Space, Geometry, and Kant's Transcendental Deduction of the Categories [1 ed.] 019938116X, 9780199381166

Table of contents :
Cover
Space, Geometry, and Kant’s Transcendental Deduction of the Categories
Copyright
Dedication
Contents
Acknowledgments
Introduction
1 A Priori Form vs. Pure Representation in Kant’s Theory of Intuition
1 The A Priori Form of Intuition and the Container View
2 Pure Form of Intuitions vs. Pure Formal Intuition
3 Summaries of the Three Grounds for the Container View
2 The Metaphysical Expositions and Transcendental Idealism I
1 Introduction
2 Three Accounts of the Metaphysical Expositions
3 Kant’s Arguments from Geometry in the Prolegomena
4 The Nongeometrical Expositions
4.1. First Reading
4.2. Second Reading
5 Why the “General Concept of Spaces in General” Is Not a Concept for Kant
3 Kant’s Theory of Intentionality
1 Kantian Intentionality as Brentano Intentionality
2 Kant’s Projectionism
3 Spatial Form and the Representational Capacity of Intuitions in General
3.1 The Map Analogy
3.2 Applying the Map Analogy to Kant’s Theory of Intentionality
4 Kant’s Theory of Geometry and Transcendental Idealism II
1 Introduction
2 Kant’s Doctrine of Geometrical Method in the Critique of Pure Reason
2.1 Kant’s Geometrical Method
2.2 The Necessity of Geometry as Counterfactual Necessity
3 Alternative Interpretations
4 Objections
4.1 Objections from Friedman
4.2 Objections from Waxman
5 The Transcendental Exposition of the Concept of Space
5.1 The Proof of the Objective Reality of Pure Geometry
5.2 The Second Geometrical Argument for Transcendental Idealism
6 Kant and Modern Physics
5 The Transcendental Deduction of the Categories I
1 Introduction: What Is the Transcendental Deduction of the Categories About?
2 What Are the Subjective Conditions of Thinking?
3 The Affinity Argument
3.1 Introduction
3.2 The Affinity Argument: Background
3.3 The Affinity Argument
4 Transition to the B Edition Deduction
6 Appearances, Intuitions, and Judgments of Perception
1 Appearances: The Undetermined Objects of Empirical Intuition
1.1 Are Appearances Constituted by the Understanding? A Preliminary Argument
1.2 What Are Appearances?
2 Intuitions in General
2.1 Introduction
2.2 Section 15: Synthesis, Intuitions, Judgments
3 Judgments of Perception, the Doctrine of Schematism, and Aesthetically Unified Intuitions
3.1 Judgments of Perception in the Prolegomena
3.2 Longuenesse and the Case for Finding a Doctrine of Judgments of Perception in the Critique of Pure Reason
3.3 Judgments of Perception, Empirical Schemata, and Empirical Concepts
3.4 Aesthetically Unified Intuitions
3.5 The Problem of Sensory Illusion for Kant
7 Transcendental Deduction II: The B Edition Transcendental Deduction
I The First Half of Kant’s B Edition Transcendental Deduction of the Categories
1 Introduction
2 The Analytical Power of Apperception
3 The Propositional Form of Judgments of Perception
4 Problems from Sections 17 and 18
5 The Analytical Principle of Apperception
6 Synopsis of the First Part of the B Edition Deduction
7 Conclusion of Part I and Transition to Part II
II The Second Half of Kant’s B Edition Transcendental Deduction of the Categories
1 Why the Deduction in the B Edition Needs a Second Part
2 The Second Part of the B Edition Deduction
2.1 Introduction
2.2 The Argument of Section 26
2.2.1 Introduction
2.2.2 Proving That the Unity of Space Is an Intellectual Condition: The Subjective Phase of the Deduction in the B Edition
2.2.3 The Proof That the Unity of Space Has Empirical Objective Validity; the Proof of Nomic Prescriptivism; and the Proof That the Unity of Empirical Intuitions Is the Unity of the Categories
2.2.4 Kant’s Explanation of How Logically Unified Empirical Intuitions Come to Be in Accord with the Unity of Space and Time
2.2.5 Some Final Thoughts on the Strength of Kant’s Argument
REFERENCES
NAME INDEX
SUBJ ECT INDEX
LOCORUM INDEX

Citation preview

Space, Geometry, and Kant’s Transcendental Deduction of the Categories

Space, Geometry, and Kant’s Transcendental Deduction of the Categories THOMA S C. VINCI

1

1 Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford New York Auckland  Cape Town  Dar es Salaam  Hong Kong  Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trademark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016 © Oxford University Press 2015 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. Library of Congress Cataloging-in-Publication Data Vinci, Thomas C., 1949– Space, geometry, and Kant’s transcendental deduction of the categories / Thomas C. Vinci. pages cm Includes bibliographical references and index. ISBN 978–0–19–938116–6 (hardcover : alk. paper)  1.  Kant, Immanuel, 1724–1804. Kritik der reinen Vernunft.  I.  Title. B2779.V56 2014 121—dc23 2014007456

1 3 5 7 9 8 6 4 2 Printed in the United States of America on acid-free paper

To my late mother, Ellen Suzette Vinci (née Auerbach), and father, Ernesto Vinci (né Wreszynski). It ended well.

CONTENTS

Acknowledgments  

Introduction  

xi

1

1.  A Priori Form vs. Pure Representation in Kant’s Theory of Intuition   9 1.  THE A PRIORI FORM OF INTUITION AND THE CONTAINER VIEW   9 2.  PURE FORM OF INTUITIONS VS. PURE FORMAL INTUITION   11 3.  SUMMARIES OF THE THREE GROUNDS FOR THE CONTAINER VIEW   20

2.  The Metaphysical Expositions and Transcendental Idealism I   23 1.  INTRODUCTION   23 2.  THREE ACCOUNTS OF THE METAPHYSICAL EXPOSITIONS   25 3.  KANT’S ARGUMENTS FROM GEOMETRY IN THE PROLEGOMENA   27 4.  THE NONGEOMETRICAL EXPOSITIONS   36

4.1. First Reading   37 4.2. Second Reading  

38

5. WHY THE “GENERAL CONCEPT OF SPACES IN GENERAL” IS NOT A CONCEPT FOR KANT   40

3.  Kant’s Theory of Intentionality  

46

1.  KANTIAN INTENTIONALITY AS BRENTANO INTENTIONALITY   46 2.  KANT’S PROJECTIONISM   52 3. SPATIAL FORM AND THE REPRESENTATIONAL CAPACITY OF INTUITIONS IN GENERAL   55

3.1. The Map Analogy   55 3.2. A pplying the Map Analogy to Kant’s Theory of Intentionality   60 vii

viii C o n t e n t s

4.  Kant’s Theory of Geometry and Transcendental Idealism II  

64

1.  INTRODUCTION   64 2. KANT’S DOCTRINE OF GEOMETRICAL METHOD IN THE CRITIQUE OF PURE REASON   66

2.1. Kant’s Geometrical Method   66 2.2. The Necessity of Geometry as Counterfactual Necessity  

69

3.  ALTERNATIVE INTERPRETATIONS   77 4.  OBJECTIONS   80

4.1. Objections from Friedman   4.2. Objections from Waxman  

80 83

5. THE TRANSCENDENTAL EXPOSITION OF THE CONCEPT OF SPACE   88

5.1. The Proof of the Objective Reality of Pure Geometry   5.2. The Second Geometrical Argument for Transcendental Idealism   95

94

6.  KANT AND MODERN PHYSICS   96

5.  The Transcendental Deduction of the Categories I  

101

1. INTRODUCTION: WHAT IS THE TRANSCENDENTAL DEDUCTION OF THE CATEGORIES ABOUT?   101 2.  WHAT ARE THE SUBJECTIVE CONDITIONS OF THINKING?   108 3.  THE AFFINITY ARGUMENT   116

3.1. Introduction   116 3.2. The Affinity Argument: Background   3.3. The Affinity Argument   126

118

4.  TRANSITION TO THE B EDITION DEDUCTION   131

6.  Appearances, Intuitions, and Judgments of Perception  

134

1.  APPEARANCES: THE UNDETERMINED OBJECTS OF EMPIRICAL INTUITION   134

1.1. A re Appearances Constituted by the Understanding? A Preliminary Argument   134 1.2. What Are Appearances?   145 2.  INTUITIONS IN GENERAL   150

2.1. Introduction   150 2.2. Section 15: Synthesis, Intuitions, Judgments  

151

3. JUDGMENTS OF PERCEPTION, THE DOCTRINE OF SCHEMATISM, AND AESTHETICALLY UNIFIED INTUITIONS   157

3.1. Judgments of Perception in the Prolegomena   157 3.2. L onguenesse and the Case for Finding a Doctrine of Judgments of Perception in the Critique of Pure Reason   159 3.3. Judgments of Perception, Empirical Schemata, and Empirical Concepts   161

Contents

3.4. Aesthetically Unified Intuitions   169 3.5. The Problem of Sensory Illusion for Kant  

ix

172

7.  Transcendental Deduction II: The B Edition Transcendental Deduction   176

I. The First Half of Kant’s B Edition Transcendental Deduction of the Categories   176 1.  INTRODUCTION   176 2.  THE ANALYTICAL POWER OF APPERCEPTION   180 3.  THE PROPOSITIONAL FORM OF JUDGMENTS OF PERCEPTION   182 4.  PROBLEMS FROM SECTIONS 17 AND 18   187 5.  THE ANALYTICAL PRINCIPLE OF APPERCEPTION   190 6.  SYNOPSIS OF THE FIRST PART OF THE B EDITION DEDUCTION   195 7.  CONCLUSION OF PART I AND TRANSITION TO PART II   195

II. The Second Half of Kant’s B Edition Transcendental Deduction of the Categories   196 1.  WHY THE DEDUCTION IN THE B EDITION NEEDS A SECOND PART   196 2.  THE SECOND PART OF THE B EDITION DEDUCTION   206

2.1. Introduction   206 2.2. The Argument of Section 26   207 2.2.1. Introduction   207 2.2.2. Proving That the Unity of Space Is an Intellectual Condition: The Subjective Phase of the Deduction in the B Edition   214 2.2.3. The Proof That the Unity of Space Has Empirical Objective Validity; the Proof of Nomic Prescriptivism; and the Proof That the Unity of Empirical Intuitions Is the Unity of the Categories   220 2.2.4. K ant’s Explanation of How Logically Unified Empirical Intuitions Come to Be in Accord with the Unity of Space and Time   221 2.2.5. Some Final Thoughts on the Strength of Kant’s Argument   228 References   235 Name Index   239 Subject Index   241 Locorum Index   247

ACKNOWLEDGMENTS

I would like to thank the De Gruyter Press of Berlin for permission to use material from an article, “Solving the Triviality Problem in the B-Edition Deduction,” first published in Kant und die Philosophie in weltbürgerlicher Absicht I (October 2013), 471–482. I would also like to thank those many Kant scholars whose support in conversation and correspondence has helped a great deal in the thinking that went into this book and the actual writing of it, including Henry Allison, Karl Ameriks, Nathan Bauer, Jeff Edwards, Lorne Falkenstein, Paul Guyer, my Dalhousie colleague Michael Hymers, Robert Howell, Béatrice Longuenesse, and especially Richard Aquila. Thanks also to an anonymous referee for Oxford University Press. I am also indebted to the members of my department, especially those who have come to hear me talk about Kant in numerous colloquia during the last twenty-five years as this project slowly came to fruition. Their comments helped immeasurably to shape my understanding of Kant and of philosophy. Much of the fundamental thinking about Kant that went into this book originated in preparing my courses on Kant over that period, and so I also owe much to the students who attended the lectures and shared their ideas with me. Most recently, I am indebted to my friends, colleagues, and students at Tel Aviv University, where I presented an earlier draft of the manuscript to students in a graduate seminar. I wish to thank those who attended the seminar, especially Nir Friedman, Ori Rotlevy, and Nadav Rubenstein. I also wish to thank my friend Noa Naaman-Zauderer and the chair of the department, Eli Friedlander, for inviting me to come to Tel Aviv. I single out for special mention the Israeli Kant Group and its organizer, Ofra Rechter, for inviting me to present on May 10, 2013, material from an earlier draft of the chapter on Kant’s theory of geometry (Chapter 4). The twenty scholars who attended the event gave me four hours of the most exciting and intense xi

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philosophical dialogue about my work on Kant, an intellectual highlight of not only my visit to Israel but of my entire philosophical career. Thanks to you all. Thanks also to Judith Sidler and my other friends and colleagues in the German Department. Finally I wish to thank Peter Ohlin, the editor for Oxford University Press who managed the refereeing and acceptance procedures for the manuscript and saw it through the press. The presentation of the text owes much to an excellent copy editor, Thomas McCarthy and indexer, Diane Barrington. Thanks also to Emily Sacharin and Geetha Parakkat, so pleasant and easy to work with, who organized various stages of the publication process.

Introduction

In section 5 of the Discourse on Metaphysics Leibniz explains to his readers the sense in which the actual world is the best of all possible worlds: it is the best of all possible worlds because it optimizes two values: the simplicity of the means and the diversity of the effects. In this case the means are the laws of nature and the ends are the number of different natural kinds in nature. Leibniz attempts to explain the notion of optimization by a number of examples; perhaps the most effective is that of an author of a treatise who seeks to optimize the values of brevity in the number of sentences and extensiveness in the number of truths. This example makes it clear that Leibniz is not talking about maximization of each value independently of the other, for that could be done in a book of one sentence, if the goal was to maximize brevity, or infinitely many, if the goal was to maximize the extensiveness of the number of truths. But maximizing any one of these values minimizes the other, so the problem is to explain a sense in which there is just the right amount of both to yield an optimal result. This problem arises only when the values are competing with one another, and a solution is possible only when an equation relating the values can be plotted on a curve having the right characteristics. Let’s say that the right characteristics are an equation that can be plotted in a Cartesian coordinate system that starts close to the y-axis with high y-values and curves down and to the right as it approaches the x-axis. An example familiar from macroeconomics is the plot of quantities of war material versus domestic consumables in a wartime economy. The solution is also familiar: define the optimal point on the curve as the x, y coordinate that determines the largest area under the curve, where the area is a rectangle the top of which is the value of x and the side of which is the value of y. An a priori means for determining the optimal point is afforded by the mathematical theory of the calculus. There is, of course, also an empirical way of discovering at what point on the curve the economy actually is producing the two kinds of commodities. We would not expect these points to coincide unless we had taken steps to make them do so and no doubt would find it intriguing if the empirically determined point and the optimum mathematically determined point actually did coincide. If these two points always coincided for all economies and all pairs of competing commodities, we would be astounded. We 1

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would seek ways of explaining this fact, an explanation that would undoubtedly require a revolution in economics. Leibniz’s interest in optimization theory was, of course, on a grander scale than economics—it was on the scale of cosmological values, the simplicity of the means versus the diversity of the effects that God uses and seeks to realize for the universe as a whole. For the nature of optimization to be defined in the way indicated, these values have to be competing values and governed by an equation that yields the right kind of curve. It is reasonable to suppose that the first condition is met, since the more laws one has, the greater the number of combinations of laws, and the greater the number of combinations of laws, the greater the number of different natural kinds that can be produced. Let’s also suppose that there is in principle an equation that determines the right kind of curve, a concave curve sloping down and to the right, with the y-axis registering degrees of simplicity—the higher the y-value, the more simple the system1—and the x-axis registering numbers of natural kinds. It is a good thing for Leibniz’s metaphysics that he had invented the calculus—later than but apparently independently of Newton—for it gives him a way, at least in principle, of solving the cosmological optimization problem he has set for himself a priori. But here too there is an empirical way of determining where on the plot of possible means/ effects values the actual world is to be located, and here too we would be surprised to find that the empirically determined point and the mathematically determined point coincide. But this is exactly what I think Leibniz supposed we would find—that the actual world is the best of all possible worlds.2 When we are advanced enough to be able to carry out both the mathematical analysis and the empirical research to establish this fact, we are faced with the need to explain it—another explanation that would need to be revolutionary. For Leibniz that revolution consisted in a reinstatement of an element of Aristotelian teleology in the new mechanistic natural science. In case the reader thinks I  may have mixed up this introduction with one for a book on Leibniz, I would like to reassure her that this is not the case; this is indeed intended as an introduction to the present book, a book on Kant’s Transcendental Deduction of the Categories. Some indication of this is already here in my use of the contrast between the a priori and the empirical, a contrast at the center of Kant’s thinking about the problematic of the Deduction.

1 The y-axis measures degrees of simplicity of the system of laws, and the degree of simplicity is inversely proportional to the number of laws; so the smaller the number of laws, the higher the degree of simplicity. A point of maximum simplicity would be one law, registering the highest y-value. The plot of points starts at this y-coordinate and curves down and to the right. 2 Leibniz could also derive this conclusion a priori from his conception of God, but that would be a different proof from the one proposed here.

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To make the analogy between the Leibniz optimization example and Kant’s Deduction closer, I can modify the Leibniz example by supposing that the curve of the competing values of simplicity (of the laws of nature) and diversity (of the natural kinds in nature) does not reflect the actual, objective relationship between these two values but a relationship in how we have to think about these values. Suppose, for example, that the theories we are able to construct are intellectually stable only for certain combinations of numbers of laws and numbers of natural kinds. For example, it may be that if we need, say, five fundamental laws of nature to explain things, we can conceive of only 500,000 natural kinds. There is no logical incoherence in postulating five fundamental laws and 501,000 natural kinds; it is just that any theory that does postulate this combination becomes intellectually unstable in various ways and in the end is not sustainable. Suppose, as in the Leibniz example, that we determine by a priori means a curve having the right characteristics reflecting these relationships and that we determine the optimal point mathematically (by a priori means as well). Now suppose, also as in the Leibniz example, that we empirically determine how many laws we need in order to account for the things that need accounting for in the actual world and we empirically determine how many natural kinds there are in the natural world, finding (as you can by now anticipate) that this pair of values happens to coincide with the mathematically optimum pair. (It is important for all of these examples that the means by which we determine the two pairs of values are epistemically independent: the determination of the curve and its optimal point is done one way, by a priori mathematical reasoning, and the determination of the values for the actual world is done another: empirically.) Again, we would be surprised at this outcome, perhaps putting our question in the following way: Why should subjectively optimal conditions of (theoretical) thinking have an exact correlate in objective reality? Again, when we search for an answer we might ultimately find that the best explanation is a revolutionary one: rather than the laws of nature explaining why human intellectual optimality is as it is, human intellectual optimality must explain why the laws of nature are as they are. In formulating “our question” in these terms I am, of course, attempting to express an idea in terms parallel to that Kant uses at GW 222 (A 89–90/B122) to express the problem of the Deduction: “Thus a difficulty is revealed here that we did not encounter in the field of sensibility, namely, how subjective conditions of thinking should have objective validity . . .” Of course, the problem of the Deduction does not concern subjective conditions of thinking relevant to the number of laws of nature and the number of natural kinds. But it does concern intellectual conditions on having a coherent conception of a world order in which we exist and things other than we exist,

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and it does concern the question why (“how”) the subjective order should have an objective correlate. In Kant’s case the question falls in the domain of metaphysics and the revolutionary consequences are just like the first thoughts of Copernicus, who, when he did not make good progress in the explanation of the celestial motions if he assumed that the entire celestial host revolves around the observer, tried to see if he might not have greater success if he made the observer to revolve and left the stars at rest. Now in metaphysics we can try in a similar way . . . (GW, 110; Bxvi–xvii) Kant continues in the rest of the passage (GW, 110–111; Bxvii–xix) to say that both for intuitions and for concepts, the best way to achieve success answering his question is to suppose, first, that the objective order must conform to the subjective conditions of thought (which he understands to have a priori dimensions) and, second, that this in turn is possible only if the objective order is an order of objects that are our “creatures” in a special Kantian sense: these objects are our creatures because the very existence of these objects depends on the existence of representations of them, and the form of these objects depends on the form of their representations—space and time. Kant does not have a name for the first of these doctrines—I call it “Nomic Prescriptivism”—but he does, of course, for the second:  it is the famous (and much maligned) doctrine of Transcendental Idealism. In the following chapters I attempt to show that achieving the Copernican revolution in metaphysics, understood on the subjectively modified Leibnizian analogy, is the main goal of the argument of the Transcendental Deduction of the Categories in both editions. I also try to show that the structure of this argument is different—and rather better philosophically—than has been thought by the commentators on this aspect of Kant’s work whose work I  know. The progress of argument in these chapters follows closely the progress of argument in the Critique itself, from the first page of the Transcendental Aesthetic in the A edition to the final page of the Transcendental Deduction in the B edition. Chapter 1 introduces the notion of an a priori form in a general way, allowing for the possibility that it is a form of our sensibility as well as of empirical objects that are mind independent. This general characterization then allows us to look in subsequent chapters for arguments Kant might have for his conclusion that the a priori form of empirical objects is a form of our subjective capabilities. The notion of a priori form I introduce here may be likened to that of a container that imparts its structure to the objects it enforms—the “Container View” as I call it—and I devote the third section of the chapter to arguing that Kant’s account of the form of intuition is a Container View in this sense. Section 2 takes up a

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distinction that Kant draws between pure intuition understood as an a priori form of representations and pure intuition understood as a representation of pure objects in its own right. Chapter  2 develops an interpretation of the numbered Metaphysical Expositions and is divided into two main parts. In Sections 2 and 3 I develop an interpretation of Kant’s argument for Transcendental Idealism, reading the relevant paragraphs (3 in the A edition, the section called “The Transcendental Exposition of the Concept of Space” in the B edition) in light of part I of the Prolegomena, especially sections 7–9. I find an argument there I call the “First Geometrical Argument for Transcendental Idealism” in order to distinguish it from a second argument I uncover (in Chapter 4) from later portions of part I. In the second main part of the chapter I analyze Kant’s argument in the remainder of the numbered expositions, postulating two possible readings. On the first, the claim that we cannot derive our representation of space from empirical experience is a conclusion from the claim that our representation of space is a pure intuition; on the second, the claim that we cannot derive our representation of space from empirical experience is a premise for the claim that our representation of space is a pure intuition. My own conclusion is that the second reading better captures Kant’s intentions. In order to establish this I argue for the thesis that the “concept” of spaces in general is not a concept in Kant’s technical sense but something that I call a “conception.” Chapter 3 presents a projectionist account of Kant’s theory of intuitional representation. Following the lead of Aquila,3 I treat the immediacy of intuition for Kant as a sign that the objects of intuition are intentional objects, a conclusion that is also supported by the First Geometrical Argument for Transcendental Idealism. On the projectionist account developed here, I show that the form of intuition-representations must be a spatial form if the objects of those representations are spatial objects (as Kant shows they must be), also arguing that intuitions for Kant are not sensations nor are they composed of sensations as their matter. To explain what intuitions are on this conception and in what sense they have spatial form, I develop an analogy between a system of intuition representations and the symbols on an ordinary geographical map. Chapter  4 divides into three main parts. The first and longest develops an account of Kant’s doctrine of geometrical method based partly on work by Philip Kitcher,4 which I call the KV account. The KV account allows for epistemically independent applications of geometrical method to objects in pure space—the mind-dependent space of imagination—as well as to objects in a putatively objective (mind-independent) empirical space, both of which, I  argue, Kant 3 4

Aquila 1983. Kitcher 1975.

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allows for. In the former case the application constitutes pure geometry; in the latter, applied geometry. In the second main part I argue that Kant compares the theorems of both kinds of geometry, finds that they are identical, and seeks to explain this coincidence. He considers the possibility that the empirical space explains the pure space but rejects it:  the pure space must thus explain the empirical space. Since empirical objects are in empirical space, empirical objects are ultimately mind dependent, thus establishing Transcendental Idealism. This argument is different in structure from the First Geometrical Argument; accordingly I call it the “Second Geometrical Argument for Transcendental Idealism.” With this argument a structure of reasoning is revealed in Kant that is analogous to that in the modified Leibnizian example and is the forerunner to the structure of argument in the Transcendental Deduction of the Categories itself. In the final part of the chapter I briefly consider the question how Kant’s theory of geometry fares in light of the modern account of the structure of space, finding that Kant’s view is still defensible. In Chapter 5 I make my first approach to the Transcendental Deduction of the Categories, beginning with a general discussion of what a deduction of the categories is for Kant. Critical to an understanding of that is an understanding of what problem the deduction is designed to solve, and as indicated, I take that to reside in his question “how subjective conditions of thinking should have objective validity.” In the next section I discuss Kant’s understanding of what subjective conditions of thinking are. In the final section I develop a reading of passages in the A edition Deduction dealing with Kant’s notion of the affinity of the manifold of intuition, arguing that in these passages there is to be found an argument with a structure analogous to that of the Second Geometrical Argument for Transcendental Idealism, though the argument deals in intellectual conditions rather than geometrical theorems and its conclusion is Nomic Prescriptivism rather than Transcendental Idealism. Chapter 6 presents a detailed discussion of Kant’s theory of intuitions and their relationship to synthesis and judgment. Briefly, my conclusions are that while all intuitions are unified by synthetic activity, this activity is of two kinds:  category-governed and non-category-governed. Intuitions unified by category-governed synthesis serve to potentiate objective judgments (“judgments of experience” in Kant’s parlance from the Prolegomena); intuitions unified by a noncategorial synthesis serve to potentiate nonobjective judgments (“judgments of perception” in the parlance of the Prolegomena). I call the former class of intuitions “logically unified intuitions” and the latter “aesthetically unified intuitions.” The chapter concludes with a discussion of Kant’s account of illusions, finding that as intuitions, they are aesthetically but not logically unified, and as potentiators of judgment, they potentiate both judgments of perception

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and judgments of experience—but only a special kind of judgment of experience, a judgment that applies to intuitions externally rather than internally. Chapter 7, the final chapter of the book, is a long chapter divided formally into an Introduction, Part I, and Part II. Part I  deals with the first part of the Deduction in the B edition, sections 16–20, and with the central concepts animating those sections: thinking, consciousness, and apperception. Section 16 introduces these concepts with the famous words “The ‘I think’ must accompany all my representations . . .” But what is the I think? Why is it introduced as an entity? Is it not an action? It is somehow connected with apperception. What is that? Is it to be understood as Leibniz understood it, as a second-order act, with its unity as the unity of an act? But then why is the unity of apperception connected with the unity of the self, an object apparently? To help explain the at times bewildering number of different directions in which Kant’s argument in this section seems to be heading, I propose that Kant may be engaged in two main projects here, both connected with the unity of judgment (thinking) and with the unity of the self; one is concerned with the unity of judgment as the unity of a system of judgments and with the unity of the self as the unity of a system of representations of objects, the other is concerned with the unity that an individual judgment has, a propositional unity that is revealed by the act of apperception. In this book, setting aside the possibility that Kant is engaged in the first project, I consider only the second. I take this unity to constitute the unity of apperception; that is, the unity revealed by apperception. From this beginning in section 16 I show how Kant constructs a sequence of arguments ending in the conclusion of section 20: “Thus the manifold in a given intuition also necessarily stands under the categories” (GW, 252; B 143). Part II has two main divisions. In Section 1, I consider a problem that must confront any interpreter of the B edition Deduction: if, as Kant says in section 20, it has now been shown that intuitions in general are subject to the categories and if the job of the second part (§§22–27) is to show that empirical intuitions are subject to the categories, why does Kant say at the start of the second part, in section 21, that only a “beginning” has been made of the overall task of the Deduction? After all, if by “intuitions in general” (Anschauungen überhaupt) Kant means “all intuitions,” then it is a trivial matter to infer from “All intuitions are subject to the categories” and “Empirical intuitions are intuitions” to the conclusion that “Empirical intuitions are subject to the categories.” Since Kant tells us that the rest of the task is anything but trivial, his readers confront a problem. My solution to the problem is quite direct: I deny that “intuitions in general” is a term that is intended to designate all intuitions; rather, it designates only a restricted class of intuitions that excludes empirical intuitions. The job of the first part of the Deduction is to show that intuitions in general have the unity of

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the categories; the job of the second is to show that empirical intuitions have the unity of the categories. I call this the “Bifurcation Interpretation.” This point can be put in terms of the two types of intuition unity introduced in Chapter 6 by saying that the first part of the Deduction shows that logically unified intuitions are unified by the categories and the job of the second part is to show that while it may seem that empirical intuitions are merely aesthetically unified, they are in fact logically unified. Now it is a trivial matter to infer that empirical intuitions are unified by the categories. The second division in Part II, consisting of Section 2, presents my interpretation of how Kant shows that empirical intuitions are logically unified. I take this claim to follow from another: that Nomic Prescriptivism is true. Demonstrating this latter claim is the main burden of the Transcendental Deduction of the Categories, though not its final outcome. We will see that the argument for Nomic Prescriptivism has a structure analogous to the Second Geometrical Argument for Transcendental Idealism and has the same structure, save for two main differences, as the version of the A edition Deduction that I have called in Chapter 5 “The Affinity Argument.” First, with the A edition Deduction I argue that the part of it concerned with intellectual conditions has the structure of what Kant has called a “subjective deduction” but the corresponding part of the B edition Deduction has the character of an “objective deduction” (in the A preface: GW 102; A xvi–vii). Second, with the Affinity Argument in the A edition, there is a specific category of the understanding providing the intellectual condition at issue in the argument, the category of cause, whereas with the B edition Deduction the proof focuses on the topological unity of space. In order for the topological unity of space to be able to serve this role in the Deduction, it has to be an intellectual condition even if it is not a category of the understanding, a status it does not enjoy in the A edition Deduction but comes to enjoy in the B edition. Kant thus proves that we prescribe the laws of the topological unity of space to nature, and consequent to this conclusion, it becomes possible to argue that we do the same with the categories of the understanding. In the final sections of Part II, I show how it follows from this for Kant that the unity of empirical intuitions is a logical unity, concluding with some reflections on the philosophical merit of Kant’s Deduction as I understand it.

1

A Priori Form vs. Pure Representation in Kant’s Theory of Intuition

1.  The A Priori Form of Intuition and the Container View My primary subject is an interpretation of the Transcendental Deduction of the Categories.1 The argument is complex, its precise nature obscure, and it comes in several forms, both within and between the A and B editions. To have some small hope of laying out the argument structure of the several versions of the deduction with reasonable clarity and simplicity, it is necessary to clear the decks as much as possible of antecedent matters, one of the most crucial of which is Kant’s doctrine that space is the form of outer intuition or sensation. (I later distinguish between the form of intuition and the form of sensation, but that distinction is not an issue here.) A leading idea of this book is that the form of intuition for Kant is a structure in which the mind can construct objects or receive impressions, for example, images, and it is a priori in the following two senses. (1) It has the power to induce structural properties, or form, in the objects2 constructed

1 My source in English for Critique of Pure Reason is Immanuel Kant, Critique of Pure Reason, P.  Guyer and A.  Wood, trans. and eds. (Cambridge:  Cambridge University Press, 1998; hereafter GW). Page references to the German text of Kritik der reinen Vernunft (KrV) are in the standard Akademie pagination, indicated as Ak, for the A and B editions. Other sources in English are Immanuel Kant, Prolegomena to Any Future Metaphysics, G.  Hatfield, trans. and ed. (Cambridge:  Cambridge University Press, 2004; hereafter Hat.); Immanuel Kant, Critique of Judgment, W. S. Pluhar, trans. and ed. (Cambridge: Cambridge University Press, 1987; hereafter Plu.), and Immanuel Kant, Lectures on Logic, J. M. Young, trans. and ed. (Cambridge: Cambridge University Press; hereafter Young). For sources in German, see References. 2 Here the term objects means representing-objects rather than represented-objects, in case representation is at issue.

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or received within it; for example, properties satisfying Euclidean geometry:  something like a jelly mold imposing shape on the jelly poured into it. This power can simply be a primitive potentiality or can be a family of actual properties; for example, actual spatial properties satisfying Euclidean geometry from which the power derives. This structure is a priori in Kant’s first sense, in that it “precedes its objects,” and it precedes its objects because it is asymmetrical: the objects whose form is induced by this power do not have a corresponding power to induce properties in the structure. I develop this distinction and explore various interpretive issues arising from it in Chapter 2. (2) This structure is a priori in a second sense for Kant in that it is a pure structure; that is, a structure that is not composed of matter—for example, physical matter or the matter of sensations—nor does it depend for its form-inducing power on matter. This structure is also asymmetrical:  it can exist without containing any matter, but not vice versa. For convenience, I  call this understanding of Kant’s conception of the form of intuition or sensation the Container View. In the remainder of this chapter I  do two main things. First, in Section 2 I  argue for the Container View as a working hypothesis on the basis of an exegesis of texts at the beginning of the Transcendental Aesthetic. I also confront and resolve a deep puzzle about those texts: how something that is said by Kant to be a form3 of representations can also be said by Kant to be a representation in its own right. The Container View is in itself only a theory about the former. Second, in Section 3 I explain in a preliminary and summary way how the Container View serves three main purposes for Kant that cannot be served by any alternative construal of the form of intuition:  (1)  it is necessary to the mind’s ability to develop a concept of three-dimensional space; (2) it underwrites the mind’s ability to represent a world of spatiotemporal objects distinct from itself and its states; (3)  it is a necessary part of Kant’s explanation for the a priori synthetic character of geometrical knowledge. All of these arguments are either given or foreshadowed in the Metaphysical Exposition in the A  edition, in the Metaphysical and Transcendental Expositions in the B edition, and in part I of the Prolegomena. If these arguments are successful I regard them as turning the Container View from the status of a working hypothesis into that of a final hypothesis. Chapter 3 develops (2), the representational purpose, and Chapters 2 and 4 develop (3), the geometrical purpose.

