necessary features of all the objects of experience. This reading falls out of the mistaken way Vaihinger and Kemp Smith interpret 'a priori' (see chapter 2, above) and is not otherwise justified by the text. Nowhere in the Second Exposition does Kant link either the necessity or the priority of space and time to anything uniquely contributed by the subject. (Not surprisingly, after having attrib-

Notes to pages 193-4

4°5

uted this conclusion to Kant, Vaihinger and Kemp Smith go on to criticize him for failing to adequately establish it.) 7 A number of commentators have claimed that the Second Exposition is, in fact, a 'second "a priority" argument' - a second argument for the thesis already established by the First Exposition. Kant is supposed to have written the Second Exposition either to repair a deficiency in the First (this is the view taken by Walker, 29) or to bolster his case for the conclusion of the First by adding another argument that makes the same point in a different way. Kemp Smith, 103, maintained that the first argument was intended to establish the merely negative conclusion that space and time are not obtained from sensation. The second argument then adds the positive conclusion that they are a priori. Allison, Transcendental Idealism, 86, agrees with Kemp Smith's reading, maintaining that the second argument proves the same thing as the first, but in a different way. However, as Humphrey, n. 34, has pointed out, since 'not obtained from sensation' and 'given a priori' are equivalent expressions for Kant, this is hardly a significant difference. The First Exposition is not, in fact, flawed or in need of support (at least, not the kind of support supplied by the second), and the sense of 'a priori' that is involved in the Second Exposition is not the same as that involved in the First. 8 Allison, Transcendental Idealism, 86-7, also observes that there are these problems with either reading of Kant's claims. Allison also notes that there is an alternative to taking Kant's premises to have absolute necessity or strict universality. This to take them to be claims about an introspectively observed limitation on our representative capacities - a psychological incapacity to represent aspatiotemporal objects, as Allison quite rightly stresses. But Allison rejects this alternative as well, preferring to read Kant's claims in a fourth way. Kant is supposed to be 'concerned with the determination of epistemic conditions' (p. 87). This is certainly true. In the Second Exposition, Kant claims that space and time are conditions of the possibility of appearance. But this claim is drawn as a conclusion from the Exposition. If Allison's proposal is that we should read the premises of Kant's argument as already asserting that space and time are 'epistemic conditions,' then he makes Kant beg the question in the Second Exposition. In his presentation of Kant's argument, Allison cites three sentences from the time exposition as evidence for his interpretation (cited in what follows in Allison's translation). The first 'We cannot, in respect of appearances in general, remove time itself, though we can quite well think time as void of appearances' - proves nothing either way since the question at issue is precisely whether this sentence ought to be taken as asserting a psychological inability to think otherwise or something stronger. The remaining two sentences - 'In it [time] alone is actuality of

406 Notes to pages 194-6 appearances possible at all' and '[time is] the universal condition of their [appearances'] possibility' - do indeed support Allison's claim that Kant is 'concerned with the determination of epistemic conditions,' but they are concluding sentences from the Exposition that tell us nothing about the grounds on which Kant draws this conclusion. If Kant is not appealing to a 'merely psychological' inability to remove time or space from experience, Allison has not shown us why not. 9 In addition to Allison, whose views were discussed in the previous note, see Parsons, 'Transcendental Aesthetic,' 68-9; Hatfield, 89; Kitcher, Transcendental Psychology, 48-9; Guyer, 347; Pippin, 63; Walker, 29; Strawson, 58-9; Kemp Smith, 103,105. The remark about the adolescent thought experiment is Hatfield's. 10 Parsons ('Transcendental Aesthetic'), Guyer, Walker, Strawson, and Kemp Smith are in the latter camp; Hatfield, Kitcher, Allison, and Pippin in the former. 11 See especially Strawson, 58-9, and Parsons, Transcendental Aesthetic,' 69, for very eloquent statements of this objection. 12 For this see Guyer, 347; Walker, 29; and Kemp Smith, 105. 13 Kitcher, Transcendental Psychology, 6. 14 Kitcher, ibid., 48-9, 40-3,44-5, accepts that the second argument rests on some empirical principles, but tries to avoid the implication that the principles are grounded in the introspectively observable results of the experiment of trying to induce a sensory experience that is not spatial or temporal. Her alternative is to take the first sentence of the Second Exposition to be the real premise of the argument. Kant is supposed to start off by assuming that space and time are a priori and then use this to attack the Leibnizian view that space is a determination dependent upon objects, and the argument is supposed to have no other end than this attack on Leibniz. The premise, for its part, is supposed to be based on what Kitcher takes to be certain established facts of the empirical psychology of spatial perception (this is where the appeal to experience plays a foundational role). These facts are not based on introspection - at least, not obviously or directly. Instead, they are drawn from Berkeley's theory of vision and Leibniz's response to Locke's and Molyneux's account of the relation between sight and touch in the New Essays. Kitcher takes it that these two works jointly established that space perception is not in any way dependent on visual or tactile sensation and that Kant simply took over this common background assumption when claiming that space is a priori. Ingenious as this account of the Second Exposition is, it is difficult to accept as a likely reconstruction of Kant's actual path of thought. The evidence Kitcher is

Notes to page 197 407 able to offer for the thesis that Kant knew of Berkeley's theory of vision (pp. 34-5) is very lean. The evidence that he paid any attention to it, even if he was acquainted with it, is non-existent. (In fact, the discussion of the focus imaginarius in Traume [Ak, II 344; note that this comes not from the ironic first and second chapters of Part I but from the sober third chapter] demonstrates a complete insensitivity to Berkeley's core argument - how could anyone who was impressed by what Berkeley had said claim to be perplexed by the fact that the lens of the eye alters the perceived angles of incidence of the lines of impression coming from the source in such a way as to make it appear that the source originates in the fund of the eye? - Ak, II 344n.) And I know of no evidence that Kant or any of his contemporaries had the clever thought to combine Berkeley's position with Leibniz's in such a way as to draw the implication Kitcher does - certainly none that would merit elevating this implication to the status of a common background assumption. Indeed, so far as I can see, Kitcher's implication simply does not follow from what Berkeley and Leibniz wrote - notably where Berkeley is concerned. Kitcher reads Berkeley's argument in NTV as establishing that space is not directly known by vision, a conclusion that she takes to be directly entailed by his claim that distance is not directly known by vision. This is certainly true - for what 'opticians and astronomers' (as Mill was later to put it) refer to as 'real' or 'objective' space. But there are two kinds of space for Berkeley. Real or objective space, which is measured in feet and inches, and apparent space, which is measured in the number of minima visibilia on the visual field. Apparent magnitude is directly and immediately perceived for Berkeley, and nothing he says tells against this doctrine. Indeed, much of what he does say, notably about the impossibility of forming abstract ideas of space and figure, presupposes that apparent magnitude is immediately seen. For more on this see my 'Intuition and Construction.' 15 This reading is motivated, first, by a failure on the part of commentators to distinguish the inextricability argument from the independence argument (a quite natural mistake to make, given Kant's manner of presentation) and, second, by an extravagant interpretation of the meaning of the concept of priority, which is central to the conclusion of the independence argument. Above, it was shown that, in the Second Exposition, 'a priori' just means 'given independently of the recognition of objects,' but it is commonly taken to entail a thesis about the subjectivity of space and time. For classic statements of this interpretation of the argument see Kemp Smith, 104, building on 103, and Vaihinger, II193, building on II186-7. 16 Kemp Smith, 105.

408 Notes to pages 197-200 17 Guyer, 347. 18 Walker, 29. 19 Here, 'think' does not mean simply 'conceive without contradiction'; it means 'recognize that a particular representation could possibly be of a certain kind of thing, and hence that this thing could be the object of an actual experience.' 20 Thus A27/B43: 'Since we cannot take the particular conditions of sensibility to be conditions of the possibility of things, but only of their appearances, it follows that while we can indeed say that space comprehends all things that can appear outwardly to us, we cannot say that it comprehends all things in themselves, be they intuited or not.' 21 It bears repeating, however, that recognizing Kant's conclusion in the inextricability argument to be a contingent fact about 'our psychology' should not lead us to follow Kemp Smith in taking the argument to establish the peculiar psychological thesis that the subject is in possession of innate ideas of space and time that it antecedently injects into its experience. There are many ways to account for our 'psychology.' Besides innate ideas, appeal can be made to innate cognitive or sensory mechanisms, to the innate constitution of the receptor system, to the constraints imposed by physiology, or to global, structural features of the environment. Whatever views Kant may have about the ground of our 'psychological' necessity to represent in space and time, they are not established by the Second Exposition. 22 Vaihinger, II196, put the distinction well when he said that, whereas the point of the first argument is that appearances are not given prior to space (at least, in the sense that space is not abstracted from sensation), that of the second is that they are not given without space. See also Humphrey, 503-4, though Humphrey tries to draw more from the argument - a demonstration that it is not possible for us to have intellectual intuitions - than it contains. The question is not whether we might know objects that are not in space or time, but just whether we might have sensory intuitions that are not spatio-temporal. Kant's claims are carefully worded in this regard: 'Space is a necessary a priori representation that serves as a ground of all outer intuitions. One can never make a representation of outer intuition that is not a space ... It is ... a condition of the possibility of appearances' (A24/ 638-9, my italics). Time is a necessary representation that serves as a ground of all intuitions. With respect to appearances ... one cannot remove time' (A31/846, my italics). These claims are restricted to sensory experience and do not prejudice any claims that might be made for intellectual intuition of things as they are in themselves, independently of how they might appear to our senses.

Notes to pages 203-4 4°9 23 For discussion of the thesis that empty space and time cannot be thought without contradiction see Vaihinger, II191 (following Riehl); Kemp Smith, 105; and Pa ton, 1113. For discussion of the claim that empty space and time cannot be experienced or even imagined see Vaihinger, 191, and Kemp Smith, 104-5. Paton, 1113-14; Ewing, 35; Dryer, 175; Pippin, 63; and Allison, Transcendental Idealism, 86-90, are so persuaded by the objections that they try to reinterpret Kant's text to evade them. According to Paton, Kant's point was not that we can represent or even think empty space or time, but just that there is no particular object that we need to experience in order to be able to do so (in contrast, the space and time we need to experience in order to be able to represent any other object always has the same topological and affine structure). Ewing offers the fantastic speculation that Kant must have taken there to be some third sense, neither conceptual nor figurative, in which we can be aware of empty space or time. Dryer and Pippin hint at, and Allison makes explicit, the suggestion that Kant's purpose is not to establish that we can imagine or conceive empty space or time, but just to show that space and time are epistemic conditions. 24 See ID, §1415, §15 ID (Ak, II 400,404), Kant's letter to Marcus Herz of 21 February 1772 (Breifwechsel, 104-5 [Ak, X 133-4]), R5879, 5880 (Ak, XVIII), A39-417656-8. 25 Physical Monadology, Proposition III (Ak, I 478-9); Ai65-6/B2o6~7; Anfangsgriinde (Ak, IV 505); Entdeckung (Ak, VIII202). 26 ID, §1414 (Ak, II 399), Ai69-70/B2ii. 27 Anfangsgriinde (Ak, IV 506). 28 Physical Monadology (Ak, I 477), ID, §1 (Ak, II 38912_14; Entdeckung (Ak, VIII 202). The demand is based on the notion that not having simple parts (i.e., being infinitely divisible) is tantamount to not having any parts at all, and so being made up of nothing. The reason being infinitely divisible is tantamount to not having any parts is that, in an infinitely divisible magnitude, the division goes on forever without ever terminating at any simple part, so that the infinitely divisible is, in effect, a network of relations without there being anything that stands in these relations. The way around the absurdity is to insist that space and time are not substances but merely networks of relations. As such, they are not composed of parts but are tota that are originally given as wholes. See A438/B466. This is not an option, however, where space and time are considered to be substantival. 29 ID, §1414 (Ak, II 399). 30 ID, §14 15, §15 ID (Ak, II400,404); letter to Herz of 21 February 1772 (Briefwechsel 104-5, (Ak, X 133-4); ^5^79, 5880; A32/B49; A39~4i/B56-8. 31 See in addition A429/B457, A487/B515.

4io Notes to pages 204-19 32 Kant explicitly drew the distinction between apprehension of the manifold of appearance and apprehension of the manifold in an object at Ai89~9i/ 6234-36, though he did so only with reference to time and not to space. 33 Principles, II Art. 18. 34 For more detail on this view, see chapter 3, above. 35 The necessity of a counterbalancing attractive force is demonstrated at Ak, IV 508-9. However, Kant speculates that there might be one kind of matter, the ether, that has incomparably great repulsive force in proportion to its quantity of matter, so that this material naturally tends to expand to fill all empty spaces. See Ak, IV 534 and 563-4. However, he regards this as merely a hypothesis, and as not adequate to impugn the possibility of empty space. 36 Here, Kant attaches a footnote that follows as the next citation. 37 Feder, 29-30, appealed to Berkeleyan intuitions about the impossibility of thinking space without some content. Later, Kemp Smith, 104-5, appealed to Berkeleyan intuitions to criticize Kant's argument on this score, taking it to be obviously false that we could imagine (apparently in the sense of 'picture') a space or time that has no sensory-quality content whatsoever. 38 Principles, 116; De Motu, 55. 39 That this is still admittedly a conception and not an intuition does not impair the result, as I go on to remark in more detail in a moment. 40 The Opus Postumum, with its ether deduction, is another matter. Chapter 7 \ Logic, §6 n. 2 (Ak, IX 95). CompareEntdeckung (Ak, VIII i99~2Oon) and ID, §6 (Ak, II 394). 2 What if, included in the concept, is a reference to a spatial location and a temporal history of motion from this location to past and present ones? Locke took the principle that two substances of same type (two bodies or two souls) cannot be in the same place at the same time to entail that spatiotemporal location should be an adequate basis for the individuation of particles and souls (Essay, 2.27.1-3), but Kant's position against lowest species in the note to Logic, §11 (Ak, IX 97), entails that there can be no uniquely individuating features. Though this result may appear counterintuitive where spatiotemporal locations are concerned, it can be rendered less so by considering that without presupposing any particular account of what space and time are Kant could easily have argued that we are not able to experience objective locations in space and time apart from reference to some sort of landmark or clock. Thus, individuation by spatiotemporal location presupposes an