Boldface is used herein to emphasize texts. Italics are used to introduce special terms and make names out of principles or concepts; they are also used for foreign terms, names of books, and other such uses. 3



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2.  Pure Form of Intuitions vs. Pure Formal Intuition I begin with a commentary on five familiar sentences at the beginning of the Transcendental Aesthetic (GW, 155–156; A20/B34). (1) I call that in the appearance which corresponds to sensation its matter, but that which allows the manifold of appearance to be ordered in certain relations I call the form of appearance.4 (2) Since that within which the sensations alone can be ordered and placed in a certain form cannot itself be in turn sensation, the matter of all appearance is given to us a posteriori, but its form must all lie ready for it in the mind a priori. In the first of these sentences Kant says that form is that which allows the many things making up appearance to be intuited as ordered, but in the second sentence Kant speaks of sensations as the items that are ordered. Although in the sentence just prior to (1) Kant has just characterized appearances as the object of an intuition and in (1) seems to say that sensations correspond to, rather than constitute, the matter of appearances and that it is the latter that are ordered by the form in question, in (2) Kant says that sensations are the matter for which space is the form. I take it provisionally that this is the position Kant means to be asserting here: form is whatever allows sensations to be ordered. (I argue later that Kant also thinks that intuitions in general have a form and that the form of sensations and the form of intuitions in general are not one and the same.) Sensations are what are given to us by sensibility, so the doctrine seems to be that the raw data for cognitive operations comes to us as in some way order-deficient. Order-deficient in what way? One thesis is that the data is entirely without spatial order when it affects our sensibility. Falkenstein calls this the “heap thesis” and distinguishes two forms of it, “forms as mechanisms” and “forms as representations,” the latter of which he attributes to Vaihinger and Kemp Smith, the former to various interpreters.5 On Vaihinger’s reading the form is understood as a “ready made spatiotemporal container”6 that plays a role in allowing sensations that are received as unordered to acquire an order once they are placed in, or correlated with, positions in this container. On the forms-as-mechanisms reading, It is the B edition translation that I follow here. Perhaps most notable among (relatively) recent interpreters is Patricia Kitcher. Her notion of “process form” corresponds to Falkenstein’s “forms as mechanisms.” See Kitcher, “Discovering the Forms of Intuition” (1987, 218). For a discussion of Kitcher’s position, see n. 13. 6 Falkenstein 1995, 80. 4 5

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what allows for the ordering of sensations is a set of rules (“mechanisms”) or procedures followed by the understanding; for example, the rules of Euclidean geometry, which take unordered data and yield sensations arranged in Euclidean space. A third view, which treats forms as relations among sensations as they are given to sensibility, “forms as orders of intuited matters,” is contrasted with the heap thesis and is the view that Falkenstein himself defends. Sentence (2) may be consistent with both versions of the heap thesis, perhaps also with Falkenstein’s own thesis,7 but because of the passivity of the faculty of receptivity whose form is at issue here, it is a stretch to say that the form might be a set of mechanisms actively applied by the mind in constructing an ordered array of sensations. It is also difficult to see how a set of relations ontologically dependent on sensations as their relata could be characterized as a form that “must all lie ready for it in the mind.” This leaves the Container View as the most plausible reading, and it is my working hypothesis that this is Kant’s intended doctrine in these passages.8 Now consider the next three sentences in the Aesthetic: (3) I call all representations pure (in the transcendental sense) in which nothing is to be encountered that belongs to sensation. (4) Accordingly, the pure form of sensible intuitions in general is to be encountered in the mind a priori, wherein all of the manifold of appearances is intuited in certain relations. (5) This pure form of sensibility is also called pure intuition. Sentence (4) strengthens the container thesis: not only is the form said to lie “a priori” in the mind to sensations—this could be true of geometrical principles—but is said to be something “wherein” (worin) the manifold of appearances (we are taking this to be sensations) are intuited. What else could this be but a container? But now, as we prepare to sail away with our catch, we notice a small cloud on the horizon in the form of the introduction of the notion of a “pure representation” in sentence (3). What could this be? The context makes it seem as if Kant is talking about the form of sensations, a container of (sensory) representations, yes, but itself a representation? This cloud becomes larger with sentence (5): the container/form “is also called pure intuition.” This would not cast much shadow over the container thesis if Kant were simply introducing As he argues in Kant’s Intuitionism, 81. There are many other passages in CPR that support the container reading; e.g., this from the A edition Paralogisms: “Space and time are of course representations a priori, which dwell in us as forms of our sensible intuition before any real object has even determined our inner sense through sensation in such a way that we represent it under those sensible conditions” (GW, 428; A373). 7 8



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alternative terminology for the container, as is suggested by Kant’s words. However, since the notions pure and intuition are technical terms already given a definition independent of form and sensation, this seems unlikely. So we seem to have two quite different things here—a special kind of nonsensory intuition, a special container for sensory intuitions, and an apparent identification of the former with the latter. (The text at GW, 428; A373, quoted above, also makes this identification.) Our present concern is whether there really are two things here or is Kant, after all, just talking about one thing with two different terminologies. A distinction between “form of intuition” and “formal intuition” that Kant makes in an important note to B160 seems to put the matter beyond doubt: they are two different things. Here is the passage: Space, represented as object (as is really required in geometry), contains more than the mere form of intuition, namely the comprehension of the manifold given in accordance with the form of sensibility in an intuitive representation, so that the form of intuition merely gives the manifold, but the formal intuition gives unity of the representation. In the Aesthetic I ascribed this unity merely to sensibility, only in order to note that it precedes all concepts, though to be sure it presupposes a synthesis, which does not belong to the senses but through which all concepts of space and time first become possible. For since through it (as the understanding determines the sensibility) space or time are first given as intuitions, the unity of this a priori intuition belongs to space and time, and not to the concept of the understanding. (GW, 261, n.; B160–161, n.) The formal intuition of B160 corresponds to the pure intuition of A20/B34, the form of intuition of B160 to the form of appearance of A20/B34. In addition to clarifying the distinction, the B160 passage adds something and subtracts something from the earlier passage. It adds that the pure intuition of space is an artifact of activity by the mind, its’ “unity” derives from synthetic activity (though not from “the concept of the understanding”);9 it subtracts the impression that I  take the reference to “the concept” to be to the pure concepts of the understanding, the twelve concepts mentioned in the table of categories. However Kant also says, puzzlingly, that the understanding determines sensibility. This suggests that there is something in the understanding performing this role that is not one of the twelve categories. I argue in Ch. 7 that this something is the principle that all spatiotemporal objects are in topologically connected space, a unity treated in the Aesthetic as not part of the intellectual conditions needed for us to think coherently about a world; but in §26 of the B edition, it is absorbed into those conditions. For an alternative reading that still seeks to preserve the idea that the formal unity of space is somehow preconceptual, see Longuenesse (1998, 214–227, esp. 222–223). 9

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this unity is given or that it is identical with the form of intuition. If we take this recantation and find places in the Aesthetic to which to apply it, one candidate would be sentences (3)–(5). Kant would now be distinguishing between pure intuition and the form of intuition. Nevertheless, the language of sentences (1)– (5) continues to suggest that Kant somehow treats the form of intuition as itself a pure intuition, and these sentences reappear unchanged in the B edition. I propose to begin to account for this suggestion by arguing that there are two kinds of pure representations of space in Kant, one that is a representation of a single local space containing the appearances that empirical intuitions represent in a given perceptual act, the other that is a representation of global space, the single space in which all local spaces are topologically connected. Though conceptually still distinct from the form of intuitions of locally perceived objects, the pure intuition of local space is now identified by Kant with that form—that is, with the form of the sensations of those objects (the latter is still understood on the Container View). However, the pure intuition of global space is not identified with this container; indeed, it is not an intuition as Kant has defined it at A19/B3310 at all11 but is, rather, a rule requiring that intuitions of local spaces be connected into topologically unified wholes. A local space in this sense is not described or identified in the Critique of Pure Reason (CPR), but it does appear in two passages from section 26 of The Critique of Judgment (CJ, 107; Ak 5, 251). Our estimation of the magnitude of the basic measure must consist merely in our being able to take it in [fassen] directly in one intuition and use it, by means of the imagination, for exhibiting numerical concepts . . . (Critique of Judgment: Plu., 107; Ak 5, 251) This mathematical estimation of magnitude serves and satisfies the understanding equally well, whether the imagination selects as the unity a magnitude that we can take in at a glance, such as a foot or a rod, or whether it selects a German mile, or even an earth diameter, which the imagination can apprehend but cannot comprehend in one intuition (by a comprehensio aesthetica, though it can comprehend it in a

“In whatever way and through whatever means a cognition may relate to objects, that through which it relates immediately to them, and at which all thought as a means is directed as an end, is intuition.” 11 In a note to the Antinomies Kant refers to “space” as a “formal intuition” but denies that it is “a real object that can be outwardly intuited.” Rather, it is “nothing other than the mere possibility of external appearances, insofar as they either exist in themselves or can be further added to given appearances” (GW, 471–473; A429/B457). This “mere possibility” is a rule-governed possibility due to the rule of topological connectedness. 10



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numerical concept by a comprehensio logica). (Critique of Judgment: Plu., 110–111; Ak 5, 254) Local spaces are here characterized as having a special kind of unity Kant calls comprehensio aesthetica, in contrast to comprehensio logica, the kind of unity involved in the unified intuitions of CPR, section 15, and following in the B edition Deduction (GW, 246ff; B130ff.)—or so I  argue below.12 Local space thus understood is a pure object presented to us by the pure intuition of local space rather than the pure formal intuition of space (a representation of pure global space). Both entities are spaces, the latter constructed, the former given. However, I am arguing that it is only the pure intuition of a local space that is somehow said to be also the form of the sensations of the objects perceived in that local space. There is an analogy to these three elements of Kant’s theory of pure intuition in the elements that make up a system of ordinary geographical maps.13 Maps are systems of symbols, which symbols derive some of their spatial-structural characteristics from the structure of the surface on which they are drawn. This structure is, thus, an a priori form of representations in the sense of the Container View: it is a spatial structure whose geometrical and topological properties are imparted to the things in the structure, and in this case, the things in the structure are symbols that stand for, thus represent, objects on the ground. But the structure itself also projects some of its general spatial characteristics onto the region of space it maps, a local region, regardless of specific topographical features. For example, the distance between two city symbols on the map will typically be proportional to the distance between the designated places in the local region mapped. In this respect the surface is itself a representation of local spaces outside the map. So we here have an intuitively accessible example of a form of representations that is also a representation in its own right.14 Notice also that when we are creating a system of local maps, there is a presupposition that every local map we draw conforms to the rule requiring that it (or rather the See Ch. 3, §3. Richards claimed that Kant’s theory of space derived from his interest in geography. (Richards 1974, 1–16). I am indebted to G. J. Mattey for this reference made in a commentary to Vinci, “A Kantian Theory of Representation,” presented at the Central Division Meetings of the American Philosophical Association, Cincinnati, 1988 (see Mattey 1988, Vinci 1988). The psychologists O’Keefe and Nadel have argued that there are spatial maplike representations in the brain (O’Keefe 1978). Although they do not apply this idea to Kant, Patricia Kitcher does (Kitcher 1987, 245–247). She considers the role that maplike representations, in the technical sense given to this notion in O’Keefe and Nadel, might play in Kant’s theory of perception. My account considers the role of such representations, in their ordinary geographical sense, in Kant’s theory of intuitional representation in general. 14 In Ch. 3, when we come to discuss Kant’s theory of intuitional representation in detail, I develop more fully the theory of map representation that I am drawing on here. 12 13

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spaces it represents) be topologically connected with every other local map that we draw, wherever and whenever we do so. This presupposition amounts to our belief in a global space, but for Kant at least, our commitment to the latter corresponds to the “intuition” that is not (really) an intuition—that is, corresponds only to a rule for connecting intuitions of local spaces that Kant calls a “formal intuition” in the note at B160. I introduce this analogy partly to help clarify and, to some extent, justify Kant’s paradoxical idea that a form of representations can also be a representation in its own right but also partly because I draw upon this same analogy to elucidate Kant’s general theory of representation. That this analogy does double duty in explaining these areas of Kant’s philosophy is some evidence that Kant himself may have had this analogy in mind when he developed them. But this is to get ahead of our story. For now, I want to refocus attention on the notion of a form of appearances that is introduced by Kant in sentence (1)  at the beginning of the Aesthetic (at GW, 155–156; A20/B34), where it is understood as a form of sensations. Setting aside what specific reading we might give that notion— for example, the Container View—I want now to consider what arguments might have impelled Kant to think that a form in general had to be postulated to explain the possibility of the ordering of sensations in the first place. Even some generally sympathetic interpreters throw up their hands at this task, finding or supplying arguments that even they find suspect. Let us look at a couple of examples taken from books written at the opposite ends of the twentieth century: Smith’s Commentary (1923) and Falkenstein’s Kant’s Intuitionism (1995). According to Smith, in the first of the numbered Expositions, we are . . . confronted by a[n]‌ . . . extremely paradoxical view, which may well seem too naïve to be accepted by the modern reader, but which we seem forced to accept, none the less, to regard as the view actually presented in the text before us. Kant here asserts, in the most explicit manner, that the mind, in order to construe sensations in spatial terms, must already be in possession of a representation of space, and that it is in light of this representation that it apprehends sensations. The conscious representation of space precedes in time external experience.15 Smith attributes the following argument to Kant for the position that is consequent to this in the second of the numbered Expositions: “we cannot in

15

Smith 1962, 102.



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imagination intuit it [space] as absent, the only explanation for which is that there is this special consciousness of pure space that is part of the representational capabilities available to cognition a priori.” Smith denies the premise:  “With the elimination of all sensible content space itself ceases to be a possible image.”16 One of the difficulties with this objection is that Smith is not factoring into his reading of these expositions the corrective note to B160:  there are two things to be distinguished, space as the form of intuition and space as the formal intuition. The latter is the pure representation of space. Nor is he recognizing the distinction between the pure intuition of local space and the pure intuition of global space that I  have introduced above. We may assume that Smith’s “representation of space” corresponds in our terminology to the pure intuition of local spaces, and it would not be unfair to say that Kant does identify this with an “image of space” that somehow remains after we scrub out the sensations. I myself find this possibility quite plausible, though Smith appears to regard it as self-evidently preposterous “to the modern reader.” But the main difficulty is that, even if there were a successful objection to the necessity of a pure representation of local spaces, it would not automatically carry over to an objection to Kant’s doctrine that the representations themselves (understood as sensations) need a form and that that form “is space,” since representations (including pure representations) and the form of representations are conceptually distinct elements of Kant’s theory. Now let’s consider the more recent objection to the need for Kantian forms of intuitions—forms understood as things whose origin (within the mind) is different from that of sensations (outside the mind)—from Falkenstein. The objection arises from the “localization problem” for the objects of empirical intuitions: Why should I represent one collection of matters as square, another as triangular; one as oval, another as round? 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 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 another— no answer, that is, if he takes form and matter to originate from distinct sources.17

16 17

Ibid., 104–105. Falkenstein 1995, 85.

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Falkenstein’s own view is that sensations are matters that are given in experience in spatial form (form as “orders of intuited matters”); there are not two ontologically or temporally distinct elements that are somehow combined into an appearance.18 Falkenstein thus rejects the Container View. Indeed, Falkenstein finds a passage at A429n/B457n where Kant himself seems to do the same:19 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. According to Falkenstein, Kant maintains this doctrine not because of some immediate introspective apprehension that this is how the material of visual consciousness is arrayed20 but because Kant thought that positing sensations as being received with an inherent spatial ordering is required to explain where we get our concept of space from. It may well be the case that space is only ever given to us along with the matter of appearance in an empirical intuition. 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?21 In answering this question, Falkenstein attributes to Kant the view 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.”22 (The “matters themselves” are the qualitative aspects of

18

Yet Falkenstein also says this: that the subject’s “constitution” determines certain structural features of the order of intuition—those that 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 within these structures. (Ibid., 295–296)

This position is very close to the one I advocate and seems to warrant the appellation “a priori container.” 19 Ibid., 295–296. 20 Ibid., 185. 21 Ibid., 173. 22 Ibid., 174.



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sensation separated from the spatial or temporal form these matters may take on. Sensationism is the general theoretical position that our spatial concepts are somehow derived from these qualitative matters. It is against a reading in which Kant himself is supposed to be a sensationist, which Falkenstein attributes to George,23 that Falkenstein is here arguing.) Falkenstein thinks that Kant makes this case, to the limited extent to which he actually formulates an argument, in the First Metaphysical Exposition. I agree with Falkenstein that Kant countenances an “array” (Falkenstein’s term for Mannigfaltige,24 usually translated as “manifold”) of sensory data that is ordered as data for the mind’s use in constructing its representations of the objective spatial world and that there is a sense of “form of intuitions” that just is this order of intuited matter. I also agree that the spatial structure of this array is needed to solve (what corresponds in Kant to) the localization problem for empirical intuitions. I  also agree that Kant does not need to account for our sense experience of the spatial order in which we encounter particular empirical objects by postulating a preexisting spatialized container (in my sense) for the data. However, I disagree with his contention that Kant thought that an appeal to an ordered array of empirically given sensations could serve as the ground for our understanding of the concept of space itself—especially the concept of three-dimensional space, which makes an objective world possible. I am about to claim that this is one place where an appeal to the form of intuition as an a priori container in my sense is indispensable. If explaining the order in which we experience empirical objects were the only ground which Kant had for the Container View account, then there would be no necessity to assign it to Kant, but I do not accept the antecedent: there are, in addition to the need to provide a ground for the concept of three-dimensional space, at least two additional grounds for the Container View. These together are the three purposes for the Container View mentioned in Section 1, repeated here: 1. Our ability to have a concept of three-dimensional space requires a three-dimensional spatial container in which the imagination can construct three-dimensional objects. 2. Our ability to represent a world of objects in space requires that there be representations arrayed in a container having intrinsic spatial structure. 3. The a priori synthetic nature of geometry requires the form of intuition to be a spatialized container.

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George 1981. Falkenstein 1995, 102.

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3.  Summaries of the Three Grounds for the Container View (1) The first ground for taking the form of intuition as a container rests on the assumption that our ability to think about a three-dimensional spatial world requires that we have the concept of a three-dimensional spatial world. As I  have argued elsewhere,25 showing how we might arrive at such a concept proved elusive to radical empiricists like Berkeley and Hume, using the meager resources they were willing to allow the mind to employ. I think that Kant saw this, added the premise that we do have such a concept, and then derived the inevitable conclusion that the mind must have additional resources available to it. Since he rejects the possibility that there are innate concepts,26 he had to find another mechanism by which the concept of three-dimensional space could be derived. This other mechanism had to be consistent with his general theory of concepts as rules—procedures for putting things together (synthesis) in certain unifying ways (GW, 210; A77/B103–A77/B104). What he found to fit the bill was the ability to construct three lines each perpendicular to the other: “we cannot represent the three dimensions of space at all without placing three lines perpendicular to each other” (GW, 258; B154). Finally, Kant saw, as his empiricist predecessors did not, that the mind could not do this unless there was a three-dimensional spatial container antecedently available to the mind in which to perform this construction.27 This, recall, is

Vinci, (2006). See the Entdeckung (Ak 8, 221–222; quoted in Falkenstein 1995, 79). 27 Patricia Kitcher has also argued (Kitcher 1987) that Kant introduced his account of space as the form of intuition to account for the origin of our idea of three-dimensional space. However, on her account, the form of intuition is a “process-form,” a set of rules and procedures that the mind uses in constructing a representation of three-dimensional objects based on the two-dimensional sensory data on the retina (215). See also Kitcher, Kant’s Transcendental Psychology (1990), for a book-length development of this idea. This is Falkenstein’s “forms as mechanism” interpretation, and she attributes it to Kant for three main reasons. The first is that she finds the forms-asmechanisms view in the Inaugural Dissertation and asserts that the same view is to be found in CPR (216–217). The second is a historical/theoretical reason. She notes that it was accepted by Berkeley in the New Theory of Vision that “distance could not be registered in the visual system because the sense data on the visual sense organ (the eye) is two-dimensional” or “true visual images are flat.” She maintains that Kant knew this and accepted it, and also was in a position to discount Berkeley’s claim that distance was immediately detected by touch (223–226). Therefore the representation of three-dimensional objects had to come from something other than the data of sense. Kant’s choice was in the doctrine of a priori forms of intuition, understood as rules for the construction of three-dimensional representations from two-dimensional objects. Third, she offers an interpretation of the First of the Metaphysical Expositions (A23/B38) that supports her reading: 25 26



A P r ior i For m vs. P ure R ep re s e ntati on

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how Kant describes the form of sensibility: “its form must all lie ready for it in the mind.” I am arguing that Kant’s best case for this is not that localizing the objects of sensible intuition requires that the mind include among its resources an a priori container for sensations but that our ability to have the concept of three-dimensional space requires it. (2) The second ground is the most fundamental in Kant’s overall transcendental philosophy, though it relies in part on the first ground; indeed this argument is the transcendental philosophy in its most central form—an argument uncovering the basic presuppositions of our ability to think about a world we inhabit. Here Kant’s argument is relatively simple to state: our ability to do so presupposes an ability to represent an objective world of things distinct from each other and from ourselves; our ability to do the latter presupposes that we represent a world of spatiotemporal objects; and the latter presupposes that spatiotemporality be already present in the form of the representations themselves. (We see in Chapter 2 that this latter doctrine is the foundation of the special, idealist character of Kant’s metaphysics.) This amounts to a claim that there must be more than a mathematical isomorphism between what represents and what is represented; there must be a commonality of structure:  spatial objects must be immediately represented by things that are themselves spatial entities. These “things” are Kantian intuitions, and Kant’s doctrine that the form of intuitions is space and time provides the necessary conditions for representation to occur in We can acquire the concept of space from outer experience only if our outer senses can register three-dimensional spatial properties like distance, size and shape. However, as we have seen, everyone acknowledges that three dimensional spatial properties are not registered by vision [or by touch] . . . So, the perceptual representation of spatial features like distance, size and shape must have some source other than the senses. (231; my interpolation) In response to this reading may I say that I do not find in the text of Exposition 1 an argument that starts with two-dimensional sensory stimulation of the retina and ends with the construction of three-dimensional space by means of an inferential process Kant calls the form of intuition. As indicated in my discussion, above, where Kant specifically addresses the question how we get our concept of three dimensional space (GW, 258; B154), it is based on our ability to set three lines together in perpendicular alignment. I take the ground of this possibility itself to rest on the form of intuition, understood in the container sense. However, in the First Metaphysical Exposition I argue that Kant’s primary concern is to explain our ability to refer sensations to objects outside our subjective faculty (see point (2), in the body of this chapter and in Ch. 3)  and to give the beginnings of a general argument why our “concept” of spaces is not a concept (see point (3), here and in Ch. 2, §3), an argument, incidentally, that would apply to two-dimensional spaces as much as to three-dimensional space. The distinction between these two is simply not a part of Kant’s concerns here or elsewhere in the Aesthetic. Finally, I note that Kant takes our perception of space to be “immediate” rather than “inferred” (see the Refutation of Idealism, n. 1: GW, 327; B276) I take the space that Kant is talking about there to be the space of ordinary physical objects; that is, three-dimensional space.

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the first place. This form must contribute its own general structural characteristics to the symbols that occur within it; it is thus an a priori form in the sense of the Container View. It is important to see that this doctrine of the requirements for representing external objects is not the same as the doctrine that our ability to have spatially ordered sensations or sensorily perceive external objects requires that there be an antecedent form for sensations, since we can represent things that we are not sensing. Thus I can represent the moon to myself and make judgments about it even while I am not seeing it; that is, not having sensations of it. Kant explicitly allows for a distinction between sensation and intuition—the former is a “modification” of a subject, the latter “is immediately related to the object and is singular” (GW, 398–399; A320 /B367–377), so I do not take the form of intuition and the form of sensibility to be simply one and the same thing in Kant.28 They both are spatiotemporal forms, but arguing for this in each case requires a separate argument and a separate account of form. This I make in the next chapter. (3) The third ground for taking the form of space to be a container derives from Kant’s doctrine of mathematical method. Following Philip Kitcher,29 I take Kant to maintain that geometry is a theory of the properties of space. In determining the truth of geometrical propositions Kant uses a version of inference to the best explanation from data about figures that we construct spontaneously in space. The best explanation is that there is a structure in which these figures are constructed and that this structure is an a priori Euclidean form in the sense of the Container View. This doctrine of method then provides a premise in Kant’s explanation for the synthetic a priori character of geometrical knowledge. This latter explanation forms part of the Transcendental Exposition of the Concept of Space in CPR and part I of the Prolegomena. This is an important result for the later parts of the argument in this book concerning the Transcendental Deduction of the Categories since, following Ameriks,30 I maintain that the structure of this argument serves as an analogy for the argument of the Transcendental Deduction of the Categories. I develop this reading of Kant’s doctrine of mathematical method in Chapter 4.

28 29 30

Falkenstein disputes this distinction (see Falkenstein 1995, 81–82, 106ff.). Kitcher 1975. Ameriks 1978.

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The Metaphysical Expositions and Transcendental Idealism I

1. Introduction In the previous chapter I  drew a distinction between the form of intuitions, not itself a representation of an object, and a pure intuition, something that is a representation of an object. I submit that one of the reasons for the notorious difficulty in discerning the structure of Kant’s arguments in the Aesthetic for Transcendental Idealism, the main conclusion of the Metaphysical Expositions, which in turn is the main series of arguments in the Aesthetic, is that Kant anchors some lines of argument for that doctrine in his account of the form of intuitions, others in his account of pure intuitions, without clearly disentangling them. The heart of the interpretive problem is showing the connection between Kant’s claim that space is an a priori form of intuitions and his claim that space is nothing more than a structure within the resources of our minds— Transcendental Idealism. I will be assuming a standard, ontological reading of this doctrine, so the problem is to show what connection Kant took there to be between forms of intuitions and the mind dependence of the objects of intuitions. Since there is an ambiguity in Kant’s writing between the pure form of intuitions and pure intuitions in their own right, we will need to be careful to specify which kind are in question in which of Kant’s arguments. In Chapter 1 I began by giving an account of the form of intuition. The form of intuition is a structure in which objects can be received or constructed and is a priori in two senses: (1) it induces structural properties (form) in the objects that come within it; and (2) it is a pure structure, not consisting of or dependent on matter. Suppose for the moment that we focus on the role of this structure as one in which we can draw images of objects. Although I did not comment on this at the time, it is evident that nothing necessitates, or even much suggests, 23

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that the structure in question be a subjective structure. Why could not the structure be objective, an “absolute being” in Kant’s own words from a 1768 article,1 something like Newtonian absolute space? (The structure-inducing feature might have to be added into the Newtonian account, but that would not in itself bring space “indoors”). Among recent commentators, Warren and Allais have had different answers to this question.2 Both have a somewhat different account than mine of the sense in which a priori intuitions are a priori, but both take the inference from Kant’s doctrine of a priori intuitions to his doctrine of Transcendental Idealism to be a nontrivial inference requiring support from substantive additional premises that Kant does not make clear (or clear enough). Warren argues that these additional premises are available in the texts of the geometry arguments of the third of the numbered Metaphysical Expositions in A, the Transcendental Exposition in B or in part I of the Prolegomena. In favor of this reading we can note that Kant’s “Conclusions from the above concepts” follows immediately on the heels of the Transcendental Exposition (B41– 42) and the first of these conclusions is that “space represents no property of things in themselves.” Warren is right about this, as I argue in Section 3. Allais, of course, is aware of the texts in which the geometrical arguments are made but maintains that their structure is sufficiently unclear at a crucial point where Kant is giving the connection between the aprioricity of intuitions and the idealist conclusion that we cannot tell whether Kant takes the texts in which the argument from geometry is given (Metaphysical Exposition 3 in the A edition, the Transcendental Exposition in the B edition, and part I of the Prolegomena) to contain all the premises needed for the proof. Her position is that Kant in fact does not consider the various geometrical arguments to be self-contained and that he imports into the geometrical argument a crucial premise from elsewhere. I argue at some length in Section 3 that Allais is wrong about this. In the next section I lay out the basic, positive accounts of Kant’s purposes and arguments in the Metaphysical Expositions due to Allison, Warren, and Allais. Both Warren and Allais relate their own accounts to Allison’s—Warren’s is broadly critical, Allais’s is broadly supportive—so I begin with Allison, focusing on his account of what makes the a priori intuition of space and time a priori for Kant.3

“Concerning the Ultimate Ground of the Differentiations of Directions in Space”; full publication data are in the References section. 2 Allais 2010; Warren 1998. 3 Allison 1983, 80–90 (unaltered in 2004 ed.). 1



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2.  Three Accounts of the Metaphysical Expositions By means of outer sense (a property of our mind) we represent to ourselves objects as outside us, and all as in space. (A22/B35)

So begins the first paragraph of the first section of the Transcendental Aesthetic. This paragraph precedes the five numbered paragraphs in the A  edition Metaphysical Exposition (four in B) as a kind of preamble. The sentence quoted above is an important basis for interpreting Kant’s intentions in the Aesthetic, including the Metaphysical Exposition proper, but it presents interpreters with a problem: it is seems to be tautological, saying that, in virtue of outer sense, we are able to represent objects that are outside of us (in space) as being, all (outside of us), in space. Now, Allison notes a tautological rendering of the sense of this sentence is not only undesirable as a reading of Kant’s meaning, it is unnecessary. If what is outside of us means simply “distinct from ourselves,” with ourselves understood as the “I” of “I think”4 and where the latter is understood in a quasi-Cartesian way,5 then saying that objects distinct from ourselves are all in space is anything but a tautology. It lays down a condition on what kinds of representations constitute representations of an objective order, things that in turn make experience possible in Kant’s sense.6 In virtue of this, Allison calls space “an epistemic condition”: The argument shows, however, that this ability presupposes (although not logically) the representation of space. Consequently, Kant’s argument can be said to show that the representation of space is a priori by showing that it functions as an epistemic condition. (Allison 1983, 86) [The argument in question is the one attributed to Dryer.] I am in broad agreement with Allison’s reading of the key sentence from the preamble, though with an important caveat. Allison says that our ability to distinguish self from other presupposes “the representation of space.” Now, in light of the distinction between the form of intuition, which is not a representation as such, and the pure intuition of space, which is, it is clear that Allison is attributing to Kant the idea that intuition as representation rather than intuition as form is what lies at the basis of this ability. But I think a closer look at the texts shows that it is actually intuition as the form of sensibility rather than intuition This term is used in §16 of the B edition Deduction (GW, 247; B131–132). I say “quasi-Cartesian” because Kant’s account of the first-person self in both editions of the Paralogisms (GW, 411–425, A342–567; GW, 445–453, B406–423) makes for a self that has some but not all of the characteristics Descartes ascribes to the self in his cogito arguments. 6 Allison (1983, 86) cites Dryer as the source of this idea (Dryer 1966, 174). 4 5

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as singular representation that Kant puts forward as the ground of this ability here, for “outer sense” is said to be the means by which we distinguish self from others, and outer sense per se is a form of sensibility, not a representation. However, it is intuition as pure representation rather than form that figures in the Exposition proper, especially Expositions 1, 2, and 4. Moreover, Allison is not very careful about distinguishing those texts he cites from the preamble versus those he cites from the Exposition proper. Warren’s main criticism of Allison is that if we stick just to the numbered paragraphs of the Exposition proper, we find no evidence that Kant is concerned with explaining the difference between self or other, little evidence that he is mainly concerned with distinguishing one object from another, and overwhelming evidence that he is concerned to give an account of how we are able to represent spatial (and in the other Exposition, temporal) relations among objects. Warren makes a good case for this, which I in the main accept. He goes on to say7 that part of Kant’s explanation of the nature of relations between physical objects is given in geometry, and Kant’s account of geometry—in particular, his account of the a priori synthetic character of the propositions of geometry—is given in arguments in Exposition 3 in the A edition and in the Transcendental Exposition paragraph in the B edition. It is from these geometrical arguments that Kant moves to his idealist conclusions about space (and time). Allais is critical of Warren’s account for finding the nerve of Kant’s argument for Transcendental Idealism in the geometrical arguments of the numbered Expositions proper, arguing for a different structure for Kant’s argument. Here is what she says: On my reading, before he gets to the Metaphysical Exposition, Kant takes himself to have established the following points: (1) Cognition or knowledge of an objective world requires both intuitions and concepts. (2) Intuitions are representations which essentially involve the presence to consciousness of the objects they present. (3) Empirical (sensible) intuition requires a priori intuition, which gives it its order or form. (4) A  priori intuition does not represent a mind-independent feature of reality (from 2). If we take these claims as established and then argue (as Kant does in the Metaphysical Exposition) that our intuition of space is an a priori

7

Warren 1998, 207–208.



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intuition, it will follow that our representation of space does not present us with a mind-independent feature of reality, so that the space that we represent is merely the a priori form of our intuition.8 Allais’s analysis is insightful, drawing explicitly on the distinction between premises asserted in the arguments of the Exposition proper and premises imported from earlier material in the Aesthetic. Her central thesis is that the mind dependence of the objects of pure intuitions (pure vs. empirical intuitions) as representations in their own right is something that Kant affirms for reasons arising from his general theory of representation, not from anything specific to the geometrical arguments.9 She argues for her thesis partly on the grounds that the geometrical argument allegedly to be found in Exposition 3 in the A edition and in the Transcendental Exposition in the B edition (not exactly the same geometrical argument, she maintains) is so obscure that it “leaves us still asking how we get from the claim that our representation of space is an a priori intuition to the claim that space is merely an a priori form of intuition.”10 In this sentence Allais indicates that she sees part of the strength of her own interpretation deriving from the weakness of the geometrical argument as she thinks it goes for Kant. But here I think the weakness lies not with Kant’s inference but with Allais’s understanding of it, as I now propose to show.

3.  Kant’s Arguments from Geometry in the Prolegomena Kant’s most developed account of his philosophy of geometry and of the argument from geometry to Transcendental Idealism occurs in part I  of the Prolegomena. Most of my discussion of Kant’s philosophy of geometry occurs in Chapter 4, but some preliminary considerations are appropriate here, chief among which is noting a distinction implicit in Kant’s texts between two topics for the argument from geometry: pure geometry (i.e., the geometry of pure spatial objects) and applied geometry (i.e., the geometry of empirical objects). The main title of the whole section (“Part I”) is: “How is pure mathematics possible?” The term “pure mathematics” occurs prominently in sections 6, 7, 10, and 11, and in note 1 after the numbered sections. This term does not occur in sections 8 and 9, which concern the sense in which it is possible to intuit something a priori. The titular question is answered in section 7 with Kant’s invocation of Allais 2010, 57–58. Ibid., 62–66. 10 Ibid., 56. 8 9

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an a priori intuition, which is explained in section 8 as an intuition that can “precede the object itself,” which possibility is explained, in turn, in section 9: “There is therefore only one way possible for my intuition to precede the actuality of the object and occur as an a priori cognition, namely, it contains nothing else except the form of sensibility, which in me as subject precedes all actual impressions through which I am affected by objects” (Prolegomena: Ak 4, 281–283; Hat., 32–34). Notice that Kant has in section 9 shifted the topic away from pure geometry, which is the topic of the prior sections and apparently of the whole of part I, to the geometry of empirical objects. Why has he done this? Is it perhaps that Kant is confused about his own argument? I suggest not. What this shift of topic indicates is that Kant has two arguments for Transcendental Idealism from geometry in part I, which he is intermingling section by section in part I but not confusing. The arguments are quite different from one another: it is a case of feeling different parts not of the same elephant but of two different elephants. The arguments in question achieve the same purpose—showing that the objects of both kinds of geometry are mind-dependent entities—but they accomplish this purpose in quite different ways. One of these arguments, which I take to be Kant’s primary and best argument, relies on his accounts of pure and applied geometry taken together and is centered on note 1, a text that occurs after the numbered sections in part I of the Prolegomena. This argument I consider in detail only later, when I present a comprehensive discussion of Kant’s philosophy of geometry.11 The second of these arguments, which I take to be the weaker of the two, relies only on applied geometry and occurs mainly in section 9. It must be admitted that seeing two arguments for Transcendental Idealism in part I of the Prolegomena is not standard fare for interpretations of Kant’s argument for Transcendental Idealism, even for those that focus on the geometrical arguments, as Allais’s and Warren’s do. I believe that this is partly because these interpretations miss a key problem that arises for any attempt to find in this text an argument that takes us nontrivially from pure mathematics to the doctrine of Transcendental Idealism. The problem is raised implicitly by Kant himself in section 7 when he explains that the “first and highest condition” of the possibility of mathematics is that “it must be grounded in some pure intuition or other, in which it can present, or, as one calls it, construct all of its concepts in concreto yet a priori*.” (Ak 4, 281; Hat., 33) The asterisks directs us to a note (Kant’s note) which in turn directs our attention to a page in (the A edition) CPR, 713. If we turn to that page we find in a general discussion of mathematical construction the following sentence: “Thus I construct a triangle by exhibiting an object corresponding to this concept, either through mere imagination, in pure intuition, or on paper, in 11

The argument itself is given in Ch. 4, §5.



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empirical intuition, but in both cases completely a priori, without having had to borrow the pattern from any experience.” (GW, 630; A713/B741) This sentence implies a major problem for the standard reading of the argument in part I of the Prolegomena. The problem is that Kant identifies in this text the domain of objects of pure intuition as the imagination; that is, as a domain of objects of thought. Of course objects in the domain of imagination are mind dependent:  the flying horse that I  sketch in my imagination is a thought object, an intentional object whose existence depends on being thought. (I am here distinguishing the imagistic representation of the horse I draw in imagination from the object of that representation, the horse itself. The latter is a thought object, dependent on mind for its existence.) So is the triangular figure that I construct in my imagination. There is also evidence from note I to part I of the Prolegomena that Kant is conceiving the objects of pure mathematics, those occurring in “the space of the geometer,” as thought objects in just this sense (Hat., 39; Ak 4, 2876). This account of pure mathematics in Kant poses a problem for interpreting Kant’s geometrical argument for Transcendental Idealism only if we think that that argument makes a direct connection from the presuppositions of pure geometry (and the necessity of its theorems) to the doctrine that all empirical objects are mind dependent. Obviously the argument from pure mathematics to Transcendental Idealism is more complex than that, bringing in considerations of applied geometry as well (see Chapter 4). We are still left with section 9 and its approach to the aprioricity of intuitions. Notice that here there is no mention of pure mathematics. Here the focus is all on applied mathematics, on the geometry of objects represented by empirical intuitions and their form, the form of sensibility. The form of sensibility is what “precedes the actuality of the object,” Kant says in this section. Now there are two options for understanding what the form of sensibility is a form of: Is it a form of the empirical representations themselves, perhaps the images we construct in empirical intuition, or the impressions that arrive from the senses? Or is it a form of the objects of those representations, the things in the world (as we think of them) that are presented to us by the representations? This is a notoriously difficult ambiguity to resolve in most of Kant’s writings on intuition, but here the form which Kant’s argument will take requires that we treat the form of sensibility not as a representation of pure space as object in its own right but as a form of subjective things, things occurring within our own minds. Kant will argue in section 9 that only if this is the case can the problem that he has set for himself at the outset (in section 6)—to explain how there can be a priori synthetic propositions of geometry—be solved. Centrally in focus in this problem is the source of the necessity of the geometrical propositions of applied geometry,

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considering that it does not come from analyticity. How might an account of the form of empirical representations provide a solution to this problem? Suppose that, for Kant, the way we determine what properties an empirical object has is by constructing an image of it in a structure that has the power to induce structure in the objects constructed therein. This would count as an a priori form of intuition in the sense adumbrated in the previous chapter. Let us say that the form of sensibility Kant is talking about in section 9 is an a priori form of intuition in this sense and that the form which it induces in the images constructed within it is Euclidean form. This would guarantee with apodictic certainty that the images are Euclidean, but what of the objects—appearances in Kant’s sense—which these images represent? Kant would need a principle connecting the form of the representations themselves (a subjective form) to the form of the objects represented (an objective form). I believe that Kant has such a principle and it is a principle of projection: just as the representations pick up their structural properties from the structure in which they are constructed (or received), so the objects of those representations pick up their structure from the structure of the things which represent them. But there is a prior question: Why should the a priori structure be a subjective structure? As noted in Chapter 1, there is no necessity in supposing that form-inducing structures must be subjective structures, no necessity for assuming that pure form-inducing structures must be pure subjective structures. A realist version of absolute space, for example, would seem to fit the bill admirably. What, then, is Kant’s argument against this possibility? We seem to be back where we started. Allais has a reading of Kant that provides a nice answer to this question. Assuming that a priori forms of intuition are pure intuitions, she says that she is “attributing to Kant the thought that the only way a mind-independent object could be directly present to us would involve its affecting us, so something which is present to us independently of anything affecting us is not a mind-independent object.”12 Reformulated to make its logical form clearer, this statement says that if something is an external-to-mind object and is present to us, then it affects us. This is a principle—call it statement (A)—of Kantian metaphysics that, Allais supposes, Kant brings with him to the argument of the Metaphysical Exposition. Of course anything that is a pure object, hypothetically even one outside of us, is free of material dependence, and if matter is the only thing that can affect our external senses, this adds up to an argument for the proposition that pure objects cannot affect us—call this statement (B). This is also an assumption imported into the geometrical argument from elsewhere. Allais also argues briefly here,

Allais 2010, 63. She credits Willaschek (Willaschek 1997) with providing the basic insight here (Allais 2009, 57). 12



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more extensively elsewhere,13 for another general metaphysical principle in Kant; namely, that all forms of intuition, including the pure intuition of space, present their objects to us—call this statement C. Finally, in statement D, Kant asserts that there are pure intuitions of space. This is the main result of Kant’s reasoning in the geometrical arguments of the Expositions and Prolegomena part I. Combining these four statements yields the final result: the objects of pure intuition cannot be mind independent. This is the argument from geometry to idealist metaphysics that Allais attributes to Kant in the Metaphysical Expositions of the Aesthetic and in part I of the Prolegomena. It can be granted that this is an argument for the conclusion that the object of pure intuition is mind dependent from premises that are Kantian and seem plausible, but I do not believe that it is Kant’s argument, at least not Kant’s argument in section 9 of part I of the Prolegomena, the text that forms the basis of Allais’s interpretation.14 There are four main reasons I offer for this, stemming from four difficulties with her account. First difficulty. When Allais comes to discuss the argument in section 9, she thinks that Kant does not tell us how the transition from a priori intuition to idealism occurs but we can explain this if we bring in the metaphysical principle which, she maintains, Kant has endorsed in material in the Aesthetic prior to the numbered paragraphs of the Metaphysical Exposition proper and prior to the argument of part I of the Prolegomena. This principle, which we have already considered above, is the “controversial claim (4); the idea here is that when you combine the idea of intuition, as I have explained it, with aprioricity, you get a representation which cannot present us with a mind-independent feature of reality.”15 When Allais says that Kant’s general account of intuition does not entail the mind dependence of space, this is because she is focusing on intuition as a representation whose object is space rather than intuition as a capacity for sensibility whose form is space.16 But it is the latter, not the former, that is the account of intuition at issue for Kant in section 9. Second difficulty. The conjunction of statement A  (“If something is an external-to-mind object and is present to us, then it affects us”) and statement B (“Pure objects cannot affect us”) is not something that Kant endorses. To make this case I begin by considering the first sentence of section 9: If our intuition had to be of the kind that represented things as they are in themselves, then absolutely no intuition a priori would take place, but Allais 2009. Her discussion is from 62–65. 15 Allais 2010, 62. 16 Allais is aware of the difference between intuition as form and intuition as representation. She discusses it in n. 16, 57. 13 14

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it would always be empirical. For I can only know what may be contained in the object in itself if the object is present and given to me. So far this is in accord with Allais’s reading. The passage continues: Of course, even then it is incomprehensible how the intuition of a thing that is present should allow me to cognize it in the way it is in itself, since its properties cannot migrate over into my power of representation; but even granting such a possibility, the intuition still would not take place a priori, i.e., before the object were presented to me, for without that no basis for the relation of my representation to the object can be conceived . . . (Ak 4, 282; Hat., 34) What is “incomprehensible” here is evidently some kind of ScholasticAristotelian theory of the influx of properties from external sources to the mind, something Kant rejects presumably for the usual reasons early modern philosophers from the time of Galileo have rejected it. But his point in the second quotation is made under the assumption that the incomprehensible is in fact the case, that properties of external objects can migrate to our minds, thus can be presented to us immediately in the way required for intuition. Now Kant does not say what kind of properties are supposed to be migrating in this assumption, but why could it not be pure properties? After all, if one accepts the Influx Theory, one is accepting a mystery (for mechanists) for the influx of all properties, even qualitative properties like color. Why would it exceed the permissible level of mystery to include pure properties in the domain of “influxed” items as well? My thought is that Kant does not think that it would. If so, then pure spatial properties could be directly present to us in intuition under the influx assumption, but even under this assumption Kant maintains that intuition is not taking place a priori. This only happens when the intuition is a form of our subjective capability to receive sensations rather than an intentional device for representing pure objects. This was the source of the previous difficulty for Allais’s reading. The present difficulty is that the conjunction of statements A and B is rejected by Kant. Completing the case for this hinges on what things are included among things that “affect us.” In particular, is the influx of properties from external sources included? If it is, then B is false: for pure properties, which can be present to us under the influx assumption but are free of material dependence, would affect us. If it is not, then A is false: something is an external object, is present to us, and yet is not affecting us. So Allais is wrong to attribute the conjunction of A and B to Kant.17 17 I should note that in making this complaint about Allais’s reading of Kant’s argument, I am not disputing that Kant holds to the conclusion of the argument: that the objects of the pure intuitions