Notes to pages 219-22 411 account of individuation of objects (landmarks and clocks) and cannot therefore be used to establish such an account. 3 The justification for these claims is to be found in the argument summarized at the outset of chapter 6, §iv.a, above. Since space and time are infinitely divisible, there can be no such thing as an ultimate, independently given part of space or time. Such parts as there are only emerge through delimitation of a large whole, within which they are all given. 4 See most notably Quinton; Swinburne, Times' and 'Conditions for Bitemporality'; and Hollis. 5 This is merely an observation, not a criticism. 6 'Mereology' is a term first used by S. Les'niewski, 'O podstawach matematyki/ Przeglad Filozoficzny 33 (1933), 77-105, to describe a theory of the part/ whole relation. The term was adopted by Wilson, 252-6, to mark a contrast between the way the parts of an extended magnitude are related to one another in the whole and the way the specific differentiae of an abstract concept are related to one another under the concept. In Wilson's terminology, this is described as a distinction between 'mereological' and 'set-theoretical' relations of parts. 7 Though I have cited Kirk Wilson as the chief exponent of this account of the Later Expositions, the notion that Kant's argument in the Later Expositions turns on the central distinction between the part/whole relation and the instance/genus relation has been made independently of appeal to the terminology of mereology, both before Wilson and after. For examples see Allison, Transcendental Idealism, 90, 92-3; Pippin, 65,67; Kemp Smith, 105; and Vaihinger, II 205. 8 In fairness, Quinton and company do not set out to do this but merely pick on Kant's text as an occasion to introduce their own discussion of the question of whether there can be discrete spaces. But the point still needs to be made because their claims could be taken as an attack on the singularity argument. 9 For more on Kant's reasons for rejecting discrete spaces see Falkenstein, 'Spaces and Times.' I maintain that these reasons are sound, but, because the point is moot, I will not repeat my arguments. 10 Kant might appear to foreclose this possibility with his claim that the parts of space are not components that precede the whole and out of which the whole has been constructed. But, in this case, it is not the singularity of space on which his argument turns, but the priority of the whole of space to its parts. We are then dealing with a different argument - one that will be examined below. Here, however, I would like to concentrate just on what follows from Kant's claims concerning the singularity or particularity of space.

412 Notes to pages 222-5 11 Some ambiguous support for this comes from the parallel passage in the time section ^32/647), which will be considered in a moment. There, Kant writes that representations that can only be 'given' by singular objects are intuitions. The support is ambiguous because, a representation's being given by a singular object and being of a singular object (i.e., a singular representation) are not the same thing. 12 For instances of this reading of the singularity argument see Prichard, 44; Kemp Smith, 105,107; Paton, 1115; Ewing, 37; Walsh, 18; Al-Azm, Time, 57; Strawson, 64; and Pippin, 64. See also Vaihinger, II211-12,223, and Dryer, 176. For reservations see Allison, 91, and Walker, 43. 13 Though I have chosen to use Wilson's account for purposes of illustration (and because it provides a nice occasion for reiterating certain points about the nature of Kantian intuitions), he is by no means the only commentator on the Later Expositions who fails to come to terms with this problem. For instance, Allison, Transcendental Idealism, 92, recognizes the difference between concepts generated by abstraction and those generated by composition but, like Kant, fails to carry through and continues to suppose (p. 93) that concepts can be only taxonomically related to instances. 14 Kirk Wilson, 256, 258. 15 Ibid., 256-7. 16 Ibid., 258. 17 The view that objects of ordinary experience such as 'my desk' are not immediately intuited but are the products of judgment was widely held in the seventeenth and eighteenth centuries. Think in this regard of Berkeley's account of visual perception (Principles, 43-4), Locke's discussion of the Molyneux question (Essay, 2.9.8), or Descartes's Second Meditation example of 'seeing' people in hats and cloaks walking beneath a window (AT, VII 32). 18 8202-3, Ai63/B2O3~4. Note more generally Bi6o, where Kant defines perception as empirical consciousness of intuition and claims that it occurs through a synthesis of apprehension, and 6162, where he claims that the synthesis that makes perception possible is subject to the categories. 19 Kirk Wilson, 256. Some of Wilson's pronouncements imply that he might hold that it is only synthesis 'in its most sophisticated form' (p. 256) that generates concepts. But to admit this much is still to admit that representations of objects such as 'my desk,' indeed, perceptions such as 'this rectangular brown colour patch,' are the products of a process performed upon more primitive given materials. They are not, therefore, intuitions in the sense of immediate representations. 20 Kirk Wilson, 257. 21 Kemp Smith, 106-7, realized this. He charges (quite correctly) that Kant's

Notes to pages 226-30 413

22

23

24 25

26

argument in the Later Expositions rests on the assumption that there are only two kinds of representation, intuition and concept, and (most significantly) that Kant takes all concepts to be of just one type: generic, class concepts. Hence the argument establishes only that space is not a generic, class concept, not that it belongs to receptivity (intuition) rather than spontaneity (intellect). This should not be confused with the closely related thesis that when there is only one particular object a representation can refer to, that representation must be an intuition. Kant is willing to allow that concepts can be used to refer to singular objects (Logic, §1 Anm. 2 [Ak, IX 91]); he only denies that a concept could in principle be given by just one object. Even if there is only one object that in fact gives us a concept, it would have to be the case that in principle there could have been others that could have done so as well. Since Kant believes that our representations of space and time are representations of the forms of our intuition, which are grounded in the constitution of the subject and not in any object that affects the senses (641), it is rather odd to speak of space and time being brought about by an object. But the locution is merely loose, not absurd, as Vaihinger, II 373, chooses to read it. We can take the 'object' that supplies our representations of space and time to be the constitution of the receptive organs of the subject. See chapter i, above. Impressed by having found a reference to whole/part priority in the last exposition of the time section after missing it in the time singularity argument, Vaihinger, II 378, writes: 'Aber die Freude dieser Wiedererkennungsscene wird uns getriibt durch den Gedanken an die enorme Ungenauigkeit Kants, die er sich somit hier hat zu Schulden kommen lassen: es fehlt vollstandig an dem richtigen Parallelismus membrorum. Indessen - wir sind solche Ungenauigkeiten des grossen Mannes zu sehr gewohnt, als dafi wir uns Weiteren dariiber aufhalten sollten.' Vaihinger's complaint is both bitter and completely justified. Over the course of the later Metaphysical Expositions and the Transcendental Expositions, the 'great man' shows himself to be the most slovenly author of philosophical work since Aristotle. He betrays not the least concern to edit his work properly and bring the parts of the exposition together systematically. The lack of parallelism between the spacesingularity argument (or, for that matter, the last exposition of the space section) and the last exposition of the time section is just one example of this. We will see many more. And when he revises the texts for the second edition, the incongruities are multiplied rather than diminished. Uberweg, as cited by Vaihinger, II256-7.

414 Notes to pages 230-40 27 Some commentators have gone so far as to see this as evidence either that Kant's views of the nature of space and time underwent a fundamental change between the Aesthetic and the Analytic, or that his views in the Aesthetic were preliminary and naive and supplanted by the more developed theory of the Analytic. For specimens of all these views see most notably Vaihinger II 224-31, esp. 227-9; Kemp Smith, 94-7; Garnett, 207-35; Wolff, 228-9; and Al-Azm, Time, 64-7. The claim that there was a shift in Kant's views between the Aesthetic and the Analytic is, however, rendered completely untenable by the fact that Kant continues to reaffirm whole/part priority in the Anticipations (Ai69-7O/B2ii). For yet another, later, 'critical' affirmation of whole/ part priority see Anfangsgriinde (Ak, IV 508). 28 The resolution consists in pointing out that the Axioms claim only that a successive synthesis of previously given part to previously given part is necessary to measure, count, or otherwise make determinate a space or time, not for the space or time to be given originally in intuition. Thus, space and time can originally be given as indeterminate wholes within which limits can be introduced, and the act of introducing these limits (e.g., drawing lines) can be considered as the successive synthesis of part to part, generating a cognition of a determinate space and time, the latter being the only kind of space or time that Kant is concerned with in the Axioms. For instances of this line of thought, see Guyer, 193-4; Allison, Transcendental Idealism, 94-5, citing Melnick, 11; Nagel, 87-8; Pippin, 66. 29 See Physical Monadology (Ak, 1478-9) for the proof he relied upon throughout his career. 30 See chapter 6, §iv.a, above. 31 For instances of Kant's awareness of and early adherence to this argument see Physical Monadology, Props, i and 2, and ID, §§i and 14.1 (Ak, 1477 and II 387 and 399). 32 And if, on the other hand, this is not how he is understanding 'concept/ then it is not obvious why the B version of the third premise should be accepted as true. 33 This is something Kant claimed from his earliest days and appears never to have questioned. See the demonstration of the infinite divisibility of space in Physical Monadology Prop. 3 (Ak, 1478-9) and compare A524/B552. The B infinity argument does not actually make explicit whether space is supposed to extend to infinity or be divisible to infinity. Some commentators (e.g., Bennett, 66-7) have supposed that infinite extension was what he intended. Others (Vaihinger, II253) have claimed that it was infinite divisibility. I have followed Vaihinger because Kant's distinction between regressus in indefinitum and regressus in infinitum ^512-13/6540-1) would appear to

Notes to pages 240-51 415 restrict him to affirming just the infinity of the division of a given space (as he does at A524/B552), not the infinity of its extension. 34 How the representation of a whole of space would first come to be thought by the intellect is a separate question and is considered below. Here the issue concerns just how the concept of infinity could be known to pertain legitimately to this representation. 35 This has previously been noted by Parsons, 'Infinity/ and Strawson, 66-7, who observe that Kant's position on the infinity of our intuitions of space was, in fact, determined by an antecedent reliance on geometrical demonstrations and mathematical induction. 36 Representation at the first level requires two types of synthesis, one for the representation of form or pattern and one for the representation of content or quality. This is why, while there are four kinds of synthetic procedures, there are only three kinds of representations put out by these procedures. 37 This holds for subjective space and time: the space and time in which sensations or matters of appearance are originally presented. Objective space and time is constructed along with objects. Though Kant at one place observes that the subjective succession is derived from the objective (Ai93 76238), what he most likely means by this is that we postulate a certain objective order of events as underlying and bringing about the subjective order in which our experiences are originally given to us. To use Aristotelian terminology, while the subjective order is given first in the order of knowing, it is derivative in the order of being. It is the order of knowing that counts, however, since, if subjective space and time were not originally given, there would be no way to represent an underlying, objective space or time. 38 Reason might demand the existence of absolute space and time as a regulative principle, but it is not something we could ever claim to know to actually exist. For more on Kant's views of absolute space, see Okruhlik. 39 For Kant, it is essential that there be features of the space that are simply given and beyond my control. For it is these features, ultimately, that are the ground of all necessary truth in geometry. It is because we discover, when doing a construction, that we are constrained to outline the object in a certain way in space, and cannot make it other than a certain way that we are able to say that there are certain things that are necessary and universal. See A717-18/B745-6. 40 For a concurring reading of Kant's position in the Axioms see Allison, Transcendental Idealism, 94,95-6. 41 Vaihinger, II180-1, gives an exposition of the problem. 42 For example, Allison, Transcendental Idealism, 95-6. 43 For example, Guyer, 193-4.

416 Notes to pages 256-7 Chapter 8 1 Kant adds something here that I want to bypass for the moment: the thesis that the invariant feature is contributed by the subject. I return to this question in §ii, below. 2 This is the sense of 'in so far as we are affected by this object' in the definition 'The effect of an object on the representative capacity, in so far as we are affected by this object [and not some other], is sensation.' 3 See also A373-4. 4 I am referring here just to the Second Exposition's independence argument. As noted in chapter 6, above, the Second Exposition contains two arguments, the independence argument, devoted to proving that space and time are a priori, and the inextricability argument, devoted to proving that they are necessary. The inextricability argument actually provides evidence for the starting hypothesis of the priority argument, that the propositions of geometry and axioms of time are, indeed, apodictic. But, in the Second Exposition, Kant takes the inextricability argument only so far as to establish necessity, not so far as to establish the stronger sense of priority discussed here. 5 Allison, Transcendental Idealism, 99, is therefore wrong to claim that the argument of the Transcendental Expositions is an unnecessary addendum to Kant's reasoning and can simply be bypassed. The sense of priority the Transcendental Expositions establish for our concepts of space and time is different from and much stronger than anything the Metaphysical Expositions are able to establish. The argument of the Transcendental Expositions could be ignored only if this stronger result were not required for anything. But, as will be shown below, this is not the case. In so far as Kant is committed to establishing, not just that spatiotemporal form originates independently of the matter of experience, but that it is grounded on the constitution of the subject and not on the manner in which we happen to be affected by objects, he needs to appeal to the Transcendental Expositions. 6 Helmholtz, The Facts of Perception/ 378-81. For a recent restatement see Kemp Smith, 118-19. 7 See Humphrey, 509-10, for evidence that Kant countenanced the logical possibility of non-Euclidean geometries (where 'logical possibility means simply that the geometry does not contain a contradiction), but compare Guyer, 359-62. Humphrey and Guyer do not disagree about the facts (note especially Humphrey's claim that truth ultimately depends on constructability, and Guyer's n. 19 in this regard), but they draw very different implications from them concerning the centrality of Kant's commitment to Euclidean geometry. 8 Strawson, 281-91; Walker, 60-5. This view has been attacked by Hopkins,

Notes to pages 257-8 417 who charges that our experience of phenomenal space underdetermines the propositions of geometry. For example, according to Hopkins, the proposition that parallel lines do not converge or diverge cannot be either verified or falsified by visual experience because the visual field is not acute enough. At close distances we cannot detect small convergencies or divergencies. But, if we extend the lines to great lengths, then we have to step back to get the whole length in our visual fields at once and, when we do this, the lines become so thin and faint that they vanish - either that, or they must be thickened so much that they present the same phenomenal aspect as parallel lines viewed at close distances, and we still cannot tell whether they converge or not. Thus, Hopkins concludes that, far from being described by a single set of principles, visual or imaginary space can be described by a wide range of alternative, incompatible geometrical principles. Hopkins has been answered by Harper, 156, who remarks that it is still significant that the spaces we can visualize or imagine cannot be described by any principles whatsoever, but only by principles that entail indiscriminately small variations from Euclidean results. So, for example, even if visual or phenomenal space is not necessarily described by Euclid's parallel postulate, principles that entail that space must be highly curved may be ruled out. Rather than being committed to a single principle, we are committed to a family or 'envelope' of principles that all yield the same results within certain tolerances. Kant in no way countenanced this result, but it is only a slightly weaker version of his point. 9 For example, a long cylindrical tube and a ring present an identical appearance when each is viewed from an appropriate angle. We distinguish them, not on the basis of this appearance, but on the basis of how we imagine they would look were they turned to the side or were we to move around them. But, when we imagine this, we presuppose, in advance of the actual experience, that the space in which these objects are embedded is consistently well behaved with regard to certain basic topological, affine, and metrical features. 10 Harper, 147-57. A version of this view was earlier articulated by Nagel, 45-51. Nagel gives his version in the process of trying to demonstrate that we possess a body of spatial knowledge more primitive than that codified in Euclidean geometry, whereas Harper (I think rightly) has no concern to absolve Kant's argument of its reliance on Euclidean axioms. For problems with Nagel's approach see Guyer, 359-62. 11 Harper, 156-7. The claim is made under the proviso that the propositions hold valid only for the gross, local structure of space, not for the fine or global structure. 12 Unfortunately, Kant remarks, not merely that the necessity of the proposi-

418 Notes to pages 259-60 tions of geometry and the axioms of time is grounded on the Second Exposition, but that their priority is as well. As noted above, this is a point on which he was mistaken. 13 Logic, §18. 14 Ibid., §17. Kant expresses this by saying that, in the judgment, the concepts of the objects and the concepts of the relations are all united in a higher concept. I avoid this way of expressing the synthesis in what follows. As will become clear momentarily, only error can result from collapsing the distinction between concepts and judgments in this way. A judgment is best viewed simply as a higher-order representation generated by connecting a number of object or predicate concepts with relational concepts. 15 Kant is not quite this careful at distinguishing representation and object. The Logic, §§17 and 18, speaks simply of the representations being unified in the judgment, not of a connection between the representations being used to designate a relation between their objects. I offer this more precise formulation merely to obviate minor objections. 16 Logic, §§35-6; A6-7/Bio-n, 11-12. Note that, in the passages from the Logic, Kant draws two sets of distinctions, one between judgments derived from concepts and judgments derived from intuitions, which he calls 'discursive' and 'intuitive/ respectively, and one between judgments asserting or denying relations of identity and judgments asserting or denying other kinds of relations, which he calls 'analytic' and 'synthetic,' respectively. However, it seems to turn out for Kant that the only judgments that can be obtained through analysis of and deduction from concepts are those involving the relation of identity, so that judgments involving any other relation (synthetic judgments) are all intuitive. Kant is not entirely clear on this point, however. The Logic, §36 n. 2 (Ak, IX 111), tells us that analytic principles are discursive, but it also hints that there may be synthetic principles that are discursive as well ('synthetische Principien sind auch nur dann Axiome, wenn sie intuitiv sind' - my italics). But there are other passages (among them, A32/B47 and 640-1) that seem to imply that all synthetic judgments must be intuitive. 17 I say 'perception or image' because there are two ways this can be done, one passive, the other active. The passive way is to wait for an experience that instances the truth of the concept (A8 and Bn-12 give good descriptions of this method). The active way is to manipulate one's environment so as to induce such an experience. The paradigm example of the latter way (imaging) is the drawing of diagrams on paper, but Kant is willing to allow that we may bypass the physical drawing process in favour of simply imagining how it would be carried out ^713/6742). 18 Logic, §35; A8,611-12. Note that Kant uses different terminology at A8 and

Notes to pages 260-2 419 Bn-i2. What are called 'intuitive' judgments in the Logic, and simply 'intuitions' in the Expositions, are called 'judgments of experience' at Bi2. 19 Though see note 16, above. 20 Of course, it is possible to stipulate arbitrarily a concept of 'triangle' or of 'different time' on which the relation would follow by analysis of the concept rather than by construction of a percept or image. But, for Kant, analytic judgments about arbitrarily stipulated concepts have no truth value and cannot, therefore, be asserted as necessary or contingent truths, even though they follow by analysis of their component concepts. The reason for this is that not all arbitrarily stipulated concepts are concepts of an object of a possible experience. The only constraint on the stipulation of a concept is that one not contradict oneself. But not all consistent concepts refer to objects of a possible experience (Bxxvi n). (At A22O-176267-8, Kant instances the concept of a figure enclosed by two straight lines, which he claims can be stipulated, since it involves no contradiction, but which cannot be instanced in any possible experience. Cf. A47/B65, and ID, §15 ID [Ak, II404].) Since there is always a chance that a stipulated concept may be a nonsense concept, that does not refer to any possible object of experience, only concepts abstracted from experience or concepts whose objects have been constructed at least in imagination can be accepted as figuring in judgments that have truth value. (At Logic, §30 n. 3 [Ak, IX 109], Kant draws a distinction between judgments and propositions, saying that only when a judgment is affirmed as contingently or necessarily true can it be called a proposition. In conformity with this, judgments drawn from stipulated, but not constructed concepts can never be propositions.) Thus, even analytic propositions are grounded in pure intuition or a posteriori experience for Kant. They may be a priori and non-empirical in the sense that no experience of the relation between the objects of the concepts needs to be given in experience to determine the truth of the proposition (the relation can be discovered merely by analysis of and deduction from the component concepts in advance of any such experience), but they are grounded in pure intuition or empirical experience in the sense that the component concepts need to be given in experience, or at least constructed in imagination, before the judgment can be admitted. 21 Logic, §35, is similar. 22 I say this Logic, §17, notwithstanding. Kant only confuses himself and his readers by conflating the distinction between concepts and judgments, as he does here. 23 For a more detailed presentation of this point see Sklar, ch. 2, esp. §§B and E. Compare Friedman, Kant and the Exact Sciences, 55-66. 24 So far as I know, the first person to make this point was Strawson, 283-4. It

420 Notes to pages 263-8 has since been popularized and more fully developed by Friedman, originally in 'Kant's Theory of Geometry' and now in Kant and the Exact Sciences, ch. i. 25 Though Kant does not do so in the Critique, he hints in ID, §14 ^5, that a similar argument could be run for time, appealing to synthetic a priori laws of mechanics and proceeding by arguing that they are based on time in the way geometry is based on space: '[The Leibnizian hypothesis that time is something real that has been abstracted from the succession of inner states], thus, throws into confusion all use of sound reason, for, rather than requiring that the laws of motion should be determined by reference to the measure of time, it demands that time itself should be determined, in respect of its own nature, by reference to things which are observed to be in motion or in any series of internal changes. In this way, all the certainty of our rules is completely destroyed' (Ak, II401). 26 In both passages, as well as in the detailed recapitulation of their content that Kant presents over Prolegomena, §§6-12, the argument relies heavily on an appeal to the example of geometry. This argument from geometry has long been taken to be Kant's only or his best argument for the subjectivity of space and, by implication, time. See, for instance, Strawson, 57-8 and Guyer, 349-5427 The paradox is removed when one considers that it is sensation alone that is the properly empirical or a posteriori element in experience (A42/B6o). An a priori experience is not a contradiction in terms, though an a priori sensation would be. 28 See the previous remarks on the priority argument (pp. 255-7, above) for a fuller discussion of this point. 29 This is not the only way to interpret Kant's following statement. One alternative (favoured by Guyer, 361, 363-4, as an accurate representation of Kant's position in the Aesthetic, though not as a representation of a view Kant ought to have taken) is that we are so constituted as to impose spatiotemporal form on our intuitions. The issue of the exact nature of Kant's subjectivity thesis will have to be postponed until chapter 11, below. In the meantime, I offer the reading that I maintain is most natural and most likely correct, with the proviso that a further defence will have to be offered later. 30 This argument is also to be found in Prolegomena, §9, and the Fortschritte, Ak, XX 266-7. 31 Guyer, in his discussion of the view that Kant might be affirming merely the conditional necessity of the principles of geometry (pp. 363-4, 367), seems to fail to appreciate that there are these two different ways in which a conditional necessity can be cashed out (indeed, at p. 364, he claims that 'it is

Notes to pages 268-73 421

32

33

34 35 36 37

38

indeed natural to explain perception of an object understood as satisfaction of this conditional necessity by the assumption that any object actually perceived is spatial [and Euclidean] independently of our perception of it/ apparently recognizing only the objective way of cashing out the condition). Consequently, his ultimate criticism of Kant (p. 367) for arbitrarily attributing absolute necessity to geometrical propositions, and failing to adhere to the project of exploring the limits of our reason and cognitive faculties, misses the mark. The necessity Kant ascribes to the propositions of geometry is conditional necessity and it could be conceived to be backed up by an investigation of the limits of our cognitive constitution. But it is a conditional necessity of type S, which Guyer fails to recognize, rather than the O-type he rightly sees Kant rejecting. Compare, however, 6167-8. Obviously, Kant was not willing to make the same allowance for the categories. These, he claims, are not just forms necessary for us as we are now constituted, but for all beings that have intuitions of any kind whatsoever. See 6148 and 150. This comment applies just to 640-1 and 48-9. The other texts that have been discussed in this chapter were not explicitly characterized in this way. In particular A24, A25/B39, A31/B47, and A32/B47 are buttressing arguments, and A46-9 7663-6 was intended as a subjectivity proof and as a further demonstration of the thesis that the objects of geometrical knowledge are only appearances and not things in themselves. Prolegomena, §10, adds that arithmetic, in so far as it depends on the temporal operation of counting, is similarly dependent on time. This particular way of cashing out Kant's subjectivity thesis is defended in chapter 11, below. This omission is remedied by the subjectivity argument of A48—9/555-6. 'Mathematics hurries immediately to intuition, in which it considers the concept in concrete, though not empirically, but merely in the sort of intuition that it... has constructed and in which that which follows from the universal conditions of the construction must hold generally of the object of the constructed concept': A7i5-i6/B743~4. Compare ID, §15 f C (Ak, II402-3); Prolegomena, §13 (Ak, IV 285-6); and Anfangsgrunde i (Ak, IV 483-4). One way is to draw the triangle so that, as you move clockwise around its perimeter from the right angle, you make the thirty-degree angle first. There is no way to draw a triangle like this on a piece of paper so that it will exactly overlap any triangle drawn by making the sixty-degree angle first. But, though the two triangles are incongruent, precisely what the difference consists in is very difficult to specify. In my description of the difference, for example, I used the term 'clockwise/ which

422 Notes to pages 273-6 really begs the question by supposing that the difference is already understood. What is the 'clockwise' direction and how is it to be defined? Is it the direction in which the fingers of the left hand curve from palm to fingertip? But this presupposes a well-understood notion of the difference between left and right, and so on. 39 Kant cites the example of a construction demonstrating the equivalence of the internal angles of a triangle to two right angles. See A7i6-i7/B744~5. 40 'For [in constructing a concept] I ought not attend to that which I actually think in my concept... (this is nothing more than the bare definition). Rather I ought to go beyond it to characteristics that do not lie in this concept, but that still belong to it. And this is not otherwise possible, than by determining my concept in accord with the conditions either of empirical or pure intuition': A718/B746. Summary and Conclusions to Part II 1 In making this claim I am running counter to a long tradition, grounded ultimately in Kant's own remarks in the Prolegomena (Introduction and §4, [Ak, IV 263,274-5]), that sees the Metaphysical and Transcendental Expositions as carrying out two, quite different synthetic and analytic methods. For an exceptionally thorough presentation of this view see Al-Azm, Time, 29-38. However, Kant's own presentation of the distinction between the two approaches does not establish the sort of clear opposition of methods he and subsequent commentators have tried to draw from it. According to Prolegomena, §4, what makes an investigation synthetic is that it goes from elements to principles, whereas what makes an investigation analytic is that it starts from something clearly known and goes back to its sources. Put in this way, the Transcendental Expositions are synthetic in so far as they appeal to the existence of certain elements (subjectively grounded forms of intuition), to explain how certain principles are possible (those of geometry and mechanics) whereas the Metaphysical Expositions are analytic because they take something clearly known (that we are in possession of concepts of space and time) and seek to uncover its sources in the cognitive system (a form or order in which matters are originally given in intuition). 2 What follows is a summary of the argument of the Metaphysical Expositions, not as Kant presented it, but as Kant ought to have presented it, had he exhibited the care and concern to edit his text properly. 3 Kant proves this point in what I called the 'singularity argument,' by appealing to the fact that we cognize spaces and times as mereologically related to space and time in general.