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Third difficulty. When Allais says that Kant’s general account of intuition does not entail the mind dependence of space, she does so because she is understanding the a priori intuition of space as a representation of a pure object (space), in the domain of pure mathematics. But in CPR at A713/B742, Kant distinguishes between two approaches to geometry, one taking pure objects as its domain (pure mathematics), the other taking empirical objects (applied mathematics). Kant’s concern in section 9 is with the latter approach rather than the former.18 Fourth Difficulty. The passage in which Kant draws his idealist conclusion, part of which we have seen before, is the following: [1]‌There is therefore only one way possible for my intuition to precede the actuality of the object and occur as an a priori cognition, namely if it contains nothing else except the form of sensibility, which in me as subject precedes all the actual impressions through which I am affected by objects. [2] For I can know a priori that the objects of the senses can be intuited only in accordance with this form of sensibility. (Hat., 34; Ak 4, 282; my interpolations) In the phrase “the actuality of the object” it is not clear what object Kant is talking about: is it the object of an empirical intuition (a physical thing in the world that is outside us), or is it perhaps the empirical intuition itself? While it is natural to suppose that Kant means the former, I am going to suppose that he means the latter—that the object in question is an actual sense impression. (The term “sense impression” as I use it is a sensory image with spatial form, thus an object of geometry. Kant countenances such things, though not under that rubric. A sensation proper for Kant apparently does not have spatial form [GW, 290; A165/B208]) That is, after all, what he says in the last part of the sentence. If we take this interpretive gambit, however unnatural it may seem, then the meaning of the remainder of the argument is cast in quite a different light, one in which it is possible to discern an argument, indeed an interesting and not obviously fallacious of space (and of time) are thought objects. But this is not because Kant endorses the argument she reconstructs but because he conceives all objects of intuition to be thought objects on principles deriving from his general theory of representation. (Of course, the latter presupposes the falsity of the Influx Theory.) I make this case in Ch. 3. It may be that Allais misses the difference between the two approaches because she misses the distinction Kant draws between a priori constructions in pure intuition (imagination) and a priori constructions in empirical intuition that Kant makes at A713/B741. Recall that this is a text to which Kant himself directs his readers in section 7 of the Prolegomena. It is curious that Allais misses this distinction, since she herself quotes this very same passage. However, in giving the quote she omits the distinction and also omits the ellipses that would have alerted her readers to the existence of missing material in the sentence. This is how she presents the passage: “Kant says that ‘I construct a triangle by exhibiting in intuition an object corresponding to this concept’ (A713/B741)” (Allais 2010, 62). 18

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argument from these premises to Kant’s idealist conclusion in sentence [3]‌that does not rely on premises not in the text. The argument is this. First the conclusion: Kant’s ultimate goal is to show that the only way that the properties of the objects of empirical representations are necessarily correspondent with the properties of the empirical representations themselves is that the former depend ontologically on the latter. That is Transcendental Idealism. Getting there depends on a hypothesis that he does not argue for nor explicitly state in sentence [1]‌; namely, that the empirical intuitions (impressions received)—not the objects of empirical intuitions—necessarily have the actual properties of Euclidean geometry. Sentence [1] then explains that this could be so because there is a form that induces Euclidean properties in anything that comes to reside in it and all impressions we can experience reside in it. This form is, of course, the a priori “form of sensibility” he mentions in the sentence. This is what Allais does not see: that the a priori form of sensibility is not intended by Kant to be a form of empirical objects, putatively mind independent, in the first place: all along it has been the form of sensibility Kant has been relying on in the argument. Allais provides a good answer to a question Kant was never asking. Allais is right that Kant is not primarily interested in the geometry of impressions or images; indeed, this is just a step along the road to saying something about the geometry of objects of these intuitions, what he calls “the objects of the senses” in sentence [2]‌(here this phrase is to be interpreted in its natural sense), which in turn is a further step along the road to the ultimate conclusion. Here it is also not a question of showing that the objects of the senses have Euclidean structure necessarily—that is already assumed—but of showing how it is possible. With the corresponding claim for the empirical intuitions themselves, Kant employs the notion of the form of sensibility to show this, but for their objects he uses a different explanatory device. First he explains that if the objects of empirical intuitions necessarily have Euclidean properties (which they are assumed to have at the outset of the argument), they must be necessarily correspondent with the properties of the empirical representations themselves, since the latter also have Euclidean properties. I take this to be the (rather obscure) sense of sentence [2]. Now, Kant asks, for a final time, the key question: How is this possible? Kant’s answer is that, unless the objects of these representations somehow inevitably get their properties from the representations themselves, there will be no guaranteeing with apodictic certainty that the objects of those representations will conform to Euclidean geometry.19 19 We may reasonably ask if what gives the high grade of necessity to the geometry of sense impressions that Kant seeks for the geometry of empirical objects is the fact that sense impressions are in a mind-dependent Euclidean-inducing a priori form of sensibility, why could not the same high grade of necessity be afforded empirical objects that occur in a mind-independent Euclidean a priori external form? In case it could, then there would be no need to invoke a separate mechanism—the



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This still does not quite get us to Kant’s transcendental idealist conclusion, but with help from comments Kant makes in the B edition Preface (Bxvi–xviii; GW, 110–111), we can see how the final step goes: this getting of properties by objects of representation from the representations themselves in turn is possible only if these objects are dependent on us. And that is Transcendental Idealism. At last! So Kant’s argument in section 9 is precisely not that the objects of empirical intuition are mind dependent because the objects of pure intuitions are mind dependent and the former somehow depend on the latter, as Allais maintains; rather, it is that the objects of empirical intuition are mind dependent because we could not otherwise explain their necessary correspondence with the geometry of the empirical intuitions themselves.

getting of geometrical properties by empirical objects from the form of intuitions—to account for the (assumed) presence of this high grade of necessity in the geometry of empirical objects, and the argument would fail. It will not do, of course, to answer here that Kant thinks that empirical objects are dependent on forms of sensibility; that is supposed to be a conclusion of the present argument, not one of its premises. Since Kant does not consider this possibility in section 9, it may be that he just assumes that only mind-dependent forms could induce structure in the things that are in them. If so, that would allow Kant to avoid this serious objection. It may seem that Allais’s interpretation would provide just what is needed here: a proof that there cannot be an a priori form for mind-independent objects. But this is not quite what her interpretation says: it says that there cannot be a pure intuition of an external object (space) since the object would have to be present to us and could be so only if it affected us, which it can’t because it is free of matter—that is what makes it “pure.” But even if this argument is accepted, it does not show that there could not be an a priori form of external objects since a priori forms of things (in my sense) and pure representations of things can exist apart since they are conceptually distinct. Why shouldn’t there be an a priori form of empirical objects even if there is not a pure representation of the form of those objects? Indeed, this latter point is precisely Kant’s doctrine: Kant does not think that we can perceive a pure form by itself (a point he makes for time at GW 304, B233, and for space at GW 184, A41/B58) but that we infer its existence from the properties and behavior of the objects within it; but why should those objects not be mind-independent objects in a space which is a mind-independent a priori form? Kant certainly thought that they could be in 1768 when he wrote “Concerning the Ultimate Ground of the Differentiation of Directions in Space”—that was his own view then. I see no reason to think that Kant came to regard this position as incoherent by the time he wrote CPR. Kant does not discuss the question one way or the other in the preceding sections of Part I—but he does refer us to the passage at A713, where he seems to allow for two kinds of a priori construction, one for pure objects of the imagination, one for empirical objects. I take it from this that Kant did not see, prior to the conclusion of his argument for Transcendental Idealism, an in-principle objection to the possibility of an a priori Euclidean-inducing form for mind-independent objects. If we take the doctrine in the CPR, thus understood, to be the governing doctrine, we will look for another argument for Transcendental Idealism that allows for the possibility in principle that there is an a priori Euclidean form for empirical objects. In what I call “The Second Geometrical Argument for Transcendental Idealism” (Ch. 4, §5), I maintain that we find just such an argument.

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If we suppose that the argument as represented for section 9 of the Prolegomena is the one operating in Exposition 3 of the A edition and in the Transcendental Exposition in the B edition, then we now have an understanding of how Kant can assert his idealist conclusions. This is of course of much importance, dispelling a perplexity in Kant’s argument in the Aesthetic, but it does not really tell us much about what else is going on in the other four of the numbered paragraphs in the Metaphysical Exposition. It is to this task that I now turn.

4.  The Nongeometrical Expositions Now we return to the Aesthetic and the Nongeometrical Expositions. I  take there to be two main theses that the Metaphysical Exposition argues for in addition to the idealist conclusions he draws from the geometrical argument: Main Thesis 1:  A  denial that our representation of space is an empirical concept. Main Thesis 2: An affirmation that the representation of space is an a priori intuition. It may seem that we have already covered Kant’s argument for Thesis 2 in the preceding section, and since Thesis 1 follows from Thesis 2 by the very meaning of the terms “intuition” and “concept” for Kant, it may seem that our work is done. This is, of course, a very attractive prospect, as attractive as it is rare in Kantian exegesis. Unfortunately, it is a mirage that arises from the fact that Kant is working in this part of the Aesthetic with two different notions of a priori intuition, that of the a priori form of representations versus that of a pure representation of an object in its own right. In the preceding section we have been working with arguments that show that space is an a priori intuition only in the first sense, but in the Nongeometrical Expositions (1, 2, 4, 5 in the A edition; 1, 2, 3, 4 in the B edition), Kant is trying to show that space is an a priori intuition in the second sense. So our work on the Metaphysical Expositions is far from done: we need additional analyses to come to an understanding of Kant’s arguments for these two main theses. What of the second point: that Thesis 1 simply follows from Thesis 2? Could we not at least simplify our work by understanding Kant’s main burden to be the establishment of Thesis 2, allowing Thesis 1 to follow as a matter of course? What I call the First Reading of the Metaphysical Exposition assumes just such a strategy.



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4.1.  First Reading Thesis 2 has two components: that the representation of space is an intuition, and that it is also a priori. Let us focus on the first of these characteristics. Here, Kant needs to show that space is an object of some kind and that the representation we have of it has the immediacy needed for it to be an intuitional representation. In Exposition 1, Main Thesis 2 follows from another claim: “For in order for certain sensations to be related to something outside me (i.e., to something in another place in space from that in which I find myself), thus in order for me to represent them as outside one another, thus not merely as different but as in different places, the representation of space must already be their ground” (GW, 157; A23/B38). There is some difficulty with the reference to “them” since the German is sie, meaning either “it” (feminine singular) or “they” (plural in any gender), whose closest grammatical matching would be Empfindungen (fem. pl.), “sensations” in English. The sense of the passage would then be that the representation of space is the ground of the possibility of referring our sensations (empirical intuitions?) to external objects. Another possibility is that Kant intended to say what the standard translation renders; namely, a reading that would require the referent of “them” to be to “something” in the parenthetical phrase, rendered as etwas in the original (the whole phrase is: d.i. auf etwas in einem andern Orte des Raumes, als darin ich mich befinde). Unfortunately, this possibility is grammatically impossible, since etwas is a neuter-gendered, singular pronoun that does not match either of the two possible meanings of sie. In his discussion of Exposition 1, Allison prefers the first sense,20 but Warren prefers the second and (incorrectly it appears) attributes the second to Allison.21 Although relying on a grammatical impossibility, Warren’s reading seems to fit better with what Kant says elsewhere in the four numbered expositions, so we will go with that for now.22 This will be the third main thesis: Main Thesis 3: Our ability to represent objects in spatial relations with one another depends on our ability to represent space as such. Kant also has an interest in the parts of space in a later exposition (4) and in the relation between parts of space and space as a single whole, arguing that the former depends on the latter. We can connect these two themes if we suppose that our ability to represent things in spatial relations with one another Allison, 1983, 83. “(1a) The representation of space is presupposed by the representation of objects as outside of me or as outside one another.” This claim he attributes to Allison. Warren, 1998, 183. 22 However my own position will ultimately be that the first option for the referent of “sie” is not only better from a grammatical point of view but better reflects Kant’s meaning, something I defend in Ch. 3. 20 21

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depends on our ability to represent parts of space (Subthesis 1)  and that the latter depends on our ability to represent space as a single whole (Subthesis 2). Subthesis 1 and 2 give us Main Thesis 3. Main Thesis 3 entails the intuition part of Main Thesis 2. Since single-object-directed cognition (intuition) is opposed by Kant to common-characteristic cognition (concepts), Main Thesis 1 follows immediately from Main Thesis 2.  When we add to this an account of the aprioricity of the intuition of space, we have the a priori part of Main Thesis 2. This gives the structure of Kant’s reasoning in the nongeometrical arguments in the Metaphysical Exposition according to the First Reading.

4.2.  Second Reading The Second Reading differs from the first in that it finds in Kant’s text an independent argument for Main Thesis 1:  A  denial that our representation of space is an empirical concept, made by Kant in the first sentence of Exposition 1. “Space is not an empirical concept that has been drawn from outer experiences.” The Second Reading seeks to find a nontrivial argument for this claim among the nongeometrical expositions. One strategy for doing this seeks to establish Main Thesis 1 first, using it as a premise to argue for Main Thesis 2.23 In Exposition 4 Kant’s argument appears to employ just this strategy. In Exposition 4 Kant introduces the idea of “many spaces” in connection with his discussion of the dependence of parts of space on space as a single object. Later in this same paragraph he introduces the idea of “the general concept of spaces.” So Kant is concerned with two kinds of spatial representations: the intuition of space as a single thing and the concept of spaces. He says that the latter “rests merely on limitations” of the former. In the next section we take a more detailed look at what this might mean and what significance it has for the kind of concept that the general concept of spaces turns out to be. We shall see that it is not a concept in Kant’s ordinary sense. For now, however, the question is whether Kant has shown that there is indeed “an a priori intuition (which is not empirical) [that] grounds all concepts of them” (GW, 159; A25/B39). The reason that there might be a problem with this is that Kant’s argument has the form of an inference to the best explanation where the explanandum is our possession of the general concept of spaces and the explanans is an a priori intuition of a single all-encompassing space. With inferences of this kind the conclusion is given by the explanans only on the assumption that it is the 23

Warren’s account of the argument also finds this strategy in Kant. See Warren 1998, 206.



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only explanation possible (or at least the best one). This is a problem because it seems that it is not the only explanation possible. Why, for example, should the concept of spaces not simply be derived by abstraction in the same way as any other concept? We look at several spaces—this one, that one, the one over there—find what is common to them and abstract. What is left would be the common characteristic, “a space,” and that is a concept. Kant does not explicitly deny that the concept of spaces can be arrived at by abstraction, so perhaps he accepts that they are arrived at by abstraction. But if they can be arrived at by abstraction, why not by empirical abstraction? There is this empirical object here and that empirical object there, and we simply take away (abstract from) what is different between them, the matter in this case, and are left with the common element: the general concept of spaces. If this indeed were to be how Kant thought we arrive at the general concept of spaces, then that would deal a fatal blow to his argument in Exposition 4 that the representation of space is an a priori intuition, for it is no longer the case that the latter is the only explanation, indeed even the best explanation, for our possession of the general concept of spaces. If, however, Kant had an independent argument against the possibility that our general concept of spaces is arrived at by empirical abstraction, then he could argue for the thesis that we have a nonempirically-arrived-at cognition of an all-encompassing space as follows: 1. Our general concept of spaces can be arrived at in one of two ways:  by abstraction from experience or by limitations in an all-encompassing space represented by an a priori intuition. 2. It cannot be arrived at by abstraction from experience. Therefore 3. It must be arrived at by limitations introduced in an all-encompassing space represented by an a priori intuition. Therefore 4. There is an a priori intuition of a single, all encompassing space. A reading of the nongeometrical numbered Metaphysical Expositions that conforms with this structure constitutes what I am calling the Second Reading of these expositions. It is such a reading that I defend in the next section. My defense takes the form of finding indications in Kantian texts that he asserts the second premise of this argument and then elaborating those indications into an interpretation of Kant’s account of the general “concept” of spaces and the relation of this to the unity of space.

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5.  Why the “General Concept of Spaces in General” Is Not a Concept for Kant In the preceding section I propose a reading (the Second Reading) of the argument structure of the Nongeometrical Expositions according to which Kant argues by disjunctive syllogism for the claim that the general concept of spaces in general is derived by limitations introduced in a singular comprehensive space. The “minor” premise of the syllogism rules out the alternative possibility: that our general concept of spaces in general is derived from experience. I  now want to make this picture more precise by making the notion of concept derivation more precise: for Kant concept derivation is achieved by a process he calls abstrahieren, the theory of which is developed most thoroughly in Kant’s Logic.24 One of the ingredients of this theory is the concept of a mark (Merkmal). A mark is something which is “common to many things,” also characterized as “that in a thing which constitutes a part of the cognition . . . insofar as it is considered the cognition of the whole representation” (Young, 564; Ak 9, 564). Kant develops a fairly extensive account of marks in section VIII of the Introduction to the Logic, which account need not detain us. The main point is that marks are representations of property-like entities shared by things in virtue of which we understand them to be the kind of things that they are. Marks are partial concepts. In the first section of the body of the Logic, “Of Concepts,” Kant develops a theory of concepts, the fundamental elements of which are concisely given in the first six sections. (The paragraphs about to be considered are in Young, 589–593, Ak 9, 91–96) Concepts are distinguished from intuitions:  the former are universal, the latter singular representations. (¶1) Concepts are pure or empirical:  empirical concepts are abstracted from experience. (¶3) With respect to concepts, what are given or made—the “matter” in question—are the objects of the concepts; moreover, in an empirical concept the objects are given by sensation. (¶4) But the form of concepts, their universality, is always made by a threefold process: comparison, reflection, abstraction: “The origin of concepts as to mere form rests on reflection and on abstraction from the differences among things that are signified by a certain representation” (¶5). This is true of all concepts, pure and empirical: To make concepts out of representations one must thus be able to compare, to reflect, and to abstract, for these three logical operations of the 24

I use the Jäsche Lectures on Logic.



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understanding are the essential and universal conditions for generation of every concept whatsoever. Kant then gives an example of this process: I see, e.g. a spruce, a willow, and a linden. By first comparing these objects with one another I note that they are different from one another in regard to the trunk, the branches, the leaves, etc., but next I reflect on that which they have in common among themselves, trunk, branches, and leaves themselves, and I abstract from the quantity, the figure, etc., of these; thus I acquire the concept of a tree. (¶6) My claim will be that what Kant calls “the general concept of spaces in general” cannot be derived from experience by abstraction because it cannot be derived by abstraction at all, and this because there is no thing (“nothing”) in common among spaces. The “thing” that there would have to be would be a universal of some kind but spaces are thoroughly particular:  they contain in themselves no universals—thus, a fortiori, share no universals. Indeed, since they are not derived by abstraction, they are not, strictly speaking, concepts at all. I later use the term “linguistic conceptions” to characterize what Kant calls “the general concept of spaces in general,” but for now the essential point is that this concept / linguistic conception cannot be created by abstraction. Longuenesse25 also takes seriously Kant’s account of concept formation in the Jäsche Logic but denies that there are for Kant universal items immanent in the items upon which the threefold process of comparison/reflection/abstraction operates. I agree with her if we understand universals as Platonic forms but submit that Kant’s examples are consistent with another conception of the common elements; namely, what Sellars has called qualitative “repeatables.”26 Kant’s own examples of common elements include colors—“With a scarlet cloth, for example, if I think only the red color, then I abstract from the cloth . . .” (Ak 9, 95; Young, 592)—a qualitative repeatable in Sellars’s sense. It is true that the example of color is used in a way that is metaphysically naive here (from the point of view of the metaphysics of CPR), but in CPR itself Kant uses color as his example of an analytical unity of consciousness in section 16 of the B edition Deduction (GW, 247; B133–134). We shall see that this is the kind of unity characteristic of concepts, in the strict sense, for Kant.

1998, 116–117. This is the term he uses in “Empiricism and the Philosophy of Mind” (Sellars 1963) for the universal character that he thinks the British empiricists attributed to perceived qualities. See 157 ff. 25 26

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Longuenesse’s view is that the items to which we apply the threefold operation are schemata. Schemata are rules that we use to construct the particular spatiotemporal form that particular empirical objects possess. From finding what is in common to the schemata used, for example, to construct triangles, we derive the concept of triangle. Kant calls these “pure sensible concepts” in the Schematism: GW, 273; A140/B180. Now schemata are rules for the construction of images, and we can distinguish rule tokens (this application of a rule vs. that application) from rule types. If we treat rule types as repeatables, we can say that each application of the schema for a triangle contains a common element abstracted from all the different schemata used to construct all the different types of triangles; this common element is the rule type for constructing elements. So the term “pure sensible concepts” is entirely apt here. There is a single element that all triangle images have in common, the rule type for constructing them; thus the pure sensible concept of a triangle is a concept in the strict sense for Kant. But this is not the question we have for Kant in Exposition 4. Our question is whether the concept of spaces in general is a concept in the strict sense for Kant, not whether the general concept of particular spatial shapes is a concept in the strict sense for Kant. Here I think that the answer must be negative; it is so for the simple reason that while there is a schema for every figure we can draw in space, there is no schema for spaces in general, hence no universal schema type for spaces in general to serve as the common element isolated by the threefold process for developing concepts. Figures are constructed in space, but space is not itself constructed in space. Space may be a feature of our cognitive capabilities but not of our constructive-cognitive capabilities; rather, the latter presuppose the former. This means that if there is in Kant an account of the generality of our language for spaces, it cannot be in his account of concepts per se. Kant does indeed have such an account, but it is to be found in his theory of definitions rather than concepts—again, most fully developed in the Logic, paragraphs 99 and thereafter.27 Of formal definitions there are two main kinds: analytic and synthetic. The former are given, the latter made (¶100). There are two kinds of analytic definition: a priori and a posteriori (¶101). There are also two kinds of synthetic definition: (a) those that are made through “exposition,” and (b) those that are made through “construction.” These latter are the “mathematical” concepts. The main difference between analytic and synthetic definitions seems to be that synthetic concepts are open ended in one of two ways: either because they are based on constructions that we can arbitrarily extend as much as we like (the mathematical kind) or because they involve an open-ended process of 27

Young, 632–633; Ak 9, 142.



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discovering new defining characteristics of “empirical concepts” (the expositional kind). Kant’s examples are, “water, fire, air”—what we nowadays would call natural kinds. Analytic definitions seem to take a set of characteristics antecedently fixed in language and uncover them by what we nowadays would call philosophical analysis. If the concept of spaces is to be introduced by definition, the definition will be a synthetic definition by construction. If we now return to Exposition 4, the meaning of “limitation” will be a line drawn in accord with the definition of a particular figure, a rule of construction. This rule is the “pure sensible concept” we have just been discussing. What is important about synthetic definitions for my present purpose is that it allows us to introduce a notion of generality in language that is not dependent on concepts in the strict sense. Kant can, for example, give an account of the meaning of the general term “parts of space” without having to link the term to a concept of parts of space. This is a good thing for Kant, of course, since (as I have just been arguing) there is no such concept. The term “spaces” is short for “parts of space.” The definition of the latter term is this: s is a part of space iff there is a whole-space W and s is a region enclosed by lines drawn in W. Particular spaces, triangles, rectangles, spheres, cubes, and the like are then defined by lines drawn by rules associated with those figures. For these particular parts of space, there are concepts in Kant’s strict sense, derived as earlier indicated. In section 103 of the Logic, Kant’s term for explanations of the meanings of general terms that are not (necessarily) concepts is “declarations” [Declarationen] (Young, 633; Ak 9, 142). We may call the condition that is defined by such declarations synthetic conceptions (conceptions for short) to indicate their affinity with concepts while preserving their distinctness from concepts. These items make essential reference to language, whereas concepts proper do not. The whole entity that serves as the ground of the synthetic conceptions—the whole-space in the case illustrated here—may be called a “synthetic-conception ground.” There is some additional textual evidence for seeing in Kant a distinction between two kinds of generality: concept generality proper and another kind. Consider first Kant’s account in a note to section 17 of the B edition Deduction of the “unity” of space and time as a synthetic unity: Space and time and all their parts . . . are not mere concepts by means of which the same consciousness is contained in many representations, but rather are many representations that are contained in one . . ., and consequently the unity of consciousness, as synthetic and yet as original, is to be found in them. (GW, 248–249; B136)

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Consider next a distinction in section 16 of the B edition Deduction between two kinds of unity: analytical unity of consciousness and synthetic unity of consciousness. The analytical unity of consciousness pertains to all common concepts as such, e.g. if I think of red in general, I thereby represent to myself a feature that (as a mark) can be encountered in anything, or that can be combined with other representations . . . A representation that is to be thought of as common to several must be regarded as belonging to those that in addition to it have something different in themselves; consequently they must be conceived in synthetic unity with other (even if only possible representations) before I can think of the analytical unity of consciousness in it that makes it into a conceptus communis. (GW, 247; B133–134) The notion of an analytical unity seems to be the same as the notion of a general concept. The notion of a synthetic unity is explained here in terms of the possibility of combining one representation with another, something that occurs in synthetic definitions of the mathematical kind. (When I draw a line I combine points one after the other to make the line.) When, therefore, Kant characterizes the unity of “space and time and all their parts” (my emphasis) in the note at B136 as a synthetic unity, he is contrasting the possibility that the unity of the parts of space is an analytic unity (which he rejects) with the possibility of it being a synthetic unity (which he endorses). In denying that it is an analytic unity, Kant is denying that our understanding of the general term “parts of space” amounts to a concept. In affirming that it is a synthetic unity, Kant is saying something different. If I have interpreted his doctrine correctly, what he is saying is that the meaning of the general term “parts of space” is given in a synthetic definition: we have a linguist conception but not a concept of space and its parts. To bring this back to where we left off at the end of the previous section, we needed there to see how Kant might defend the second premise in our reconstruction of the Second Reading of the Metaphysical Exposition, reproduced here for convenience, with one modification indicated in bold. 1. Our general concept or conception of spaces can be arrived at in one of two ways: by abstraction from experience or by limitations in an all-encompassing space represented by an a priori intuition, respectively. 2. It (the concept) cannot be arrived at by abstraction from experience.



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Therefore 3. It (the conception) must be arrived at by limitations introduced in an allencompassing space represented by an a priori intuition. Therefore 4. There is an a priori intuition of a single, all-encompassing space. By showing in the present section that our understanding of spaces in general is not arrived at by abstraction (hence is not a concept), we have established premise (2), as promised. This concludes my discussion of the numbered paragraphs of the Metaphysical Exposition (the Metaphysical Exposition proper) but does not exhaust our interest in the Exposition, since in the preamble to it and also in the second sentence of the first of the numbered Expositions, there remains material critical to the development of Kant’s theory of intentionality that we are yet to discuss. It is to this theory I turn in Chapter 3.

3

Kant’s Theory of Intentionality

1.  Kantian Intentionality as Brentano Intentionality Intentionality is usually characterized as “aboutness,” that property of something in virtue of which it “has an object.” But what is it for something to “have an object” in the requisite sense? Perhaps we can say that something has an object in case it is an idea of x, where x is the object? But what then is an idea? We are in danger of a vicious circle here. Let me suggest an alternative approach: define intentionality not by what it is but by what it does. What intentionality does is make objects available for further cognitive action. Let’s say that when something makes an object available to the mind for cognitive action, it is the “vehicle” of intentionality.1 For example, when we see something, the seeing makes an object available to us to make judgments about. The seeing in this case is the vehicle of intentionality. Since seeing is a relation between an observer and an object, the vehicle is in this case a relational vehicle. But it also seems possible for a nonrelational vehicle to make something available to us for cognitive action. This is where “ideas” traditionally come into the story.2 I may have an idea of a nonexistent entity, a unicorn say, which idea makes that entity the subject of judgment (e.g., it doesn’t exist), where the idea is not a relation between the holder of the idea and that object. The object, nevertheless, is distinct from the idea: the unicorn is an animal, whereas my idea of a unicorn is not. There are many theories of how intentionality is possible, including how nonexistent things may be intended. I want to characterize one such theory, one I associate with the work of Brentano,3 as follows:

1 2 3

Term is due to MacKenzie 1990. See Wilson 1978, 102. Brentano 1874. 46



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An intentional vehicle V has Brentano intentionality iff (1) V is a mental state (2) The intended object of V is an intentional object In the first sentence of part I  of the Transcendental Aesthetic, Kant introduces the notion of intuition: In whatever way and through whatever means a cognition may relate to objects, that through which it relates immediately to them, and at which all thought as a means is directed as an end, is intuition. (GW, 172; A19/B33) Aquila4 has maintained that when Kant characterizes intuitions as immediately related to the objects of cognition, he means to ascribe (what amounts to) Brentano intentionality to them. If so, then whatever objects intuitions represent (we’ll use Kant’s standard terminology here for intentionality), they depend on being intuited. This gives them a decidedly non-thing-in-themselves status. On Kant’s view intuitions represent spatiotemporal objects, so if Aquila is right, spatiotemporal objects are intentional objects. As argued in Chapter  2, this same conclusion is established by an independent line of argument by Kant in the geometrical arguments of the Metaphysical Exposition (Exposition 3 in the A edition, the Transcendental Exposition in the B edition) and in section 9 of part I of the Prolegomena. I am therefore going to take it as established that Kantian intentionality is Brentano intentionality.5 But the geometrical argument has a great weakness: it assumes the necessity of applied geometry, a necessity that Kant assumes but does not demonstrate in all of these proofs. We will see in Chapter 4 that Kant has another version of these arguments that does not assume this, thus making for a stronger form of the geometrical argument for a form of Transcendental Idealism, but he does not give that argument in the Aesthetic. I argue that what he does give in the Aesthetic, while not a direct argument for Brentano intentionality, is an account of the “ground” of this conception of intentionality, part of the theoretical scaffolding necessary for showing how it is possible that there be Brentano intentionality in the first place. The argument structure is that which some modern interpreters of Kant have come to call “transcendental arguments.”6 I begin my discussion with a brief characterization of an intentional object. Aquila 1983, 73. See Aquila 2003 for a discussion of other intentionalist readings of Kant: Vaihinger, Prauss, Sellars, Pereboom. 6 See, e.g., Stroud 2000, chs. 2 and 13. Stroud attributes the first use of this term to J. L. Austin in 1939 (203). 4 5

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An intentional object is a strange entity. It is the immediate object of the intentional vehicle, it depends on the intentional vehicle for its ontological status (“intentional inexistence”), but it is not identical with its vehicle. It may or may not be real. This doctrine is plausible enough if applied to nonexistent objects: we intend them, they don’t exist, so they are somehow dependent on the mental act. But what of objects that do exist—the man standing in front of me with the blue cap and red trousers? We surely do not mean to say that this object depends on the mental act. In this case, we want to say, the object of our thought is not an intentional object (an object with the property of intentional inexistence) but an actual, material object ontologically independent of our mental acts: a thing in itself. But there is a problem with this view, brought out by bifurcating the example into two cases. Suppose that I am hallucinating a particular man in a blue hat and red trousers. Since the man does not exist, he is an intentional object, whom we shall call “intentional-Jones.” My act of intending this object has a certain metaphysical structure: an act, the subject of an act, an object distinct from the act and subject yet ontologically dependent on same. Now suppose that a man looking just like intentional-Jones—call him “real-Jones”—steps into my field of view and my brain starts to be stimulated in the visually usual way by real-Jones. We can suppose that one of two things happens:  (i)  intentional-Jones is replaced by real-Jones as the immediate object of my perception and, correspondingly, the nonrelational intentional vehicle is replaced by a relational intentional vehicle; or (ii) the distal cause of the nonrelational intentional state changes—it is now real-Jones rather than an internal cause—but the immediate object of my intending remains intentional-Jones. Which should we prefer? A version of the argument from hallucination popular with sense-datum theorists can be pressed into service here. For any veridical sense experience there is a hallucinatory experience such that the first is indistinguishable to immediate consciousness from the second. This requires explanation, and the explanation is that (a) in each case there is an object of immediate awareness and (b) the immediate awareness of the object in each case must be a token of the same mental-state type, it being understood that (c)  the immediate awareness of the same mental-state type must share the same metaphysical structure. Since it is out of the question that in the hallucinatory case the metaphysical structure is relational (a seeing of a real object), the only alternative is that in both the veridical and the nonveridical case the metaphysical structure of the mental act is nonrelational; that is, the object of the mental acts in both cases is an intentional object. Since intentional objects ontologically depend on the mental acts that intend them, in all cases the objects of our mental acts depend ontologically on them. I find an argument along these



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lines in Descartes, in the passage in Meditation II where he discusses men in the streets in hats and coats.7 The notion that objects of ideas are intentional objects is an important feature of the Cartesian theory of ideas. This property—the ontological-dependence property—is important for our purposes since it could provide an elucidation of Kant’s positive doctrine of Transcendental Idealism, and it is correspondingly important to find Kant’s other (other than the geometrical argument) reasons for assigning this property to the objects of intuition. There is evidence in Kant’s writings that he was attracted to a Cartesian account of ideas insofar as it relates to the immediate objects of perception. An example is a passage in the Prolegomena, part I, note III, where Kant takes up the task of explaining Transcendental Idealism. He here seems to endorse reasoning similar to the argument from hallucination (in the first half of the sentence) and also to give a phenomenalist account of the distinction between reality and nonreality (in the second half): The difference between truth and dream, however, is not decided through the quality of representations that are referred [bezogen] to objects, for they are the same in both, but through their connection according to the rules that determine the connection of representations in the concept of an object, and how far they can or cannot stand together in one experience. (Hat., 42; Ak 4, 290; my emphasis; my interpolation) I take these passages to show that there is at least a tendency in Kant to endorse the argument from hallucination:  all objects of representations are mind dependent (in this case, possessing intentional nonexistence), some have the property of being real. In one of its meanings at least, I am inclined to say its central meaning, “Transcendental Idealism” is just Kant’s name for this theory of intentionality. Kant’s theory of intentionality tells us what intentionality is—it is Brentano intentionality—and he provides an argument why we should accept this theory rather than an alternative. This argument appeals to intuitively appealing principles—(b) and (c) in my reconstruction above. In this respect the argument is like the argument Kant gives in the Prolegomena (part I) for the contention that space and time are forms of intuition: it starts from the intuitively appealing idea that arithmetic and geometry constitute judgments that are a priori synthetic. Kant also maintains in this case that we do not need to show that mathematical propositions, as synthetic a priori propositions, are “possible,” since “there are plenty of them actually given, and indeed with indisputable certainty” (Hat., 7

Descartes 1984 (CSM II, 21; AT VII, 32).

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27; Ak 4, 276). However, this is not the case with philosophical propositions, propositions like the ones stating Kant’s theory of intentionality. Concerning these propositions all that we have so far in their favor is an intuitively plausible argument that falls considerably short of “indisputable certainty.” It would seem, therefore, that Kant would insist on asking and answering the question how such a theory is possible, beyond simply asking whether it is logically consistent. The insistence on asking and answering How-possible? questions that invoke a notion of “real possibility” beyond mere logical possibility is the central task of Kant’s transcendental method and is perhaps his most abiding contribution to scientific epistemology. In investigating Kant’s transcendental method applied to the theory of intentionality, there is less to go on in Kant’s texts than we would like—we may even doubt that Kant has a theory of representation in the usual sense since he says in the Lectures on Logic (Young, 535; Ak 9, 34) that the notion of representation cannot be defined. But this may not matter much since Kant is looking for the conditions of (real) possibility for something to realize the concept. When Kant is asking about the possibility conditions for something, he usually expresses this by asking for the “ground” of the thing. In CPR Kant explains the idea of representation in the first sentence of the first section of the Transcendental Aesthetic (A22/B37):  “By means of outer sense, a property of our mind, we represent to ourselves objects as outside of us, and all without exception in space” (GW, 157). This is intentionality: a cognitive state representing something outside of itself to the mind. He goes on to offer an account of how this is possible—what the ground of intentionality is. This account makes up part of Exposition 1 of Space: For in order for certain sensations to be referred8 to something outside me (i.e. to something in another place in space from that in which I find myself), thus in order for me to represent them as outside one another, thus not merely as different but as in different places, the representation of space must already be their ground. (GW, 157; A27/B 38) In Chapter 2 I noted that the pronoun “them” (sie) can grammatically only refer back to “sensations” (Empfindung), but I  there set aside that concern to suppose that the sense of the sentence could somehow be that I was representing objects as outside one another (etc.), “them” thus not referring to sensations but to some imaginary noun earlier in the sentence for objects. Giving this sentence this sense fits in well with what our analysis of the other parts of the Metaphysical Exposition proper tell us of Kant’s intended argument. But if we 8

Translation altered: “referred” substituted for “related.” Original is bezogen.



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now set these other parts aside and read this sentence in conjunction with the opening sentences of the previous paragraph, the “preamble” to the Expositions proper, it then appears that the reference to sensations might indeed be what Kant intended since the theory of intentionality, not the theory of spatial relations, is now in the foreground. If so, we might give the sense of the sentence to be that what has the representation of space as its ground is my ability to have sensory representations (empirical intuitions) of objects in space (“outside one another, thus not merely as different but in different places”). This brings out the general relevance of the first part of the sentence to the rest of the sentence—not easy to do on the alternative reading. This is another advantage of this reading. Let us look more closely at the first part of the sentence. Note especially the phrase “in order that sensations be referred to something outside me” in the second sentence. Being “referred to” here (bezogen) should be understood as a semantic relation, something akin to representation.9 The meaning of this sentence, then, is that the representation of space is what makes it possible for us to represent objects in space.10 Since this is also the only grammatically permissible reading for this sentence, I take it that this is indeed Kant’s meaning here.

9 Guyer and Wood do not translate bezogen as “referred” but as the less semantic-sounding “related” (GW, 157/175). However, bezeihen (the infinitive form of bezogen) is used with the sense of referring in a representational sense at Bxvii:  “Yet because I  cannot stop with these intuitions, if they are to become intuitions, but must refer [bezeihen] them as representations to something as their object . . . (GW, 110; Bxvii). I take the same sense of this verb to be in play in the passage under discussion from the Metaphysical Exposition. Bezeihen also appears in the first sentence of the Transcendental Aesthetic, twice, again translated by GW as “relate.” Here is the German: “Auf welche Art und durch welche Mittel sich auch immer eine Erkenntnis auf Gegenstände bezeihen mag, so ist doch diejenige, wodurch sie sich auf dieselben unmittelbar bezeiht . . . die Anschauung” (B33). Here is the GW translation: “In whatever way and through whatever means a cognition may relate to objects, that through which it relates immediately to them . . . is intuition” (GW, 155; my italics). Again, the very generic translation “relate” does not convey the idea that the relation is “as representation”; thus, it is best translated for the modern analytic philosopher as “refer.” I discuss this issue further in Chapter 6 in relation to Kant’s use of “relation to an object” in several texts in the Transcendental Analytic that seem to some interpreters to make trouble for the idea that intuitions refer to objects. 10 This point seems to have been missed by George (1981). In making a point in relation to this passage George first quotes from a lecture of Kant’s (Metaphysik L, Ak. 28, 235), which “ suggests that the object that causes the sensations is itself spread out in space and that its spatial features are discovered by scanning it with the eye.” He continues,

The sensationist premise [which George attributes to Kant], does not allow this assumption. Initially only the succession of sensation is present, and we may speak of a generation of the spatial features of objects by putting the sensations in relation to each other, setting them “outside and alongside each other, and referring them to something outside me” as Kant puts it at the beginning of the Transcendental Aesthetic. (240)

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There is, however, some question of how the “representation of space” should be taken in light of our twofold distinction, introduced in Chapter 2, between a representation of a unitary global space and a representation of a unitary local space. I have argued on the basis of the note to B160 that the former is not an intuition at all, in the sense of the Aesthetic (that is, it is not given11 and in immediate relation to its object), but is, rather, a rule for constructing a representation of a topologically unified space from local spaces. It seems clear from the analyses in Sections 4 and 5 of Chapter 2 that the kind of space represented in the Expositions is an object of intuition in the sense of the Aesthetic, so I take the space in question to be a local unitary space. But I also argue in Chapter 2 that a pure intuition of a local space is also regarded by Kant as a form of intuition (recall the discussion of the map analogy in Ch. 1), so I propose that when Kant says that the ground of the possibility of referring our sensations to things outside us is the representation of space, he may also be thinking of that representation as a form of intuitions or sensations. In that case, since the form of intuitions is spatial form, what apparently grounds the possibility of referring sensations to things outside us is the fact that the sensations occur in a spatial form themselves. There are two questions emerging from this. In second priority is, Why should Kant maintain that the spatial form of our intuitions grounds our ability to refer sensations to things outside us? In first priority is, Why should Kant maintain that the form of our intuitions is spatial in the first place? We will see that the answers to these two questions are closely linked and depend on a notion of projection.

2.  Kant’s Projectionism Kant says that what makes it possible for us to refer sensations to things outside us is a prior representation of space. This representation can at the same time be understood as an a priori form of sensibility. Even before Kant argues in the Expositions proper that space and time are nothing more than this form, George is of course speaking of the passage quoted above. While Kant does indeed not speak here of “scanning” objects, he also is clear that what enables this referring of sensations to things outside us is not some operation of the imagination that somehow, and mysteriously for George,* creates spatial objects from nonspatial sensations but that it is our prior ability to represent spatial objects that enables the reference. This prior ability is itself grounded in the form of intuition that is space. (*“It seems that [Kant] wanted to claim that the imagination somehow knows how to identify and reproduce just that subset of a given sensory manifold that forms an image for an appropriate concept. . . . Kant thinks of this ability as deeply hidden and makes no attempt to explain how it works” [247].) 11

Cf. Longueness 1998, 214–227, esp. 216–217.



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he says that this form is spatial and temporal. Let’s reconsider why Kant maintains this. One answer, discussed in Chapter 1 and to be further discussed in Chapter 6, is that Kant maintained this to account for our ability to perceive objects in space. This is certainly part of the answer, but this is not what the passage in the First Metaphysical Exposition says; it says that the form of intuition is needed to account for the referral of sensations to things outside us. Another answer, given in Exposition 3 in the A  edition, the Transcendental Exposition in the B edition, is that it is only if our empirical intuitions come in a spatial form, in particular a Euclidean spatial form, that we can explain how it is possible for the objects of empirical intuition to necessarily conform to the same geometry as the intuitions themselves. This explanation requires the assistance of a metaphysical principle, a principle saying that the objects of empirical intuition must get their geometrical structure from the geometrical structure of the intuitions themselves. When objects of representation get their structure from the representations themselves, that is a kind of “projection” of the subjective onto the objective. This is not quite yet Transcendental Idealism but, as noted in Chapter 2, it is only one step away from it. Referral is an intentional act. It explains how external objects come to be objects of cognitive action. So could Kant perhaps be saying here, in the second sentence of Exposition 1, that spatiality, understood as the form of sensibility, is the ground of intentionality in general? My view is that that is exactly what he is saying. But how, then, is the form of sensibility the ground for intentionality? My suggestion will be that it derives from the same metaphysical principle Kant relies on for the penultimate step to idealism in the geometrical argument: the principle of projection. I have accepted that intentionality for Kant is Brentano intentionality and that intentionality depends on a projection principle, which I state as follows: Kant’s Projection Principle: What makes it possible for a mental state m to be a Brentano representation of an object o with structural characteristics (a “form”) F is that m also exemplifies F. This principle allows for an answer to the second of our two questions: Why does Kant maintain that the spatial form of sensations grounds our ability to refer sensations to objects outside us?, now refined as the question Why does Kant maintain that the spatial form of intuitions allows for the Brentano representation of objects outside us in general? The answer is that the objects of Brentano representations are intentional objects, and the structural features of intentional objects derive from the structural features of their representations. The first remains as it was originally:  Why does Kant maintain that the form of intuition is spatial to begin with? Here the answer is that the objects sensibility presents to us are antecedently

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postulated by Kant to be spatial objects, a point established by transcendental argument in the first sentence of the first section of the Aesthetic.12 Since the objects sensibility presents to us are intentional objects, Kant correctly infers from his projectionism that they could be spatial in form only if the representations themselves are spatial in form.13 Formally, the argument can be laid out as follows: (1) Assume that we have singular representation of objects distinct from each other and from ourselves. (2) All singular representations of objects distinct from each other and from us are representations of objects in space (Kantian transcendental postulate). (3) We have singular representations (intuitions) of objects in space (logical inference, 1, 2). (4) All singular representations (intuitions) of objects in space are Brentano representations (Kantian postulate). Therefore, (5) All singular representations (intuitions) of objects in space are themselves in spatial form (4, Kant’s Projection Principle). Kant’s theory of intentionality also provides an account of the two components of Transcendental Idealism, a doctrine Kant derives immediately after completing the numbered Metaphysical Expositions. The theory consists of two main metaphysical doctrines. The first is that spatial objects are mind dependent:  this follows from the assumption that spatial objects are the objects of Brentano-like intentionality. This is the “idealist” part of Kant’s Transcendental Idealism. The second is that the form of external objects is derived from the form of the intuitions that represent them. This is the projectionist strand in Kant’s theory of representation reflected in Kant’s Projection Principle. Since the projection capability of the mind is the ground of the possibility of the idealism, this contributes the “transcendental” part of Transcendental Idealism.14 In advancing this as a Kantian postulate I am taking sides with Allison on his interpretation of the significance of the famous first sentence in the preamble to the Expositions at GW, 157; A22/ B37: “By means of outer sense (a property of our mind) we represent to ourselves objects as outside us, and all as in space.” See Ch. 2, §2. 13 This account locates the principle of projection in the form of sensibility rather than in the spontaneity of cognition. For a reading that locates the source of projection in the latter, see Dickerson 2004, 51 ff. See Aquila 2003 for a discussion of various other interpreters that attribute forms of projectionism to Kant. 14 The form of Transcendental Idealism defended here is the ontological form: appearances and things in themselves form two disjoint classes of entity. There are alternative readings, notable among which is that the distinction between things in themselves and appearances is not a distinction between two classes of entities, as I maintain, but a distinction in ways of considering a single class of entities. Considerations of space and focus prevent me from further considering this alternative here 12



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3.  Spatial Form and the Representational Capacity of Intuitions in General 3.1.  The Map Analogy In the First Metaphysical Exposition sensations seem to be the vehicles of intentionality; it is through them that we are able to refer to things outside us. Now, this is true of empirical intuitions (empirische Anschauungen), of which there turn out to be two kinds: empirical intuitions of categorially undetermined objects (“appearances”) and empirical intuitions of categorially determined objects (“empirical objects”). With the first kind, sensations constitute the matter of the intuitions, and they are unified by their spatiotemporal form—“aesthetically unified intuitions” as I shall be calling them.15 With the second kind, the situation is more complicated, depending on yet a third kind of intuition, “intuitions in general” (Anschauungen überhaupt). These intuitions are unified by the understanding in a form that I call “logical unification.”16 That Kant sees a distinction between empirical intuitions and intuitions in general is required for a proper understanding of his intentions in dividing the B edition Deduction into two segments. Empirical intuitions are a composite of aesthetically unified intuitions and logically unified intuitions, the demonstration of which is the objective of the second part of the deduction. That intuitions in general are logically unified is the objective of the first part. I explain and argue for this in what follows.17 Logically unified intuitions are still intuitions:  they represent objects in space, and it is part of Kant’s projectionist theory of intentionality that they must have spatial form to do so. This is what the isomorphism argument demonstrates theoretically. My purpose is to make this idea intuitively plausible by means of an analogy with symbols on an ordinary geographical map. I propose to do so for intuitions in general, leaving the question of empirical intuitions to later chapters. The idea, then, is that intuitions in general may be likened to symbols on a geographical map—spatial marks that, in the context provided by other marks and conventions, represent objects distinct from themselves in space. This suggestion is helpful heuristically because it provides a common-sense analogy that will help us gain an initial and intuitive understanding of Kant’s doctrine of representation. But it also provides an additional motivation for several postulates of but I have done so elsewhere. See Vinci, “Appearances vs. Things in Themselves: Dual Aspects of a Single Thing or Two Kinds of Entity?” unpublished MS. 15 16 17

See Ch. 6, §3.4. See Ch. 6, §2. See Ch. 7, Part II, §1.

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Kant’s theory of representation already discussed. For example, as mentioned in Chapter 2, the analogy allows us to explain Kant’s puzzling claim in the Aesthetic that the form of intuitions is at the same time a pure intuition, a representation taking space (local spaces, as I argue) as its object. The analogy also provides an intuitive motivation for Kant’s Projection Principle: if intuitions are like symbols on a map, part of their capacity to represent spatial regions derives from the spatial form of the system of representations itself. Yet another motivation derives from the fact that a map is a human construction, a system of symbols based on sensations we receive from the objects to be mapped but not identical with those sensations. If the analogy between intuitions and maps holds, this would explain why Kant takes intuitions to be based on but not identical with sensations.18 An ordinary geographical map is a spatial object with determinate properties. It has a certain topological structure but also a determinate size and shape; distances between points on the map are also metrically determinate. In order for these metric properties to specify metric properties of the space being mapped, a scale is specified for the map: say, 1 inch equals 2 miles. In addition to these metric features, a map also has symbols that stand for things like mountain ranges, large cities, small towns, rivers, and roads. All of the features of the map that have representational properties acquire those properties at least in part through a system of conventions that specify meanings for the symbols. For some of the symbols, at least, their representational effects are also acquired through spatial characteristics of the symbols themselves: the distance between two city symbols on a map, for example. Distances between points are properties intrinsic to the map itself, and when the representational effect of a symbol depends systematically on such properties, I  call these symbols or representations “intrinsic.” When the representational effect does not systematically depend on such properties, I call such symbols or representations “purely conventional.” The points in the spatial structure of the map itself and relations defined on them are intrinsic symbols. For example, the fact that a 2-inch space separates two points on a map is at least partly responsible for the fact that that space represents a space of 4 miles on the ground. In general, it seems that when a determinable property P of the map is assigned a representational role such that determinate features of what is being represented can be systematically read off from determinate intrinsic features of the map, the property P is an intrinsic representation in my sense. Other examples of intrinsic symbols are created when relative sizes of circles on a map indicate relative sizes of populations in the towns represented and when relative degree of color intensity of a region of the map indicates relative degree of intensity of agricultural development. On 18

As he does in the “classification passage” at GW, 398; A320/B376.



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the other hand, proper names (e.g., New York) are purely conventional: nothing about the determinable intrinsic features of the names themselves is relevant to their representational properties. I’ve said that both purely conventional symbols and intrinsic symbols acquire their representational properties in part due to semantic conventions; thus “New York” stands for New York, and relative size of circle stands for relative size of population. With the notion of “standing for” staring us so squarely in the face here, it might seem that we are looking at a semantic notion, perhaps the notion of linguistic reference or denotation. Something along these lines seems to be Goodman’s view in The Languages of Art. Consider an example from that work: [We must not] overlook the fact that denotation by a picture does not always constitute depiction; for example, if pictures in a commandeered museum are used by a briefing officer to stand for [denote] enemy emplacements, the pictures do not thereby represent [depict] these emplacements.19 Goodman was not of course interested in arguing for a distinction between intrinsic and purely conventional symbols: the whole thrust of the argument in his first chapter is in the opposite direction. His purpose is to deny that an individual picture depicts an emplacement while allowing that it may denote (“stand for”) one. We may, however, turn his example to our own purposes by thinking of the whole arrangement of the pictures as a depiction (model) of the whole setting of the emplacements. I note, to begin with, that this notion of depiction seems to have very little to do with causal relations between the pictures and the setting for a battle to be fought in the future. Rather, “standing for” seems to mean something like “standing in for.” The pictures stand in for the prospective battlefield emplacements for certain purposes; for example, to help commanders visualize what the emplacements would look like to an attacker, what the attack would look like to defenders situated in the emplacements, or to make certain calculations about the lines of fire, length of barbed wire needed, and so on. When a depiction system stands (in) for what it depicts, certain operations are performed on the intrinsic structure of the depiction system and the results of that operation are then transferred, mutatis mutandis, to the system being depicted. This transformation heuristic should be contrasted with the semantic relationship between sentences subject to inferential procedures and the objects to which those sentences refer.

19

Goodman 1968, 41.

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In addition to the transformation component, a depiction must also have a coordination component. This component allows us to relate the depiction to an actual or possible setting; in this case, the scene of a battle. One way to do this is to designate each of the pictures as a name denoting a particular emplacement to be constructed on the scene. A second way to achieve coordination would be to physically transport the model to its designated site and then physically orient it in the intended direction. This procedure does not rely on a notion of the individual denotations of the individual objects in the depiction system. I mention the existence of an alternative to a denotational solution to the coordination problem in the present context because a denotational solution will likely depend on a causal connection between the symbols and the things denoted by the symbols, something that would be ruled out for a theory of Brentano intentionality like Kant’s. A third feature of a depiction is its degree of accuracy (the veridicality feature). Suppose that in our present example, the depiction is coordinated to an actual battlefield setting with ten emplacements situated in a certain way with respect to one another. In keeping with our heuristic program we could try to establish veridicality in the same way we established coordination (viz., physically) by transforming the model into what it represents by certain geometrical operations implied by the transformation component. We can tell by inspection whether our depiction has been accurate:  are pictures where and only where there are emplacements? I should note here that this explanation works only if the pictures are somehow representative of things satisfying the general description of an emplacement. This is the fourth component, the descriptive component. My suggestion is that we think of geographical maps as depiction systems having the four components introduced above: (1) the transformation component, (2) the coordination component, (3) the veridicality feature, (4) the descriptive component. The most problematic components are the second, third, and fourth; I now turn to them for closer consideration, beginning with the second. In order to avoid reliance on a notion of denotation, I choose a version of the physical solution to the coordination problem. In our example from Goodman this solution consisted of actually transporting the depiction to the designated site and then physically orienting it. In the case of maps this procedure is impractical and, in addition, leaves us with the matter of explaining what a designated site is. We do not want to be required to say that it is the whole geographical region denoted by the map. But if we do not say this, how then are we to connect the map with its designated site? The answer I  propose is that any given map must be seen as fitting into a system of maps one member of which is, shall we say, an “indexical map.” An indexical map is like any other map, except that it says of a point in the region mapped and a point in the plane of the map itself: “This (pointing to the plane



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of the map) is this (pointing to the region mapped).” This point on the map has the property that it is identical with the place in the region mapped. Thus, if things are set up properly, this is a point that is both a symbol and its designated site. Call this the “transparent point.” There will be just one such point in any system of maps.20 In addition, there must be certain other indexical conventions establishing orientation of the map (e.g., “this is north”). Once these indexical conventions are in place, the intrinsic spatial properties of the map together with the scale (1 inch equals 2 miles) establish designated sites for other points on the indexical map. By means of the rules connecting nonindexical maps into a system, any given map has its designated sites fixed. In characterizing the transparent point I employ the notion of designated site, and in explaining that notion, I make reference to the transparent point. There may appear to be a circularity here, but if there is one it is not a vicious circularity, for we can specify a set of procedures for constructing maps that determines designated sites in a recursive way. First, we specify an index for the map that contains the descriptive symbols and algorithms. Then we arbitrarily designate a certain point in the plane of the map as the “transparent point.” Together with the orientation conventions, this serves as a frame of reference for locating descriptive symbols on the map by use of the specified algorithms. All of the designated sites for the symbols, including that labeled the transparent point, are then simultaneously determined by the intrinsic properties of the map and the algorithms. It is worth emphasizing that it is not until the map as a whole has been constructed that any of the points in the plane of the map acquire their representational properties. Depiction is in the first instance a property of a whole depiction system and only derivatively does it apply to individual symbols. In this crucial respect depiction differs from denotation. So the fact that the transparent point is identical with its designated site is derived from the depiction system as a whole rather than specified ab initio. It is only if we had to do the latter that the account would be viciously circular. This solution to the coordination problem also implies an account of the veridicality feature somewhat analogous to the “transformational” solution suggested in our example from Goodman. The difference is that we do not, of course, require an actual transformation of the map into the region mapped but only a kind of “virtual” transformation. The idea here is that we perform calculations based on the intrinsic properties of the map and the interpretation algorithms to determine whether the symbols would actually come to spatially coincide with the features represented. Naturally there is no advance guarantee

The transparent point is known in mathematics as the “fixed point”; its existence is proved by a theorem of the same name. Thanks to Gillman Payette and Robert Paul for this. 20

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that all symbols will coincide with their objects, thus allowing for the possibility of inaccuracy in the map. This, of course, is as it should be.

3.2.  Applying the Map Analogy to Kant’s Theory of Intentionality The main points of the map analogy for Kantian representations are these: intuitions in general are like symbols on the map, and pure intuitions of local spaces (understood both as forms of intuition and as pure representations) are like the blank page on which the map is constructed. What gives a map its capability to represent specific features of the terrain is the intrinsic spatial structure of the blank page. But the map needs to be brought into relation to its intended object by a real relation—this is the coordination problem—and I  have suggested a relation of identity between some element of the map and an element in the terrain that is mapped: the transparent point. The advantage of solving the coordination problem with a transparent point is that it does not require causal relations between the representational system and the things represented, as would be the case, for example, with a denotation solution like Goodman’s. This is an advantage, because Kant’s Transcendental Idealism seems to preclude causal relations of this kind. So solving the coordination problem with a transparent point is in principle an attractive option for a Kantian theory of representation. If we try to implement a maplike representational system with a transparent point in the materials of modern cognitive psychology, we take the blank slate to be spatial structures in the brain, representations to be brain states arrayed in these structures in an order partly determined by sensory inputs, partly by other functions associated with indexing conventions and other forms of inference, and the transparent point to be a brain state that represents itself. There is no essential mention of causal affection by things in themselves outside the brain. The role of affection, if there is one, is to explain why the order of representations is as it is, not how they can be representations. There is, however, a text in section 25 of the B edition Deduction where Kant says that the self is not an object of intuition: In the transcendental synthesis of the manifold of representations in general . . . hence in the synthetic original unity of apperception, I am conscious of myself not as I appear to myself, nor as I am in myself, but only that I am. The representation is a thinking, not an intuiting. (GW, 259; B157)



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So, apparently, I cannot be the transparent point: the thing that represents itself. But the proposal is not that I, the unitary self of apperception, am a symbol representing itself but that a fragment of myself, a particular intuition contained within the matter of my faculty of representation, represents itself. I do not see that the doctrine of section 25 automatically precludes this. Still, the spirit of Kant’s objection seems to be that we cannot take the representational system as we know it to be a thing in itself, and so it would seem to be in accord with a conservative approach to interpreting Kant to say, if we are conservative of his doctrine of Transcendental Idealism in relation to the constructing mind, that the transparent-point solution is not one that Kant would accept.21 There are, however, other ways in which Kant might hope to solve the coordination problem. What is needed is some nonarbitrary, empirically grounded way of determining a you-are-here point on the map that does not require extensional relations between representational elements and represented elements. This is a natural place to introduce a role for sensations, not as representations themselves (corresponding to intuitions in general in Kant’s account), but as data that can be used in inferences allowing the representational system to locate the objects it represents in particular spatiotemporal locations in the objective environment.22 For example, if we assume that sensations occur in a spatial array for Kant—Kant does say that space and time are the form of sensibility as well as intuition—and that this array constitutes a visual field in the sense of a field of visual data when we are seeing something, then Kant can require rules correlating locations in the visual field with locations in the objective map. Intuitively, the you-are-here point is that place in the objective map correlating with the center of the visual field. The perceptual system could also take sensation data of speed and direction generated by our walking somewhere to continuously update the you-are-here point—a kind of dead reckoning. These are all empirical sources available to Kant to solve the coordination problem in a way consistent with even the most conservative interpretation of the role of things in themselves in Kant’s metaphysics. I conclude that the map analogy without the transparent-point solution to the problem of coordination can be implemented within Kant’s theoretical system. This is the model (I shall call it the Intentional Map Model) that I assume Kant employs in understanding human intuitional representation. This model However, if we are not conservative of this and allow for the spatialization of the mind as constructing mind, a development I advocate elsewhere (in an unpublished manuscript), then the transparent-point solution to the Kantian coordination problem may be possible. 22 As Falkenstein has insisted, only if sensations have a spatiotemporal form themselves can we give a reasonable explanation of how this could happen. (See Ch. 1, §1.) I maintain that, for Kant, sensations in spatiotemporal form are intuitions in their own right but, unless logically unified, they represent only schematic objects in a perspectival nonobjective space. (See Ch. 6, §3.4.) 21

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is a representational system with Brentano intentionality: it represents objects distinct from itself, which objects nevertheless are ontologically dependent on the representational system, and it achieves representation without depending on causal or identity relations between itself and the things it represents. This amounts to Kant’s positive doctrine of Transcendental Idealism. There are some other points in the implementation of the analogy that also require comment. In the development of the theory of the intentionality of maps, I draw a fundamental distinction between depiction and description. Depiction is a property that a representational system as a whole possesses in virtue of its intrinsic spatial form; description is a property of terms acquired in some other way. This distinction corresponds in important respects to Kant’s distinction between intuitions and concepts. We shall address Kant’s theory of concepts and the relation between intuitions and concepts in detail in the chapters 6 and 7 that deal with the Deduction—indeed that is the principle issue there discussed—so I  leave further comment on this topic until then. There is one final topic that the map analogy can help with: Kant’s doctrines of pure intuition. There are, as noted previously,23 two notions of pure intuition for Kant: one is the notion of the form of intuitions, the container in which intuitions are arrayed; the other is the notion of an intuition of a unitary space, both a local space and a global space. In the note to B160 Kant calls the second of these intuitions of unitary spaces a “formal intuition.” The object of the formal intuition is depicted in the Aesthetic as a single entity. But, as previously explained, in the note to B160, Kant requires a modification in this doctrine of the Aesthetic of pure intuition: it is not due simply to sensibility, as suggested there, but requires mental activity to construct. Kant is saying in this text that our ability to represent a unitary spatiotemporal world (the formal intuition) depends not just on the form of intuitions (i.e., intuitional representations) but also on a synthetic activity of the mind. We might take this as an indication that concepts (i.e., rules of intellectual synthesis) would after all play an essential role in intuitional representation were it not for Kant’s explicit disavowal. Our map model may shed some light on this puzzle. Recall that any given map achieves its reference only by being put together with other maps into a system that includes an indexical map. This “putting together” is a procedure governed by certain rules but, at least apparently, is independent of any specific interpretation for the conventional description symbols. Perhaps something like this is what Kant had in mind by the preconceptual synthesis— a putting together of intuitions of local spaces into a representation of global space. The second point has to do with the idea of a metric or measure function that assigns determinate sizes and distances to spatiotemporal objects. In the map 23

See Ch. 1, §1.



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model, this function has purely epistemic import: it allows us to epistemically determine distances in the terrain by application of the scale of the map to the “intrinsic” metric of the map itself. However, both the map and the terrain are objects with the same ontological status and subject to the same assumed metric; the scale function simply takes the units of measurement on the map and projects it into a greater number of units in the same system of measurement for the terrain. I argue in Chapter 624 that in the case of the “map” of intuition, there is reason for thinking that Kant did not suppose it to have an intrinsic metric. I suggest, therefore, that we think of pure intuition as analogous to a system of blank maps, without a metric, that serves as the structure in which intuitions (singular representations) are embedded. Particular arrays of singular intuitions are connected with one another by a set of preconceptual rules to generate a unified system of intuitional maps representative of a topologically unified spatiotemporal world order. Transforming this world order into an objective empirical order with determinate metric and other properties is the task of the faculty of understanding applying concepts.

24

Specifically, Ch. 6, §3.3.

4

Kant’s Theory of Geometry and Transcendental Idealism II

1. Introduction I argue in Chapter  2 that Kant countenances two domains for geometry, a pure domain of thought objects existing in the space of the imagination, a second domain of empirical objects existing in empirical space. The former are mind-dependent objects by definition, the latter are not. The geometry of objects in the first of these Kant calls “pure geometry,” the geometry of objects in the second of these he does not specifically name, but I have called it “applied geometry.” The main role of the discussions of geometry in both the Aesthetic and in the Prolegomena is to make a case that space is not an entity that exists in itself, outside our minds, but is a subjective entity of some kind, in this case a form of our capacity to have empirical intuitions. I have understood “form” in this sense as a structure that has the power to induce in the objects that reside within it certain structural properties; in this case the properties of Euclidean geometry. This power may lie in this structure as a mere potentiality or derive from actual possession of Euclidean, or Euclidean-like, properties by the structure itself. I have yet to develop this theory of form in detail or defend its attribution to Kant. This is one of the main tasks of this chapter. We have seen from our analysis in Chapter 2 of Prolegomena section 9 that Kant’s position there is that figures that appear in this structure are guaranteed to have the geometrical properties that the form induces in them, but it is another question whether, if we treat these images or impressions as representations of external objects, these external objects themselves also have Euclidean structure and are guaranteed to have it. Since Kant assumes for the sake of the argument in section 9 that the answer to both questions is affirmative, the only task

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remaining is to explain how this is possible. There is only one way, Kant argues, that these claims would be true, and that is if the structure of the representations determines the structure of the objects of the representations. This is but one step away from Transcendental Idealism, which is obtained when Kant declares that the only way a representation can determine the properties of its objects is if those objects are ontologically dependent on the representation. This is the final conclusion of the Metaphysical Exposition of the Aesthetic and the corresponding argument in part I of the Prolegomena. This result shows that the empirical objects of applied geometry are also objects of thought, like those in the domain of pure geometry. But although the section 9 argument demonstrates this similarity between the objects of pure and applied geometry, it does not in itself invoke pure geometry. Moreover, the argument suffers from a serious weakness. The critical premise of necessity for the theorems of applied geometry is simply assumed for the sake of argument, not proved. It will be my contention in this chapter that there is also an argument in part I of the Prolegomena that does exploit the other geometry—pure geometry—as well as applied geometry and avoids the weakness just mentioned of the First Geometrical Argument for Transcendental Idealism, as I  call it. This argument, the Second Geometrical Argument for Transcendental Idealism, trades on a correlation between the two geometrical domains—of pure and applied geometry—a correlation that requires explanation. As with the corresponding explanandum in the First Geometrical Argument, the only explanation is also a form of Transcendental Idealism, but unlike the first argument, the Second Geometrical Argument requires Kant to derive geometrical theorems from the principles of his doctrine of mathematical method and to demonstrate that they have the status of a priori synthetic propositions, something the first argument simple assumes. Accordingly, another major task of this chapter is to develop an account of Kant’s mathematical method in its application to geometry and to show how the theorems of Euclidean geometry are demonstrated of both pure objects of the imagination and empirical objects. This dual application of mathematical method serves as a premise for the Second Geometrical Argument and its ultimate result, the doctrine of Transcendental Idealism. Once this is established, I  then claim that this argument has a structure analogous to that of the Transcendental Deduction of the Categories. Since the Second Geometrical Argument is easier to understand and state perspicuously than the Transcendental Deduction of the Categories itself, I  use the former as a template from which to develop the latter. The next section begins my account of Kant’s doctrine of Geometrical Method.

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2.  Kant’s Doctrine of Geometrical Method in the Critique of Pure Reason 2.1.  Kant’s Geometrical Method In the B edition Introduction to the CPR (GW, 146; B19) and also in the Prolegomena, I:6 (Hat., 32; Ak 4, 280), Kant asks how it is possible for human reason to produce mathematical judgments that are synthetic a priori. In the latter work (Hat., 33; Ak 4, 281, note) Kant refers us to a doctrine of mathematical method requiring the existence of pure intuition. The passage, which I have used before, is an important one. Here it is again, quoted more fully: Philosophical cognition is rational cognition from concepts, mathematical cognition that from the construction of concepts. But to construct a concept means to exhibit a priori the intuition corresponding to it. For the construction of a concept, therefore, a nonempirical intuition is required, which consequently, as intuition, is an individual object. . . . Thus I  construct a triangle by exhibiting an object corresponding to this concept, either through mere imagination, in pure intuition, or on paper, in empirical intuition, but in both cases completely a priori, without having had to borrow the pattern for it from any experience. The individual drawn figure is empirical, and nevertheless serves to express the concept without damage to its universality, for in the case of this empirical intuition we have taken account only of the action of constructing the concept, to which many determinations, e.g., those of the magnitude of the sides and the angles, are entirely indifferent, and thus we have abstracted from these differences, which do not alter the concept of the triangle. (GW, 630; A713–14/B741–42) In this passage we find an analogy between drawing lines on paper and drawing them in pure intuition: just as the paper is a spatial structure that exists prior to and independent of the drawing of a line thereon, pure intuition is a spatial structure, a kind of three-dimensional mental slate apparently, that exists prior to and independent of the drawing of an imaginary line therein. This analogy embodies the idea that pure intuition is a spatial container, as discussed earlier, an idea that serves as a premise in Kant’s theory of representation and formation of certain spatial concepts. Since this activity originates spontaneously from within our mental faculties rather than being guided by sensation (the matter of sensibility rather than the form), Kant characterizes the activity as a priori. Moreover, the analogy also suggests that just as the structure of the paper



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imparts itself to the structure of the line in certain respects—bumpy paper makes for a bumpy line—so the structure of pure intuition imparts itself in certain respects to the line drawn within it. Kitcher has developed a reading of Kant’s doctrine of mathematical method that allows us to exploit this aspect of the analogy.1 The idea is something like this. First take the case of drawing figures in empirical intuition; that is, figures drawn in the usual way on paper or other physical surfaces. Since we have immediate knowledge2 of facts about various properties that the image possesses, we are in a position to ask for the source of these facts. The source for some of them resides in the rule of construction. For example, the source of the three-sidedness of the triangle I have just drawn is that the rule of construction I implicitly employed in drawing it is Draw a figure having three sides such that . . . Following Kitcher3, I call these “R properties” (and the corresponding facts “R facts”). But not all properties I observe in the image are R properties. Some of the remainder are clearly accidental properties (e.g., the length of the sides). These are “A properties.” But some—for example, the property that the sum of interior angles of the figure equals the sum of two right angles—are neither A nor R properties. These are the S properties—S for “space.” The fact that the image possesses S properties must also have a source, and following Kitcher, I take it that Kant locates the source of these facts in the existence of intrinsic properties of the spatial structure in which the image is drawn. Consequently, applications of this procedure can be regarded as epistemically determining the set of intrinsic properties of intuition— the subject matter of geometry. An important presupposition of this reasoning is that the spatial structure in which I  draw the image has the power to imprint its own geometrical structure (however this will eventually be understood; discussion of some options follows) on the image it contains. Not all containers have this property: a rectangular container into which, for example, we put some marbles does not imprint rectangularity on the marbles. When a space s with a set of properties P containing a set of objects O determines the members of O to have P, I say that s is a form-space for O.4 See the interpretation in Kitcher 1975. Kitcher does not base his reading on this passage but on one from B138 with similar content. However, my version differs from Kitcher’s in substantial ways that allow for a defense of Kant’s method from objections Kitcher himself raises to it. For general criticism of the adequacy of this kind of interpretation, see Friedman 1992, esp. 98–104. See §5 for a discussion of Friedman’s critique. 2 It is controversial among commentators whether Kant endorses a doctrine of immediate knowledge but there are several texts in which Kant affirms such a doctrine: in the Logic at Young, 574–575; Ak 9, 70–72; and in the section “On the principles of a transcendental deduction of the categories in general” (GW, 221; A87/B120). Hatfield also sees that Kant employs a “visual inspection model.” See Hatfield 1990, 92–93. Another commentator who sees Kant as committed to a doctrine of immediate knowledge is Shabel (2006, 105). 3 Kitcher 1975, 43. 4 This follows Kitcher’s terminology; ibid., 30. 1

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In cases where the properties are geometrical properties, I say that the form space is a geometrical form-space. The presupposition can be formulated using the notion of form-space as Thesis A: Thesis A:  Empirical space is a geometrical form-space for the objects constructed in it. The existence of this method yields more than just an explanation of the truth of first-order geometrical propositions; it also yields a corollary that geometrical propositions are both synthetic and cognized a priori. Since Kant says that a priori cognition is cognition independent of experience and is of necessary propositions (A1–4/B4–5), this explanation should account for all three of these properties. For the synthetic property the explanation is this: geometrical propositions are synthetic because their truth is to be explained by intrinsic properties of space, a constituent of the world, and not simply by appeal to the analytic rules governing construction of figures in space. But in what sense are they necessary? According to Kitcher the necessity of geometry consists not in an absolute necessity but in a conditional necessity:  in all possible worlds that humans can experience (given their actual constitution), geometrical propositions are true. This is so because human experience rests on human intuitions of objects in space: But Euclidean geometry is true in virtue of the fact that space is Euclidean. . . . Thus there are laws which describe the spatial structure of any possible world—of any world, that is, of which we can have experience.5 It is not clear to me that this is a satisfactory account of the necessity Kant attributes to geometrical propositions. As Kitcher puts it, geometrical propositions are a set of laws governing the structure of space. Laws are formulated as necessary conditionals (in some nonlogical sense of necessity); for example, “Necessarily for all x if x is a straight line, then x is the shortest distance between two points.” What does the supposed necessity of human experience to rest on intuition of spatial objects have to do with this? If it is true, it does not explain the lawlike character of geometrical propositions; if it is false, it does not show that the laws of geometry are false—if something were a straight line it could still necessarily be the shortest distance between two points even if spatiality is not a necessary condition on how humans experience the world. 5

Ibid., 29.



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Having just proposed the structure of Kant’s geometrical method, Kitcher now finds a problem with it:6 in order to avoid circularity, the method requires that we determine what the accidental properties are independently of determining what the S properties are (S properties are non-A, non-R properties). Kitcher thinks that this cannot be done; he argues that in addition to determining the R properties, we must also determine the S properties prior to determining the A properties (A properties are non-S, non-R properties). This makes any appeal to A properties in the determination of S properties viciously circular. But I  believe that Kant has another option:  treat the necessity of the non-A/ non-R properties as (what we would now call) counterfactual necessity, and provide a criterion of counterfactual necessity that is independent of S properties. If this solution is tenable, it automatically gives an account of the lawlikeness of geometrical propositions: geometrical propositions are lawlike because lawlikeness consists in necessary counterfactuality. I believe this is the option Kant actually takes.

2.2.  The Necessity of Geometry as Counterfactual Necessity I take the account of mathematical method presented in Kant’s article “Concerning the Ultimate Ground of the Differentiation of Directions in Space”7 to provide an instance of Kant’s general mathematical method, even in CPR, and to support my contention that Kant regards the lawlikeness of geometrical propositions as a form of counterfactual necessity. In this paper Kant makes his famous argument from incongruent counterparts. One object x is a counterpart of another object y if they are structurally isomorphic to one another; a pair of counterparts is incongruent if the outline of one cannot be made to perfectly coincide with the outline of the other by a continuous rotation. Kant offers a pair of hands as an illustration of incongruent counterparts. His first conclusion from the existence of the phenomenon is stated thus: Since the surface which limits the physical space of the one body cannot serve as a boundary to limit the other, no matter how that surface be twisted and turned, it follows that the difference must be one that rests on an inner ground. The inner ground cannot, however, depend on the difference of the manner in which the parts of the body are combined with each other. 6 7

Ibid., 42. Kant 1992, 361–372.