Notes to pages 276-90 423 4 Another way to put this is to say that the form is homogeneous. There is no part of it that is slotted for any one particular matter in opposition to any other. 5 Kant proves these points in the First Exposition. 6 Kant proves these points in the independence argument of the Second Exposition. 7 This is not to say that space and time could not possibly exist as relations between things in themselves (that question will have to be addressed in chapter 9, below). It is just that it is out of the question that this is all that they are in so far as they figure in our cognition, since they can be found in our experience independently of any reference to objects. 8 Kant proves these points in the infinity and whole/part priority argments. 9 See Harper, 147-57. 10 For example, Allison, Transcendental Idealism, 99. 11 Guyer, 347-8. 12 Hume might have anticipated Kant in it when he defined space and time as 'manners of disposition of impressions' in Treatise, 1.2. Introduction to Part III 1 These words deleted in B. 2 Given the priority relations expressed in both paragraphs, it would seem fairer had the community chosen to refer to it as 'empirical realism.' Chapter 9 1 See A39/B56 and ID, §15 ID (Ak, II 404). 2 Allison, Transcendental Idealism, 105, has recently argued that Kant's claims here turn merely on the thesis that space and time are a priori and not on any specific commitment to the necessary truth of the principles of Euclidean geometry or of specific axioms concerning time. The error in this view has already been exposed in chapter 8, and the Summary and Conclusions of Part II, above: the priority established by the Metaphysical Expositions and the priority established by the Transcendental Exposition are of two different kinds. The priority of the Metaphysical Expositions is priority simply to all the matters that we discover through experience to be presented in space and time (matters that, given blindness, are already a product of intellectual synthesis). It is not priority to the matter of intuition, and it is certainly not priority to sensation considered as 'the effect of an object on the representative capacity so far as we are affected by it.' The argument of the Metaphysical

424 Notes to pages 291-2 Expositions fails to establish that spatiotemporal form could not be just as much an effect of objects on us as the matter of appearance. It establishes only that this form is not drawn from the matter. To establish the stronger thesis that space and time are given independently of reference to the specific sorts of effects that objects have upon us, Kant needs to invoke the priority argument of the Transcendental Exposition. 3 Kant comes closest to arguing in this way in Prolegomena, §9: 'Were it the case that our intuition is of such a kind that it represents things as they are in themselves, then no intuition whatsoever would take place a priori, but they would always be empirical. For I can only know what might be contained in the object in itself if it is present and given to me. Admittedly, it is even then inconceivable how the intuition of a present thing should give it to me to know as it is in itself, since the thing's properties cannot wander over into my representative capacity. But, even admitting this possibility, such an intuition would still not take place a priori, that is, prior to the object being represented to me, for apart from that no ground of the relation of my representation to the object can be thought - such a prior intuition would have to be based on revelation [Eingebung]. There is therefore only one way possible by which my intuition can precede the actuality of the object and take place as knowledge a priori, namely, when it contains nothing other than the form of sensibility in my subject, which precedes all actual impressions, whereby I am affected by objects' (Ak, IV 282). 4 Guyer, 349, 363, has rehabilitated an interesting objection to this conclusion. What, he asks, if it were the case that the subject's sensory system is merely constituted in such a way as to blind us to any objects that are not in space or time (or, more precisely, not in a space or time that correspond to the forms of our intuition)? Let us call this the 'selection hypothesis.' If the selection hypothesis is correct, then, while it would still be true that the forms of our intuition are ultimately determined by the constitution of the subject and not by the affecting object (though determined only in the sense that the subject selects objects that already exhibit these forms and rejects all others), and while the principles of geometry and axioms of time would retain their apodictic status (since the subject's constitution would still prohibit any falsifying instances), we could still infer that whatever objects we do perceive really have the spatiotemporal properties we perceive them as having. But, while Guyer's selection hypothesis may be admitted as a possible account of the manner in which the subject's constitution works, this is not sufficient to undermine Kant's conclusion. Knowledge cannot be based on speculative hypotheses. Simply because it is 'at least possible' that the workings of our sensory system may be described by the selection hypothesis, it does not fol-

Note to page 292 425 low that our sensory system does work this way or that we can affirm that it does. Not only is it a mere possibility, it is an unlikely one. Whether the subject's constitution selects only certain objects for representation and rejects others, or instead imposes spatiotemporal order on all its representations, regardless of the nature of the affecting object; whether it filters out some things in any given object that it can map into spatiotemporal order and rejects others, or whether it follows some sort of algorithm to project everything in the object onto a spatiotemporal grid, the way a camera transforms an object in three dimensions into a representation in two - these are just four among a large number of different ways of explaining how the spatiotemporal form of our intuition is determined by the subject. And, of them, the selection option is far from being the most likely. If anything, projection ought to be chosen before selection on the grounds that a cognitive system that is able to project as much information about the environment as possible onto its sensory array would be evolutionarily advantaged over one restricted to displaying just those objects that already happen to be arrayed in conformity with its own innate forms. But projection rules out any inference from the spatiotemporal features of our experience back to spatiotemporal determinations of things in themselves. 5 Even though this may not be the conclusion Kant wants to draw as the non-spatiotemporality thesis, it is a conclusion that follows directly from the Prolegomena, §9, argument (see note 3, above) and the related priority argument. Guyer, 349, 362-3, is therefore right to claim that these arguments fail to rule out the possibility that things in themselves might have spatiotemporal properties and relations corresponding to the spatiotemporal features of our intuition, but if he also thinks that these arguments fail to prove that we can have no knowledge of spatiotemporal relations of things in themselves, he is wrong. Whether things in themselves might be in space or time is one question; whether we could have any justification for supposing that they are is another, and while Guyer might be right to follow Trendelenburg in charging that Kant fails to justify a negative answer to the first question, Prolegomena, §9, and the priority argument establish that we cannot take the spatiotemporal features of our experience to be determined by things in themselves, and so rule out any possibility of causal inference from the spatiotemporal features of our experience to spatiotemporal determinations of affecting objects. (Guyer's attempt to circumvent this result by floating the selection hypothesis as an account of how the subject's constitution works to determine the forms of its intuition [see note 4, above], would be successful only if the selection hypothesis were the only or the most likely way of accounting for the manner in which the subject's constitution determines the forms of our intuition, and that is not the case.)

426 Notes to pages 292-6 6 The charge has been made, most famously by Adolf Trendelenburg, that Kant took the subjectivity of space and time (as established by the Transcendental Expositions) to entail that they could not be features of things in themselves and simply neglected to consider the alternative, that space and time might be both subjectively determined forms of our intuition and features of things as they are in themselves. Trendelenburg's objection and its extensive treatment in the literature is exhaustively detailed by Vaihinger, II134-51, but see also Kemp Smith, 113-14; Allison, Transcendental Idealism, 111-14; and Guyer, 363. 7 It is possible to give a trivial demonstration that things in themselves could not possess spatiotemporal relations by claiming that to consider things in themselves as related to one another in space and time is not to consider them as they are in themselves but only as they are in relation to something else. Kant himself throws this consideration in at 666-7. But that it is mere chicanery is evident from the fact that the relevant notion of a thing in itself is that of a thing as it is independently of how it appears to us. The only relations that are relevant to destroying the 'in itself status are relations to the cognizing subject. Were a thing related to other objects, and were it to possess these relations independently of being cognized by a subject, space and time would not be 'nothing' apart from all reference to us and our modes of intuition, and it is this that Kant wants to deny. 8 The Reflexionen contain no lack of more directed uses of the argument, however. Witness R5876: The mathematical properties of matter, for example, infinite divisibility, prove that space and time do not belong to the properties of things but to the representations of things in sensory intuition. For since the essential aspect of these representations is composition, when I abstract this nothing (and consequently also nothing simple) is left over' (Ak, XVIII 374). See also R5879 and 1*5880 (Ak, XVII 375). 9 This claim is echoed at 870-1. 10 Kant claimed to have done this in Anfangsgrunde2 (AK, IV 803-5). Note, however, that, in the Second Antinomy ^440/8468), he explicitly denied that this argument applies to alterations, claiming that an alteration does not consist of a number of smaller alterations that are its parts. 11 Yet a third version (perhaps the oldest) is to be found in Physical Monadology, Prop. 4, Schol. There Kant claims that infinite divisibility would entail that however many fundamental parts were put together in a body, they would not sum up to a particle of any determinate magnitude. This is an appeal to the classical composition paradox, which goes back to Bayle, and even farther to Zeno of Elea, and quite different from the later arguments, which

Notes to pages 296-302 427 appeal to division of the composite down to the simple rather than to aggregation of the composite from the simple. 12 Here, Kant seems to intend a contrast with the case of objects of experience. When an object is given to a cognizing subject, it can be given as a whole in which the parts are indistinct (due to the limited powers of discrimination of our senses) and so in this sense can be given prior to its parts. But when we are dealing, not with how objects appear to us, but with how they are, then we have to admit that it is impossible for a thing to be composite unless it actually has at least two parts, and that it is impossible for its parts to be composite unless they each actually have at least two parts. 13 Though Kant speaks of an infinite magnitude as one the completion of which can never be represented, it is doubtful that the word implies any tacit appeal to the limits on human cognitive capacities. Kant is most likely simply speaking figuratively of what we find upon analysis of our concept of infinity. We do not have to carry out the division ourselves, or even imagine it, and it does not have to be supposed to be carried out over time. The division goes on 'forever' just in the sense that there is no end to the number of iterations (where the parts generated by a previous division are made in turn objects of a further division), not in the sense that it would take forever for us to perform it. (The latter is a consequence of the former, but it is the former that is relevant to the point, not the latter.) 14 Witness the way Kant himself indiscriminately tosses about the terms 'unendlich' and 'uneingeschrankt' in the last of the Metaphysical Expositions for time. 15 See note 32 to chapter i, above. 16 The words 'in thought' are extraneous and can be ignored without doing any damage to the argument. The point here, as in ID and the Entdeckung, is just that if there is to be a composite thing then there has to be something that thing is made up of, but if the thing is infinitely divisible, then it has no parts of its own. 17 Physical Monadology, Props. 5-8 (Ak, I 480-2). 18 See note 32 to chapter i, above. 19 Those who have not already done so are urged to read chapter 5, above, especially its appendix, before proceeding. 20 I stress that the causal laws I am considering here are specific causal laws, not the general causal principle that every event in time must be preceded by some other event from which it follows in accord with a rule. See A766/B794. 21 For more on these various types of order see the Appendix to chapter 5, above.

428 Notes to pages 305-8 22 Of course, Kant himself never intended the Metaphysical Expositions to contribute to this goal. As far as he was concerned, a strong sense of the non-spatiotemporality of things in themselves is established by the decomposition argument. But, as noted above, while the decomposition argument applies to space and time, it can be applied to objects in space or time only if it is assumed that the latter must be divisible into as many parts as the space or time they occupy, and that is a thesis that he never adequately justifies. 23 Allison, Transcendental Idealism, 113-14, attempts to argue that, since the space and time of our experience are 'essentially related to a mind,' they could not be qualitatively identical or even similar to a space or time of things in themselves, which could not share this property. Thus, things in themselves could only be in space and time in that trivial sense where being in 'space' or 'time' just means being ordered in whatever way it may be that things in themselves happen to be ordered. But, though he may be right that lack of 'essential relation to the subject' rules out identity of experienced space and time and a space or time of things in themselves, his argument is forced when he tries to claim that the two could not even be similar. Being 'essentially related to the mind' or 'completely independent of the mind' is (not withstanding the question-begging use of the word 'essentially') only one feature a space or time might have, and it is a relational feature at that. Space and time have many other properties. In the Metaphysical Expositions alone, Kant remarks that space and time are orders in which various matters are disposed, not properties that various matters may have in common or kinds to which they might belong, that they are unlimited, and that they have mereological structure. In the Anticipations, he remarks that they are infinitely divisible. Other remarks he makes in the Transcendental Analytic entail that the moments of time are successively individuated by a transient 'now.' He seems as well to have believed that space has Euclidean metric and affine structure. Why should not a comparative order of things in themselves that shares these features or some subset of them not be taken to be similar to experienced space and time? 24 Ruling out, for the sake of argument, the possibility that the space could be a causality space. 25 This might not be true where variations in hue are concerned, since these differ qualitatively and could not be anticipated in advance. But it could be imagined where the variations are purely intensive, as with saturation and brightness. 26 Thus, Guyer, 349,363, is right to observe that the Transcendental Expositions do not rule out the possibility that our subjective constitutions may merely blind us to objects that are not arrayed in accord with the forms of our intu-

Notes to pages 309-16 429 ition, so that our perceptions of the form of appearance could, in fact, be direct perceptions of the spatiotemporal features of the remaining things in themselves - though the Transcendental Expositions are able to establish that even if this was the case we could never know it, and that this possibility is a sheer speculation and not the 'most likely explanation' Guyer would have us believe it to be. See note 4, above. 27 But not more than he thought his arguments, in particular the decomposition argument, were able to support. Had Kant been able to prove that objects in space and time must be divisible into as many parts as the space or time they occupy, he would have had a much better case for his strong conclusion one that only the modern distinction between infinity and unboundedness could undermine. Chapter 10 1 It is likely that he was greatly assisted in this regard by his tendency to confuse sensations considered as matters of intuition with sensations as exemplified through our empirical concepts of the matters of intuition - concepts like the colours of roses and tastes of wines. (See chapter 3, above, for more on this distinction.) Had he clearly conceived of sensations as feelings of the intensity of force rather than as sensible qualities, he might have been less sanguine about his position. 2 Guyer, 336. 3 See also Prolegomena §36 (Ak, IV 3i811_13). 4 See Vaihinger, II 35-55; Allison, Transcendental Idealism, 247-54; and Jacobi, 220-3 f°r discussion of this objection. 5 It should perhaps be stressed that the issue here is just one of whether Kant needs to talk about affecting objects, not whether he needs to talk about things in themselves. Kant is explicit in a number of passages that, even though we may not know anything about things in themselves, the notion of a thing in itself must at least permit of being thought, if only because, otherwise, the concept of an appearance (which involves a contrast with things in themselves) would be lost. See, for instance, Bxxvi-xxvii; 8306; 6307-8; A254/B3io; Prolegomena, §32 (Ak, IV 315); §57 (Ak, IV 352); A251-2. But whether these things in themselves need also to be thought (or even known) to be affecting objects is what is at issue. 6 Berkeley, of course, supposed that objects do exist outside of us and determine our ideas independently of our wills. He simply denied that these objects are material, and took our language of material objects to be merely a 'vulgar' way of describing the manner in which the divine spirit is disposed

43O Note to page 316 to cause ideas in us. I do not know whether Kant objected to Berkeley because he objected to the caricatured view of Berkeley as someone who had tried to reduce all experience to illusion, or because he found the system of immaterial spirits influencing one another's ideas through the mediation of God as supreme causal principle (a close analogue of what he would have found in Swedenborg) to be deeply offensive. The former motive is indicated by his characterization of Berkeley's position in the Appendix to the Prolegomena: The dictum of all genuine idealists, from the Eleatic school to Bishop Berkeley, is contained in this formula: "All knowledge through the senses and experience is nothing but sheer illusion, and only in the ideas of the pure understanding and reason is there truth"' (Ak, IV 374; Beck's translation. Compare Principles, I §§35-6, for Berkeley's actual position.) But the latter motive is present as well in his characterization of Berkeley's idealism as 'mystic' and 'enthusiastic' (Ak, IV 293) and in his reflection that 'idealism consists in the assertion that there are none but thinking beings, all other things that we think are perceived in intuition, being nothing but representations in the thinking beings, to which no object external to them in fact corresponds' (Ak, IV 288-9). The first part of this sentence does reflect Berkeley's 'spiritual realism' (though Kant should have added that, besides thinking things, their ideas also exist); the second, however, would reflect Berkeley's position only if a further qualification were added: it is not that no object in fact corresponds to our representations; it is just that no material object corresponds to them; and the 'things that we think' are correspondingly not 'nothing but representations,' but rather are signs signifying the manner in which something outside of us will be disposed to affect us, depending on how we proceed to act (see Berkeley's New Theory of Vision, §147, for a paradigmatic statement of this position). This is not, in the end, so different from the 'critical idealist' position Kant attributes to himself in Prolegomena, §13 Anm. iii, since that position consists in affirming the existence of things in themselves but simply denying that we can know anything about them. This certainly leaves open the possibility that things in themselves may be spiritual rather than material. Indeed, Kant's emphatic denial (in Anm. ii [Ak, IV 289-90]) that things in themselves could be spatial would appear to entail Berkeley's result. If there is a difference between Kant and Berkeley, it is just that Berkeley is willing to describe things in themselves, like God and the soul, and claim that they are causally related to one another, whereas Kant wants to withhold assent from all such discourse. Kant and Berkeley are therefore not that different - though not because Kant is more of an idealist than he is willing to admit, but because Berkeley is much more of a realist than Kant realizes. In fact, in so far as there is a difference at all between the two, it is that

Notes to pages 317-22 431 Berkeley is more dogmatic in his pronouncements about the nature of the world of things in themselves, and Kant much more sceptical about the legitimacy of any such pronouncements. 7 This has been demonstrated by Harper. 8 This remark certainly serves to point out a respect in which Kant's approach to providing for the objectivity of reference differs from Berkeley's, but the claim that only a priori foundations can provide for objectivity of reference goes undefended and is certainly one that any empiricist, including Berkeley, would deny. The charge that Berkeley reduces everything to illusion would have to be underwritten by an attack on Berkeley's alternative way of providing for a distinction between reality and illusion over Principles, 26 and 28-33, before Kant could justly present his position as the only way to provide for objectivity of reference. 9 It is on this issue that Kant makes some of his most 'manifestly idealist' pronouncements - those on the topics of affinity and the ground of the laws of nature in the A deduction (Aii3-i4, Ai2i~3, Ai25~7). Here Kant speaks almost as if he considers the intellect to have the power to impose a single, coherent order on all our experiences. However, Kant himself subsequently struck these idealistic passages from B. There are no references to affinity in the B deduction and the laws of nature are described as necessary only in so far as experience is to be intelligible to us (6164-5). 10 Prolegomena (Ak, IV 290-1). 11 That this answer may none the less not be completely satisfying is nowhere better illustrated than by the life and work of Heinrich von Kleist. The Critique of Pure Reason, so the story goes, convinced Kleist that it is possible that the appearances might be radically at variance with the true facts of guilt or innocence of an accused, and despair over this result led him to kill himself. See David Luke's and Nigel Reeves's Introduction to their translation of Heinrich von Kleist, The Marquise of O and Other Stories (Harmondsworth: Penguin, 1978), 7-10. 12 Prolegomena, §13 n. 3 (Ak, IV 293), Ak, IV 374-5, 669-71, 8274. 13 A249, A251-2, Prolegomena §32 (Ak, IV 3i52-3)/ 6306. 14 Bxxvi-xxvii, 6306, 6307-8, A254/B31O, Prolegomena, §32 (Ak, IV 315) and §57 (Ak, IV 352), A251-2. 15 It may none the less be possible to go some way towards recognizing the legitimacy of a claim about affection by things in themselves as well. However, since that is strictly not required for the purpose of Auseinandersetzung with Berkeley, I relegate further speculation on this topic to an Appendix. 16 In making this claim I am interpolating somewhat. What Kant strictly says is that the a posteriori is that which is known through experience (62-3).

432 Notes to pages 322-3 But this is an unfortunate way of putting the point, and only creates confusion when one recalls Kant's remark that experience contains a priori as well as a posteriori elements (Bi) - and that the a priori elements can be isolated 'only after long practice has made us aware of them and capable of separating them' (62). So, careful inspection of what is given in experience appears necessary to know its a priori elements as well! It is merely Kant's exposition that is infelicitous, however, and that is why I have offered the alternative given in the body of the text. What justifies the interpretation are two passages: first, Kant defines sensation as 'the effect of an object on the representative capacity, in so far as we are affected by it' (Ai9/B34), by which he means that sensation is not just 'the gross effect of an object on the capacity' (since that effect includes things like spatio-temporal form, that are properly seen as contributions of the constitution of the subject's cognitive system and not as due to the object). Sensation is rather 'that portion of the effect that is properly due to the activity of the object' - this is the import of the 'in so far as' clause. The second passage is A42/B6o, where Kant remarks that it is the presence of sensation that makes our knowledge a posteriori. Taken together, the two passages entail that the a posteriori is that which depends on the specific manner in which an object happens to affect us. 17 Kant says something very much like this: that the concept of an appearance in general carries with it the notion of something of which it is the appearance (notably at those passages cited in note 13, above) - but apparently he does not say it for the reason that sensation cannot be defined apart from reference to an external, mind-independent affecting object. What moves him is rather the notion that a reference to things in themselves is analytically contained in the concept of an appearance. 18 This is the very term Kant had used in ID to describe the illegitimate application of the forms of the sensible world to objects in the intelligible world. In the Critique, where intelligible objects are not possible objects of knowledge for us, subreption resurfaces as the illegitimate conflation of sensation with space and time. (Though the Introduction to the Dialectic contains a single reference to 'the unobserved influence of sense on intellect' [^294/6350], the cause of transcendental illusion is swiftly located elsewhere.) 19 'The pleasant taste of a wine does not belong to the objective determinations of the wine, and so to an object, even considered as appearance, but to the particular constitution of the senses in the subject that tastes it.' 20 'Colours are not characteristics of bodies that are intuited as being coloured, but likewise only modifications of the sense of sight, which is affected in a certain way by light.'

Notes to pages 323-4 433 21 Taste and colour are not necessary conditions, under which objects can alone be Objects of the senses for us. They are only contingently injected effects of the particular organization, bound up with the appearance.' 22 The pleasant taste [of a wine is] in fact grounded on feeling (of pleasure or displeasure) as an effect of sensation.' 23 'Further, no one can have a representation of a colour or any taste a priori.' 24 See Sextus Empiricus, 54-65. 25 The sceptics used the modes against spatiotemporal properties too, noting, for instance, that the apparent shape, size, position, and duration vary with the location and circumstances of the perceiver (witness Sextus's fifth mode, or Berkeley's use of sceptical arguments to attack primary quality realism over Principles, 110-15, or the middle part of the First Dialogue in Three Dialogues between Hylas and Philonous. But Kant is after something more primitive: regardless of how big the object looks to be or what shape it appears to have, it always appears as a collection of parts arrayed in space, and the space itself (so Kant) has certain constant and invariant features (i.e., those described by Euclidean geometry). Similarly, regardless of how long an event may appear to a subject to endure, it always appears as taking up an expanse of time, and this time has certain constant and invariant features (e.g., it is linear and anisotropic). 26 Of course, causal reasoning allows us to anticipate the matter of experience, but only by proceeding from some presently given datum and applying a causal law to it. With space and time, no such reference is necessary. 27 Indeed, Locke goes so far as to observe that, for all we know, different people could get different simple ideas when affected by the same object (Essay, 2.32.15, cf. 3.2.1-4). Since none of us could ever enter others' minds to experience what they experience when their senses are affected in the way ours are by a certain object, we could never be sure that the simple ideas of others resemble our own. (The difference would be moot, however, since the several people would all use the same name to refer to their individually different simple ideas, and thus all end up naming the same stimulus source with the same word.) Here Kant's remark (vii) comes up in a slightly different context. 28 It is interesting to note that appeals to the Molyneux question and experiments with newly sighted blind people were used by Kant's opponents to attack his claim that space is a priori. These considerations were taken to establish that the concept of space is different depending upon which sensory organ, vision or touch, is operative, and hence that this concept is (or, more properly, these concepts are) specific products of specific sensory modalities, not a single form of intuition in general. See, for instance, Feder, 57-9.

434 Notes to pages 327-45 29 The argument of this section has been strongly influenced by Rolf George's work in progress on conceptions of causality in Kant and Hume. While I am not sure that he would agree with the line I am taking here, I am indebted to him for the insight into the analysis of causality that permitted me to take it. Chapter 11 1 The historical material discussed in this section has been gone over before. Most notable among recent treatments are Altmann, esp. 329-31, and Guyer, 22-3. 2 Lambert's and Mendelssohn's objections are to be found in their letters to Kant of 13 October 1770 and 25 December 1770, respectively (Briefwechsel, 7685,87-90; Ak, X 105-10,114-15). Schultz's objection was made in a review of ID published in Konigsbergischen Gelehrten und Politischen Zeitung 95 (25 November 1771), 373-5, reprinted in Brandt, 63-6. 3 Brandt, 64-5. 4 This objection keeps recurring in the secondary literature on Kant. See Strawson, 38-9, for a recent restatement. 5 It is interesting to note that, when Kant came to write the Critique, he reversed the order of exposition, first dealing with space. (In ID, the discussion of time came first.) It is as if he hoped to make his case first for space, where the objection does not naturally arise, and then rely on his reader's previous assent to carry the point for time as well. 6 See pp. 301-2, above, for a fuller exposition of this point. 7 This argument has been encountered before, in chapter 3, §ii.b, where it was shown to indeed be a consequence of Kant's own position (whether Kant appreciates the fact or not). Kant cannot deny the argument without giving something up, and he will not do so (thus, this answer in §7 of the Aesthetic is prefaced with the remark that he concedes the whole argument); what he will do instead is try to mitigate its conclusion so that it cannot be extended to things as they are in themselves. 8 It is interesting to note, in this regard, that Kant took Lambert's statement of the objection, and not Mendelssohn's, as paradigmatic. It is Lambert's statement, for instance, that he reiterated in §7 of the Critique ^36-7/653), and in the letter to Herz, it is Lambert and Schultz alone who are mentioned as proponents of the objection - Mendelssohn's name is unaccountably omitted. Despite these circumstances, it is Mendelssohn's version of the objection that I have chosen to oppose to Kant. I have done so because, as I said, it is briefer, clearer, and more elegant. But Mendelssohn was also, in the end, more profound. According to Lambert's version, change, and therefore time, must be

Notes to pages 349-61 435 undeniably something real because no one, not even an idealist, can deny that there is change, if only in the beginning and passing away of our inner representations (Briefwechsel, So; Ak, X 107). According to Schultz, our intellectual and conative acts, as well as our outer sensations, change in time, so time must be a real form of the intelligible as well as of the sensible world (Brandt, 64-5). Thus stated, the objection invites the response that what is the case with our representations and what is the case with the objects those representations represent may be two different things, and that the representations may be 'really' successive, though the objects are not. Mendelssohn's version of the objection, which stresses that, in so far as the representations are 'really' successive, the subject that has them must change over time, makes it immediately clear that the difficulty has not been evaded in the least. If Kant ignored Mendelssohn, then he did so at his cost. 9 I have learned from an unpublished paper by Donald Felipe that the phrase 'I concede the entire argument' (concede totum argumentum) was a standard response employed by participants in scholastic disputations. The phrase was used to charge that the opponent had reached an irrelevant conclusion. 10 This is a thought that cannot be ruled out of bounds for things in themselves. It involves only the 'unschematized' categories of substance and inherence (A242-3/B3OO-i) and does not import any reference to permanence in time. Afterword 1 For reasons more fully expanded upon in chapter 2, above, it is a misinterpretation of the Analogies to suppose that the objective temporal series precedes the subjective. In the order of knowing, the subjective series is given first as datum for judgments about objective spatio-temporal relations (the objective series). It is just that, in the order of being, the objects in their relations are thought as the cause of the subjective series, even though the objective relations are what is known last. 2 See Vaihinger, II180-4, for an exposition.

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Citation Index

Physical Monadology Ak, I 477 36, 372, 409, 414 Ak, I 478-83 371-2 Ak, I 478-9 241, 373, 414 Ak, I 479 372, 426 Ak, I 480-2 300-1

Ak, II 388n.2 Ak, II 388-9 Ak, II 389

'Negative Magnitudes' Ak, II 165-204 116

Ak, II 393-4 Ak, II 394 Ak, II 394-5 Ak, II 395 Ak, II 396 Ak, II 396-7 Ak, II 398-406 Ak, II 399

Prize Essay Ak, II 278-79 Ak, II 291

33, 375 33

Traume Ak, II 344-8

381, 390, 394

'Quadrants in Space' Ak,II 37 8 374 Ak, II 383 34, 41 Inaugural Dissertation title 32-3 Ak, II 387 37, 42, 414 Ak, II 387-9 35 Ak, II 388 38

Ak, II 391-2 Ak, II 392 Ak, II 392-3

Ak, II 400 Ak, II 400-1 Ak, II 401 Ak, II 401 n Ak, II 402 Ak, II 402-3 Ak, II 403

40 372 36, 38, 45, 48, 409 35, 373 41, 42, 44, 46 46-7, 79, 3H, 337 373, 373-4 374, 375, 4io 374 45, 80, 374 51 43 49-52 36, 38, 168-9, 228, 293-4, 372, 373, 379, 399, 409, 414 171, 294, 337, 409 169 379, 397, 420 397 228, 397, 398 421 337

446 Citation Index Ak, II 403-4 Ak, II 404 Ak, II 405 Ak, II 405-6 Ak, II 406 Ak, II 415-16

294, 369, 373, 398 409, 419, 423 397 398 80, 402 35, 36

Critique, Prefaces to Bxxv 81 Bxxvi n 187, 193, 404, 419 Bxxvi-xxvii 429, 431 Bxxvi-xxix 187 Bxxxiv 389 Critique, Introduction to Ai 193, 255 A2 256 Bi 84, 86, 92, 173, 256, 432 Bi-2 131 62 432 62-3 432 83 193, 255 63-4 322 A6-7/Bio-n 418 A8 418 Bn-i2 418 Bi2 419 Ai5-i6 / 629-30 17, 21-6, 368 Aesthetic §1 Aig / 633 Ai9-20/B34