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From here Kant moves to his second conclusion: Our considerations make it plain that the determinations of space are not consequences of the positions of the parts of matter relative to each other; and then to his final conclusion: Our considerations, therefore, make it clear that differences can be found in the constitution of bodies; these differences relate to absolute and original space, for it is only in virtue of absolute and original space that the relation of physical things to each other is possible. (WM, 371; Ak 2, 283) Notice the phrase “no matter how that surface be twisted and turned” in the first of the three passages just quoted. This phrase introduces into the discussion a notion of counterfactuality, one in which the assumption involves human actions in manipulating objects, the purpose of which is to show that a certain observable result can be obtained. In this case the intended result is the rotation of one counterpart object (the outline of my left hand) into another (the outline of my right hand). Kant asserts that the intended result cannot be achieved. This conclusion is reached not simply because it has not been achieved—that would be a non sequitur—but because of the great variety of ways that he tries to achieve the result. In effect, Kant is claiming to have carried out a series of experiments under varied conditions. The varied conditions are relevant because they allow Kant to claim that the results are representative of those that would be achieved under all humanly realizable conditions. This is a necessary counterfactual arrived at by a nondeductive inference and constitutes the first step in Kant’s proof. Why must it be nondeductive? If Kant had started with the claim in the 1868 paper that space is an entity in itself with certain absolute topological properties then Kant could derive the result that he would not be able to get one hand to turn into another no matter how much he would twist and turn them deductively from this premise (given certain topological principles). That would indeed be a deductive argument for the counterfactual necessity (not one based on “experimental conditions”), but it would treat absolute space as the premise rather than the conclusion of his reasoning; yet it is the opposite that is expressed in Kant’s text. So the basis of his reasoning to the counterfactual must be nondeductive. The next step seeks a “ground” for the first step: what explains the counterfactual necessity? Kant’s answer is that it is something “internal” to the object; that is, something in its structure. The third and final step is an explanation for



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the second step: what explains this inner ground? Kant’s answer is that the structure of space itself, space as an original and absolute entity, explains this inner ground. Precisely what it is about original and absolute space that explains step two is unclear from the text, but I follow Buroker in seeing a topological argument for this based on the three-dimensionality of space as a likely candidate.8 We can apply this same method to the geometrical case as follows. We construct a triangle following the usual rules. The three-sidedness is an R property explained as an immediate consequence of following the rule for constructing triangles. It happens that the three lines have a certain length, l1, l2, and l3, and that the angles have a certain size, a1, a2, and a3. These are “accidental properties,” because if I were to try to produce a triangle with different line lengths and angle sizes, I would be able to do so. So these properties are not counterfactually necessary. But try as I might to produce a triangle with the sum of interior angles not equal to 180 degrees, I cannot succeed. From this I infer that it is counterfactually impossible to do so, thus that it is counterfactually necessary that the sum of interior angles is 180 degrees. Since this property is not an R property nor an A property, we must seek an explanation for this in the structure of the space in which the figure is constructed. The explanation is that “space is Euclidean” in a sense still to be discussed. This is the result achieved by using the method of the 1768 paper as a template for the mature doctrine of geometrical method. It accords with the intended outcome of Kitcher’s method9, without incurring the objection of circularity, and provides an account of the lawlikeness of geometrical propositions missing Because this is a very long footnote, I relegate it to Note A at the end of this chapter. Palmquist 1987 offers some criticisms of Kitcher’s account. Since these also apply to my own account, I consider them here. Palmquist quotes a passage from Bxi–xii concerning “the true method” of doing geometry: it “was not to inspect what he discerned either in the figure, or in the bare concept of it, and from this, as it were, read off its properties; but to bring out what was necessarily implied in the concepts that he himself has formed a priori, and had put into the figure in the construction by which he presented it to himself.” Commenting on this, Palmquist says: “Here the a priori process of constructing concepts and putting them into the figure is clearly distinguished from the a posteriori process of actually drawing a sample figure and reading off its properties” (17, n. 23) In reply I say, first, that Kant does call the process of drawing a figure spontaneously an “a priori construction” at A713/B741. Second, my proposal is not that we determine the geometrical properties of pure intuition simply by reading off the properties of a single figure that we construct but that we attempt to construct, under experimentally producible conditions representative (we think) of all possible conditions, a figure from which we can “read off ” properties inconsistent with Euclidean geometry. Failure to do this indicates something about the nature of space. While it can be admitted that there is an experimental dimension to this process, even that it is “empirical” in a modern sense, it is not an a posteriori method in Kant’s sense, since it relies on a priori, not a posteriori, constructions and it does not depend only on results obtained from what is true of figures, even of all figures, we happen to have encountered in experience. 8 9

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from Kitcher’s own interpretation. All things considered, this rather nice result makes it attractive to attribute the 1768 method to the mature method of CPR. So far this imputation is without direct textual support, but in the Prolegomena, part I, section 12 (Hat., 36; Ak 4, 284–285), Kant directly and explicitly connects the argument from incongruent counterparts to the mature doctrine of mathematical method. Of course the metaphysical status of space has changed from being a thing-in-itself in the 1768 article to being a form of intuition in the 1783 Prolegomena, but mutatis mutandis, if read in light of the interpretation of the 1768 method just offered, I contend that this text provides strong support for the imputation. However, there remains the question whether reading the necessity of synthetic a priori propositions as counterfactual necessity is consistent with Kant’s characterization of the nature of this necessity in central texts, like those in the Introduction to CPR. For example, at B3–4, Kant distinguishes between “strict universality” and “empirical universality”; both are kinds of universal generalization, but only strict universality is a criterion of aprioricity. With strict universality “no exception is allowed as possible.” Kant does not mean that no exception is logically possible (in that case the proposition would be analytic). So what does he mean? One possibility, consistent with what he says elsewhere in the Introduction, is that no exception is possible under all imaginable experimentally varied conditions (including imagination–experimentally varied conditions), thus yielding an equivalence between Kant’s notion of strict universality and the notion of counterfactual necessity that I am employing. Kant’s example of an empirical universality is “All bodies are heavy.” Even if this is a true generalization and even if it supports a true counterfactual generalization relative to normally occurring background circumstances, it does not follow that for every experimentally possible circumstance (including imagination–experimentally possible circumstances) if a body were placed in such circumstances, it would be heavy. For example, although not practically feasible in Kant’s day, he might have supposed it possible to manipulate bodies so that they become weightless—say, by locating them in spaces not affected by the gravitational pull of other objects. In this case, “all bodies are heavy” is not a necessarily true counterfactual generalization. To take another example not from Kant, the statement “No apple tree produces pears” may support the true counterfactual “In all normally occurring circumstances if something were an apple tree it would not produce pears,” but it does not entail that there are no experimentally possible conditions in which we can get an apple tree to produce pears. So this too is not a case of a necessarily true counterfactual generalization. If I am right about the equivalence of strict universality and counterfactual necessity, then Kant’s epistemic doctrine is that counterfactual necessity is a criterion of aprioricity.



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Many readers of Kant will doubt that the modern-day account of counterfactual necessity is strong enough to represent the necessity Kant has in mind for nonanalytic a priori propositions. I believe that these doubts are based in large part on a number of questionable assumptions about Kant’s understanding of necessity that we might formulate as follows. (1) “Counterfactual necessity has the implication of causal necessity and, for Kant, pure geometry is free of causal elements, so counterfactual necessity cannot be the kind of necessity Kant had in mind for geometry.” My reply is that the implication is false: counterfactuality does not always express a causal relation between antecedent and consequent. (2) “According to the present interpretation, the evidence to which Kant appeals for an assertion of a counterfactual geometrical necessity is an observed factual regularity obtained under a variety of experimental conditions, but Kant says that you can never get from experience to necessity.” This is not quite right. It is true that Kant says that strict universality cannot be “derived from experience” (B4) but “experience” (Erfahrung) here is used in a special Kantian sense: “Experience is, beyond all doubt, the first product to which our understanding gives rise, in working up the raw material of sensible impressions” (in the A edition formulation, A1). This is a technical, narrow conception of experience, emphasizing the constraining effects on cognitive action from what is given by external objects to the faculty of sense, not the broader nontechnical conception of experience at work, for example, in the proposition (as we might express it) that we can immediately experience the properties of images drawn in space. As long as we initiate the drawing and it is guided by rules lying within our mind, there are no constraining effects coming from sensation essential to the production of the particular figure. This broader sense of experience is the one at issue in the doctrine of geometrical method. (It is true that even the broader notion of experience does not entail necessity, but I am attributing to Kant only the position that experience of the right sort can provide evidence for attributions of counterfactual necessity.) I shall call the account of Kant’s doctrine of geometrical method just developed the Kitcher-Vinci account (“KV” for short.) The KV account has been developed in connection with a particular application: figures drawn a priori in empirical space. But Kant has said in the text on mathematical method at A713/ B741–42, that one can draw figures a priori in both empirical and pure intuition, calling pure intuition in that text an “individual object” (Object).10 When drawing a figure in pure intuition, it is the imagination that carries this activity out within the structure that constitutes the form of intuition, a kind of mental slate corresponding in the case of imagination to the container in which sensations

10

This is a point also recognized by Hatfield in Hatfield 1990, 93.

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are arrayed in the case of sensibility. This may seem to be a strange doctrine, although I note Descartes’s Rules for the Direction of the Mind as a historical precedent for a doctrine of mathematical method relying on the imagination constructing figures on some kind of spatial structure, in this case a slate provided by a part of the brain (the phantasia, or corporeal imagination).11 Strange or not, he expresses the doctrine in the central text in CPR dealing with this matter. We have already, in previous chapters, seen two other reasons why his theoretical commitments require the form of intuition to be a spatialized structure—now we have a third. The KV reading of the method can be applied, mutatis mutandis, to figures drawn in pure intuition as long as they are a priori constructions. In the special case of imagination experiments conducted on figures drawn in pure intuition, the results of these experiments are known through experience in the broad sense, from which results Kant infers a strict universality (counterfactual necessity) of S-property facts; for example, that it is counterfactually necessary that all triangles have the sum of interior angles equal to 180 degrees. This necessity itself requires explanation, a requirement that, once the analytic explanation is eliminated, leads Kant to posit the existence of a nonempirical (“pure”) form-space possessing S properties. If this application of the KV interpretation is right, then Kant accepts a distinction between two kinds of necessity: a. Logical necessity: “All triangles have three sides” is true in all logically possible worlds. b. Counterfactual necessity: For all x if x were a triangle constructed under a diverse range of experimental conditions, then x would have the sum of interior angles = 180 degrees. Both assertions are logically stronger than the corresponding empirical generalization: “For all x if x is an actually constructed triangle, then x has the sum of interior angles = 180 degrees.” But this is not sufficient to account for all of what Kant says about the necessity of geometry. In addition we need one other distinction: 2. Two kinds of Euclidean geometry a. Object geometry: This is a system of statements claiming of objects in space and time that they conform to the principles of Euclidean geometry.

11

Descartes 1984, esp. Rule 14 (AT X, 440–41; CSM I, 58).



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b. Space geometry: This is a system of statements claiming of space itself that it has Euclidean structure in a sense to be explained. These two sets of distinctions generate four applications of geometry: 3. Four applications of Euclidean geometry a. Empirical. This an application of either (a1) Euclidean object geometry or (a2) Euclidean space geometry to objects or space, respectively, in empirical intuition. b. Pure.12 This is an application of either (b1) Euclidean object geometry or (b2) Euclidean space geometry to objects or space, respectively, in pure intuition. From “It is counterfactually necessary that all objects in space (either empirical or pure) have Euclidean properties” it does not follow that “It is counterfactually necessary that space itself (either empirical or pure) is Euclidean.” (To see this, try the implication out on the example; from “for all x if x were to be a triangle constructed by someone, then x would be Euclidean (have the sum of interior angles = 180 degrees)” it does not follow that “for all x if x were a space, then x would be Euclidean.”) The reason for this is that counterfactual necessity is assessed relative to constructing figures in space (pure or empirical) as it actually is. But none of this entails that space as it actually is is necessarily Euclidean. The conclusion that should be drawn from this reading of Kant’s doctrine of geometrical method and these three sets of distinctions is that object geometry is counterfactually necessary but space geometry is not. There is, thus, a contingency at the bottom of Kant’s theory of geometry. The contingency is due to reliance of Kant’s account of space on the form of human

There is a distinction between “pure” and “applied” geometry that many commentators have found in Kant. Here are some alternative treatments of that distinction in Kant. (I am indebted in most of what follows to a recent discussion of the distinction in Hagar 2008, 80–98, esp. 85–89.) For Broad (1941) pure geometry is assumed-to-be-true geometry, applied geometry is proven-tobe-true geometry. For Carnap (1949) pure geometry is semantically uninterpreted, applied is interpreted. Carnap does not apply this distinction specifically to Kant, but there is an interpretation of Kant due to Butts that would make this way of drawing the distinction applicable to Kant (see Butts 1969). For Strawson (1966, part V) pure geometry is the geometry of “appearances” (the way things look), applied geometry is that of physical objects. For Brittan (1978, 82–83) pure geometry gives constraints on the class of “really possible” constructions, applied geometry applies to actual objects. For Friedman (1992, ch. 1) pure geometry is employed in underwriting constructive procedures, applied geometry applies to empirical objects. 12

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subjectivity, a form that is not logically inevitable for Kant.13 That is why Kant does not regard geometrical propositions as logically necessary. I do not see that this is a problem either for Kant or for my interpretation of Kant.14 Our task has been to see how Kant’s doctrine of first-order geometrical inference can explain how geometrical propositions can acquire the dual status Kant ascribes to them: (a) nonanalytic but necessary and (b) known independently 13 This contingency arises because I interpret pure intuition as a form-space that has Euclidean structure; that is, as a container that contributes Euclidean structure to the objects constructed or sensed within in it. However, there are passages in the Prolegomena, part II, 38 (Hat., 73; Ak 4, 321– 322) that seem to contradict this reading, indicating that the form of intuition is amorphous, possessing no structure that it can transmit to things occurring in it. I discuss this passage and the reading it suggests later in this chapter. On this reading, all geometrical properties that objects constructed in pure intuition possess are due to the concepts that guide the construction. On this account there is no room for contingency of the kind that arises on the KV interpretation. Thus Brittan writes:

 . . . it is not the (“topological”) conditions of space mentioned in the Aesthetic, but the determining (“metrical”) conditions which are at the core of the Analytic that support whatever case can be made for Euclidean geometry, and are the conditions in terms of which the concept of constructability is to be understood. (Brittan 1986, 66) These conditions are supplied by the understanding, not encountered in the form of intuition or empirically. This explains: why non-Euclidean figures cannot be constructed . . . [it] is . . . because there is not an appropriate metric for them . . .. And there is not an appropriate metric for them, Kant thought, because it is only on the presupposition that a Euclidean metric is supplied by us, a priori, that we can understand how it is that Euclidean geometry applies with perfect precision to the objects of our experience . . . (65) Melnick 2004, 8–9, defends a similar position to Brittan’s, as does Waxman (I discuss Waxman’s position below). Although, as I explain, this reading is not inconsistent with the attribution of the structure of a correlation inference (as in the Second Geometrical Argument) to Kant’s argument for Transcendental Idealism—my primary interest in Kant’s discussion of geometry—on balance I believe that the textual evidence indicates some contribution from the form of intuition to the geometrical properties of the objects constructed in it. 14 However, not all commentators have agreed. Thus, Van Cleve, discussing similar objections from Russell (1912) and Moore (1962), says that these objections give us a dilemma, “[the proposition] that our form of intuition is Euclidean is necessary or contingent,” both sides of which are destructive for Kant: If it is contingent, then geometrical truth depends on a contingency of human nature, and its necessity is thereby abolished. If is necessary, the question arises as to how we are to obtain knowledge of this necessity (as presumably we must, if we are to base geometrical knowledge on it.) Kant’s theory does not account for knowledge of necessary facts about our own nature. Therefore Kant must renounce either the existence of necessary truths or his explanation of how we come to know them. (Van Cleve 1999, 41) For further discussion of Van Cleve’s views, see §4 in this chapter.



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of experience. We have just seen how Kant might have established (a); I now turn to how he establishes (b). The answer I  favor is this:  “independent of experience” means “independent of sensation.” This seems to be what Kant has in mind when he explains the notion of a priori construction at A713/B741. An a priori construction is one not guided (determined) by sensation. (Tracing an outline of a figure onto a sheet of paper would be an example of a construction that is wholly guided by sensation.) And what is sensation? “The effect of an object upon the faculty of representation, as far as we are affected by it, is sensation” (A19/ B33) So a priori cognition is cognition the construction of which is not at all guided by the effects of objects on our understanding; a posteriori cognition is cognition the construction of which is at least partly on the basis of those effects. (Knowing that there is an apple on the table is a cognition at least partly guided by the sensory effects of the apple on my sense organs; hence this is a posteriori cognition.)

3.  Alternative Interpretations It might be useful to compare the present account with some others. I choose two accounts that are broadly sympathetic with the idea that Kant’s account of geometrical method is constructivist in a sense of construction that involves visualizability and is experimentalist in that it involves a range of attempts to construct possible counterexamples. The first is due to Van Cleve.15 Van Cleve gives a formal version of the argument for Transcendental Idealism, based mainly on A46/B64–A49/B66, though he also claims that it captures the argument in the passages in the Prolegomena that we have been discussing. I give a compressed version of the argument, in Van Cleve’s words, as follows: 1. The inference from “We cannot construct any cubes with more than eight corners (or any polygons that do not have at least three sides, etc.) to “There cannot be any cubes with more than eight corners” must be legitimate— otherwise, there would be no accounting for our knowledge of geometrical truths such as [the conclusion of the inference].16 2. But the inference in (1)  would not be legitimate if cubes were things in themselves. 3. Therefore, cubes are not things in themselves, but only appearances. (35)

Van Cleve 1999, 34–37. Here I compress the first three statements into a single premise. In Van Cleve’s version the first two statements are not given as premises. 15 16

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According to Van Cleve, premise (1) is true on the basis of a “transcendental argument”: “(1) if the inference . . . were not legitimate, I could not know that any cube anywhere has eight corners, but (ii) I do know this” (35) As with my own account, Van Cleve takes the impossibility of being able to carry out certain constructions to be the evidence on which an inference to the impossibility of a corresponding proposition is made. However, my own account differs from Van Cleve’s in that it takes the inference to involve an intermediate step: the postulation of a form-space with Euclidean structure. Since the immediate outcome of Kant’s argument from geometrical knowledge in the Prolegomena (part I, §§9– 10) is postulation of a pure intuition of space, I take it that my own interpretation fits the texts (those texts) better. It is because geometrical objects are in or are constructed in pure intuition that knowledge of their geometrical properties is synthetic a priori. This is the position I have been defending. However Van Cleve offers an alternative explanation. Explaining Kant’s justification for (2), he writes: The assumption that immediately suggests itself is this: cubes, and spatial figures generally, exist only in the construction of them. That is why the constraints on what we can construct are also constraints on all spatial objects: such objects exist only in being constructed. This is a plausible explanation for figures that are constructed in pure intuition—they are indeed objects that “exist only in being constructed.” But what of empirical figures? They are not objects that exist only in being constructed; part of their “existence” is given in sensibility. Van Cleve takes account of empirical figures in his proposal by noting a qualification:  . . . a cube need not be constructed (exhibited in pure intuition) in order to exist; it can also exist in virtue of being perceived (exhibited in empirical intuition). This qualification does not affect the argument from geometry, since in Kant’s view empirical intuition and pure intuition are governed by the same constraints.17 Indeed they are (governed by the same constraints), but why are they? Van Cleve presents this as a brute fact for Kant; it has nothing to do with the argument. On my own view, on the contrary, it is precisely this coincidence of structures that provides the explanatory problem to which the solution is that the objects of empirical intuition must exist in the same (numerically the same) form-space as that in which pure objects are constructed. This coincidence provides the 17

Both passages are from Van Cleve 1999, 36.



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explanandum for the Second Geometrical Argument for Transcendental Idealism. Van Cleve’s analysis thus misses the nerve of Kant’s argument. The second account I consider is due to Dryer.18 As my account does, Dryer sees the basic evidence for geometrical conclusions in Kant’s doctrine of method to lie in experimenting with various constructions carried out by the imagination: Being conscious of how one must imaginatively construct an equilateral triangle does not consist merely in thinking that one cannot represent an equilateral triangle without representing it as equiangular. One is conscious of the necessary procedure of imagination in representing an equilateral triangle only by using ones imagination to exhibit an immediate representation and finding from it that an equilateral triangle can only be represented as equiangular. (280) But how do we find this impossibility? My answer is that we find it experimentally: we try constructing the figure in a full range of possible conditions, conclude that these conditions are representative of all conditions we could produce, and draw a counterfactually necessary conclusion. Dryer offers a different answer:  . . . nothing can arise to refute the conclusion that a cube must have twelve edges, for if one tries to represent a cube differently one is conscious that one cannot. To be conscious of the necessary procedure of imagination in representing a spatial configuration, one does not need to wait on what the senses present and one need not fear refutation by them. One becomes conscious of the procedure by pure intuition. (282; my emphasis) Pure intuition here is not understood, as I do, as a kind of mental form-space but in a more traditional (Cartesian) way as a special kind of awareness of necessary truths. It is because of this special awareness of the impossibility of being able to construct certain figures that we “need not fear refutation.” This account explains why we need not have this fear in what may seem to be a satisfyingly certain manner. But this is pure Cartesian intuition, the light of the mind directed to necessary truths, not pure Kantian intuition. Also unlike my account, Dryer’s does not see a fundamental difference between drawing a figure in thought (in mental space) and drawing it on paper, since in both cases the lines we draw have width and color. They are both 18

Dryer 1966, 268–282.

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empirical intuitions, “whether one draws a figure of it on paper or furnishes oneself a mental picture of it” (273). Pure intuition enters the account in some way other than as the space in which mental lines are drawn. In one way it enters as the practice of abstracting from accidental features of empirical lines like width and color. In another “a configuration can be represented in pure intuition without drawing a figure of it on paper or even forming a mental picture of it” (273). I take the Cartesian-like intuition of the previous passage to be this second kind of pure intuition. The first kind involves something we might call “abstracting intuition” applied to both kinds of figures. In support of this Dryer quotes from the doctrine of mathematical method (B741): “For the construction of a concept . . . we need a non-empirical intuition,” adding that what makes the construction pure is that “in what we have drawn or pictured we attend to the relations among positions apart from any empirical features” (273–274). Unhelpfully, he does not tell the reader about Kant’s next sentence, by now very familiar to us:  “Thus I  construct a triangle by exhibiting an object corresponding to this concept, either through mere imagination, in pure intuition, or on paper, in empirical intuition, but in both cases completely a priori . . .” (GW, 630; A713/B741). Kant is saying that what makes a construction pure is that the space in which it produces its figure is a pure space, not that the process involves abstraction from accidental properties of the figures. The latter point is made in the next sentence and applies to all figures, those constructed in pure intuition and in empirical intuition alike. Dryer’s interpretation of what pure intuition means simply does not fit these texts. Since these are the most central texts dealing with this subject in all of Kant’s writings, we must conclude that Dryer’s account of Kant’s doctrine of geometrical method is also not satisfactory. I now turn to objections from interpreters not broadly sympathetic to the approach I take here: Friedman and Waxman.

4. Objections 4.1.  Objections from Friedman Friedman19 considers a class of interpretations of Kant’s doctrine of mathematical method similar to the KV interpretation and rejects them on two grounds: (a) “ . . . it is not pure intuition, but only empirical intuition that is capable of providing a model for the truths of mathematics” (101).20 Friedman 1992. If there are objects in pure intuition that serve as a model for geometry, these objects will be constructed by the imagination following rules defining various geometrical figures. Because 19 20



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and (b) “The problem is then to see how pure intuition can select one . . . possibility from the class of all logically possible axiomatizations, and this, I think, is quite impossible” (103). Reply to (a). Friedman cites two texts in support of this contention, one from the chapter on Phenomena and Noumena (GW, 340–341; A239/B298–299), one from the Postulates of Empirical Thought (GW, 324–325; A224/B271). Since the second one is easier to handle, I begin with it. It may look, to be sure, as if the possibility of a triangle could be cognized from its concept in itself . . . for in fact we can give it an object [Gegenstand] entirely a priori, i.e., construct it. But since this is only the form of an object it would still always remain the product of the imagination, the possibility of whose object would still remain doubtful, as requiring something more, namely that such a figure [Figur] be thought solely under those conditions on which all objects of experience rest. Now that space is a formal a priori condition of outer experiences, that this very same formative synthesis by means of which we construct a figure in imagination is entirely identical with that which we exercise in the apprehension of an appearance in order to make a concept of the experience of it—it is this alone that connects with this concept the representation of the possibility of such a thing. (GW 324–325; A224/ B271; my emphasis) Kant here asserts that we can give an object to our concept of triangularity entirely a priori. He calls these objects figures, and figures are geometrical objects. So the class of figures serves as a domain of objects modeling geometry. Figures are pure objects, corresponding to pure sensible concepts (see Schematism: GW, 273; A141/B180). They are pure objects because they are not given in sensibility, the way in which ordinary empirical objects are perceived. If this reading of the passage is right, then Kant’s concern is not to deny that figures in pure intuition instantiate geometry; quite the reverse—he says Friedman rejects interpreting Kant in this way, he rejects this account of the role of construction in Kant’s doctrine of mathematical method. This is not to say that Friedman rejects altogether a role for construction in Kant’s mathematical method; on the contrary, he sees Kant using this device to provide a critical element in his account of concepts of infinity corresponding to elements available in modern quantification theory but not available to Kant in his day (see Friedman 1985).

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that they do—but rather it is to prove the possibility of an empirical object corresponding to a given figure, thus removing this possibility from the doubtful status it has absent such a proof. The proof is given in the last part of the passage and depends on his claim that the same “formative synthesis” we use to create spatial figures in imagination is also at work in the “apprehension of an appearance in order to make a concept of the experience of it.” I  take the experience in this case to be sense experience that is given to us; that is, that contains sensory data which we interpret and classify. This process is not described in detail here, but however it goes, Kant says that we employ the same procedures to determine and classify the given sensory data we use productively in the generation of figures. Perhaps the idea is that when we encounter an array of given sensory data, we try to draw a line around it, as it were, employing the various rules (“formative synthesis”) available to us for drawing figures, noting which rule achieves the result successfully. The doctrine of the Schematism chapter is that such rules correspond to pure sensible concepts (GW, 273; A140/B180). For example, if the rule we successfully use to outline a certain array of sensible data is the pure concept of a triangle, we judge that the appearance presented to us is a triangle. This is what the “apprehension of an appearance” in the passage above amounts to. I discuss this account more fully later,21 but even from this brief discussion I think we can see two crucial points emerge for Kant. The first is that pure figures of the imagination do indeed serve as a model for geometry, contrary to Friedman’s contention; and second, that there is a requirement that sensory content given in perception have its own spatial array prior to the operations of synthesis. This latter point is of critical importance to achieving a correct understanding of Kant’s objectives and argument in the Deduction. I now turn to the other passage (from the chapter on Phenomena and Noumena): Now the object cannot be given to a concept otherwise than in intuition, and, even if a pure intuition is possible a priori prior to the object, then even this can acquire its object, thus its objective validity, only through empirical intuition, of which it is the mere form. Thus all concepts and with them all principles, however a priori they may be, are nevertheless related to empirical intuitions, i.e. to data for possible experience. Without this they have no objective validity at all, but are rather a mere play, whether it be with the representations of the imagination or the understanding. One only need to take as an example the concepts of

21

See Ch. 6, §3.3.



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mathematics, and, first indeed, in their pure intuitions. Space has three dimensions, between two points there can only be one straight line, etc. Although all these principles, and the representation with which this science occupies itself, are generated in the mind completely a priori, they would not signify anything at all if we could not always exhibit their significance in appearances (empirical objects). (GW, 340–341; A239/B298–299) In this passage Kant says two main things: (1) he seems to allow that the mind can “generate” representations “in the mind” on the basis of the principles of geometry in pure intuition; but (2) these things would be “a mere play,” would lack “significance” or “objective validity” unless the principles could also be exhibited in the domain of empirical objects. In this passage Kant seems to allow that there are nonempirical representations, the “figures” of pure intuition of the previous passage. However, Kant later adds: “Mathematics fulfills this requirement [of making an abstract concept sensible] by means of the construction of the figure, which is an appearance present to the senses (even though brought about a priori) (GW, 341; A240/B299; my interpolation). In this sentence Kant alludes to “the figure” (Figur), as he did in the passage from the Postulates of Empirical Thought considered previously, but here the figure is “present to the senses.” What does this mean? It could mean (i) that no construction in mathematics takes place in pure intuition absent sensory stimulation from external sources or (ii) that figures constructed by the imagination, whether in pure intuition or in empirical intuition, are sensuous representations. Kant’s overall intentions in this text are unclear. However, in another familiar passage dealing with mathematics Kant’s intentions are clear—he mentions constructing figures in both kinds of intuition, empirical and pure: “Thus I construct a triangle by representing the object which corresponds to this concept either by imagination alone, in pure intuition, or in accordance therewith also on paper, in empirical intuition—in both cases completely a priori” (A713/ B741). This latter passage comes from the official account of Mathematical Method and would presumably reflect Kant’s most careful and precise formulation of the relevant doctrine. I thus propose to resolve the tension between the two passages in favor of the second interpretation. Since the passage from the Postulates of Empirical Thought also embodies this reading, I conclude that it represents Kant’s considered view.

4.2.  Objections from Waxman A central contention of the KV interpretation of Kant’s doctrine of mathematical method is that the form of intuition is a geometrical form-space, a space that has

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geometrical structure and imparts that structure to the objects occurring in it. Waxman objects to such a reading as follows: The apodeicity of geometrical propositions, whether axioms or theorems presupposing a particular geometrical space . . . has nothing to do with the properties intrinsic to metaphysical space. On the contrary, the necessity of these propositions depends first and foremost on discursive understanding operating conformably to the categories.22 Since the contention that pure intuition is a geometrical form-space is an integral part of my reconstruction of the proof of the objective reality of geometry, it will be necessary to deal carefully with Waxman’s objection. It is based on two texts, the first from the Prolegomena, part II, 38: Now I  ask:  do these laws of nature lie in space, and does the understanding learn them in that it merely seeks to investigate the wealth of meaning that lies in space or do they lie in the understanding and in the way in which it determines space in accord with the conditions of the synthetic unity . . . Space is something so uniform, and so indeterminate with respect to all specific properties, that certainly no one will look for a stock of natural laws within it. By contrast, that which determines space into the figure of a circle, a cone, or a sphere is the understanding, insofar as it contains the basics for the unity of the construction of these concepts. The bare universal form of intuition called space is therefore certainly the substratum of all intuitions determinable upon particular objects, and, admittedly, the condition for the possibility and variety of those intuitions lies in this space; but the unity of the objects is determined solely through the understanding . . . the understanding is the origin of the universal order of nature . . . (Hat., 73; Ak 4, 321–322), The second is from a letter to Kästner: Metaphysics must show how one can have the representation of space, but geometry teaches us how to describe space, i.e., exhibit it (not by drawing it) in representation a priori. In the former space is considered as given, prior to receiving any determination conformable to a definite concept; in the latter it is constructed . . .23

22 23

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On Waxman’s reading of the account that Kant offers in the Prolegomena passage, objects are such that the understanding makes them be in accord with Euclidean principles rather than are such that their Euclidean properties are due to the Euclidean form of the structure in which these objects are given. This is a prescriptivist reading rather than a form-space reading of the way in which subjective sources contribute geometrical structure to objects constructed in pure intuition. Now, it is true that a prescriptivist reading would also explain the necessary coincidence of the satisfaction of Euclidean properties by both pure and empirical objects. It also would also lead to a form of idealism: empirical objects are made by the understanding to obey the laws they in fact obey (Nomic Prescriptivism). However, there is a difficulty with this reading in regard to the structure of the argument it attributes to Kant. For as reported in the introductory chapter, Kant regards it as a presupposition of Nomic Prescriptivism that the things to which the laws apply are appearances: the understanding cannot prescribe laws or anything else to things as they are in themselves. So the doctrine that empirical objects are appearances must be established first, as indeed it has been in part I of the Prolegomena. This means that the prescriptivist explanation cannot be operating in part I. The only remaining option for Kant is that pure intuition is a form-space for both pure and empirical objects, as it is in the KV interpretation. But what then are we to make of the passages from Prolegomena, part II, 38, and the letter to Kästner which both appear so unequivocal in their denial of this? Surely Kant cannot have it both ways? I offer three resolutions of the conundrum, in decreasing order of conservatism with respect to the original KV interpretation. (1) Pure intuition is not an object that has Euclidean properties by itself—it is thus geometrically amorphous in its actual structure—but has a structure with the potential for contributing Euclidean structure to objects that are constructed within it. In this sense it remains a geometrical form-space, as in the original KV interpretation. (2) Pure intuition remains a geometrical form- space in the sense of (1); the claim that the pure intuition of space is amorphous is not understood as the lack of actual Euclidean structure, as in (1), but as the claim that the pure form of intuition is indeterminate with respect to unified geometrical intuitions. (3) Space is not a geometrical form-space, as in the original KV interpretation, but is a topological form-space, imparting its topological structure, including specifically three-dimensionality, to the objects that are constructed in it. If any of these interpretations correctly capture Kant’s intentions, they allow versions of the Second Geometrical Argument for Transcendental Idealism (discussed in §5) to go through, altered where necessary to reflect modifications to the original KV interpretation as indicated. Any version of the proof altered in these ways preserves the idea that pure intuition is a form-space, thus a container

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of some kind. Any version of the proof altered in these ways has the structure of a correlation-explanation argument, thus preserving one part of the analogy between the Deduction and the Transcendental Exposition that holds for the original version of this proof. Any version of the proof altered in these ways allows for an analogous version of the Argument for Transcendental Idealism to be derived from it, thus preserving the second part of the analogy between the Deduction and the Transcendental Exposition. I now undertake a more detailed discussion of these alternatives. Re (1). In the letter to Kästner, Kant distinguishes what is required for describing a figure from what is required for drawing it. If we draw a straight line it will be the shortest distance between the points terminating the line. To describe this line as the “shortest,” we need to subsume it under the category of quantity: something that requires the use of the understanding, not pure intuition. Still, something must explain why a straight line necessarily has this property. This is a synthetic proposition, and Kant’s doctrine is that pure intuition is needed to explain the truth of synthetic necessary propositions. Even if we say that there are no line segments in pure intuition, thus no actual Euclidean structure in pure intuition, something in that structure has the potential for making straight lines drawn in it also satisfy the procedures we use to determine shortest distance between two points. The following passage from the Postulates of Empirical Thought supports reading Kant in this way: “ . . . in the concept of a figure that is enclosed between two straight lines there is no contradiction . . . ; rather the impossibility rests not on the concept itself but on its construction in space, i.e., on the conditions of space and its determinations; . . . (GW, 323; A221–222/B268). Mention of the contribution of “the conditions of space” to the impossibility of constructing the figure in question is sufficient for us to call pure intuition a geometrical form-space, even if we can also say, in terms of actual geometrical structure, that it is amorphous Re 2. The conundrum posed by the texts from the Prolegomena and the letter to Kästner is part of the larger puzzle of the relationship in Kant involving intuition, sensibility, and the understanding. Kant does not deny that intuition has a contribution to make to what is given in sensibility and that sensibility has a form, but he also affirms that the unity of intuition is due to the understanding, not sensibility. (This doctrine is asserted explicitly in §15 of the B edition Deduction; GW, 245–246; B129–131.) In the troublesome passages from section 38 of the Prolegomena, it is “unity of the construction” of geometrical figures that is due to the understanding, the “unity of the objects [that] is determined solely through the understanding.” I will argue24 that unified intuitions

24

See Ch. 6, §2.



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are implicit judgments and that this is a key premise in Kant’s development of the argument of the Transcendental Deduction of the Categories. When in the Deduction Kant talks about topologically unified space, assigning it a key role to play in the argument of the B edition Deduction in section 26, Kant is speaking of it in the mode of a unified intuition; that is, as an implicit judgment about the topology of space. In the letter to Kästner, geometry is the means by which we “describe a space” and in so doing we presuppose that space is a single, unified entity. Here again judgment is in the foreground, and the space in question is the formal and unified intuition of space, not space as the form of intuition that is at issue. When Kant says in the Prolegomena passage that it is the understanding that “determines space into the figure of a circle,” he is talking about the circle “insofar as it contains the basics for the unity of the construction of these concepts”; that is, insofar as the intuition of the circle is considered an implicit judgment to the effect that it is a circle. When Kant says that space does not contain a stock of natural laws within it, he means that the form of intuition is not composed of principles lying ready made to be discovered by investigation: principles are necessary judgments and judgments are made, not found. This is not to say, however, that space is not a geometrical form-space in the sense of (1). Re (3). Kant says clearly and unequivocally in the passage from the Prolegomena that “[t]‌he bare universal form of intuition called space is therefore certainly the substratum of all intuitions determinable upon particular objects, and, admittedly, the condition for the possibility and variety of those intuitions lies in this space . . .” Perhaps space is nothing more than this and so does not contribute to the geometrical properties of objects constructed in it. Still, it does contribute something: “the condition for the possibility and variety of those intuitions.” What else but an entity with dimensionality could do that, and what else but an entity with at least three dimensions could accommodate the range of objects of possible sensations that humans are capable of receiving? Such an entity is space in three dimensions, and by saying that it is a condition for the ordering of sensory givens, Kant is saying that it imparts its dimensionality to the things that are contained in it. This makes space a topological form-space but not a geometrical form space. In Kant’s 1768 paper it is the topological property of incongruence in objects that derives from the topological property of the three-dimensionality of space. Meerbote25 and Brittan have defended interpretations of Kant’s doctrine of space that bifurcates spatial properties between the metrically determinate and the nonmetrically determinate, assigning the former to the synthetic activities of the understanding. So it might be true that pure intuition is actually three

25

Meerbote 1981; Brittan 1978. See Ch. 6, §3.3, for discussion and specific references.

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dimensional or at least somehow contains three dimensions potentially, even if it is entirely metrically (and geometrically) amorphous. There is, finally, an extreme reading of these passages on which pure intuition lacks any inherent spatial characteristics at all, including dimensionality. This is Waxman’s position26 and, if correct, refutes a key element of my interpretation of Kant’s theory of geometry. However, if we do allow this reading, we either have to demolish Kant’s doctrine of the independent contribution that intuition and, especially, the forms of intuition make to knowledge or indict Kant for an inconsistency, repeated through both editions of CPR and in the Prolegomena, at the heart of his general philosophy of space and time. But if we disallow it and accept the original KV interpretation or one of the three conservative modifications, then we maximize the coherence of the different things Kant says about space and geometry in part I versus part II of the Prolegomena and in the Aesthetic versus the Analytic in CPR. We also make it possible to explain Kant’s view about the formation of our concept of the three dimensionality of space and, thus, about the conditions that make it possible for us to understand and represent an objective world outside ourselves. For the extreme view, the exegetical costs are great, the benefits small; it should be rejected. My interest in Kant’s general doctrine of space and mathematical method is as a background to the metaphysical conclusion that Kant draws from these doctrines. With that background now in place, it is time to turn to see how these conclusions are drawn. The name that Kant gives to this argument overall in the B edition Aesthetic is “the transcendental exposition of the concept of space” (GW, 176; B40). I shall use this term to describe the version of Kant’s argument developed in the next section, although the textual basis for that argument is in part I of the Prolegomena, not the text with that title in the Aesthetic.

5.  The Transcendental Exposition of the Concept of Space We have already seen (Ch. 2) how Kant argues for a version of Transcendental Idealism in section 9 of the Prolegomena. This we called the First Geometrical Argument. This argument does not directly invoke the notion of a pure representation of space but, rather, the notion of a pure form of empirical representations, a form that is spatial in the sense that it induces spatial (Euclidean) properties in the objects in which it occurs. It is possible that the form of intuition is itself 26

Ibid., 89.