28-71 (esp. 29), 61, 104, 404 86,103-34, 126, 131, 280, 314, 322, 326, 327, 432

A2O / 634

10, 72-102, 105, 109,

135-7

isolation passages A20-1 / 635 A2in / B35n A22/B36

82, 124, 125, 388 29 55-6,63,82, 148-9, 275

Aesthetic §2, Introduction 637 63-4 A22/B37 387 A22-3 / 637 163 A23 64 A23/B37 364,390 A23 / 637-8 146-7 638 64, 150, 269 Space Metaphysical Expositions A23/B38 111,159-85, 393, 387 A24 7638-9 186-216 A24 202, 254-8, 264, 421 A24 / 639 393, 408 A24-5 / 839 217-26 A24-5 / 639-40 82 A25 57, 65, 237-9 A25/B39 65,229, 258-63, 393, 421 639-40 67, 237-8, 239-41 640 57, 65, 393 Space Transcendental Exposition (§3) 640 229-70, 395

Citation Index 447 640-1 641

3, 263-9, 4i8, 421 93, 272, 393, 413

Space Conclusions from the Above Concepts A26/B42 64,288, 289-309, 334-55, 369, 393 A26 / 642-3 292 A26-7/ 642-3 334-55 A27 / 643 193, 199, 200, 202, 267-8, 408 A27-8/ 643-4 287-357 A28 / 644 292 Space Empirical Exposition A28-9 108, 156, 311, 323-4, 357, 396 A29 124, 357, 388, 392 644 124, 156, 311, 323-4, 357, 388, 396 A29-30/B45 156,311, 323-4, 357, 391, 396 Time Metaphysical Expositions (§4) A30/646 159-85,393 A3i / 646 186-216, 393, 408 A3i 202 A31/647 80,393, 254-8, 421

A31-2 / 647 A31-2/ 647-8 A32/647 A32 / 647-8 A32/648 648

56, 66, 226-8, 377, 412 82 258-63,418, 421 229-37, 427 57,65-6,393 64

Time Transcendental Exposition (§5) 648-9 270-1, 421 Time Conclusions from the Above Concepts (§6) A32/649 64,373,409 A32-3/649 289-309,393 A33/649 334-55 A33-4/ 649-50 390 A34 / 650 162, 387, 397 A34-5 / 651 334-55 A36-7/652 287-357 A36 / 652 292 Empirical Exposition (II) A36 7652-3 323-4 Aesthetic §7 A36-7/653 A36-8 / 654-5 A37/ 653-4 A37/854 A38 7654-5 A39-41 / 656-8 A39 / 856 A41/858

339,434 320 350-1 292 349-50 409 80, 294, 300, 369, 373, 423 396

Aesthetic §8 A42/859 A42 / 659-60

292 80, 107, 111

448 Citation Index A42/B60

A42-3 / 859-60 A44 / B6i A45/B62-3 A46-9/B63-6 A47/B65 A48-9/ 665-6 A51/B75 666-7

669 669-71 670-1 671-2

672

86, 104, 109, 161, 256, 322, 420, 432 310-14, 315

303 335-6 263-9, 421

419 266-7, 421

104 426

Ago / 6122

A92-3 A93-4 A-Deduction A97 A98-9 A99 A99-ioo Al02

335-6 319, 431 369, 426

Aio8 Am

369 268

Aii3-i4 An6 An6-i7 Ai 19-20

Transcendental Logic and Transcendental Analytic A50/674 53,6i 10 A50-1 / 674-5 A5i/6 75 149 23 A52-3/B77 21-5 A52-64 7676-88 A55-6 7679-80 23-4 242 A64-5 / 689 Earlier Analytic of Concepts A67-8/692-3 29 A68/693 60 A69/694 10 A76-7 / 6102 74 A77 / Bio2-3 149 A77/B103 218 A77-8/8103 60 A8o-i/ 8106-7 242 A85/8ii7 394 A86-7/ 8118-19 364 A87/5120 80 A89-91 / 8122-3 59

Al2O

Ai2i-3 A125-7 B-Deduction 6128 8129-30 6130-1 8132-3 6133 6134-5 8135 8136 Bi36n 8136-7 8137 6137-8 8138 6145 8146-7 8148

55, 73, 108, 190 76 242

74 387

74-7 78 78 224 55, 59, 83, 99, 224 43i 55,59 224, 246 161 78 431 431

242 54, 60, 61, 68, 383 149 54,68 224 224 224

61, 100

67 224, 246 81 55, 78, 99 193 vii, 59, 74 84 81, 421

Citation Index 449 B148-9 Bi50 6150-2 8151-2

54 421 60,61

6152 6154-5 Bi54

83 78 99 78

Bi59 Bi6o

394-5

6156

Bi6on

6162 6164-5 Bi67-8

78,98

80, 81, 161, 207, 412 20-1, 78, 90-1, 383 412 43i

421

Earlier Analytic of Principles Ai3O-i / 6169 260 Ai38/Bi77 387 Ai4i / Bi8o-i 123 Ai43 / 6182 78 Ai47 / 6186-7 54 Ai50-8/ 6189-97 187 Axioms of Intuition Ai62~3 / 6202-4 6202 6202-3 Ai62 / 6203 Ai62-3 / 6203 Ai63 / 6203-4 Ai63 / 6204

244-52 80, 249 412 230 245-6 412 247-8

Anticipations of Perception 6207 74, 108, 109, 119, 190, 207, 389 6207-8 107 6208 111

Ai66-7/B2o8-9 Ai67 / 6208-9 Ai6y / 6209 Ai68/B2O9 Ai68 / 8209-10 Ai69/B2ii Ai69~7O / 6211 Ai7i-2 / 6212-13 Ai72 / 6214 Ai73/B2i5 Ai75 / 6217

126 109, 280, 322 107, 109, ill 115,117 127 116,125 231-2, 409, 414 209 207, 208, 213, 379 213 124, 388

Analogies of Experience 6218 207 6219 207, 379 6225 207, 379 Ai82 76226 112 Ai83 76226 207 Ai88/623i 2O7 6233 207 112, 113 AiSg / 6234 Ai89~9O / 6234-5 191 Ai89-9i / 6234-6 41O Aigo / 6235 1OO Aigo-i / 6235-6 224 Aigi / 6236 74, 109, 190 Ai92 / 6237 207, 224 Ai93 76238 96-8, 415 A202 / 6247-8 100, 224 A207-9 / 6253-4 205, 209 6257 207, 379 A214 / 6261 209, 379 Postulates and Reftitation A220-1 / 6267-8 187, 419 A223 / 6270 107 A226 / 6273 198, 346 6274 319, 389, 43

45O Citation Index A230 78283 A230/B283

43

Phenomena and Noumena A23&-44 / 6297315-16 302 6297 161 A239 76298 84 A242-3 / 6300-1 353, 354, 357, 435 A243 / 6301 331-2 A249 43i A251-2 429, 431 6306 429, 431 6307-8 429, 431 A254 / 6310 268, 321, 429, 431 Amphibolies A266-8 / 6322-4 A267 / 6323 A267-8 / 6323-4 A27i / 6327 A272 / 6328 A275-6 76331-2 A276-7 78332-3 A286 / 6342-3 A292 / 6349 Earlier Dialectic A294 / 6350

403 80 343, 387 30 81 387, 403 304 268 174 432

Classification Passage A320 / 6376-7 66, 67, 68, 105, 113-15, 119, 191, 389 Paralogisms A355 A373 A373-4

354 80, 81 256

A383 8421 B422n

388 389 68

Antinomies A429/B457 A429n / B457n A43i / 6459 A43in / B459n, 46in A43i, 33 / B459, 61 A434 / 6462 A438 / 6466 A438, 440 / 8466, 468 A44O / 6468 A487 76515 A493-4 78521-2 A512-13 / 8540-1 A521/B549 A523-4 / 8551-2 A524/B552

299, 426 207,379,409 346-8 414 207,379 240 414,415

Ideal A58i / 8609

105

Later Dialectic A6g6 / 8724

54

Doctrine of Method A712-24 / 6740-52 A713 / 8741 A713 / 6742 A715-16 / 8743-4 A716-17 / 8744-5 A717-18 / 8745-6 A7i8 / 8746 A723 / 8751 A727-30 / 8755-8 A766 / 8794

273-4 29, 66 418 421 422 415 422 105 151 330, 427

409 85, 86, 87 204 210, 213 210, 232-4 298-9, 300 235 370, 409

Citation Index 451 Prolegomena Ak, IV 263 Ak, IV 274-5 Ak, IV 279 Ak, IV 280-5 Ak, IV 281 Ak, IV 282 Ak, IV 283 Ak, IV 284 Ak, IV 285 Ak, IV 285-6 Ak, IV 287 Ak, IV 288 Ak, IV 288-90 Ak, IV 288-9 Ak, IV 289

Ak, IV 289-90 Ak, IV 290 Ak, IV 290-1 Ak, IV 291 Ak, IV 291-2 Ak, IV 293 Ak, IV 293-4 Ak, IV 304-5 Ak, IV 306 Ak, IV 306-7

201, 422 201, 422 201 420 69, 90, 260, 377 311, 388, 420, 424, 425 421 108 81 421 4/93 81 319 430 314-15, 318, 327, 388, 391 430 124, 318, 388 318 3i8 372 430, 431 430 358 115 109, 111, 116, 124, 212

Ak, IV 308-10 Ak, IV 309 Ak, IV 3O9n Ak, IV 314-15 Ak, IV 315 Ak, IV 318 Ak, IV 333 Ak, IV 350-1 Ak, IV 351 Ak, IV 352

1O9, 111 107 124

315, 318, 327 429, 431 327, 429 40

268 388

429, 431

Ak, IV 363 Ak, IV 374 Ak, IV 374-5

Anfangsgrunde Ak, IV 481 Ak, IV 483-4 Ak, IV 497 Ak, IV 499 Ak, IV 501 Ak, IV 503-5 Ak, IV 504-5 Ak, IV 505-8 Ak, IV 506 Ak, IV 506-7 Ak, IV 508 Ak, IV 508-9 Ak, IV 513 Ak, IV 516-17 Ak, IV 517 Ak, IV 524 Ak, IV 534 Ak, IV 534-5 Ak, IV 535

388-9 430 318, 431

Ak, IV 563 Ak, IV 563-4 Ak, IV 564

81 421 132 133 132 426 298, 301, 37 296-8, 300 409 240, 373 132, 414 132, 410 333 133 132 333 410 206 208, 213-14, 215 213 214, 410 215

Critique of Judgment Ak, V 18 Ak, V 20 Ak, V 205-6 Ak, V 351

"3, 387, 39 113, 391 113-14, 391 375

Anthropology Ak, VII 119 Ak, VII 153-7 Ak, VII 154 Ak, VII 156-7

122, 131

12O-3 387, 391 391

452 Citation Index Ak, VII 161 Ak, VII 167-8 Ak, VII 167-9 Ak, VII 168 Ak, VII 177

Entdeckung Ak, VIII i99-2Oon Ak, VIII 202 Ak, VIII 202-3 Ak, VIII 203 Ak, VIII 221-2 Ak, VIII 222 Logic Ak, IX 33 Ak, IX 36 Ak, IX 59 Ak, IX 61-2 Ak, IX 91 Ak, IX 91-100 Ak, IX 93-4 Ak, IX 94-5 Ak, IX 95 Ak, IX 97 Ak, IX 101 Ak, IX 109 Ak, IX no Ak, IX 110-11

121, 122 122

396 388 368

374, 375, 396,

410 409 294-6, 297-8, 300 83 79, 80, 85, 91-3 4

68 61, 70

43 394

29, 44, 67, 218, 225, 227, 413 43,66

243 43,222 410 43, 4io 418, 419

419 418, 419 418

Ak, IX 140 Ak, IX 142-3

151 151

Correspondence Ak, X 130-1 Ak, X 133-4 Ak, X 134

409, 434 339-42

Reflexionen Ak, XVII 293 Ak, XVII 349 Ak, XVII 352 Ak, XVII 356 Ak, XVII 364-5 Ak, XVII 366 Ak, XVII 371 Ak, XVII 505 Ak, XVII 648-9 Ak, XVII 699 Ak, XVIII 13 Ak, XVIII 156 Ak, XVIII 374 Ak, XVIII 375 Fortschritte Ak, XX 266-7 Ak, XX 267 Ak, XX 268 Ak, XX 268-9 Ak, XX 269 Ak, XX 276

53

159 378 378 378 378 124 378 186 384-5 205, 206, 404 117-18, 390 2O6, 211 426

409, 426

420

193, 268 107

124, 388

4,93 107

Person Index

Adelung, Johann Christoph, 375 Adickes, Erich, 366, 371, 378 Al-Azm, Sadik, 370, 381, 412, 414, 422 Allison, Henry, 365,370,376,386,389, 391, 392, 393, 395, 397, 399, 403, 405-6, 406, 409, 411, 412, 414, 415, 416, 423, 424, 426, 428, 429 Aquila, Richard, 386, 387, 391 Aristotle, 6-9, 21-2, 29, 46,138, 364 Armstrong, D.M., 400 Arnauld, Antoine, 394 Aschenbrenner, Karl, 394 Bailey, Samuel, 8 Bain, Alexander, 64 Baumgarten, Alexander Gottlieb, 30, 48,163, 394 Bayle, Pierre, 35, 385, 426 Beck, Lewis White, 374, 375 Bennett, Jonathan, 364, 375, 376, 386, 392, 395/ 414 Berkeley, George, 7, 8,12, 64-5,145, 175,176, 210-12, 316, 318-22, 324, 376, 369, 381, 394, 401, 402, 406-7, 412, 429-31, 433 Beth, E.W., 369

Boler, John F., 367 Boring, Edwin, 363 Boscovitch, Roger, 126 Brittan, Gordon, 369 Broad, C.D., 395 Brook, Andrew, 378 Buchdahl, Gerd, 393, 395 Buroker, Jill, 397 Butts, Robert E., 381 Caird, Edward, 364, 375, 395 Cassirer, Ernst, 370, 376, 378 Cassirer, H.W., 365, 375, 395 Cohen, Hermann, 84, 86 Condillac, Etienne Bonnot, 30,48,385, 386, 388, 394 Crusius, Christian August, 163 Descartes, Rene, 6,7,12, 30, 48,115, 122,145,192,206, 329, 369, 388,404, 412 de Vleeschauwer, Hermann Jean, 369, 370, 374 Donagan, Alan, 400 Dryer, D.P., 397, 409, 412 Eberhard, Johann August, 295, 365