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a representation of a space, pure or otherwise, but that is not part of the First Argument. Kant believes that there is a pure representation of space because he believes that there is a pure intuition of space, something that he argues for in sections 10 and 12. The argument in section 12 is perhaps the clearest: That full-standing space (a space that is itself not the boundary of another space) has three dimensions, and that space in general cannot have more, is built upon the proposition that not more than three lines can cut each other at right angles at any one point; the proposition can, however, by no means be proven from concepts, but rests on immediate intuition, and indeed on pure a priori intuition, because it is apodictically certain. (Hat., 36; Ak 4, 284–285) I take Kant to be arguing that the certainty that attaches to geometrical propositions requires the immediate presence to mind of objects that are characteristic of intuition; moreover, that the intuition is a pure intuition. This latter addition indicates that Kant is talking here about a domain of pure objects, hence about pure mathematics. There is nothing here about empirical objects, about whether empirical objects satisfy the principles of geometry, about how this is possible or how we know this. These are the topics of the First Geometrical Argument. There is also not much here about the method geometers practicing pure geometry use, except to say that it requires construction and immediate intuition. However, even these few remarks fit the KV account of Kant’s geometrical method I have developed, and I assume it is that method that is operating in pure mathematics as understood in this and the other sections of the Prolegomena mentioning pure mathematics. We have not yet seen how pure mathematics fits into the overall argument of part I. Kant seems to tell us in section 11: The problem of the present section [i.e., part I of the Prolegomena] is therefore solved. Pure mathematics, as synthetic cognition a priori, is possible only because it refers to no other objects than the mere objects of the senses, the empirical intuition of which is based on a pure and indeed a priori intuition (of space and time), and can so be based because this pure intuition is nothing but the mere form of sensibility, which precedes the actual appearance of objects, since it in fact makes the first appearance possible. (Hat., 35; Ak 4, 283–284) However, here Kant represents the problem of the possibility of pure mathematics as in fact being solved in part by reference to the First Geometrical Argument: that the form of our representations of empirical objects is Euclidean

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and the structural properties of the objects of those representations ontologically depend on the properties of the representations. But there is something added here: it is that the pure intuition required by pure mathematics is somehow identified with the form of sensibility:  that is how “the problem of the present section is therefore solved.” This is a paradoxical comment if we think that the problem of the present section is the one Kant gives at the outset of the entire part I argument: How is it possible that the propositions of pure mathematics are expressed in true a priori synthetic propositions? The answer to that question comes from the application of mathematical method to pure intuition, as outlined in the KV interpretation of that method. However, there is another problem for pure mathematics that does bring empirical considerations into the mix. This is first stated clearly in note I: Pure mathematics, and especially pure geometry, can have objective reality only under the single condition that it refers merely to objects of the senses, with regard to which objects, however, the principle remains fixed, that our sensory representation is by no means a representation of things in themselves, but only of the way they appear to us. From this is follows, not that all the propositions of geometry are determinations of a mere figment of our poetic phantasy, and therefore could not with certainty be referred to actual objects, but rather, that they are necessarily valid for space and consequently for everything that may be found in space, because space is nothing other than the form of all outer appearances . . . (Hat., 38; Ak 4, 287) The problem raised in this passage seems to be that assuming that geometry has objective reality, in order for this to be the case, empirical objects must have their spatial properties determined by the power of our subjective capacity for receptivity and image construction. This formulation of the problem seems to assume the truth, perhaps the necessary truth, of applied geometry. Again, this is not what Kant has assumed at the outset of part I; he has assumed the apodictic certainty (and necessary truth) of pure geometry. So again Kant has slipped up in his argument. However, later on in this same note Kant uses the phrase “space of the geometer” to refer to the phantasy (imagination) space referred to above. This is a reference, again, to pure intuition and to the pure geometry that the geometer practices. But in this place Kant seems to correct himself: [1]‌The space of the geometer would be taken for mere fabrication and would be credited with no objective validity, because [2] it is simply not to be seen how things would have to agree necessarily with the image that we form of them by ourselves and in advance. If, however, [3a] this image—or better, this formal intuition—is the essential property



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of our sensibility by means of which alone objects are given to us, and if [3b] this sensibility represents not things in themselves but only their appearances, then [4] it is very easy to comprehend, and at the same time to prove incontrovertibly:  that all outer objects of our sensible world must necessarily agree, in complete exactitude, with the propositions of geometry . . . (Hat., 39; Ak 4, 287; my numbering and emphases) In statement [4]‌Kant speaks both of proving and of explaining. Take the proof aspect first. What is being proven is an agreement between the thought world of pure mathematics and the world of empirical objects. It may seem that Kant is engaged here on a project similar to that of a rationalist philosopher like Descartes who, starting with innate geometrical ideas, seeks to discover whether there is a material world that “agrees with” those ideas. It appears from the previous passage quoted (from the beginning of note 1) that the “objective reality” (also called here the “objective validity”) of pure geometry consists in this agreement. So another way of putting Kant’s apparent project is to say that he seeks to prove the objective reality/validity of the concepts of pure geometry. In section 11, Kant speaks of “a transcendental deduction of the concepts of space and time,” which is to explain “the possibility of pure mathematics.” In light of the proving aspect of claim [4]‌here, this might be understood as the task of proving the agreement between the thought world of pure geometry and the empirical world, starting with only the certainty of the geometry of the thought world. The objective reality/validity of the concepts of space and time would then consist in this agreement. Because of the obvious parallel here (echoed in §13 of CPR [GW, 221; A87/B119]) between the phrase “transcendental deduction of the concepts of space and time” and “transcendental deduction of the categories,” it would be natural to think that when Kant characterizes the purpose of the latter as proving the objective validity of the categories, he is seeking to prove the agreement between the thought world of categories and the empirical world, starting with only the certainty of the thought world. There is much evidence in support of this reading, and many think that this is the correct reading, but it is a leading feature of my interpretation of the Transcendental Deduction of the Categories that this a serious misunderstanding of the purpose of that deduction. It is also a leading feature of my interpretation of the Transcendental Exposition of the Concepts of Space (and time) that the corresponding claim is a serious misunderstanding of the purpose of Kant’s argument here (in note 1). I say this in part because of texts in CPR27 that indicate Kant is not seized with the Cartesian project of arguing to the existence of a material world from E.g., the A edition Paralogism 4 (GW 425ff.; A367ff.) and its counterpart in the B edition: the Refutation of Idealism in the Postulates of Empirical Thought (GW 327–329; B275–278). 27

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the antecedently given certainty of a mental world, but also in part because the argument that he would be giving for the objective reality of pure geometry would be viciously circular if it depended on the First Geometrical Argument. It is true that this argument entails that the Euclidean form of sensibility must also be found in empirical objects, since the conclusion of that argument is that the properties of the latter depend on those of the former. When we add the additional point made in section 11, that the form of sensibility is the pure intuition needed for pure mathematics, it follows that the principles of pure geometry will also be the principles of empirical geometry. But as has been shown in our discussion of the First Geometrical Argument, that argument assumes the truth and necessity of empirical geometry. To now expect the First Geometrical Proof to do double duty as a proof of the objective reality of pure geometry, as well as a proof of Transcendental Idealism, would be viciously circular. We get a more charitable and, I think, more accurate picture of Kant’s reasoning if we concentrate on the other aspect of claim [4]‌, the explanation aspect. Here Kant is saying that we can explain why there is necessary and exact agreement between the domain of pure geometry and that of empirical geometry. Now this statement says that there are these two domains of Euclidean geometry: the pure domain and the applied domain. It must be, therefore, that the Euclidean characteristics of each domain have been antecedently established by Kantian geometrical method. Since both have Euclidean characteristics, it is true that the geometrical characteristics of pure geometry are reflected in the objects of applied geometry; that is, in empirical objects. But to say this is just to say that pure geometry has objective validity (sometimes, objective reality) in Kant’s sense. Notice that this property is not established for Kant by a Cartesian strategy of reasoning that applies mathematical method in an epistemologically asymmetrical way between the thought world and the empirical world but by a symmetrical application of that method.28 This point is not appreciated by other commentators. Strawson may be taken as representative. He accepts that Kant assigns a role to the construction of figures in pure intuition and that this warrants assigning geometrical properties to such figures in a “phenomenal geometry” (Strawson 1966, 282). But Kant made “a fundamental error.” 28

[It] lay in not distinguishing between Euclidean geometry in its phenomenal interpretation and Euclidean geometry in its physical interpretation . . . Because he did not make this distinction, he supposed that the necessity which truly belonged to Euclidean geometry in its phenomenal interpretation also belongs to it in its physical interpretation. He thought that the geometry of physical space had to be identical with the geometry of phenomenal space. (285) Strawson depicts Kant as just somehow, without argument, assuming that the structure of physical space “had” to be identical with that of pure intuition. But he did not assume this, he demonstrated it, if I am right, on the basis of an argument resting on a correlation between the structures of two spaces independently established by mathematical method.



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It is this very symmetry that creates something needing explanation: Why should two distinct domains of objects have just the same geometrical structure when each has been shown by independent means to have that structure? The explanation is that the geometry of the pure domain determines the geometry of the empirical domain and does so because the form of the objects of the empirical domain is identical with the form of the objects of the pure domain. Since the latter is a domain of thought objects structured by the form of imagination, empirical objects also turn out to be thought objects, contrary to our initial beliefs. And that is also a form of Transcendental Idealism. Why is this the only explanation? The answer is, because otherwise “it is simply not to be seen how things would have to agree necessarily with the image that we form of them ourselves and in advance” [2]. The image that we form of them in advance is the construction of figures in pure intuition that proofs in pure geometry depend on. We can summarize the difference in structure between the First Geometrical Argument and the Second Geometrical Argument by saying that whereas both arguments prove an idealist conclusion by explaining a strict correlation between the geometrical properties of two domains of objects, the second argument proves each side of the correlation independently, but the first argument proves only one side of the correlation independently. It is this difference that ultimately explains why the first argument is regressive and the second progressive in Kant’s sense. Moreover, it is only when we arrive at each side of the correlation independently that we are then surprised at the correlation and feel the need to explain it. The surprise in question is the sort we express when we say of something “it’s too much of a coincidence,” meaning that it is vastly improbable that the co-occurrence of the events happened by chance. Taking this stance towards two events requires that we know that each has occurred on the basis of independent evidence. That, I have argued, is the stance that Kant is asking his readers to take in his Second Geometrical Argument, but not the first, in part I of the Prolegomena. This account fits well with the original KV interpretation of Kant’s doctrine of geometrical method (A713/B742ff.). What we find there is a surprisingly even-handed approach to a priori proofs in geometry according to which the same method can be separately applied to pure intuition and to empirical space, showing how the geometrical properties of each can be epistemically determined from the nonaccidental, nonanalytic properties of figures constructed in them. Neither application by itself establishes even a factual coincidence between the structure of pure intuition and empirical intuition, but both methods taken together establish a necessary coincidence. Every triangle I draw on paper has the same nonanalytic, nonaccidental properties possessed by every triangle I draw in imagination space. (So Kant maintained. See §6 for a discussion of this claim in light of developments in modern physical

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geometry.) In fact, this holds of all triangles, no matter what kind of triangle I draw, wherever and whenever I draw it, on paper or in imagination. From this universality and diversity of experimentally induced experience, we can infer the counterfactual necessity of the coincidence of pure and empirical geometry. Assuming the success of my argument in Section 2.2 of this chapter (that counterfactual necessity is all that Kant needs or wants for the kind of necessity that characterizes a priori cognition), then we have proved the a priori coincidence of pure geometry with the objects in the physical world of sense; that is, we have proved the objective reality of geometry. This proof can be formally represented as follows:

5.1.  The Proof of the Objective Reality of Pure Geometry (1) The set of nonaccidental, nonanalytic spatial properties of empirical objects satisfies Euclidean geometry. (2) The set of nonaccidental, nonanalytic spatial properties of figures drawn in pure intuition satisfies Euclidean geometry. (3) Necessarily objects in empirical space have Euclidean properties. (4) Necessarily figures in the space of pure intuition have Euclidean properties. Therefore, (5) there is a rigorous and necessary coincidence between the geometry of objects in empirical space and the geometry of figures in the space of pure intuition. Therefore, (6) pure geometry possesses objective reality. Both (1) and (2) are substantive results of applications of Kantian mathematical method, and in the nonanalytic sense of necessity Kant has in mind for geometrical propositions, (3) and (4) follow from (1) and (2), respectively, as a result of the assumption that empirical space and pure intuition are form spaces for the objects they contain. Line (5) is an obvious consequence of (3) and (4), and (6) follows by definition from (5); QED. Because Kantian mathematical method is a progressive method of (nontranscendental) reasoning, the present argument should also be treated as progressive; it begins with something that is not knowledge (pure intuition or empirical intuition) and ends with something that is knowledge: proposition (6). This gives the first part of the definition of a Transcendental Exposition at B40.



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A regressive argument derives Transcendental Idealism from (5). Formally stated, it looks like this:

5.2.  The Second Geometrical Argument for Transcendental Idealism (7) Assume the truth of (5). (8) Proposition (5)  would not be true unless pure intuition is the space in which empirical objects are situated. Therefore, (9) pure intuition is the space in which empirical objects are situated. Therefore, (10)  empirical objects are appearances, aspects of our subjective constitution. Therefore, (11)  Transcendental Idealism is true. Line (9) logically follows from (7) and (8), and (10) follows from (9) and the fact that pure intuition is part of our subjective constitution. Because one of the main premises of this argument depends on something assumed as knowledge (line 5 from the previous argument), the demonstration of which occurred in a progressive argument, these two arguments should be characterized as progressive overall. This gives the second part of the definition of a Transcendental Exposition at B40. The key premise is (8). The argument for Transcendental Idealism is intelligible if but only if the form of sensibility is a container that imposes its form on the things that are located in it—a form-space, as I have been calling it. To explain the aprioricity of geometry, the form-space must be a geometrical form-space, as is made clear in note 1.  Speaking of certain benighted philosopher/mathematicians, Kant says: “They did not realize that this space in thought makes possible the physical space . . .” And how does it do so? Because “appearances must of necessity and with the greatest precision harmonize with the propositions of the geometer, which he extracts not from any fabricated concept but from the subjective foundation of all outer appearances, namely, sensibility itself ” (Hat., 39; Ak 4, 288). The dependence of physical space on thought space would not be intelligible if the form of sensibility were simply a form dependent on sensations—an

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“order of intuited matters,” as Falkenstein would have it—and the “extraction” of the propositions of geometry from the form of sensibility would not be intelligible if the structure of the form-space were something imposed by the application of these same propositions on an initially geometrically amorphous space. In concluding this section, let me say that Kant’s arguments are not above criticism. Even if we grant the main conclusion, that pure and applied geometry can be shown by independent application of mathematical method to satisfy the same geometry, it does not follow that we must explain the form of the empirical space in terms of the pure space rather than the other way around. My objective is not, however, to defend or attack the cogency of Kant’s position on either of these two arguments but to lay out their structure and to propose the following thesis: The Argument for the Objective Reality of Geometry is the first (and progressive) part of the Transcendental Exposition of the Concept of Space, and The Second Geometrical Argument for Transcendental Idealism is the second (and regressive) part of The Transcendental Exposition of the Concept of Space. The primary thesis of this book is that the argument structure of the Transcendental Exposition of the Concept of Space thus understood provides Kant with an analogy for the argument structure of the Transcendental Deduction of the Categories.

6.  Kant and Modern Physics How are we to evaluate Kant’s account of geometry in light of developments in modern science in which non-Euclidean geometries have been devised and one empirically confirmed? Hagar puts the issue in the form of two questions: (1) Are there any contradictions between the scientific developments of our era and Kant’s philosophy? (2) What is left from the Kantian legacy in light of our modern conceptions of logic, geometry and physics?29 Although I cannot give detailed consideration to these issues here,30 I would like to say something in general about the first question understood in relation to Kant’s claim that space is Euclidean. One suggestion as to how to immunize the Euclideanism of Kantian geometry from inconsistency with modern scientific theories of space is to treat Kantian geometry as a phenomenal geometry. This is the approach Strawson has taken. A phenomenal geometry is the geometry “of the spatial appearances of physical 29 30

Hagar 2008, 80. For a review of answers to these questions in recent literature, see Hagar 2008, 85–89.



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things and only secondarily, if at all, of the geometry of the physical things themselves.”31 Unfortunately, it is not at all clear that a geometry of how things visually appear is Euclidean. Arguments to this effect were already made in Kant’s day by Reid32 and more recently by others, among them Angell.33 Moreover, Hagar himself argues that even if Kant (Kantians) were to accept that the geometry of visible space is non-Euclidean, this leads to a fatal “trap.”34 A further, internal, difficulty for treating Kant’s theory of pure geometry as a phenomenal geometry is that the phenomena, how things look, are anything but pure phenomena; their content comes from sensations as much as from the form of sensation. For these reasons I do not regard this approach as promising. A more promising suggestion follows. Prevailing scientific opinion holds that when space is measured empirically, its structure is determined to be non-Euclidean. Now, empirical measurement is a physical operation carried out by physical means in a domain of experimentation involving forces that operate on the measuring devices (the measuring “rods”). Any inference from observations of these rods will be an inference to the best explanation involving at least two theories: a theory of the structure of space and a theory of the operation of forces on the rods. In order to arrive at determinate conclusions about the geometry of space, it has to be determined how the forces are affecting the rods. Since there does not seem to be any special access that we might have to the operation of forces on rods directly, we need to make certain assumptions about how they are operating, on the simplest of which space turns out to be non-Euclidean. Of course, it is possible that the forces are acting on the rods in such a way that measurement observations would lead us to posit a Euclidean space; it is just that this does not seem to be the simplest explanation when taking the two theories together. This picture, which I  hope is scientifically uncontroversial,35 allows for the possibility that Kant’s contention that space is Euclidean is in fact correct and that we can know that it is by means of Kant’s mathematical and philosophical methods. This is so because the former method posits pure intuition and determines its structure by means of constructing and measuring figures in an arena in which no physical forces are operating (this is what is pure about pure intuition), and the latter asserts that all physical objects have the geometrical structure of objects in pure intuition. Because no forces are operating in pure intuition, we are in an ideal position to determine the structure of space itself— we don’t have to account for the effects of a second variable. Should the results of Kant’s imagination experiments be as reported, then Kant can claim that the 31 32 33 34 35

Strawson 1966, 282. Reid 1997, esp. ch. IV, §9. Angell 1974. Hagar 2008, 91. It is based on Salmon 1980, ch. 1.

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structure of pure intuition is Euclidean. Moreover, should Kant’s philosophical doctrine of Transcendental Idealism also be correct, then empirical objects also have Euclidean structure, from which it follows that the prevailing opinion in science about the structure of space is mistaken. (This would be so because science has made the wrong guess about the force effects on measuring rods.) A related point is made by Mittelstaedt: On the basis of unrestricted mobility [of rigid objects of finite extension], it is possible to construct Euclidean geometry as an a priori theory, which is necessarily valid for all objects of the prescientific domain of experience. Similarly, Riemannian geometry can be established on the basis of restricted mobility. It too is an a priori theory in the sense explained, and is necessarily valid for all objects of experience.36 The claim made here is that Kant’s position that space is Euclidean can be defended by a dogmatic claim that there is unrestricted mobility for measuring rods and that this dogmatic claim would make Kant’s theory a priori in some sense. But dogmatic assertion of a mobility assumption is just what Kant is not doing: within the confines of his philosophical and methodological theory, he has (would have) an argument for that assertion. Unfortunately (for Kant) the argument for Transcendental Idealism becomes unsound in light of modern physics, for the central premise of this argument (line [5]‌) is that “there is a rigorous and necessary coincidence between the geometry of objects in empirical space and the geometry of figures in the space of pure intuition.” This is just what modern physics appears to have disproven. Kant could of course dogmatically invoke the appropriate mobility assumption mentioned by Mittelstaedt, but that would be unconvincing and ad hoc. Alternatively, Kant could, perhaps, rely on a weaker premise:  that there is a rigorous correspondence between figures in pure intuition and those occurring in a small scale in empirical space, arguing, as before, that even this restricted correlation needs explaining and the idealist explanation is still the only one viable. That would allow for treating the required mobility assertion as derived rather than dogmatically asserted. But, it must be admitted, this argument lacks the necessity Kant seems to want for his premises. Unless there is a geometry-independent argument for transcendental idealism, one would have to say that these modern developments would seriously, if not fatally, undermine Kant’s transcendental idealist metaphysics.

36

Mittelstaedt 1976, 81 (quoted in Brittan 1978, 85, n. 38).



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But there are geometry-independent arguments for transcendental idealism that Kant employs. One is that for the theory of intentionality itself,37 the other is implicit in Kant’s “touchstone” remark made in the B edition Deduction, mentioned in the introduction above, to the effect that idealism about appearances (Transcendental Idealism) is a necessary condition for Nomic Prescriptivism. This, taken together with the claim that Nomic Prescriptivism can be independently argued for, entails the truth of Transcendental Idealism. Perhaps few contemporary philosophers would be prepared to endorse the necessary doctrines—of pure intuition, of mathematical method, of intuitional representation, of Nomic Prescriptivism or of Transcendental Idealism itself— or the assumption about the results of the thought experiments needed to vindicate Kant’s claim that pure intuition is Euclidean. But these are all philosophical doctrine (or claims about what can be observed introspectively), and rejecting these doctrines would require a philosophical engagement with them; by itself an appeal to the deliverances of modern physics would not suffice.

Note A See Buroker 1981, ch. 3. According to Buroker’s interpretation, Kant’s argument is intended to show that a certain property P of physical objects is to be explained by the existence of a certain property Q of space. Q is not itself to be explained in terms of properties of physical objects. Space thus possesses properties intrinsic to itself and is thus “absolute.” Buroker maintains that this argument depends on two main premises: (1) “ . . . two figures would be congruent only if, in addition to (standard Euclidean congruence) some continuous rigid motion could make them identical objects” (53); (2) “ . . . an n-dimensional asymmetrical object can be turned into its counterpart if it is rotated in a space of n + 1 dimensions” (55–56).

If the space is “orientable” (as Euclidean space is), then (2) becomes a biconditional: an n-dimensional asymmetrical object can be turned into its counterpart iff it is rotated in a space of n + 1 dimensions” (55–56). I offer the following formal reconstruction of Buroker’s version of Kant’s proof. 37

Given in Ch. 3, §2.

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 1. If x and y are incongruent counterparts in 2 dimensions, then they can be made congruent absolutely* iff there is a 3 (or higher) dimensional space in which they are located (topology theorem).  2. a and b are incongruent counterparts in 2D (assumption).  3. a and b can be made congruent absolutely (assumption).   4. Thus, there is a 3D (or higher) space in which they are located (m.p. twice, 1, 2, 3).  5. If x and y are incongruent counterparts in 3D, then they can be made congruent absolutely iff there is a 4D (or higher) space in which they are located (topology theorem).  6. c and d are incongruent in 3D space (one of Kant’s main substantive premise).  7. c and d cannot be made congruent absolutely (another of Kant’s premise).   8. Thus, not: there is a 4D space in which c and are located. (m.p., then m.t.: 5, 6, 7).   9. Thus, there is a space that contains a, b, c, d that is at least and at most 3D. (4, 8). 10. Def ’n: Space is an absolute being = df. Space has intrinsic properties S that explain observable properties of physical objects but not the reverse. 11. The three-dimensionality of Space (9) explains the observable properties of congruence and incongruence of physical objects a, b, c, d, but not the reverse (1, 5). 12. Thus, Space is an absolute being (10, 11). Objects mentioned in the proof: a is a 2D circle with a left-facing broken arrow protruding upwards. b is a 2D circle with a right-facing broken arrow protruding upwards. c is a left hand. d is a right hand. *  This concept is to be understood counterfactually: there is a possible rotation R such that if the objects were rotated in accordance with R, they would become congruent.

5

The Transcendental Deduction of the Categories I

1.  Introduction: What Is the Transcendental Deduction of the Categories About? Any interpretation of Kant’s Deduction of the Categories has to give a plausible reading of a central text from section 13, entitled “On the principles of a transcendental deduction in general” (A89–90/B122; GW, 222). Here it is: The categories of the understanding, on the contrary, do not represent to us the condition under which objects are given in intuition at all, hence objects can indeed appear to us without necessarily having to be related to functions of the understanding, and therefore without the understanding containing their a priori conditions. Thus a difficulty is revealed here that we did not encounter in the field of sensibility, namely how subjective conditions of thinking should have objective validity, i.e., yield conditions of the possibility of all cognition of objects; for appearances can certainly be given in intuition without functions of the understanding. I take, e.g., the concept of cause . . . It is not clear a priori why appearances should contain anything of this sort (one cannot adduce experiences for the proof, for the objective validity of this a priori concept must be able to be demonstrated), and it is therefore a priori doubtful whether such a concept is not perhaps entirely empty and finds no object anywhere among the appearances. For that objects of sensible intuition must accord with the formal conditions of sensibility that lie in the mind a priori is clear from the fact that otherwise they would not be objects for us; but that they must also accord with the conditions that the understanding requires for the synthetic unity of thinking is a conclusion that is not so easily seen. (GW, 222–23; A89–90/B122–234) 101

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The overall sense of this passage seems to be that there is a problem encountered with the categories that is not encountered with the concepts of space (geometrical concepts) and that problem is that it is “doubtful” that there are objects that actually “accord with the conditions that the understanding requires.” It would be futile and unreasonable to deny that Kant is expressing a concern here about the existence of objects outside our thought (Kant’s example is cause), but it is not futile and unreasonable to ask what significance Kant attaches to the fact that this existence is said to be doubtful. One very natural understanding treats Kant’s concern as being with the absence of proof of the existence of such objects outside our representation of them. Accordingly, his objective in the Deduction is to provide such a proof and, moreover, to do so from the nature of our representations themselves. That this is indeed Kant’s intention seems to be borne out by a study of the main texts of the Deduction in both editions, which, we seem to be told, show that when our representations are brought under the unity of consciousness, as they must, it follows from this unity that there also must be actual objects in the objective world corresponding to those representations. In an article that is seminal to my own work,1 Ameriks has called this “the traditional view”2 and mounts a powerful, multithrust attack on it. One thrust is directed (in effect) to the assumption that the significance of calling the existence of actual objects outside our representations doubtful in the passage just quoted is to remove that doubt by means of a proof from representations of objects to actual objects, a proof that constitutes the Transcendental Deduction of the Categories. He proposes an alternative reading, deriving from a consideration of the two-part structure of the B edition Deduction of the Categories. Briefly, his reading is that Kant needs to make the point that empirical intuitions might, in principle, not be subject to the categories in order to give the second part of the B edition Deduction something major to accomplish; namely, that empirical intuitions are in fact subject to the categories. He adds that this reading “might also explain why, in the pivotal paragraph 20 of that deduction, Kant reminds the reader to refer back to paragraph 13.”3 I am entirely in agreement with Ameriks’s reading. Since I discuss this matter at considerable length in Chapter 7,4 I say no more about it here. Another thrust makes the case that the traditional view treats Kant’s argument as progressive in form, arguing as it does from representations (under the unity of apperception) to things outside the representations, but that no such form Ameriks 1978. He attributes this view to Strawson, Bennett, and Wolff; ibid., 51. 3 Ibid., 63. Actually, it would serve Ameriks’s purpose better had Kant made the reference in §21 instead of §20. 4 Viz., Ch. 7, Part II, §1. 1 2



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of argument is found in either the Transcendental Deduction of the Categories or the Transcendental Exposition of the Concept of Space.5 Since, Ameriks observes,6 there is evidence from section 13 that Kant calls the latter a “transcendental deduction” (“We have above traced the concepts of space and time to their sources by means of a transcendental deduction . . .” [GW, 221; A87/ B119]), we would expect to find a similar form of argument in each; and since the form of argument of the Deduction of the Concept of Space is regressive, as Ameriks maintains, we would expect to find a similar form in the Deduction of the Categories. What we would expect to find, affirms Ameriks, is the following: In its most skeletal form the central argument of the Aesthetic (with respect to space) has this structure:  the science of geometry (A) requires synthetic a priori propositions which in turn requires pure intuitions (B), and these are possible only if transcendental idealism is true . . . The argument of the Analytic would have a parallel structure if it is of the form: empirical knowledge (“experience”) is possible only if the “original synthetic unity of apperception” applies to it, which is possible only if the pure concepts have validity, and this in turn requires that transcendental idealism be true.7 I accept Ameriks’s suggestion that the mention of a “transcendental deduction of the concept of space,” said in section 13 to have been earlier accomplished, is a reference to the geometrical arguments of the Metaphysical Exposition— the “Transcendental Exposition of the Concept of Space,” as it is called in the B edition—and that this creates a presumption that the form of argument of the Transcendental Deduction of the Categories will be similar. Indeed, this is a guiding idea of the book that I owe to Ameriks. But I part company with him when he claims that the form of argument of the former is “regressive.” This characterization is true of the First Geometrical Argument for Transcendental Idealism but not the Second: the Second has a progressive form since it requires establishing both the subjective and the objective sides of geometry by independent applications of mathematical method. These applications are progressive in form, and it is the Second Argument, not the first, that constitutes the second stage of the Transcendental Exposition of the Concept of Space (so I argue in Chapter 4). Thus, if Ameriks is right about the parallel between the two deductions—and I accept that he is—and I am right about the structure of the Deduction of the Concept of Space, then he is wrong about the structure of 5 6 7

He makes these arguments in §§3 and 2, respectively (54–60). Ibid., 51–52. Ibid., 54.

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the Deduction of the Categories. To find out what the structure is, we need to go back to the start of section 13 and closely follow Kant’s own account of that concern to its final resolution. Of the many themes Kant explores in section 13, entitled “On the principles of a transcendental deduction in general,” the following four seem to be most salient: (1) Discussion of the quid juris, the matter of right or entitlement to employ the pure concepts of the understanding (GW, 220; A84/B116). (2) The “explanation of the way in which concepts can relate to their objects a priori.” This explanation is called the “transcendental deduction” (GW, 220; A85/B117). (3) A comparison of a transcendental deduction of the concept of space with a transcendental deduction of the categories (GW 221–222; A87–88/ B119–121). (4) The posing of what seems to be the official statement of the problem the Deduction is to resolve:  “how subjective conditions of thinking should have objective validity, i.e., yield conditions for the possibility of all cognition of objects” (GW, 222; A89–90/B122). It looks as if (1) is, indeed, about proving that the categories are instantiated, for instantiation seems to be the issue that Kant is addressing when he speaks of proving the “objective reality” of empirical concepts by experience “without objection from anyone.”8 However, with the categories, experience cannot perform this service; that is apparently why a special argument, a “deduction,” is required. Indeed, it is but a few pages later where Kant seems to confirm this idea in the passage quoted above, when he says of the concept of cause (one of the categories) that “it is . . . a priori doubtful whether such a concept is not perhaps entirely empty and finds no object anywhere among the appearances” (GW, 222; A90/B122). But there are also reasons to doubt that proving the instantiation of the categories is Kant’s main goal in the Deduction. For one thing, while there are perhaps some arguments in the Analytic of Principles that seem to establish something like the instantiational (antiskeptical) thrust of this reading of Kant’ s intentions, no arguments of this sort are evident in the material of either the A or the B edition Deduction. This could be

“We make use of a multitude of empirical concepts without objection from anyone, and take ourselves to be justified in granting them with a sense and a supposed significance even without any deduction, because we always have experience ready at hand to prove their objective reality” (GW, 220; A84/B116–117). 8



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taken as a problem with the organization of Kant’s argumentation or it could be taken as grounds for doubting this reading of the quid juris question. A second reason for doubting this reading comes from a close reading of theme (3), the comparison Kant makes between the Deduction of the Categories and the “deduction” of the concept of space. At GW 221–222 (A88/B120–121) Kant explains that the need for a deduction of the categories is due to the lack of immediate evidence of their objects and, in the same breath, affirms the necessity of a deduction of the concept of space as well. The reason for requiring both deductions is that the pure concepts “arouse suspicion about the objective validity and limits of their use but also make the concept of space ambiguous by inclining us to use it beyond the conditions of sensible intuition, on which account a transcendental deduction of it was needed above” (GW 221–222; A88/B120–121; my underlining for emphasis). Establishing the certainty of geometrical propositions is the job of mathematical method; establishing the limits of the application of concepts to a certain class of items (appearances), a metaphysical proposition carried out by the critique of the use of these concepts, is the job of philosophy. So the concept of space does after all have to beg philosophy for an answer to the limits question. It was on this account that Kant says he needed to carry out the deductions and on this account that both transcendental deductions are necessary. I thus concur with Hatfield9 that the ultimate objective of a transcendental deduction is the establishment of the limits of possible application of our concepts, not the establishment of their objective reality in an existential sense. In light of this we should revise our understanding of the kind of entitlement that is at issue in theme (1): it is not a right to assert that the categories are instantiated; rather, it concerns the range of objects (appearances, not things in themselves) to which we have a right to meaningfully apply concepts. Section 13 is one of three main places where Kant says in advance what the Deduction is to accomplish and how, in general terms, it is to be accomplished. The other places are in the prefaces to the first and second editions. In the former Kant introduces a distinction between a “subjective” and an “objective” deduction (GW, 103; Axvi–xvii); in the latter, Kant introduces the idea that he is able through philosophical reasoning to effect a kind of “Copernican revolution” in metaphysics (GW, 110–112; Bxvi and ff.). The doctrine of the former discussion is rather obscure—a subjective deduction seems to involve a best hypothesis about the subjective side of thinking, an objective deduction seems to be more He puts it this way: “The critical investigation is intended to assess the claims of reason (and the understanding) in the field of pure speculation ‘beyond the boundaries of all possible experience.’ That is the field of speculation the Critique is intended to shut down, and, within the book as a whole, Kant here implies that the deduction is to do the job” (Hatfield 2003, 174). 9

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analytical in method and focuses on the objects of thinking—but the doctrine of the latter discussion is more transparent. If we assume that we know something about objects in advance of experience—that is, have knowledge a priori about objects—then regarding the intuition of objects, Kant says we face a choice in explaining this: either the intuition must conform to the object or the object must conform to the faculty of intuition. I call this the Copernican dichotomy. Kant does not include an explicit argument why there are only these choices: couldn’t it be the case that neither the objects determine the intuition nor the intuition determines the objects? What I think Kant is leaving out of his account here is that he supposes two domains, a subjective and an objective domain, between which there is tight correspondence of content; both are Euclidean, a point reflected in the Second Geometrical Argument for Transcendental Idealism. If we assume this correspondence of content, we then are in a position to understand why Kant would think that he faced the Copernican dichotomy—otherwise there would be an intolerably improbable coincidence. In any case, Kant’s choice is clear: If intuition has to conform to the constitution of objects, then I do not see how we can know anything of them a priori; but if the object (as an object of the senses) conforms to the constitution of our faculty of intuition, then I can very well represent this possibility to myself. (GW, 110; Bxvii) Even more important for present purposes is Kant’s claim that we confront the same dichotomy in the case of the application of concepts to objects:  . . . I can assume either that the concepts through which I bring about this determination also conform to the objects, and then once again I am in the same difficulty about how I could know anything about them a priori, or else I assume that the objects, or what is the same thing, the experience in which alone they can be cognized (as given objects) conforms to those concepts . . . (GW, 110; Bxvii) Kant’s choice is the same: the rule (which a pure concept of the understanding constitutes) “is expressed in concepts a priori, to which all objects of experience must therefore necessarily conform, and with which they must agree” (ibid.). Only in this way can we explain the possibility of concepts applying a priori to objects. I call Kant’s inference to this conclusion the Copernican inference. Kant then goes on to say that regarding things falling outside the limits of experience, things in themselves, “the attempt to think them (for they must be capable of being thought) will provide a splendid touchstone of what we assume



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as the altered method of our way of thinking, namely that we can cognize of things a priori only what we ourselves have put into them” (ibid.). Of course we cannot cognize anything a priori in things in themselves. Kant here connects the Copernican revolution in metaphysics with the stated objective of the Deduction, arguing that the limits doctrine is a “touchstone” of the revolution. Why? Because we can ascribe properties a priori to things only if we prescribe laws to them and we cannot prescribe anything to objects as they are in themselves—only God could do that—so the objects of our cognitions must be somehow limited to those that are human dependent. For Kant, this means that they are appearances. This is the Copernican revolution for intuitional representation. The Copernican revolution for intuitional representation is called by Kant Transcendental Idealism, and I call the Copernican revolution for conceptual representation Nomic Prescriptivism. We can summarize Kant’s reasoning here as follows: (1) the possibility of a priori cognition depends on Nomic Prescriptivism, and (2) the possibility of the latter depends on Transcendental Idealism, an ontological doctrine that sets limits to the kinds of things that our cognitions can take as objects. Nomic Prescriptivism is not said to be an objective of the Deduction in Kant’s introduction to the Deduction in section 13, but statements of it appear in the final stage of both the “provisional” and the final versions of the Deduction in the A edition (GW, 236; A114; and GW, 241; A125; respectively) and in the final stage of the B edition Deduction, in section 26 (GW, 261; B159–160) and section 27 (GW, 264; B166–167). The language is the same as that in the Copernican revolution passages, thus showing a tight correspondence between the latter and the Deduction. What of the express statement in section 13 that the objective of the Deduction is to establish the limits of human cognition? Drawing upon our discussion of the “touchstone” remark from the Preface, we can see that this doctrine is merely a corollary of the doctrine of Nomic Prescriptivism—only if the limits doctrine is true could Nomic Prescriptivism be true—thus the establishment of the latter is the main task of the argument of the Deduction.10 If this is right, how is it to be accomplished? One constraint that my interpretive strategy places on the answer is that it is to be accomplished in a way that parallels the accomplishment of Transcendental Idealism in the Transcendental Exposition of the Concept of Space. It might be helpful for us to have a summary of that argument before us again. The Exposition has two parts. The first is the argument for the objective reality (validity) of geometry made in remark I to part I of the Prolegomena. Here, If we distinguish the ultimate objective from the main task of the deduction, this account is consistent with Hatfield’s. 10

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I have argued that Kant countenances a separate application of mathematical method to both pure objects of the imagination and empirical objects, finding that in both cases there is a necessary applicability of the laws of geometry. When the application of a philosophical or mathematical method establishes results purely for objects of thought, I call that a “subjective application” of the method; when the application is to empirical objects, I call that an “objective application.” So the first application in the present case is a subjective application, the second is an objective application. There is, thus, a “rigorous” correlation between the structure of pure space (“thought space”) and empirical space, independently demonstrated by mathematical method. This correlation is what the objective validity of geometry consists in, the demonstration of which is the first stage of the overall Transcendental Exposition of the Concept of Space. From this correlation Kant then infers, by elimination of the alternative possibilities, that the thought space makes the empirical space possible. This is one step away from the doctrine of Transcendental Idealism (the other step is Kant’s claim that when a representation induces its object to have certain properties, the object depends ontologically on the representation), and the inference that leads to it is the Second Geometrical Argument for Transcendental Idealism, which constitutes the second stage of the Transcendental Exposition of the Concept of Space. We have also seen that in part I of the Prolegomena Kant offers another argument for Transcendental Idealism, the First Geometrical Argument for Transcendental Idealism. The key difference between these argument structures is that with the second argument, the necessity of both domains of the correlation is established independently of one another; with the first, necessity is established independently for only one domain. My central contention is that the structure Kant eventually proposes for the Deduction at the conclusion of the B edition Deduction (§26) and in at least one form of the Deduction in the A  edition is analogous to that version (“version 2”) of the Transcendental Exposition of the Concept of Space containing the Second Geometrical Argument for Transcendental Idealism rather than the first. But before we can be in a position to see what the case for this is, we need to understand what corresponds to the subjective application of mathematical method to the objects of pure geometry in the case of the Deduction of the Categories. Kant’s general answer is “the subjective conditions of thinking” or, sometimes, “intellectual conditions.”