454 Person Index Epstein, William, 400 Euler, Leonhard, 48 Ewing, A.C., 395, 409, 412 Feder, J.G.H., 172-3,175-6, 395, 396, 399, 410, 433 Friedman, Michael, 369, 370, 419, 420 Garnett, Christopher Browne, Jr, 364, 375, 414 Gassendi, Pierre, 393 George, Rolf, 109, 365, 368, 378, 38 387-8, 39i Gram, Moltke, 365, 368 Guyer, Paul, 197-8, 313, 384, 386, 39 397, 406, 414, 415, 416, 417, 4 420-1, 423, 424, 425, 426, 428-9 Harper, William, 257-8, 417, 423, 431 Hatfield, Gary, 179,181-3, 366, 376 378, 379, 381, 384, 394, 395, 4OO, 402, 406 Helmholtz, Hermann, 159, 257 Helvetius, C.A., 30, 48 Herbart, Johann Friedrich, 379 Hilbert, D., 262 Hinske, Norbert, 30-1 Hintikka, Jaakko, 57-8, 367, 369 Hollis, Martin, 411 Hopkins, James, 257 Hume, David, 4,7,10,12, 30, 48,114, 124,125,139,155,158,178, 324, 329-30, 396, 398, 423 Humphrey, Ted, 369,405, 408, 416 Jacobi, Friedrich Heinrich, 392, 429 Jacobi, Maria Charlotte, 365 James, William, 8, 402

Kant, Immanuel: answer to Hume, 330; character traits, 19; constructivism, 4; empiricism, 5,11, 53,122, 194, 282, 366n.i; goals in the Critique of Pure Reason, xv; intuitionism, xv-xvi, 3-5,10-13,26; nativism, 3-4,10,11; on Berkeley, 318-22, 429-31,43in.8; on empty space and time, 188-9; °n introspection, 196; on perception / theory of vision, 148,179, 364*1.22, 38in.29; on physiology, 122, 364n.i9; on sensation, 5,11-12; on space and time, 10-11, 72; on the faculties, 10,28-30, 31-3; on the forms of intuition, 72; philosophy of mathematics, 33; priority of physics to epistemology, 134,148, 364, 38in.29, 393n.9, 398^17; silent decade, 96; slovenliness, 289-90, 4i3n.25; sly tricks, 55, 222, 426n.7, 434n.5; transcendental idealism, xvi; use of terms, 17-18, 26-7, 29-32, 41, 70, 225, 261, 264, 365n.i Keill, J., 295 Kemp Smith, Norman, 197, 364, 366, 375, 376, 378, 381, 386, 393, 394, 39 403,404,405,406,407,408, 409,410, 411, 412, 414, 416, 426 Kitcher, Patricia, no, 196, 366, 376, 377,378,379,38i, 385,394, 395,399, 400, 406-7 Klemme, Heiner, 403 Kolb, Daniel, 376, 377 Kreimendahl, Lothar, 369, 370 Kuehn, Manfred, 369, 385, 388 Kuksewicz, Z., 367 Lange, Ludwig, 84 Leibniz, Gottfried Wilhelm, 30, 34,45,

Person Index 48, 53,126,174,175, 187, 192, 375, 381, 387, 388, 393, 394, 398, 403, 406-7 LeSniewski, S., 411 Locke, John, 7,30,45,53,114,155,158, 162,165-70,174,175,192, 324, 364, 388, 395, 402, 406, 410, 412, 433 Lotze, Rudolf Hermann, 64, 379 Maafi, J.G.E., 172, 365, 396 McRae, Robert, 386 Mahoney, Edward P., 367 Makkreel, Rudolf, 378 Marenbon, John, 367, 373, 374 Martin, Gottfried, 369, 393 Meier, Georg, 394 Melnick, Arthur, 414 Mendelssohn, Moses, 178, 385 Mijuskovic, Ben, 385 Mill, J.S., 407 Molyneux, William, 406 Morgan, Michael, 363 Nagel, Gordon, 414, 417 Newton, Isaac, 34, 393, 394 Nicole, Pierre, 394 Okruhlik, Kathleen, 415 Parsons, Charles, 367, 376, 395, 406, 415 Pastore, Nicholas, 363, 379 Paton, H.J., 376, 393, 394, 395, 409, 412 Pippin, Robert, 376,395,406,409,411, 412, 414 Pitcher, George, 400 Plato, 6 Porterfield, William, 176 Prichard, H.A., 368, 391, 395, 412

455

Quinton, Anthony, 411 Reich, Klaus, 369 Reid, Thomas, 6,8,103-4,n8,119, 177-8, 386, 388, 392, 394, 398 Riehl, Alois, 84, 86, 381, 409 Sassen, Brigitte, 375 Schmidt, Raymund, 403 Schmucker, Josef, 369 Sellars, Wilfrid, 367 Sextus Empiricus, 323, 433 Siegfried, Hans, 388 Sklar, Lawrence, 419 Steinbuch, Johann, 179-83, 379 Strawson, Peter, 368, 395, 397, 406, 412, 415, 416, 419, 420 Stuckenberg, J.H.W., 365, 369 Swedenborg, Emmanuel, 430 Swinburne, Richard, 411 Thompson, Manley, 367 Tonelli, Giorgio, 30-1, 374 Trendelenburg, Adolf, 424, 425 Vaihinger, Hans, 80, 84-7, 90, 93, 365, 366, 376, 379, 389, 392, 393, 394, 395, 396, 403, 404-5, 407, 408, 409, 411, 412, 413, 414, 415, 426, 429 Walker, Ralph, 198-9, 376, 395, 397, 405, 406, 412, 416 Walsh, W.H., 412 Waxman, Wayne, 378, 382-3, 383-4 Wilkerson, T.E., 376, 390-1, 394, 395 Wilson, Catherine, 368 Wilson, Kirk Dallas, 57-8, 223-4, 3^7, 411

456 Person Index Wolff, Christian, 30, 48, 394 Wolff, Robert Paul, 365, 375, 376, 414 Wundt, Max, 368

Wundt, Wilhelm, 64 Yolton,John,386

Zeno of Elea, 35, 296, 426

Subject Index

abstraction, 43,44-5, 59-60,62,68-70, 90,151,158, 218, 222, 225, 227-8, 235-6, 239, 243, 37411.41 adequacy, 328-9 affection: between object and subject, 46, 86-7, 89,107-8,118,121,135-7, 141-2,155-6,173, 227-8, 255-7, 280-1,282-3,290-1,312-13,314-33, 38on.24, 389n.25; between physical objects, 132-3; transcendent vs empirical, 326-7 affinity, 43in.9 analogies, 62, 96-8,112-13, 38on.25; see also entries between Ai76/B2i8 and A2i8 78265 in the citation index a posteriori, 109,135-7,154~8/ 256, 261-2, 280, 322-5, 42on.27 appearance, 44, 53-4,72-3,104-9, 128-9,141,190-1, 388n.25; as affecting object, 314; for Reid, 103-4; matter of, 104-18,140, 4O3nn.2,3; spatiality of, 191 apperception, 54, 64, 68, 76, 99,119, 224 applied logic, 23 a priori, 86-7, 90,135-7,153/ ^i/ 322;

as given independently of the matter of appearance /whatever plays the role of relatum in spatiotemporal relations (the 'negative sense' of 'a priori/ also the 'First Exposition' sense of 'a priori'), 153,172, 173,193,256,282, 403^.3,423^.2; as given independently of the matter of intuition, 423^2; as given independently of the proper effects of objects on the cognitive system (the sense of 'a priori' established by the Transcendental Expositions), 153, 255-7, 282, 423n.2; as given prior in time to all experience (the 'extravagant' sense of 'a priori'), 84-8,174; as given prior in time to intellectually processed representations (the 'Second Exposition' sense of 'a priori'), 191-2,193, 256; criteria of, 322; extravagant sense of, 174; for Vaihinger, 84; in relation to necessity, 190, 322; in relation to subjectivity, 198; negative sense of, 173,174 architectonic, 242 array, 102,139; array of representa-

458 Subject Index tions vs representation of an array, 11,76,99,249, 251-2 assembly ii, 245; see also combination axioms of time. See geometry blindness, 54-9,63-4,72-74,104,129, 137,138-9,149,160,191-2, 223-5, 215,240,242,244,260,275, 376n.57, 394n.io; levels of, 225 body, 117-18,120, 388n.23 categories, 53-4, 242-3, 315-16; schematized vs unschematized, 331-2, 353, 354, 357,435n.io causality, 328-32; as ground of temporal order, 178,184,185, 387^14, 4O2n.50,4O3n.57; schematized vs unschematized, 331-2 chiliagon, 198,208 circularity: in Allison's interpretation of the Second Exposition, 4O5n.8; in Kant's argument in ID, 51-2, 61-6; in the Anticipations, 133; in Mendelssohn's account of time, 178; in individuation by spatiotemporal location, 4ion.2; in the Leibnizian account of time, 301-2, 398^17 click experiment, 387^14, 399n.2O cognition: a priori, 109; empirical, 109; intuitive and symbolic, 375n.5i; levels of, 129, 207, 224-5, 242-3; objective, 105 cognitive theory: medieval, 29,41-2, 45-6, 50, 52,62,69; Kantian, xv-xvii, 3-5, 9-13,21-2,29-33, 35, 39-47, 53-4, 58-62,86-7,93-6, 100,118,138-42,145,224-5,242-3, 259-61; early modern, 7-10,29-30, 44-5,125,162-3,174-9 cognizability, 188

combination, 10-11, 47, 54, 59-60,62, 70,98-100,149,222-4,227, 235-6, 239,243-4,244-52; 279, 38311.31; types of, ii, 98-100,245 complete, as feature of the exposition of a concept, 150 composition. See combination concept, 22,43, 53, 59,218-19,220-1, 227; experienced vs stipulated vs constructed, 4i9n.2O; infinity of, 239; 'logical' and 'metaphysical' senses of, 70; of objects, 150, 396n.i8; of sensible qualities, 150, 396n.i8; of the forms of intuition, 150, 396n.i8; pure intellectual, 150,242, 396n.i8; two senses of, 68-71 conditions, of existence of things in themselves vs experience of appearances, 37-41,240, 312, 427n.i2 constitution (of the subject), receptive vs productive, 92-6, 268-9 constraints: on empirical intuition (perception), 248; on imagination (figurative synthesis), 247-8; on intellect, 50-1, 53-4; on intuition, 37-8; on pure intuition (productive imagination), 247 construction, 188; in mathematics, 33, 273-4 constructivism, 5-6,8-9,64-6,101, 139,145,175-6, 376n.6o continuity, 37-41; principle of, 209 coordination, 47,62,84,88, 93,182 correlation (of sensory data with space), 176-8,181-2 correspondence: of appearances to things in themselves, 319-20, 331; of sensation to matter of intuition /

Subject Index 459 matter of appearance, 104-18,128; of sensation to 'the real,' 115-17; of the intensive magnitude of sensation to force, 117,129-30; of the space of things in themselves to that of appearances, 307 Critique of Pure Reason: differences from ID, 52-4, 58,66, 68; Kant's goals in, xv; punctuation, 4O3n.i decomposition argument, 293-300, 311-12,428n.22,42gn.27; see also paradoxes of composition and division deduction, 188; and metaphysical exposition, 394^12; transcendental, 53-4, 61,64,68, 394n.i2 difference (differentia, Merkmal), 22, 30, 43-4,150-1 discursion, 37,42-3, 45; as applied to judgment, 69; distinction from intuition, 42, 68,138 distinct: as a feature of experience, 37-9,198, 240, 312, 322,427n.i2; as a feature of the exposition of a concept, 150 divisibility: of substance, 371; of space, 371 drawing, 245-9, 4i8n.i7 dualism, 119,177 edge perception, 248-9 efficacy, 328 empirism, 3-9,172,175,179-83; definition of, 6; strict, 6 emptiness, 54, 59 enthusiasm, 121 ether, 132,214, 4ionn.35,40 experience, 86-7,187-8,195,198,207, 242-3; 4o8n.i9; empirical and

a priori components of, 173,255-6, 262,264; unconceptualized, 55 exposition, 150,269-70,275-83, 422n.i; as argument for the nonspatiotemporality thesis, 290-1, 300-5,423n.2; as opposed to definition, 151; dependence of metaphysical on transcendental, 256-7, 280-1,282, 308-9; dependence of transcendental on metaphysical, 200-3,258,266,283, 308; empirical, !54-8, 322-5, 38on.24; metaphysical, 145-54, !58,269-70; purpose of, 146-8,253-4,275; standard view of, 151-4; transcendental, 146,201-3, 253,269-70; see also metaphysical exposition extension, 118,132, 388^23 faculties: higher and lower, 10,21, 25-6, 39-48, 53-4, 59-62,138, 376n.62; one-faculty theories, 29-30, 389n.27; types of higher, 21, 44-5, loo, 129,224-5,242-3 feeling (of pleasure or displeasure), 140, 392n.38 figurative synthesis, 61,62,63,70, 98-100,246-8 force, 108,125^7,129-34; and intensive magnitude, 117-18,129-30, 140; attractive, 132-3; mechanical; 132; of cohesion and rigidity, 214; original vs derivative, 214; repulsive /of impenetrability, 132-3,206, 211,214, 300-1, 371-2 form, 47,49, 375; as ground for ordering the manifold, 78-9,101, no; as order of the manifold, 77-8, 80-1,101,145,276; of intuition, 9, 56-7,62-6,72-102,135-7,139; of