2.  What are the Subjective Conditions of Thinking? In both editions Kant states a version of the main problem of the Deduction in the passage quoted at length in the previous section. The focus of my interest



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in that passage was to highlight Kant’s concern that there might not be actual objects answering to certain of the categories, for example, that of cause, and to consider whether that meant that Kant’s main job for the deduction was to prove the existence of said objects. My conclusion was that it was not. I now focus on another aspect of the passage: his characterization of the special “difficulty” that the Deduction of the Categories is to solve as the problem of showing how the subjective conditions of thought should have objective validity. Here is the relevant passage again:  . . . Thus a difficulty is revealed here that we did not encounter in the field of sensibility, namely how subjective conditions of thinking should have objective validity, i.e., yield conditions of the possibility of all cognition of objects . . . (GW 222; A89–90/B122) Here Kant seems to think that we know antecedently what the subjective conditions of thinking are; yet he does not say what they are, nor does he explain what he means by “subjective conditions of thinking”. Let us specialize this question: How is causality, for example, proven to be a subjective condition of thought? Is it perhaps by means of the fact that causality is one of the twelve pure concepts of the understanding, a case made in the first chapter of the Analytic, “On the Clue to the Discovery of All Pure Concepts of the Understanding”? In this chapter Kant lays out an account of the structure of the judgments we need in order to engage in logical inference (“general logic”). General logic is the science of inference (GW, 194; A52/ B76), and the Table of Judgments is an exhaustive taxonomy of the kind of propositions involved in logical inference11 as Kant understood it at the time of writing the Critique.12 The taxonomy is divided into four groups of three forms each. The present proposal is that the Table of Judgments is the source of the subjective conditions of thought for Kant. Yet it may seem that Kant’s conception of logic precludes this possibility, for he seems to say that logic is not a science of the subjective: Logic is . . . a science of the correct use of the understanding and of reason in general, not subjectively, however, i.e., not according 11 After giving the table of Judgments, Kant says; “Since this division seems to depart in several points, although not essential ones, from the customary technique of the logicians . . .” (GW, 206; A70/B96). See Melnick 2004. 12 He understood it to be classical Aristotelian logic: “From Aristotle’s time on, logic has not much gained in content . . . nor can it by its nature do so” (Young, 535; Ak 9, 20).

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to empirical (psychological) principles for how the understanding does think, but objectively, i.e., according to principles a priori for how it ought to think. (Young, 531; Ak 9, 16) I think that appearances are misleading here, for Kant also says in the same work (in the opening sentence): Everything in nature, both in the lifeless and in the living world, takes place according to rules . . . The exercise of our powers also takes place according to certain rules that we follow, unconscious of them at first . . . Thus universal grammar is the form of language in general, for example. One speaks even without being acquainted with grammar however; and he who speaks without being acquainted with it does actually have a grammar and speaks according to rules, but ones of which he is not conscious. (Young, 527; Ak 9, 11; emphasis added) The rules in question direct and control behavior, linguistic and otherwise, and thus would seem to fall within the province of what we would nowadays call cognitive science or psychology. The laws in question Kant calls “necessary laws,” and the science of these necessary laws in the case of reason is logic. So logic seems to be the science of the necessary and general forms of the way we actually think. Yet Kant also says, noting that “some logicians presuppose psychological principles in logic” and that this is “absurd,” adds: If we took the principles from psychology, i.e. from observations about our understanding, we would merely see how thinking occurs and how it is under manifold hindrances and conditions; this would lead to merely contingent laws. In logic, however, the question is not one of contingent but of necessary rules, not how we think but how we ought to think. (Young, 529; Ak 9, 14) We can reconcile these two descriptions of logic if we focus on Kant’s explanation of what psychology studies; like logic, psychology provides generalizations about actual thinking, but logic studies how we actually think in the “deep structure” of our thought and how we would express those thoughts under ideal conditions; psychology studies the associative (empirical) laws13 and Hatfield 1990 maintains that at this time “psychology” applied to associative principles relating events that were not described in the vocabulary of idea, judgment, and other cognitive capabilities with a normative dimension. In this I follow Hatfield (83). 13



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mechanisms of how we think and express our thoughts under real-life conditions in which various “hindrances” to ideal cognitive functioning exist. This distinction seems to be reflected terminologically in Kant’s distinction between “pure logic” and “applied logic”: In pure logic we separate the understanding from the other powers of mind and consider what it does by itself alone. Applied logic considers the understanding insofar as it is mixed with other powers of the mind, which influence its actions and misdirect it, so that it does not proceed in accordance with the laws which it quite well sees to be correct. Applied logic really ought not to be called logic. It is a psychology in which we see how things customarily go on in our thought, not how they ought to go on. (Young, 532–533; Ak 9, 18) If we are well rested, free from prejudices, operating with full information, we would actually reason and express our reasoning in a way that conforms to the rules of logic in the textbooks. This is because those rules are internalized and govern our actions unless other factors intervene. Of course other factors do intervene in real life, and so we do not always reason or do not always express our reasoning like the textbooks. For example, we may often forget when we reason hypothetically that conclusions drawn under the hypothesis cannot be affirmed categorically. This is a lapse on our part that occurs in certain circumstances, circumstances that psychology records and explains, but it is not a refutation of the thesis that in the deep structure of our understanding there lie laws of logic guiding our actions unless interfered with. So, I maintain, Kant really does think that the laws of logic are the laws of thought, the deep laws of how we actually think under ideal conditions to be sure, but laws of actual thinking nonetheless.14 So the title and subtitle of ­chapter 1 are entirely apt: logic does provide an important clue to the deep structure of our concepts. The clue is the previously mentioned Table of Judgments (GW, 206; A70/ B79). Associated with each of the judgment forms is a “category.” Kant introduces the idea of a category by means of the notion of “synthesis” (GW, 211; A78/B104). We discuss the role of synthesis in the theory of judgments and of categories in the theory of synthesis in Chapters 6 and 7. For now we simply say that categories are concepts that are needed if we are to apply judgments of a given form to objects (objects understood in a very general way). For example, if one is to apply judgments of the form Universal (“all things of a certain kind A are also of kind B”) we need to employ the concept of Unity. Kant gives an example

14

Hatfield (1990, 83) does not agree.

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of “the common ground of unity”: “Thus our counting . . . is a synthesis in accordance with concepts, since it takes place in accordance with a common ground of unity (e.g., the decad)” (GW, 211; A78/B108). I maintain that the kind of unity here is sortal unity, for if we now look at the table of categories presented in the Prolegomena (Hat., 55; Ak 4, 303), we find that the category of Unity is correlated with the schematized category of “measure,” and the concept of measure is the concept of a “sortal unity”; for example, the decad. I conclude from this that the category of Unity is the “one” in Plato’s problem of the one and the many.15 In general, Kant thinks that all thoughts—at least all judgments—must occur in at least one of the twelve forms. His doctrine of the categories asserts that for each of these kinds of judgments, a category must also be employed. Even if we accept all of this, there is still the fact that we are not required to apply all twelve kinds of judgments in every case. At most we are required to apply one (of three) judgments in each of the four main groupings, Quantity, Quality, Modality, Relation. For example, under the heading of Relation, we have to make a judgment of the hypothetical form, disjunctive form, or categorical form. The category of main interest to Kant and his readers is causality, the concept associated with hypothetical judgments. There is nothing in this account by itself that entails or even gives the slightest reason to believe that we must make hypothetical judgments.16 Maybe we can get by with simply disjunctive and categorical reasoning. (Modern symbolic logic allows that one kind of hypothetical, the material conditional, can be defined in terms of a disjunction.) Maybe, like Hume, when we feel moved to employ causal reasoning, we should just fall back on “constant conjunctions.” Statements expressing these are in universal/categorical form, one of the other logical forms of judgment allowed for in Kant’s taxonomy. Moreover, if the Table of Judgments provides the kind of propositions needed for making logical inferences, since logical inferences are hypothetical operations—assuming premises, deriving conclusions—we also face the question why we need to make any judgment on this table assertorically. With the rush on the part of Kant (and many of his interpreters) to prove that “subjective conditions of thought” have objective validity, it may seem that 15 Thus, I cannot agree with Longuenesse that Kant somehow reversed the proper coordination between the categories of quantity and the judgments of quantity. (She discusses this in connection with Prolegomena, part II, 20.) Kant has stated the coordination thus: universal form of judgment / category of unity, singular form of judgment / category of totality, whereas the actual correspondence he intends, according to Longuenesse, is this: universal form of judgment / category of totality, singular form of judgment / category of unity (Longuenesse 1998, 249). But unity is not the singularity of an object—for example, the unity of consciousness is not the singularity of an object of consciousness but is, rather, a conceptus communis*—and it is singularity of an object that would go with the singular form of judgment. I think that Kant’s statement of the correspondence should be accepted as he gave it. (*This term comes from a note at B133 and means a sortal concept of unity.) 16 See Guyer 1987, 128–129.



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Kant has neglected to provide a satisfactory proof that there are any such conditions. We should be on the lookout for something more than is on offer in the Metaphysical Deduction to provide it. We have been speaking a good deal so far of two sides to the argument of the Deduction:  one side subjective, the other objective. Kant himself speaks in the Preface to the A edition of a “subjective” and an “objective” side to the Deduction: One side refers to the objects of the pure understanding, and is supposed to demonstrate and make comprehensible the objective validity of its concepts a priori; thus it belongs essentially to my ends. The other side deals with the pure understanding itself, concerning its possibility and the powers of cognition on which it itself rests; thus it considers it in a subjective relation . . . (GW, 103; Axvi–xvii) The subjective side addresses the question how thinking is possible, which I take to be the question what the subjective conditions of thought are. There is here confirmation that in the A edition Deduction at least,17 Kant accepts the demand for a deduction of intellectual conditions; that is, the demand to show a justification for asserting that there are certain concepts necessarily governing the way we think. So far our investigation of the obvious places in Kant’s texts has not revealed what this justification might be. One strategy that Kant might be employing to demonstrate that the categories give subjective conditions of thought, in addition to whatever argument might be found in the Metaphysical Deduction itself, is an analogue of the subjective stage of the Transcendental Exposition. The first component of the Exposition is an argument for the objective reality (validity) of geometry, made in remark I to part I of the Prolegomena. Kant countenances a separate application of mathematical method to both pure objects of the imagination and empirical objects. When the application of a philosophical or mathematical method establishes results for pure objects of thought, I call that a “subjective application” of the method; when the application is to empirical objects, I call that an “objective application.” So the first application in the present case is a subjective application, the second is an objective application. But both applications have the form of inferences to the best explanation. In the subjective case the inference is from the counterfactual necessity of constructing images in the space of the imagination that have only Euclidean properties to the underlying explanation of this necessity; namely, that there is a pure structure The passage in which the two sides of the deduction are distinguished does not survive into the B edition. 17

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of the faculty of imagination in which these images are constructed and which imparts these characteristics to the images. This is the a priori form of pure intuition. There is some evidence pointed out by Bauer18 that in the A edition Deduction Kant sees a subjective side to the deduction and presents that side in that part of the A edition Deduction that deals with the concept of the affinity of the manifold, especially A111–115 in the “provisional explanation” (GW, 234–236) and again at A120–126 in the final version (GW, 238–241). I will call this the Affinity Argument. His case depends on two main points. The first is that Kant characterizes the subjective deduction as “something like the search for the cause of an effect, and is therefore something like a hypothesis (although, as I will elsewhere take the opportunity to show, this is not in fact how matters stand . . .” (GW, 103; Axvii), and the subjective side of the Affinity Argument has exactly this character. The second is that Kant regards hypothetical arguments of this kind as weak, for “ . . . it appears as if I am taking the liberty in this case of expressing an opinion, and that the reader might therefore be free to hold another opinion” (GW, 103; Axvii). Bauer points out that Kant characterizes the ultimate result of the Affinity Argument as problematic, “strange and contradictory” sounding (A114) and “exaggerated and contradictory” (A127). However, it does not seem to me that the complaint of weakness of argument made in the Preface is the same as the complaints made in the body of the argument itself —for one thing, the latter address only the ultimate stage of the argument, that in which Nomic Prescriptivism is derived, whereas the former concern the argument as a whole. Nevertheless, his first point seems to me still to stand: the subjective side of the deduction has the form of a hypothetical inference, and this is the form of reasoning we find in the Affinity Argument.19 But what is that form of reasoning? I argue in the next section that part of the task of that argument is to establish a subjective condition for thinking (an “intellectual condition”) by means of an inference to the best explanation; what is to be explained is our ability to have certain kinds of associations, what does the explaining is our possession of the concept of causality a priori. The kinds of associations in question are not just the accidental associations that might be the subject of psychological study but the kind that are requisite for our having a conception of an objective world. In “A New Reading of Kant’s Subjective Deduction” (Bauer 2005). For a more recent work, see his doctoral dissertation (Bauer 2008). 19 Locating the exact range of text for the Subjective Deduction is a matter of speculation among commentators, but none, as far as I know, locate it where Bauer does. Most favor earlier texts in the A  edition Deduction. Dyck “confidently” locates some preliminary material for it at A94–95 and the body of the argument proper at A98–110, the range of text comprising discussion of the three syntheses (Dyck 2008, 152–179, esp. 158, 162). I forgo further discussion of the location question. 18



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Can this reading be reconciled with the key passage from section 13 that has occupied so much of this chapter’s attention? The problem this time originates in the fact that Kant has just been comparing the cases of geometry and the categories with respect to their objective validity, and at least on the side of geometrical cognition, this means “mak[ing] comprehensible with little effort how these, as a priori cognitions, must necessarily relate to objects . . .” (GW, 222; A89/B121). Recall that Kant customarily regards the objects in question as empirical objects when the objective validity of geometrical cognition is at issue. There is, however, some question whether Kant’s use of “objective validity” has the same sense a few lines later in the key passage we have been considering before: “Thus a difficulty is revealed here that we did not encounter in the field of sensibility, namely; how subjective conditions of thinking should have objective validity . . . for appearances can certainly be given in intuition without functions of the understanding. I take, e.g. the concept of cause . . .” (GW, 222; A89/ B122). If the use of objective validity does conform to this interpretation, then the “difficulty” is whether there are things satisfying the concept of cause; that is, whether there actually exist causes. Now Kant does seem interested in this question, for as mentioned, he raises it in the lines immediately following the passage just quoted: “ . . . it is . . . a priori doubtful whether such a concept is not perhaps entirely empty and fails to find an object anywhere among the appearances” (GW 222; A90/B122). But there is also evidence that Kant is not using the notion of objective validity in this sense. For one thing, notice in the first passage quoted that objective validity is characterized not in terms of finding actual instances of the concepts but in terms of conditions of the possibility of cognitions of objects, events lying on the subjective side of the divide between the subjective and the objective. The emphasis seems to be on explaining what it is for a cognition to be of an object, not on whether the object of the cognition exists. Indeed, Kant expressly states this in the next section (§14):  . . . since representation itself . . . does not produce its object as far as its existence is concerned, the representation is still determinant of the object a priori if it is possible through it alone to cognize something as an object. (GW, 224; A92/B125; Kant’s emphasis) Kant’s idea may be that one kind of cognition (object-representing) may require another (conceptual cognition) governed by the categories and that this is a property of the categories constituting the objective validity of the categories. In his well-known interpretation of the B edition Deduction in the first edition of Kant’s Transcendental Idealism, Allison maintains that in the first part (§§15–20) Kant’s purpose is to show that the categories have objective validity

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in the subjectivized sense; that is, the categories take objects whose actual existence is another matter to be demonstrated later.20 Here the “objects” are contextually eliminated in favor of an “objectivity” claim. The second part (§§22–27) is the place where the demonstration of actual existence occurs. Allison also maintains that the conceptual distinction between the question whether the categories have objectivity and whether they take actual objects is marked by the terminological distinction in Kant between objective validity and objective reality, respectively. Unfortunately, the usage of this language throughout CPR does not seem consistent enough to warrant marking the conceptual distinction with this terminology.21 Nevertheless, the conceptual distinction is in Kant’s doctrine and should be marked clearly. I propose to do so by speaking of intentionally objective validity and empirically objective validity, respectively. When we now come to face the question Why should subjective conditions of thought have intentionally objective validity?, we face a question only on the intellectual side. That question is, When our thinking has intentionally objective content, that is, has the content of an objective world, what intellectual factors explain this content? My answer is that to have intentionally objective content we need the capability of having a certain kind of association, an objective association, and that our ability to have it depends on our a priori commitment to the causal law (“all events have a cause”). This is an intellectual factor, what Kant means by a “subjective condition of thinking.” My contention is that Kant’s argument for this constitutes the subjective side of the first stage (that concerned with intentionally objective validity) of the A edition Deduction of the Categories and that the place where he carries it out is in the Affinity Argument.

3.  The Affinity Argument 3.1. Introduction The notion of affinity plays a central role in the A  edition Transcendental Deduction of the categories, both in the “provisional” version and in the final version that follows. Yet this notion does not reappear in the B edition Deduction. Moreover, it seems to have a role in explaining psychological aspects of the Deduction—what makes psychological association possible—which, as such, seems to be out of keeping with the objective and conceptual modes in which Kant’s most important reasoning in the Deduction is presented. So there Allison 1983, 133–147. That is why the claim is not repeated in this form in the corresponding part of the 2004 edition of Allison. 20 21



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have been few commentators who have found it worthwhile to expend much time discussing the role of affinity in the Deduction. A recent exception to this pattern is Westphal,22 who recognizes the importance of the problem that Kant identifies as the problem of affinity—the problem of the ground of the possibility of association, the associability of the sensory manifold—but thinks that the solution that Kant provides, a form of Transcendental Idealism, is faulty. It is faulty not just on external grounds but because it creates a fatal dilemma for this doctrine: If the associability of the sensory manifold is a function of our constitutive cognitive activity, then the manifold of sensation cannot be given. If instead the manifold of sensation is given, then whether it is associable is a function of the similarities and differences among the sensations comprised in that given manifold; it cannot be a transcendentally ideal function of the subject’s structuring of its experience. (112) So Kant cannot have it both ways: be a transcendental idealist about the form (intuitional and conceptual) of experience while insisting that its content comes from nonprescribed, given elements of sensation. Westphal’s own position, one he thinks Kant could and should have embraced as a result of a proper application of the method of transcendental argument, is the second horn: If the manifold of intuition is given, then whether it is associable is a function of the similarities and differences among the sensations comprised in that given manifold . . . If this is the case . . . then two things follow. First, Kant was quite right to ascribe the principle of affinity to the “object,” or content, in that manifold . . . Second, this transcendental affinity . . . cannot be ascribed to the constitution and functioning of the relevant subjects . . . (113) Westphal also credits Kant with the identification of a problem with Hume’s associationist account of causality—there just are not enough associations present in our experience to explain the wide range of cases where we make causal attributions.23 This identification occurs in a text late in the Critique of Pure Reason (A766–767/B794–795). Kant formulates Hume’s problem in terms of the notion of affinity: “ . . . he [Hume] made a principle of affinity, which resides in the understanding, and expresses a necessary connection, into a rule of association.” 22 23

Westphal 2004. Ibid., 74–75.

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Westphal is right to characterize Kant’s objection to Hume in this way, but I believe that Westphal’s criticism of Kant’s transcendental solution to the problem of affinity and his own support for a realist Kantian solution rests on an inadequate appreciation of the weakness of the realist position and the strength of Kant’s. As noted, Kant’s criticism of Hume is that there is not enough regularity in our sensory data—and not enough of the relevant kinds—to explain the empirical laws we find in nature. What must be added to the diversity in the data comes from ourselves, Kant argues, in the form of a law of the understanding that provides the explanation of how it is possible for us to experience regularity, especially causal regularity, in nature. This explanation is called the “affinity” of the manifold, and because it is contributed by us, it is called “transcendental affinity.” I  argue that what we contribute is the causal law, understood as a law of the understanding. I should emphasize that I am not saying that the concept of “affinity” is the same as the concept of the causal law; rather, I am saying that the concept of affinity is a functional concept—whatever it is that explains our ability to engage in associative cognition—and that the causal law as a subjective condition of thought is the realization of this functional concept. If this is right, then Westphal’s dilemma is a false dilemma: the associability of the objective manifold is neither purely “a function of our constitutive cognitive activity” nor purely “a function of the similarities and differences among the sensations.” It involves both.

3.2.  The Affinity Argument: Background Affinity is discussed in detail in at least three places in the A edition Deduction: in section 2.2 (“On the synthesis of reproduction in the imagination”: GW, 229– 239; A100–102), in 2.4 (the “Provisional explanation of the possibility of the categories as a priori cognitions”: GW 235–236; A112–114) and in 3 (“On the relation of the understanding to objects in general and the possibility of cognizing these a priori”: GW, 239–242; A121–128). The argument is laid out especially clearly in the third of these places, and I focus most of my discussion of the argument on that text. However, it will be useful to also have a summary of the main line of argument from section 2.2: “On the synthesis of reproduction in the imagination.” I see five main elements to the argument of this section. (1) There is a “law of reproduction” in the association of one representation with the next when I imagine a sequence of previously experienced representations.



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(2) “This law of reproduction, however, presupposes that the appearances themselves are actually subject to a rule . . .” (3) If things in the world were not regular and predictable (here Kant gives several examples of natural chaos), then “no empirical synthesis of reproduction could take place.” (4) “There must, therefore, be something that itself makes possible this reproduction of the appearances by being the a priori ground of a necessary synthetic unity of them.” (5) To represent a sequence of past events in the present time I cannot “lose the preceding representations from my thought”: I must “reproduce them when I proceed to the following” representations. The transition from step (4) to (5) introduces the general issue of the doctrine of inner sense in Kant: the account of time in general, its relation to temporal events and to personal identity. My present focus is not on this topic but instead on the transitions from (1) to (2) and from (2) to (3). Even if we grant that there must be a psychological law that explains how we are able to generate from memory a sequence of images, it is unclear why there should be a rule in nature corresponding to the law of association. Suppose that there is a series of random events—color patches generated randomly on a screen, say, so that they obey no predictable, regular rule. Why should this prevent us from remembering them in the sequence in which they actually occurred? Suppose nature itself was random and chaotic (“on the longest day the land was covered now with fruits, now with ice and snow”); why should this affect our ability to reproduce sequences of random events that we have experienced? There is the sequence last week fruits on the land, this week ice and snow, and I recall it. Even if we somehow explain this, why the need for an “a priori ground”: why should not the natural sequence and the capacity to receive and store the impressions of these be enough to allow for reproductive memory? My answer is that it is enough for us and should be enough for Kant, for Kant misdescribes the explanandum for which an a priori ground is offered as explanans: the explanandum is not our ability to reproduce from memory a given series of experiences but, rather, our ability to produce novel series of experiences represented by certain counterfactual conditionals. I identify eight main elements in the argument running from GW 234 to 236 (A111–115), the Affinity Argument in its “provisional” formulation. (1) Unless our experiences were subject to causal order and other categories, “necessary unity of consciousness would not be encountered” and the multiplicity of representations we did experience would “be without an object and would be nothing but a blind play of representations, i.e., less even that a dream.”

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(2) These categories cannot be derived from “experience”: they lack an “empirical origin.” (3) The concept of causality is a species of necessary relations. (4) The rule of psychological association of representation is something that we must assume “if one says that everything in the series of occurrences stands under rules according to which nothing happens that is not preceded by something upon which it follows.” The latter is Kant’s schematic statement of the rule of causality (GW, 275; A144/B183). (5) “The ground of the possibility of the association of the manifold, insofar as it lies in the object, is called the affinity of the manifold.” (This is the “empirical affinity.”) (6) The explanation for this affinity is that all appearances belong to the unity of original apperception.24 (7) The empirical affinity therefore rests on a transcendental affinity, an affinity that is in the cognizing subject. (8) Commitment to the existence of a transcendental affinity requires the following of nature:  “. . . nature . . . direct[s]‌ itself according to our subjective ground of apperception, indeed in regard to its lawfulness even depend[s] on this. . . ” Step (1) here is reminiscent of steps (2) and (3) of section 2.2, but it is not problematic in the same way. Here the issue is not whether our ability to imaginatively reproduce events could be realized in a chaotic world but whether we would have a real world as opposed to something else, a “dream-world” in Kant’s language, if there were not a causal order in nature. Still, even this claim is problematic in somewhat the same way as the former: why should not the world really be chaotic? Kant himself has allowed that appearances could occur without 24 There are two things we can take “the unity of original apperception” to refer to here. The first is the unity of the self or of the states of the self in virtue of which they are states of the self. The second is a unity of the kind that the self or the states of the self possess. This is a “unity of consciousness,” a kind of unification of elements that occurs in a judgment or other act of cognition. My interpretation requires that the reference be to the second kind of unity. (For an interpretation of unity of apperception in general that emphasizes the second rather than the first reading, see Dickerson 2004, 80–131. He focuses on the B edition. For an interpretation that emphasizes the first, see Longuenesse 1998, 52–58. She focuses on the A edition.) On this reading the unity of apperception is “that sort of unity” Kant mentions in the following sentence from the discussion of affinity: “Thus the concept of a cause is nothing other than a synthesis (of that which follows in the temporal series with other appearances) in accordance with concepts; and without that sort of unity, which has its rule a priori, . . . necessary unity of consciousness would not be encountered in the manifold perceptions” (GW, 235; A112; my emphasis). I take the reference to “that sort of unity” to mean that Kant countenances various instances of it. I take the unity of the self to be one instance of the general unity of consciousness, of special importance to Kant elsewhere, but only one instance of a general kind of unity.



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causal order (GW 222–223; A90/B122–123). Kant’s answer here seems to be that if the world were chaotic in this way our experiences “would be without an object.” This suggests that Kant is making a conditional claim: assuming that our experiences are in fact about objects, then they need to be lawful in a certain way. Kant raises the question “what is meant by the expression ‘an object of representation’ ” in the previous section (2.3) at A104 (GW, 231). Kant’s answer is that the concept of an object is the concept of something that is the basis for the regularity and constancy of the manifold of intuitions that are associated with the object.  . . . we say that we cognize the object if we have effected synthetic unity in the manifold of intuition. But this is impossible if the intuition could not have been produced through a function of synthesis in accordance with a rule that makes the reproduction of the manifold necessary a priori . . . Now this unity of rule determines every manifold . . . and the concept of this unity is the representation of the object  =  X . . . (GW, 231–232; A105) This same issue is raised again in the second analogy: We have representations in us . . . Now how do we come to posit an object for these representations, or ascribe to their subjective reality, as modifications, some sort of objective reality? . . . If we investigate what new characteristic is given to our representations by the relation to an object, and what is the dignity that they thereby receive, we find that it does nothing beyond making the combination of representations necessary in a certain way, and subjecting them to a rule. (GW, 309; A197/ B242) This doctrine has some affinities with analytic phenomenalism, a doctrine that analyzes physical object concepts in terms of experiential counterfactual conditionals.25 But there are important differences between Kantian phenomenalism and modern-day “analytic phenomenalism.” An analytic phenomenalist analysis is typically a contextual definition of physical-object language; we take a sentence like “there is an apple before me” and replace it by language that is I say “affinities with” advisedly here since Kant’s actual doctrine is probably not a version of modern analytic phenomenalism. For interpreters that take Kant to be committed to analytic phenomenalism, see Bennett 1966, 126ff., and Van Cleve 1999, 91ff.; for one who does not see Kant committed to it, see Allison 2004, 38–42. For present purposes, it makes for a clearer line of exposition to 25

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(supposedly) logically equivalent to that sentence but does not contain referential physical-object language or synonyms of referential physical-object language. The purpose of such an analysis is in the first instance ontological; it eliminates the existence of a class of entities while retaining the truth of the class of statements nominally about that class of entities. Kant is not attempting to do this, for he is not attempting to deny the existence of physical objects, as his Refutation of Idealism in the B edition makes clear (GW, 326–329; B274–279). He also does not appear to be attempting to define the notion of representation itself—to give a noncircular reductive definition of that concept—for as he says in the Jäsche Logic,  . . . representation is not yet cognition, rather cognition presupposes representation. And this latter cannot be explained at all. For we would always have to explain what representation is by means of yet another representation. (Young, 545; Ak 9, 34) What he is attempting to explain is the concept of the objectivity of the objects of representation, how representation of things that are transcendentally ideal can nonetheless be of things that are more than just states of our mind. This project is echoed in section 17 of the B edition (GW, 249; B137). We shall call the rule making a representation of a certain type of thing objective a “meaning rule for _____,” where the blank is to be replaced by a specific sortal term (e.g., an apple). When I think of an apple, I associate a series of possible experiences with certain possible actions. Thus if I imagine seeing an apple sitting before me, I imagine a series of sense experiences that would occur as I move my eye to the left or to the right or over the top of the apple. Similarly, I imagine a series of sense experiences were I to cut open the apple, roll it across the floor, and so on. Now the series of sense experiences associated with the meaning of “apple” cannot be composed of just any experiences in just any order I spontaneously imagine; there must be a specific series of experiences for each initiating action, and these and only these experiences collectively constitute the meaning rule of an object of a specific type. Moreover, it is also important to note that when one internally reviews series of experiences in the meaning rules for a certain concept (the concept of an apple in our example), this review is generated spontaneously and therefore is a form of synthetic activity: we can just decide to do this whenever we want, we are not driven by sensation to do so but are guided by rules. It is this spontaneity that makes the reproduction a

assume that Kant is a phenomenalist than to attempt to introduce the qualifications needed to give an accurate reading of his actual account.



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priori. But once we decide to review a specific content, that content follows with necessity—counterfactual necessity. Something like this is also true for the concept of a particular object; my house for example. If I imagine walking around my house at ground level from right to left, my imagination generates a certain series of experiences different from those I generate if I imagine walking at the level of the second story from right to left, different again if I imagine walking at ground level from left to right. It would not perhaps be appropriate to call these “meaning rules” of the concept of my house, but my understanding of my house consists in my ability to generate a series of possible experiences.26 If Kant is successful in showing that all objective intuitions of object types and of particular objects analyze into rules for generating series of experiences and if all intuitions are objective, he will have shown that all intuitions are subject to synthetic activity. It is not entirely clear whether Kant thinks that the second of these conditions is true—a central part of my reconstruction of his argument in the B edition depends on showing that this is problematic for Kant—but even if he does think so in the A edition, that, by itself, is not sufficient to prove that all intuitions are subject to the categories: it must also be shown that all synthetic activity is subject to the categories. Kant, indeed, maintains just this: “The same function that gives unity to the different representations in a judgment also gives unity to the mere synthesis of different representations in an intuition which, generally expressed, is called the pure concept of the understanding” (GW, 211; A79/B104–105). (The use of the phrase “pure concept of the understanding” here is an allusion to the categories.) With this premise and with the claim that all intuitions of objects are subject to synthetic activity, Kant seems to have closed the deal as far as the Deduction’s chief aim is concerned:  all intuitions of objects are subject to the categories, hence the categories have objective validity. But why then go on—is this not the point to be proven in the Deduction? The answer is that there are two sides to the Deduction that Kant is developing in the A edition: a subjective side and an objective side: One side refers to the objects of the pure understanding, and is supposed to demonstrate and make comprehensible the objective validity of its concepts a priori; thus it belongs essentially to my ends. The other side deals with the pure understanding itself, concerning its possibility and the powers of cognition on which it itself rests; thus it considers it in a subjective relation . . . (Preface: GW, 103; xvi–xvii) The locus classicus for interpreting Kantian phenomenalism in this way is C. I. Lewis, Mind and the World Order (Lewis 1929). 26

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The argument just given is the objective side, the argument yet to come is the subjective side . . . and the argument yet to come is the Affinity Argument. It comes in two versions: a provisional version and a final version. The provisional version of the A Deduction, although it accurately and clearly presents many of the elements of the full treatment, is misleading in several ways, of which I shall discuss two. First. In element (4) of the provisional argument given above, Kant says that the causal rule presupposes the empirical rule. This sounds rather too Humean a view for Kant; I argue that the relationship is in fact the reverse, as indicated in one of Kant’s most extensive critical discussions of Humean causation theory. I mentioned this passage before in connection with my discussion of Westphal, and it is of special interest to us because it is one of the few places in CPR, other than the present texts from the A edition, where Kant mentions the notion of affinity. He says in that text that Hume could not see how there could be anything outside experience to justify the a priori status of the law of causality. Kant replies: In the transcendental logic, on the contrary, we have seen that although of course we can never immediately go beyond the content of the concept which is given to us, nevertheless we can still cognize the law of the connection with other things completely a priori, although in a relation to a third thing, namely possible experience, but still a priori. In the reference to “possible experience” I see a reference to Kant’s phenomenalism. Kant’s argument continues:  . . . he [Hume] confused going beyond the concept of a thing to possible experience (which takes place a priori and constitutes the objective reality of the concept) with the synthesis of the objects of actual experience, which is of course always empirical; thereby, however he made a principle of affinity, which has its seat in the understanding and asserts necessary connection, into a rule of association, which is found merely in the imitative imagination and which can present only contingent combinations, not objective ones at all. (GW, 657; A767/B795) In this segment of the reply Kant distinguishes between an affinity as such and a “rule of association.” An affinity as such is what underlies necessary connections among the objects of experience; that is, which underlies the system of phenomenalist objectivity that Kant develops in the lead-up to the provisional version of the A  deduction. The rule of association is sharply distinguished from any



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principle of affinity here, in particular from a notion of “empirical affinity” that appears in element (5) of the provisional version of the deduction. Second. Kant attributes the empirical rule of association to an “imitative imagination,” referred to in the Deduction as the “reproductive” imagination, of which Kant has had much to say in section 2.2. It is not entirely clear to me why Kant is so interested in the reproductive imagination in the provisional A deduction27—there is also the productive imagination—but in the provisional version only the reproductive imagination is at issue. This is corrected in the full version. The productive imagination explicitly appears only in the full version of the Deduction (all of §3 of the A edition Deduction), ten paragraphs in A123 (GW, 240). The tenth paragraph corresponds to element (6) of the provisional version, the element in which the unity of apperception is introduced. It is worth quoting the corresponding passage since it brings out more clearly than in the provisional version the connection between “apperception” and “synthesis in the imagination that is grounded a priori on rules”—what is identified in the next paragraph as the “productive imagination”: The objective unity of all (empirical) consciousness in one consciousness (of original apperception) is thus the necessary condition even of all possible perception, and the affinity of all appearances (near or remote) is a necessary consequence of a synthesis in the imagination that is grounded a priori on rules. The next paragraph says that the productive imagination is transcendentally productive, that is, productive of experience, thus corresponding to element (7) in the provisional version: The imagination is therefore also a faculty of a synthesis a priori, on account of which we give it the name of productive imagination . . . it is only by means of this transcendental function of the imagination that even the affinity of appearances, and with it the association and through the latter finally reproduction in accordance with laws, and consequently, experience itself, become possible; for without them no concepts of objects at all would converge into an experience. (GW 240; A123)

Kemp Smith evidently is also puzzled about the relevance of the discussion of association in §2.2; indeed, he simply leaves it out of his abridged version of CPR (1934, 83). For a study of the Deductions sympathetic to the importance of the role of reproduction in the A Deductions, see Longuenesse 1998, 38ff. 27

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In the next section I  provide a detailed reconstruction of the Affinity Argument as it occurs in the final version of the A edition Deduction.

3.3.  The Affinity Argument In a passage from A105 (GW, 231–232; just quoted in §3.2), Kant characterizes the function of the understanding that generates the rules constitutive of objectivity as “the reproduction of the manifold.” Reproduction is the function that figures in all of the passages associated with the association of representations: in sections 2.2 and 2.4 and also in the fuller version of the Deduction in section 3:  . . . if representations reproduced one another without distinction, just as they fell together, there would in turn be no determinate connection but merely unruly heaps of them, and no cognition at all would arise, their reproduction must thus have a rule in accordance with which a representation enters into combination in the imagination with one representation rather than any others . . . This subjective and empirical ground of reproduction in accordance with rules is called the association of reproductions. (GW, 239; A121) There is, however, a problem with Kant characterizing the generation of the objective series of experiences as reproductive rather than productive. In addition to the texts from the A edition quoted above, Kant draws this distinction in section 24 of the B edition Deduction: Now insofar as the imagination is spontaneity, I also occasionally call it the productive imagination, and thereby distinguish it from the reproductive imagination, whose synthesis is subject solely to empirical laws, namely those of association, and that therefore contributes nothing to the explanation of the possibility of cognition a priori, and on that account belongs not in transcendental philosophy but in psychology. (GW, 257; B152) There is, however, a difficulty in seeing where to locate the capacity of the imagination to generate the counterfactual series of experiences for particular objects in these categories; neither the reproductive nor the productive capacities seem up to the job by themselves. Like the productive use of the imagination, I can generate spontaneously a series of experiences that I would have walking around the house at ground level from right to left. But unlike a purely productive use of the imagination, my ability to generate just this particular series is



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not simply up to me, as it would be in a fictional use of the imagination. Where I actually have walked around my house from right to left at ground level, this ability can be explained as a reproduction of the remembered experiences and could, then, still be classifiable as a “reproductive” use of the imagination. But for the very large proportion of objective experiential series that I can imaginatively reproduce, I have not actually experienced the sensations I imaginatively reproduce. In our example, I will probably never have walked around my house from right to left at second-story level, though I can generate a series of experiences that I would have if I did so. How are we to classify this use of the imagination? It is not reproductive, nor is it purely productive; it is an ability that depends both on patterns of sensation I have experienced and on an understanding of the structure of my house that transcends these sensations. I call this use of the imagination a “mixed use.”28 Most of the particular-object-dependent series of experiences that I can generate will come from mixed uses of the imagination. Mixed uses of the imagination are psychologically quite interesting, and I suggest that Kant’s failure to recognize them in his terminology and in his development of the Affinity Argument lies at the root of the chaos problem identified earlier in section 2.2. I contend that if we extend Kant’s argument in the affinity passages to mixed uses of the imagination, we can reconstruct the reasoning in those passages in a way that is more clear and persuasive philosophically—and more fully suits Kant’s ultimate purposes—than is the case with the argument as written. Our example is imagining what a walk around my house from right to left (starting at the bathroom window) would be like at second-story level. I have never had this walk but think that I can accurately imagine the sequence of experiences I would have if I did. How can I do this? This is a psychological question but with philosophically deep implications. In the first place we need to note that the mixed exercise of the imagination generates novel experiential content, and the question how novel content can be generated is among the most powerful and theoretically suggestive questions cognitive science seeks to answer. The answer must in general be that I have a theory of the topic in question, a theory that allows for a generation of contents that far outstrips what specific empirical data is actually experienced. In the case of the present topic, my house, what I must have is a theory of my house, a theory that tells me how big the rooms are Aquila has an extensive discussion of the role of Kant’s notion of affinity in the A  edition Deduction and also sees a distinction between tendencies to merely associate past recollected events and tendencies to “anticipate” future ones. As here, he sees the basis for the latter to lie partly in past associations and to be due to the operations of imaginative synthesis. He does not, however, locate the ground of the latter possibility in a prior commitment to the law of universal causality as an intellectual condition, as I am about to. See Aquila 1989, 72, for the latter point; 82–106, for the broader discussion. 28

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and other features of the specific structure of the house, a theory that tells me about the causal properties of the house in particular and of houses in general, a theory that tells me how things will look when seen in daylight and with the eye level with the objects seen, moving from right to left, but also how the house will look in twilight when viewed from below moving in the opposite direction. This theory must itself draw upon other theories, theories of perception, of physics, of the properties of materials, and the like. The theories in question are empirical theories justified by empirical data, and the empirical data, although describable at various levels of cognitive penetration, are empirical because they ultimately rest on sensations actually experienced. Although the world as we think of it in everyday, common-sense thought—Sellars’s “manifest image”—is a relatively constant world of durable objects and stable events and processes, the sensory data on which these thoughts are causally based are neither durable nor stable. Sensory data, whether understood as stimulations occurring on the surface of the sensory receptors or as sensations stripped down to their basic material, vary from moment to moment, depending on such things as the angle at which an object is looked at, the ambient light, and the surrounding context of color and light. In a word, sensory data are chaotic, and we somehow cognitively generate order from them. My suggestion is that we think of Kant’s talk of reproduction and association as a somewhat confused amalgamation of two distinct elements from our account of mixed uses of the imagination; when Kant talks of the possibility of chaos he is somewhat confusedly thinking of the chaos of the sensory data; when he contrasts the chaos with the necessity of order he is thinking of the contrast between the sensory chaos and the objective experiential counterfactuals that mixed uses of the imagination generate; and when he speaks of the need for categories and a transcendental ground for affinity, he is giving expression to the need for theoretical thinking as part of the explanation for our ability to produce these counterfactuals. I offer this as a suggestion that may prove helpful in laying out the rest of Kant’s argument, the part that leads to the Copernican revolution in metaphysics represented by the final step of the Affinity Argument. The notion of an experiential counterfactual has two properties to which I draw attention. The first is that it is a factual statement: it can be true or false, and which it is going to be for a given statement is not something we can simply decide by fiat. Reasonable though it may be for me to think that the wall will look blue (the color it normally looks from the ground) as I pass the second bay window on my hypothetical trip around the second story of my house, it may in fact look green—the ambient light at that level may create this effect. Determining this is an empirical matter; ultimately I have to set up the scaffolding and actually walk around the house to see what the wall near the bay window looks like. The second is that they are contingent counterfactuals. The contrast I intend here



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is between contingent and necessary counterfactuals. A necessary counterfactual is one that holds true through the full range of experimentally manipulable initial conditions; the theorems of applied geometry are necessary counterfactuals in this sense, or so I argued in the previous chapter. But a counterfactual expressing what my house would look like if I were to move around the second story does not conditionalize on the full range of experimentally alterable conditions; it selects one of these conditions and determines what would happen if it obtained. That is what makes them “contingent counterfactuals” in my sense. The facticity of experiential counterfactuals points in the direction of an objective order in nature. Insofar as the explanation of that order is an issue, it points in the direction of brute facts lying outside the imagination. While it is not entirely clear what this is for Kant, it must somehow rest on the differentiation of the content of appearances provided by sensation. I am suggesting that Kant’s interest in empirical affinity is with what grounds the truth of the mixed uses of the imagination responsible for the set of rules constituting phenomenalist objectivity. Henceforth I will understand “empirical affinity” in this way: it is the ground, whatever it turns out to be, of the capacity we have to engage in this use of the imagination. My suggestion is that this ground is the law of causality, subjectively applied. The argument for this runs as follows. Kant’s question is how the mind generates judgments about experiential counterfactuals from the fleeting data of the senses. Suppose, when the mind takes up a series of chaotic sensations for further processing, it always takes as a background assumption the principle that every event has a cause. If so, there is a rational obligation to find a cause for these events. Because of the fleeting and chaotic nature of sensations, regular conjunction will almost always be absent, so Humean causation will almost always be absent. A theory to find causes will therefore push the active mind in the direction of postulating theories and theoretical entities whose existence will figure in theoretical nomic regularities. These theoretical regularities will then provide laws explaining the sensations even in the absence of empirical regularities, thus meeting the requirements of the causal law. Without assuming the causal law as a condition of the mixed use of the imagination, there simply would not be the set of experiential counterfactual judgments that we in fact are able to make on demand. This makes the causal law an intellectual condition and the argument in favor of it analogous to the subjective application (the application to pure objects of the imagination) of the Transcendental Exposition of the Concept of Space. This provides some support for my suggestion made earlier that the Affinity Argument counts for Kant as a “subjective deduction” in the sense of the A preface (GW, 102–103; Axvii–xviii). This provides a detailed understanding of one way in which Kant argues that a category is a subjective condition of thought.