460 Subject Index judgment, 259; of sense /sensibility, 47,54 formal intuition, 383^31 formal intuitionism, 9-13; empirist, 9-10; nativist, 10-13;see flk° intuitionism, formal forms-as-mechanisms thesis, 79-83, 85,92-3,98-101, no, 387n.i4 forms-as-representations thesis, 79-80,83-8 fusion, 180-2 general logic, 22,23 geometry, 200-3,27°; apodictic certainty of, 257-8,263, 280; intuitive ground of, 265-6; synthetic status of, 262,263,283 great light of 1769, 32-3, 369^25 heap thesis, 78-9, 91,93 homogeneous, 'the' (resembling matters), 245-9 hypothetical necessity, 198-200, 203, 267-8 idea, 114,146 idealism, 389^24; Berkeleyan, 429n.6, 43in.8; manifest, 316, 318-21; 43in.9 ideality, of space and time vs subjectivity of sensible qualities, 396n.2o image, 106; see also phantasm; object, of perception imagination, 98,122-3,246-8, 4i8n.i7; as a function of inner sense, 46; as a function of intellect, 60,62; concealed workings of, 123; constraints on the operations of, 247-8; productive, 246-8 immaterialism, 119

immediacy, 29, 31-2, 42-3, 45-7, 60, 66-7,71/37711.64 impression, 132-3 incongruent counterparts, 34,273, 376n.6i independence, 192-3,4i6n.4 induction, 199 inextricability, 192,194,4i6n.4; and necessity, 198,4i6n.4; and the a priori, 198,4i6n.4 infinity, 36-41, 51, 57, 65 innate-ideas nativism, 6,7-8,10; definition of, 6 innate-mechanisms nativism, 6-7; definition of, 6 inner sense, 46,117,120,121, 387^15; confused with outer, 121,122 intellect, 21,26; as discursive, 43-4; as the faculty for abstracting universals and laws, 42, 44, 50,66-71; as the faculty for all forms of cognitive processing, 59-60,66-71; distinction from sense /intuition, 28-41, 44-7, 49-62,70,123,138,140,145, 368n.io, 376n.62; fundamental procedures of, 242-3; limits of, 50-1, 53-4; principal function of, 149; real use of, 44-5; 53, 373n.39; relation to understanding, 367^2, 368n.i5 intellectualism, 389^27 intensification and remission, 132-3 intensity values. See magnitude, intensive; sensation, intensive magnitude of intentional object, 103-6, no, 118, 123,127-30,140,177,191, 385n.i, 386nn.2,i2, 387^18, 388n.22, 389n.25, 39^.37, 392^38 introspection, 196

Subject Index intuition, 31, 60-1, 67-71; definitions of, 29, 31-2, 66-71,138,190-1, 222-3; as applied to judgment, 69, 259-61, 263; as a physiological state, 117-20,123, 376n.62; as a preferred term for 'sense/ 60; as a subjective state, 123; conditions of, 38-41; distinguished from discursion, 37,42,138; distinguished from understanding/intellect, 10, 56-8, 60-1, 70,123,145; empirical, 104; empirical components of, 5,11, 86-7, 94-5,131; form of, 9, 56-7, 62-6, 72-102,135-7; inner, 106; intellectual, 51, 389^27, 4o8n.22; limits of, 37-8; 'logical' sense of, 70, 74,138; matter of, 9-10, 86,104-18, 127-30, 4O3nn.2,3; 'metaphysical' sense of, 70, 74,138; outer, 106; pure, 83-4, 86-7, 90,111,135,158; relation of empirical to a priori elements in, 86-9,111-12,247, 4i5n.39; relation to sense/intellect, 29, 38-9, 45-6, 60, 70, 374H-47; singularity of, 222-3, 226-7, 41311.22; spatiotemporal articulation of, 77, 80-1; speculation that each person only has one that develops over time, 230-1, 377n.2, 379^14; structural complexity of, 4-5, 37-8,74-7, 86-7,138; unconceptualized, 55 intuitionism, 3-4, 5-6, 7-13,153; definition of, 7; formal (see also formal intuitionism), 9-13,166-9,174-83, 184-5, 244-52, 276-9, 283; nonsensationist, 8; sensationist, 8 judgment 259, 260; intuitive ('of experience') and discursive /conceptual, 69,259-61, 263,4i8nn. 16,18; syn-

461

thetic and analytic, 69, 260, 263, 4i8n.i6, 4i9n.2o; vs proposition, 4i9n.2O localization, 11, 85, 94-5,111-12,136, 141,164-5,170-2,175-8,184-5, 250-1, 291, 301 local sign, 180-1, 277, 306-7 magnitude: extensive, ill, 248-9; intensive, 107,116-18,126-7, 129-34,136,140, 388n.2i, 396n.i7; negative, 116 manifold, 73-7,139; order of, 77,80-1, 139 materialism, 118-19,140, 388n.23 mathematics. See geometry matter, 47; as whatever plays the role of relatum in spatiotemporal relations, 160, 276; of appearance, 104-9,118,140, 204, 277, 4O3nn.2,3; of intuition, 86,104-6,109-18, 127-30,204,277, 403nn.2,3; of judgment, 259; of objects, 204; resembling, 245-9 mechanics, 271 memory, 167-8 metaphysical exposition, 145-54, 422n.i (see also exposition); and transcendental deduction, 394n.i2; and transcendental idealism, 283; as ground of the non-spatiotemporality thesis, 301-5; method of, 63-66 method, analytic and synthetic, 201-3, 422n.i mind, 118-19,127; see also soul Molyneux question, 395n.i6, 433^28 nativism, 3-9, 47, 62,78-80, 85, 87,

462 Subject Index 91-6,101,139,145,176-8,4o8n.2i; definition of, 6 necessity, conditional. See hypothetical necessity neglected alternative, 291-2, 393n.8 non datur hiatus, 209 non-sensationist intuitionism, 8-13; definition of, 8; empirist, 9; formal, 9-13; innate-ideas nativist, 6,7-8 non-spatiotemporality thesis, 288 noumenon, 187; in the negative sense, 315, 321, 325, 333 object, 109; and representation, 191; aspatiotemporal, 187,193; of perception (see also phantasm; image), 129,224-5,243; °f sense, 129,224-5, 243; recognition of, 164-5, 171-2, 243; spatiotemporal, 191; theoretical, 129,243 objectivity, 317-19, 322, 325 one and many, 220 order, 183-5; as distinguished from ordered elements, 89,136-7,140, as independent of the ordered elements, 173; as prior to relations, 170-2; 183-5; causal, 184-5, 3O1> 305; comparative, 170-2,184-5, 276-7,302,305-6; deductive, 184; of the manifold, 77-81,139; presentational, 170-2,184-5,277/ 3O1~3/ 305-6, 313; stipulative, 184; subjective vs objective, 62, 96-8,112-13, 139,209, 38on.25, 387n.i4, 415^37; types of, 183-5 original acquisition, 91-3,269 outer sense, 46,118,120, 387^15; causes of, 121,122 paradoxes of composition and divi-

sion (and decomposition argument), 35-41/ 231,234,293-300, 311-12, 371-2,428n.22,429n.27 particular. See singularity pattern recognition, 243 percept. See object, of perception perception, 68-70,108-9, *6i, 207, 224-5,242-3,248; for Reid, 103,107, 177; of edges, 248-9; of spatiotemporal relations, 174-83 phantasm, 42,46,62,106; see also image physiology, 122-3 possibility, 213,273,4i9n.2O presuppositions (of Kant's enterprise), 282 principle of charity, 13,19-21 proper effect, 136,141,256, 432n.i6 proposition vs judgment, 4i9n.2o psychologism: in applied logic, 23; in transcendental logic, 24,27, 366n.9 quality differentiation, 243 real, 115-17; distinct from the actual, 115; of appearance, 116-18; of intuition, 109,115-18; of objects, 117-18; of perception, 211; of sensation, 107,108,115-17,211; the 'real,' 107,113,115-17,206,211-13 reality vs illusion, 317-19, 322, 325, 429-31 receptivity, 10,46-7, 59-60, 92-6,138 recognition, ii, 245; see also combination refutation of idealism, 389^27 relata, 204 relations: adjacency, 249-50; comparative, 167; grounds of, 166-72,

Subject Index 183-5; mereological, 220-1; presentational, 167; taxonomical, 220-1 representation, 17-18,103-4,1O5/ 113-15,191; arising from abstraction vs arising from combination, 236; as opposed to thought, 187, 188,194; discursive vs intuitive, 261; levels of, 129, 224-5,242-3; particular vs generic, 220-1; representation of an array vs occurrence of an array of representations, 11, 76,99,249,251-2; representation of the manifold in intuition vs intuition of manifold representations, 76 schematism, 123 secondary qualities, 44,123-8,140, 154-8 selection hypothesis, 424^.4 sensation, 9, 86,103-34; and properties of objects, 117,125-7, HO, 31O> 388n.2i; and space /time, 49,63, 204; as a posteriori element in experience, 256,261-2,322,42on.27; as effect of an object, 131,137, 140-1,145-6,155-8, 256, 314, 322, 326; as elements of an order, 137, 139; as matter of appearance, 107-9, 116-17,4O3nn.2,3; as matter of intuition, 109-17, 4O3nn.2,3; as physiological state, 119-23,140, 146, 326-7; as psychic state, 125; as sensible quality, 123-7,140,429n.i; as subjective state, 105-6,113-15, 119,123,125,140; as 'the real/ 115-17; correspondence to matter of appearance /matter of intuition, 104-17; distinguished from effects

463

of the constitution of the subject, 131,135-7; f°r Reid, 103,177; inner, 387n.i5; intensive magnitude of, 116-17,126-7,129~34/ 14°A M5-6; objective and subjective, 121; outer, 387^15; role in cognition, 106; spatiality of, 11-13,109-12,118,124, 387n.i5, 391^34; two senses of, 113-14,121,128; views of, 106 sensationism, 8-10,165-9,174-83; definition of, 8 sense (aisthesis): as an intuitive/ receptive faculty 26, 31, 32, 38-9, 45-6, 59-60; as a physiological faculty delivering singular representations, 31-2,41-2,44, 50, 52; common, 46,60; distinction from intellect, 21,26,28-41,44-7,49-62, 138,140,145, 376nn.57,62; form of, 47-50, 54; inner and outer, 46, 117-18,120,162-3, 399n.22; matter of, 47; objective and subjective, 121; replaced by 'intuition,' 60 sense object, 129,224-5,243 sense organ, 122 sensibility. See sense simplicity, 36-41 singularity, 50, 56-9,62,65-71, 377n.64 solipsism of the present moment, 168 soul, 117-18,123,124,187, 320-1, 325 space (including references to space and time): absolute, 244; and the paradoxes of composition and division, 35-6,203-4, 37on.3i, 37in.32; as a priori representation, 161-74, 189-90,192-3,254-8,263,264; as condition of appearance, 200-1; as condition of individuation, 162, 4ion.2; as condition of localization,

464 Subject Index 164-5;as condition of sensory experience /form of intuition, 37, 39-40, 48-52,62-3,101,139,146,153-4, 157,279; as derivative from time, no, 112-13,4O2n.54; as form of outer sense, 163; as ground of synthetic a priori truth, 200-1,270-4, 4i5n.39; as independent of the matter of appearance, 160,276-7, 4O3nn.2,3; as independent of object-recognition, 192-3,215-16, 277-8; as independent of sensation, 49,157,255-6; as independent of understanding /intellectual processes, 49-52,241-4; as inextricable from appearance, 193-4; as irreducible to other representations, 147; as order of reception of data, 9-11, 62-3,72-102,146,185,276,278,281, 290; as presentational order, 185, 277; as things in themselves, 278, 289, 293-300, 311-12; as unrepresentable, 194; concepts of, 63-4; continuity of, 232, 373^37; determinate, 99,249; empirical and a priori aspects of, 5,11,94-5,247, 415^39; empty, 84,186,188,191, 203-16; features invariant with respect to circumstances, 433^25; infinite divisibility of, 40,203, 231-2,240-1,278,293-300, 311-12, 371-2, 372n.34, 373n-37; infinity of, 40, 57, 232-4,237-41; metaphysical absurdities with, 34, 35; necessity of, 26,189-90,192,196, 197,198-200,269,280; objective vs subjective, 62, 96-8,112-13,139, 145-6,157,209, 38on.25, 387n.i4, 4i5n.37; objectively vs absolutely empty, 204, 207; ontological status

of, 34,118-34,147-8,152, 203-4, 372n.34, 398n.i7; relata in, 204; role in mathematical demonstration, 33-4; singularity of, 50,219-21; subjectively full but objectively empty, 204,207; subjectivity of, 197,264-5, 266-7,281; substantival, 293-300, 37on.3i; whole /part priority of, 58, 65,66-7, 69-70,219,229 space- and time-cognition: and object-recognition, 216; history of theories of, xv, 3-13 spatiotemporal relations; and spatiotemporal order, 169-72,174; ground of, 166-72; perception of, 165-83; prior to sensation vs prior to matter of appearance, 160 special logic, 23 spontaneity, 10,46-7, 59-60,138 subject, constitution of, 86-7, 89, no, 131,135-7/ MI, 145-6,173,197, 264-5,266-9,281, 38on.24, 389n.25; see also constitution subjectivity thesis, 288 subreption, 35, 38-41, 323 substance: and accident, 36, 370^31; composite and simple, 36-41, 293-300, 311-12, 370n.3i, 428n.22; material, 118-19, spiritual, 118-19, 388n.23 synthesis. See combination theoretical object, 129,243 thing in itself, 38, 44-5, 53-4,89,141, 298-9, 313-14, 386n.i2,427n.i2; as affecting object, 314-33; as logically entailed by the concept of appearance, 321, 325,429n.5; as thinking, 320-1, 325,43on.6; non-spatiotemporality of, 148,289-93, 300-8,

Subject Index 312-13, 315, 330-1; unknowability of, 311-14 thought (see also intellect; understanding), 187, 4o8n.i9; as opposed to cognition, 187-8; as opposed to representation, 187; empirically guided, 242; of empty space or time, 212-13 time: as condition of sensory experience /form of intuiton, 154, 39on.3O; as form of inner sense, 163, 39on.3O; as ground of synthetic a priori truth, 270-2; as independent of the matter given in perception, 161; as inextricable from experience, 193,194,196; as order of reception of data, 62; empty, 189, 204-5; ontological status of, 235; relation to space, no, 112-3,397^.8, 402^54; singularity of, 56-7, 226-8; whole /part priority of, 57,229-36; see also space totality, 37-41

465

transcendental aesthetic: common views of, 12, 58, 62, 64-5, 364n.23; method of, 64-5,73,148-54; purpose of, 21-2,24-6,146-8 transcendental idealism, xvi, 283,288, 325, 38on.24 transcendental logic: considered as a discipline, 24; considered as a section of the Critique, 21-2 understanding, 367^3, 368n.i4; see also intellect vivacity, 167,178, 398^14 whole/part priority, 57, 58,65,66-7, 69-70,219,229-36; and extensive magnitude, 230; as conditions of existence of things in themselves vs conditions of appearance, 37-9, 240, 312, 427n.i2 world, sensible and intelligible, 35, 39-41,47, 52-3