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Kant now calls this subjective condition a “transcendental affinity.” I take it to be so characterized because it is something that creates nature. This characterization is justified by the last step, (8), of the provisional version of the affinity argument, the step in which the move to idealism (Nomic Prescriptivist version) is made. However, in the provisional version Kant offers no grounds for it. Why should a subjective application of any rule make nature to be in accord with the rule? This is the central step in Kant’s idealist metaphysics, the final step in the Copernican revolution, and yet Kant had provided no argument for it in the provisional version. He does so in the final version: “Thus we ourselves bring into the appearances that order and regularity in them that we call nature, and moreover we would not be able to find it there if we, or the nature of our mind, had not originally put it there” (GW, 241; A125). The key phrase is “to find it there.” It is because we (inevitably) find causal order in nature, an objective condition, and because this order corresponds to the intellectual condition (for coherently thinking about nature) of applying the rule of causality a priori, a subjective condition, and because both of these conditions have been established independently of one another that there is something interesting and surprising to explain.29 The explanation is provided by the doctrine of Nomic Prescriptivism, a form of idealism. If this is so, then this is some confirmation of the leading idea of this book: that the final stage in the overall pattern of reasoning in the Transcendental Deduction of the Categories is parallel to the Second Geometrical Argument for Transcendental Idealism, the final stage of the Transcendental Exposition of the Concept of Space. Before concluding my discussion of the Affinity Argument, it is necessary to see how well my interpretation of it fits Kant’s stated account of the nature of a transcendental deduction at A85/B117 (GW, 220), “Theme (2)” of the four themes I identified at the outset of this chapter involved in Kant’s account of its purpose. Such a deduction is an “explanation of the way in which concepts can relate to their objects a priori.” I claim to have uncovered three such ways present in the Affinity Argument as reconstructed above.

Aquila (1989, 100–101) also extensively discusses the role of affinity in the A  edition Deduction, also treating it, in one of its senses for Kant, as a correlation, or “harmony,” between the representational side and the objective side. In this we are in agreement. But Aquila treats the correspondence as a consequence of Kant’s projectionist version of Transcendental Idealism, the latter of which is established independently, whereas I treat the correlation as providing Kant’s reason for adopting the Nomic Prescriptive form of idealism, thus requiring that each side of the correlation is warranted by an independent application of epistemic method. I take this to be the chief importance of the analogy between the Transcendental Deduction of the Categories and the Transcendental Exposition of the Concept of Space. 29



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(1) One is the necessity of the conditions on the side of thinking:  intellectual conditions. These give a priori conditions on the objects of thought, whether actual or not. These conditions constitute the subjective side of the correlation to be explained by the Deduction. (2) On the side of nature, there is an inevitability to our finding nature to be in accord with intellectual conditions: no matter who we are, no matter what possible conditions are present, we always find nature to have categorial structure. This inevitability, which serves as the objective side of the correlation, has to be established independently of the intellectual conditions for it to play its role in a correlation explanation. We should not call this “aprioricity in the proper sense,” since our finding nature to be in accord with intellectual conditions does not occur independently of sensibility. So here we have a special kind of necessity lying between the strictly a priori and the strictly a posteriori—“quasi aprioricity” as I call it—not clearly delineated by Kant but indicated by his use of the language of “finding.” (3) Finally, once the explanation has been arrived at by the Copernican inference, a third kind of aprioricity emerges. This comes from the newly inferred knowledge: we know in advance of particular experience that nature will be found to be in accord with these conditions because we make nature to be that way.

4.  Transition to the B Edition Deduction This concludes my discussion of the A edition Deduction. Kant went on in the B edition to rewrite the Deduction extensively, and the obvious question is Why did he do so? I conclude this chapter with some reflections on this question. In Chapter 7 I turn my attention to the B edition Deduction. The intervening chapter, Chapter 6, contains some background for that discussion. One reason is the apparent inconsistency, broached earlier, between the doctrine of the Aesthetic, that intuitions are given independently of the functions of the understanding, and the doctrine of the Analytic, that they are not. Providing a solution to this puzzle is one of the main tasks of the B edition Deduction, and providing an interpretation of that solution is one of our main tasks in the next chapter. Another is the problem with the strength of the argument in the A  edition Subjective Deduction we have just finished discussing. Kant might have decided to recast the subjective side of the Deduction in the B edition so that it would reap the benefits of a stronger form of argument. Additionally, there is

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the puzzling way in which the “chaos problem” is introduced in section 2.1 and the misleading emphasis on the reproductive imagination that motivated us to reconstruct the Affinity Argument as a whole; it may also have motivated Kant to reformulate his intentions in a different way in the B edition. There is evidence from the text of the B edition Deduction that Kant did recast the argument on the side of the intellectual conditions of thought. Some evidence for this comes from section 26 of the B edition and the recasting that occurs there of the Synthesis of Apprehension (GW, 261–262; B159–162). In section 26 the Synthesis of Apprehension is the form of mental activity that constructs our representation of empirical objects. This account draws heavily on two objective principles. (1) Space is a topological unity: every region of space is spatially connected with every other region of space. (2) All empirical objects are in space. It also depends on three subjective principles: (a) when the mind produces a representation of a perceived empirical object, it must place it in some specific spatial region; (b) when the mind places an empirical object in some specific spatial region, the region is itself located in unitary space; that is, the region is in topological relation to all other possible regions of spaces; and (c) the rule that governs the mind in doing the second thing is (somehow) governed by the rules associated with the categories. In this way Kant believes that he has achieved the objective of the Deduction. Even with this brief sketch of the main concluding line of argument of the B edition Deduction, we can see that there is a striking contrast with the account of the synthesis of apprehension in the A edition. In the A edition Deduction (§2.1:  GW, 228; A98ff.) the synthesis of apprehension constructs intuitions of temporally extended past events; in the B edition Deduction, the synthesis of apprehension is devoted to constructing representations of spatially extended objects currently present perceptually to us. In the A  Deduction no role is assigned to principles, subjective or objective, concerning space and the placement of objects in space,30 yet these principles lie at the heart of the B Deduction. I shall argue that what has made this transition possible for Kant is a new account of the classification of the idea of unified space and time; in the A edition it is left where it is left in the Aesthetic, as due to sensibility;31 in the B edition it is removed from sensibility and assigned to the understanding as an intellectual condition. What I  take this to mean is that the topological unity of space (and time) has become part of the necessary conditions of thought about objects. These conditions constitute a layer of rules fundamental to our ability to represent the Cf. Melnick 2004, 38–39, for the opposite view. See Metaphysical Exposition (in both A  and B), A22/B36 and A25/B39 (the Fourth Exposition). 30 31



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objective order, connected somehow to the categorial rules. The topological rule now replaces affinity as the subjective condition of thought chiefly under discussion in that part of the Deduction that makes the case for Nomic Prescriptivism. The notion of transcendental affinity as it operates in the A edition Deduction is the assumption of a causal law understood as a real necessity imposed on nature. The notion of affinity is still present in the B edition in this same sense in the Doctrine of Method section (A767/B795). However, this notion does not appear in the argument of the B edition Deduction itself. What replaces it in the B edition as the source of transcendental productivity is the principle of the topological unity of space. Chapter 7 presents my reading of the B edition Transcendental Deduction of the Categories. In Chapter 6, I lay the foundation for that reading.

6

Appearances, Intuitions, and Judgments of Perception

1.  Appearances: The Undetermined Objects of Empirical Intuition 1.1.  Are Appearances Constituted by the Understanding? A Preliminary Argument It is clear that appearances and concepts both contribute to knowledge and experience for Kant: without intuitions concepts are “empty;” without concepts, intuitions are “blind.” What this dictum certainly means is that intuitions contribute the objects for conceptual activity leading to knowledge or experience. But what does it mean to say that intuitions are “blind” without concepts? It could simply mean that we cannot recognize or judge characteristics of the objects given to us in intuition without concepts. This provides a modest role for concepts, one not ultimately departing from an empiricist view like Locke’s, athough, of course, Kant’s concepts are not Locke’s abstract ideas. In this case there would scarcely be a serious challenge to taking Kant’s many pronouncements that objects are simply given to us by intuition, independent of the functions of the understanding, at face value. But if concepts or, at least, synthetic activity guided by the understanding is affirmed by Kant to create unity for all intuitions from the manifoldness of items in sense and if all intuitions must possess this property to carry out their representational function, then we must deny that concepts play a modest role with intuitions, hence deny that intuitions contribute to knowledge the representation of objects unaided by the understanding. But taking such a view, despite its apparent congruence with the texts in the Deduction and elsewhere in the Analytic, comes at a cost. It seems to require that we simply discount the Aesthetic as Kant has written it:  intuition is the faculty that gives objects to the understanding for judgment. Those objects are “appearances.” Getting clear on this 134



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issue is central to understanding the direction that Kant’s reasoning takes in the B edition Transcendental Deduction. In Section 2 of this chapter I discuss Kant’s doctrine of unified intuitions as given in section 15 of the B edition Deduction; in this section I discuss Kant’s doctrine of appearances. My conclusion will be that Kant does not think that the ability of intuitions to present the mind with appearances rests on functions of the understanding. With some exceptions,1 this view is opposed by recent Anglo-American commentators. I begin with Beck in his well-known article “Did the sage of Königsberg have no dreams?”2 Beck’s main interest in the first part of his article is with the passage in section 13 (GW, 222; A89–90/B122), discussed at length in Chapter 5, in which Kant allows that appearances might be given to the mind independently of the functions of the understanding. It is important to realize that, unlike our own treatment of it, Beck thinks this passage does not represent Kant’s ultimate doctrine of intuition, and he reports “astonishment even indignation” among Kant’s “traditional” commentators,3 who account for the troubling passage either by adopting a version of the “patchwork theory” of the composition of the CPR or by supposing that Kant “was asking a question which he imagined his readers would naturally ask and was preparing them for an argument by which this ‘difficulty’ could be averted.” Both interpretations agree that Kant finally denied the possibility left open in section 13.4 I would like to express a bit of indignation of my own at this conclusion. The texts I have quoted from section 13 are, by the usual standards, of central importance; they are fairly clear by any philosophical standard, but taking as the standard of clarity Kant’s own exposition of his arguments in the Deductions in general, they are blindingly clear (perhaps that is why they are so puzzling to the commentators). Moreover, the ideas are presented not once but twice and are developed at considerable length, including examples; the texts develop points for which an explicit and reasonably developed theoretical justification has been given in a major preceding part of the CPR, the Transcendental Aesthetic (one-half of the Doctrine of Elements in CPR); the texts appear in a section explaining in Kant’s own words the problems he seeks to solve in the Deduction; the texts appear in both the A and B editions. What could possibly justify the aforementioned dismissive treatment of these texts?

1 An exception is Aquila, discussion of whose views on Kant’s doctrine of intuition was prominent in Ch. 3. See Aquila 1983, 122–123. For criticism of Aquila, see Pereboom 1988, 349, n. 12. For another exception, see Allais 2009. 2 Beck 1978. 3 The words are from de Vleeschauer. 4 Beck 1978, 40.

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The two answers provided by Beck, on behalf of himself and the traditional commentators (whose views he in other respects rejects), lie in a certain interpretation of the central argument of the Deduction, which he takes to rule out the possibility that there could be appearances (in Kant’s sense) that are not governed by categorial lawlikeness and in a distinction he finds in Kant’s texts between two kinds of intuition. I deal with these reasons in order. Reason 1. Here is Beck’s “compressed” version of the Deduction:5 1. The “I think” must be able to accompany all of my representations of which I am conscious (B130). 2. To think is to judge (A79/B141). 3. To judge is to relate representations to one another according to a rule given by a category (B141). 4. Representations synthetically related to each other according to the rule given by a category as a concept of an object in general are the same as representations related to objects (A191/B236). 5. Therefore, relation to an object must be ascribed to all representations of which we are conscious. To the extent to which this reconstruction relies on the B edition, it rests exclusively on the first part of that argument (§§15–20), ignoring the second part (§§22–27), which Kant himself takes to be of greater importance. That aside, the argument is not an implausible reading of the first part: Kant does seem to be saying that from the necessity of apperception (the necessity of the attachment of the “I think” to all my representations), all of the objects we humans can represent exist in a world of lawlike regularity; and if the unity of apperception is some kind of necessary fact (or the “ascribability” of the “I think,” a weaker requirement Beck himself endorses,6 is a necessary fact), then it seems that appearances cannot after all exist in an unlawful world. This means at most that there is a tension between the texts in section 13 and those in the Deduction proper, perhaps a contradiction; it does not mean that the doctrine of section 13 must be abandoned. Could the problem lie with the reading of the Deduction that Beck has presented? In Chapter 7 I argue, on independent grounds, that this is in fact the case:  a reading like Beck’s is not only not inevitable, it is not the best available. But that is not my point here. My point here is that Kant’s expositions of the argument in both the A and B editions are models of unclarity, in both the effectiveness of Kant’s explanation of the meaning of his key philosophical terms (what exactly is the meaning of 5 6

Ibid., 44. Ibid., 45–47.



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“unity of consciousness”?), in systematic ambiguities (self-consciousness vs. consciousness) and in the opacity of the argument structure itself. Why should someone maintain that the deliverances of doctrines presented with such expository weaknesses be assigned greater weight than (one of the few) passages in the Deduction, indeed of the whole of CPR, which is free from these weaknesses? There are two sorts of answers that traditional interpreters have offered. One7 is that there are self-contained doctrines developed in the Analytic that are simply inconsistent with the plain meaning of the texts from section 13 and should be given greater weight since they represent more central aspects of Kantian thought. To this I reply that many of the arguments of the Analytic depend on Kant’s doctrine of Nomic Prescriptivism,8 and the latter, as I have just been arguing, depends on Transcendental Idealism. Further, I argued earlier (Ch. 3, §2) that Transcendental Idealism depends on the power of the mind to project the structure of its faculty of receptivity onto its objects and that the latter capacity is not due to the categories. From this it follows, as Kant says in section 13, that appearances could very well be given without conforming to intellectual requirements. So this reason is unsuccessful in discrediting the section 13 texts. However, some arguments in the Analytic do not (or not obviously) depend on Nomic Prescriptivism; for example, the much-admired Refutation of Idealism. The argument of this text rests on the proposition that we have immediate perception of objects in space, a proposition that is not only not incompatible with the doctrine of section 13 but seems to require it: The immediate consciousness of the existence of outer things is not presupposed but proved in the preceding theorem, whether we have insight into the possibility of this consciousness or not. The question about the latter would be whether we have only an inner sense but no outer one, rather merely outer imagination. But it is clear that in order for us to even imagine something as external, i.e., to exhibit it to sense in intuition, we must already have outer sense, and by this means immediately distinguish the mere receptivity of an outer intuition from the spontaneity that characterizes every imagining. (GW, 328; B276– 277, note; my emphasis)

Due, e.g., to Guyer, discussed later. Thus Kant writes in the Second Analogy: “I perceive that appearances succeed one another, i.e., that a state of things exists at one time the opposite of which existed in the previous state. Thus I really connect two perceptions in time. Now connection is not the work of mere sense and intuition, but is here rather the product of a synthetic faculty of the imagination, which determines inner sense with regard to temporal relations” (GW, 304; B233). 7 8

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An outer sense gives us objects independently of spontaneity; thus the objects of outer sense can exist independently of the understanding. This is the very doctrine of the section 13 texts that the traditional commentators say is ultimately repudiated by Kant. Yet there is a strategy that takes an argument made in the body of the Refutation, from the determination in time of the self to the existence of a lawful world (nn. 1 and 2, GW, 327–328; B277–278), and reads it into Kant’s intentions in the Deduction at a crucial point: the transition from the unity of apperception understood as the unity of self-consciousness to the objective unity of apperception understood as the kind of unity objects have when they exist in a world subject to the laws of the categories. A strategy of this sort has been pursued by Guyer in various places.9 Why should he think it necessary to read this into Kant’s arguments? Because the argument for the Deduction as Kant wrote it is an “embarrassment,”10 “a failure and at best sets the agenda for the detailed demonstration of the role of the categories in the determination of empirical relations in space and especially time in the following sections of the Critique of Pure Reason.”11 But with Kant’s true reasoning in the Deduction now revealed, it is argued, the conclusion of the Deduction can be appealed to as proof that Kant repudiated the doctrine of section 13. There are two objections I  wish to lodge against this strategy. The first is the one already noted, that the doctrine of the Refutation of Idealism actually depends on the doctrine of section 13. The second is more general and more fundamental. If one were to accept as an adequacy condition of our interpretation that Kant is committed ultimately to the doctrine that appearances can be given independently of the functions of the understanding, this would give one hermeneutical leverage to apply to any interpretation of the argument of the Deduction: it must be read in a way that allows for this doctrine. I do not propose to do this but I give this doctrine great weight on the basis of the clarity and centrality (in both editions) of the passages in which it is asserted. I also argue in detail in Chapter 7 for a point raised first by Ameriks (discussed in the previous chapter), that only if we accept in some sense (in a sense to be developed in §3.4) that Kant allows for empirical intuitions that are not unified by the Categories can we develop a reading for the two-part structure of the B edition Deduction as Kant (probably) intended. Moreover, on this reading, we will find not only that it does not go as indicated by the traditional commentators but that it escapes their harsh philosophical assessment.

E.g., in Guyer 1987. “The argument of Section 20, which is to crown Kant’s deduction, only compounds his embarrassment” (Guyer 1992, 152). 11 Ibid., 155. 9

10



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Second reason. It will be helpful to begin our discussion of Beck’s second reason for dismissing the section 13 text as reflecting Kantian doctrine with an account of the “two meanings” of intuition Beck sees in Kant: The Critique begins with an inspectional conception of intuition and ends with a functional conception. According to the first, an intuition is a passively received inspectable sensory datum giving consciousness of an individual object independently of all categorization. It is given to consciousness as it were ready-made and labeled.12 In saying this it seems that Beck is conflating the issue of intentionality (how objects are made available to the mind for cognitive action) and label-providing consciousness (how the characteristics of said object are made available). It may well be that consciousness of characteristics of objects given to us by intuition relies on synthetic activity (thus is not “given to consciousness as it were ready-made and labeled”) and yet the objects themselves are made available to the mind by means that do not involve synthetic activity. This possibility is precisely the one that I think best reflects Kant’s doctrine.13 When Beck comes to contrast the inspectional account with the functional account, it is intentionality rather than inspectability that is in focus. On the inspectional view, there could be intuitions which relate immediately to objects but do not conform to the categories . . . According to the functional view, representations which do not conform to the concept of the object may be experiences but are not considered intuitions precisely because they fail to conform to the concept of an object.14 (Because of the emphasis on the noncognitivist characteristics of the inspectional conception of intuition, I refer to this conception of intuitions as “noncognitivist” rather than “inspectional.”) Beck is bringing two contentions together in this last passage; one is that the idea of an object in Kant is a functional idea involving a connection of “representations” according to laws; the other is that the idea of an intuition in Kant is a functional idea of this same kind. There are Beck 1978, 41. Although Kant does not say so, I take it that the possibility that appearances are given to us independently of the functions of the understanding (category-governed functions) also requires that we could have consciousness of these appearances. This possibility in turn requires that we find in CPR the possibility of making judgments about appearances that, though dependent on synthesis, hence on concepts, are not dependent on categories. In §3 of this chapter I argue that Kant does have such a doctrine and that the concepts in question are metrically indeterminate concepts. 14 Ibid., 43. 12 13

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certainly texts in Kant that support both of these contentions, as there are texts that support the noncognitivist reading, yet the contentions are not equivalent. In the next section I discuss the second of these; here let me say something further about the first. There are three texts Beck cites that are especially telling for the functional account. The first is from the Second Analogy. Appearance, in contradistinction to the [mere] representations of apprehension, can be represented as an object distinct from them only if it stands under a rule which distinguished it from every other apprehension and necessitates one particular mode of connection of the manifold [of apprehension]. The object is that in the appearance which contains the condition of this necessary rule of apprehension. (A191/B336; quoted in Beck, 42) In the first sentence Kant’s assertion that our ability to represent [vorgestellt] appearances as objective entities depends on their “standing under a rule” is not inconsistent with the “inspectional” (noncognitivist) reading as long as “represented as an object” is understood as a kind of cognition (Erkenntnis). That it should be so understood is suggested by the qualification “as.” Kant’s doctrine is that objective cognition of appearances depends on rules governed by the categories: no surprise there. However, the last sentence suggests that the appearance is somehow constituted by the rules, and that is inconsistent with the noncognitivist reading. But it is also inconsistent with Kant’s official definition of “appearance” as the “undetermined object of empirical intuition” at A20/B34. I suggest that Kant is here (in this last sentence) thinking of the determined object of empirical intuition and using “appearance” in a different sense than is allowed by his precise usage: determined objects of empirical intuition are appearances in the transcendental sense; it is that sense I think we can reasonably attribute to Kant here.15 There remains the other class of texts, those that seem to define the concept of an object in general in a functionalist way. These texts have had a powerful effect on interpreters, pulling many of them away from the noncognitive reading of intuition and its objects. Consider; for example, a position developed by Van Cleve:16 that appearances are “virtual objects,” “logical constructions The other two passages Beck cites come from the Phenomena and Noumena chapter (his translation): “The fact that this affection of sensibility [sc. Intuition] is in me does not amount to a relation of such representation to any object” (A253/B309; Beck’s interpolation); and “Thought is the act which relates given intuition to an object” (A247/B304). These passages are surely suggestive of Beck’s interpretation, but I believe that at least the first of these can be handled by the general considerations I am about to adduce in relation to four other texts that seem to make a similar point. 16 Van Cleve 1998, 10–11. See also Allison 1983, 173ff., et.al. 15



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out of perceivers and their states.” This makes Kant a “phenomenalist.” Van Cleve offers two grounds for attributing this view to Kant. The first is that it explains how Kant can claim that appearances are dependent on states of perceivers without having to invoke Brentano intentionality, understood (see Ch. 3) as positing intentional objects with “intentional inexistence.” The second is that key Kantian texts in the Analytic in which Kant gives his account of an object are best understood as giving a phenomenalist reconstruction of the notion of object. (He cites approvingly a passage from C. I. Lewis’s Mind and the World Order.)17 Here, Van Cleve claims that there is a second class of objects—“objects2” as he calls them, material objects like houses—that are also subject to “contextual definition”:  “Objects (objects2) thus turn out to be logical constructions at one remove: they are logical constructions out of objects1, which are themselves constructions out of representations. . . .”18 Now phenomenalism, as Van Cleve understands it, is a doctrine that contextually eliminates reference to certain kinds of entities; hence eliminates the entities themselves. What is left is just an echo of the objects through our ability to assign truth value to the original sentences containing expressions ostensibly referring to the objects. Not all interpreters of these key texts see Kant as eliminating talk of objects in this way, but they do see Kant as taking various rules based in the understanding as constituting the concept of an object for Kant. In this case, too, there is no room for appearances understood as the immediate objects of intuition presented to the mind independently of the functions of the understanding. Van Cleve makes it clear that this is the approach he is taking: “ . . . Kant defines an object as something the concept of which plays a certain role.”19 As support for his contention he presents several of the key texts, saying of one from the Second Analogy at A197/B242 that this passage “makes the point as explicitly as one could like.” But this text is concerned with explaining “what new character relation to an object confers upon our representations, what dignity they thereby acquire . . .” Van Cleve assumes that when Kant explicates what it means for representations to have this character, “relation to an object,” Kant means to be defining the notion of “object” itself. I believe that if we look more closely at this and several similar passages, we shall see that the overall tendency of these passages, especially those in the B edition, does not support this reading. There are four passages that I propose to consider.

17 18 19

Lewis 1929, 140; quoted here on 92. Ibid., 93. Ibid., 92.

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Passage 1  . . . we are now also able to determine our concepts of an object in general more correctly. All representations, as representations, have their object, and can themselves be objects of other representations in turn. Appearances are the only objects that can be given to us immediately, and that in them which is immediately related to the object is called intuition. However, these appearances are not things in themselves, but themselves only representations, which in turn have their object, which cannot therefore be further intuited by us, and that may therefore be called the non-empirical, i.e., transcendental object  =  X. (GW, 233; A108–109)

Kant says that he is here giving an account of the concept of an object, the project Van Cleve assigns to this passage. I first note that Kant is here talking about two objects, the appearance and the transcendental object = X. (In both cases the term Gegenstand is used.) Kant repeats the doctrine of the Aesthetic here about appearances; they are given in intuition. So, clearly, this text is not one that gives support to the idea that Kant is denying in the Analytic that appearances are given independently of functions of the understanding. Moreover, Kant is not here offering a definition of appearance but of transcendental object. His definition is this: The pure concept of the transcendental object . . . is that in which all of our empirical concepts in general can provide relation to an object . . . This relation, however, is nothing other than . . . the synthesis of the manifold through a common function of the mind for combining it in one representation. (GW, 233; A109) The notion “relation to an object” appears here, and we need to know what it means to understand Kant’s intentions here. There are two possibilities I wish to consider: (1) Representations bear relation to an object when and only when they collectively constitute an object in virtue of that relation. (2) Representations bear relation to an object when and only when they serve as attributes truly ascribable to said object. The first of these provides a definition of the concept of an object, the second of the concept of objective predication. One of the chief differences between (1) and (2) is that (2) leaves the concept of an object as such undefined and, a fortiori, undefined in terms of functions of the understanding. I maintain that it becomes increasingly clear as we progress to passages that occur only in the



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B edition that it is the second rather than the first of these interpretations that Kant intended. Passage 2 an object, however, is that in the concept of which the manifold of a given intuition is united. Now, however, all unification of representations requires unity of consciousness in the synthesis of them. Consequently the unity of consciousness is that which alone constitutes the relation of representations to an object, thus their objective validity . . . (GW, 249; B137)

The first sentence again suggests that Kant is giving an account of the notion of an object, as in the passage from A108–109. Again, the notion “relation to an object” appears.20 If we paraphrase the last sentence to say that the unity of consciousness constitutes what it is for representations to constitute an object, we have reading (1). This is, admittedly, a reasonable reading of that sentence in light of the opening sentence, but it can also be read in accord with (2) if taken out of context. Now consider the following passage a few pages later, in section 19 of the B Deduction: Passage 3 In accordance with [laws of association] I could only say “If I carry a body, I feel a pressure of weight,” but not “It, the body, is heavy,” which would be to say that these two representations are combined in the object, i.e., regardless of any difference in the condition of the subject, and are not merely to be found together in perception . . . (GW, 252; B142)

Passage 3 comes as the penultimate installment of the first part of the B Deduction and, I  submit, must be given great weight in interpreting the passage from section 17 previously cited, since the point of the Deduction to date is realized here:  the connection between the doctrine of a unifying synthesis and judgment. Kant’s language here is of representations that are combined “in the object.” The representations being combined here are property-type representations—being a body, being heavy in this case—not an object-type representation (for Kant, the term “appearance” usually applies only to the latter). The rest of the passage makes clear that this is a reference to a way in which attributes relate to objects when they are truly predicated of the object, not merely somehow associated with it. The fusion of attribute and object into an “objective unity” (§18) seems to be task of a synthetic operation of the understanding in its 20

This is how Allison (2004, 173ff.) takes it.

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objective employment. If we read Passage 2 in light of Passage 3, we can see that “relation to an object” in the former can also reasonably be read as the relation of being “in the object” in the sense of the latter. If this is indeed the right reading of these passages, then Kant is relying on an antecedent notion of an object to serve as that to which the predicates are objectively attributed—and that is an appearance. Kant’s doctrine in the Aesthetic is that appearances are given to us by intuitions without the actions of the understanding. I now offer a final passage as evidence that this indeed is Kant’s view. This passage was added to the discussion of time in the B edition Transcendental Aesthetic. It is appended as a note to B70: Passage 4 The predicates of appearance can be attributed to the object in itself, in relation to our sense, e.g., the red color or fragrance to the rose; but the illusion can never be attributed to the object as predicate, precisely because that would be to attribute to the object for itself what pertains to it only in relation to the senses or in general to the subject, e.g., the two handles that were originally attributed to Saturn . . . if I attribute the redness to the rose in itself, the handles to Saturn or extension to all outer objects in themselves, without looking to a determinate relation of these objects to the subject and limiting my judgment to this, then illusion first arises. (GW, 190; B70)

This passage is not easy to interpret. However, if we understand what it is to attribute a characteristic “to the object” here as meaning what it is to say that a characteristic is “in the object” in the sense of Passage 3, then Kant seems to be saying that we can attribute properties to appearances (even if these are a special class of properties that must be taken “in relation to our sense”) in the same objective manner as occurs in any case of objective predication. Illusion arises when we take representations that are not “in the object” in this sense but are just associated with it and claim that they are in the object. For example, if my experience is of a rose that looks red, what is the case in my experience is that the rose appearance and the red look are associated in space and time—the look is where and when the rose appearance is—but the red look is not truly “in the rose.” There is no illusion here. However, if I see the red as being in the rose itself (see the rose as red) when the red is simply a red look associated with the object, then illusion does arise. The conclusions that I draw from this are that appearances in the sense of the Aesthetic are the objects of empirical intuition, they can be determined or not depending on the kind of attribution involved, and they are given through intuition to thought without depending on or being constituted by operations of the understanding.



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1.2.  What Are Appearances? Let me first construct a path to what I shall call “ordinary empirical appearances.” The basic language in which we describe how things appear involves a relational verb modified by an adjective; for example, “The apple appears red to me.” The word “red” in English is an adjective, not an adverb, and this is a fact that needs some explaining.21 (I am supposing that the explanation is not going to be that we somehow just leave off -ly’s from these modifiers.) Where there are adjectives, there must be nouns. In this case, the nouns are hidden somehow from view. The noun in question is “appearance.” So when I say that an apple appears red to me, in the “deep structure” what I am saying is that there is an appearance that is red that is somehow related to the apple and somehow related to me. One possibility of how it is related to the apple is by way of representation, another is by way of causation (or both), another is by way of shared qualitative character (an apple appearance), yet another is by way of identity (the apple just is the appearance). There are also various ways that the appearance could be related to us, but all have in common that they account for the perspectival nature of the appearances. A penny appearance shifts from elliptical to circular as our perspective on the penny shifts. One possibility is that appearance in Kant’s sense at A20/B34 (“The undetermined object of an empirical intuition is called appearance”) is an ordinary empirical appearance in the sense just explained. What I mean by this is that, although appearance language in Kant’s technical sense does not have the same sense as appearance language in the ordinary sense, which occurs in both contemporary English and eighteenth-century German, what Kant takes appearances in his sense to be are what we are referring to when we use ordinary appearance language. There are several advantages to this reading. One is that the notion of an ordinary empirical appearance would be familiar to Kant’s readers, and we might hope that Kant would want to use concepts familiar to his readers in explaining his ideas in the opening pages of his work. Certainly if “appearances” here meant something in a transcendental sense—an object that is transcendentally ideal—then no reader of CPR, reading it in the order in which it was written, could possibly understand Kant’s meaning the first time through; and, of course, the argument-structure of the Aesthetic would become incoherent. A  second reason is that the perspectival character of ordinary empirical appearances suits them well for the role they will ultimately play in the doctrine of empirical schematism, for as Sellars notes, empirical schemata construct perspectival images of objects.22 A third reason is that this conception of appearances allows for a This explanation, admittedly, does not work so well for German, where adjectives and adverbs need not be distinguished by word form. 22 Sellars 1978, 238n (§33). 21

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doctrine of judgments of perception, explicitly formulated in detail only in the Prolegomena, to be formulable within the theoretical apparatus of CPR. (The possibility of doing so is quite controversial; what should not be controversial is that it is an advantage for an interpretation of CPR if it can show how this is to be done while accommodating the other things that need to be accommodated.) I discuss both of these doctrines later in this chapter (§3.3). Another possibility is that appearances are ordinary empirical objects, nonperspectival entities such as tables and chairs, as we ordinarily expect them to be. There is a sentence in the Conclusion of the Aesthetic (in both the A and B editions) that may suggest this: “For in this case that which is originally only appearance, e.g., a rose, counts in an empirical sense as a thing in itself, which yet can appear different to every eye in regard to color” (A29/B45). (The case Kant refers to is the case of things like “colors, taste, etc.,” which are “completely inadequate examples” of the “transcendental concept of appearances.”) It is clear that the rose, considered as an empirical thing in itself, is an ordinary empirical object that is nonperspectival: it can appear differently to every eye. What is not clear is whether the rose is said here to be an ordinary empirical object. It seems that it is, for Kant says that what is “originally” an appearance “counts” (gilt) as an empirical thing in itself. However, please note that the status as an empirical thing in itself is something we attribute in thought to the rose-as-appearance (it “counts” as an empirical thing in itself), not something that the rose-asappearance actually is. The rose-as-appearance as it actually is, is the rose as an ordinary empirical rose appearance. There are four main objections to this view. The first is that Kant’s official definition of an object rules this reading out in principle. I have already discussed this objection. The second objection is that the theory of unified intuitions rules this reading out in principle. I  discuss Kant’s account of unified intuitions in the next section, showing that it does not have this effect. Third and of greatest importance, it will be objected that a proper reading of the argument structure of the Transcendental Deduction as whole rules out this reading.23 My reply to this is simply to ask the reader to wait until the end of Chapter 7 to decide whether this is so. The fourth objection is that this conception of the objects of intuition is incompatible with the account of objective predication, which was crucial to my argument against the first objection. I deal with this objection in the remainder of this section of this chapter. Kant clearly thinks that we can say what properties empirical objects really have; that is, have independently of perspectives we have on objects and the way Pollok (2008) has even argued that very purpose of the Deduction is to rule out the existence of judgments of perception and the notion of an uncategorially synthesized appearance on which they depend. See note below for reference. 23



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that they appear to us at any given time. It is natural to suppose that Kant provides for this by giving an account of the existence of ordinary empirical objects, tables and chairs, that are understood as nonperspectival objects. On one reading, this class of objects then would be somehow constructed out of the class of ordinary empirical appearances. This is the already mentioned view of Van Cleve. Alternatively, appearances in Kant’s sense could be taken to be, not the perspectival objects I am claiming them to be, but nonperspectival objects— ordinary empirical objects. This is the view of Pereboom.24 However they are introduced, these “objective objects,” to use language from Prauss,25 are the subjects of predication when predication is objective. But there is another way that objective predication can be accomplished by Kant, a way that does not require that the subjects of objective predication be objective objects:  take ordinary empirical objects to be perspectival objects (“ordinary empirical appearances”) and account for objectivity through a theory that allows that they are the subjects of objective predication. For example, when I  look at a penny from one angle and then look at it again from another, on the view that Kantian appearances are objective objects (Pereboom’s position), there is only one object I see. On the view that Kantian appearances are perspectival objects, there are two objects I see in sequence, but we can say that they bear to each other objectively the relation “being the same penny.” This is the position I attribute to Kant. Now it will seem odd, even contradictory, to say of an elliptically shaped penny appearance that it is really (objectively) a three-dimensional disk shape or of two objects that they are the same. Isn’t this simply a contradiction: we are saying of a certain thing x that it is both elliptical and not elliptical in shape or of two things that they are one? From a transcendental realist stance this is indeed so, for from this stance we regard all objects as things-in-themselves, including things that are subject dependent and perspectival.26 To regard something in this way is to regard subject-predicate judgments as expressing an ontological relation between object and property; for example, the inherence of a universal in a particular. Saying of a perspectival object that nonperspectivalness inheres in it is of course impossible. But Kant’s transcendental turn has not just moved space and time indoors; it has also transformed the theory of judgment from

See Pereboom 1988. Kant “makes it clear that he believes that we have immediate cognitions of objects that are permanent, which persist and undergo causal change even when we may not perceive [them] . . . Intuitions (in one sense) are the representations of ordinary objects, and it is central to Kant’s notion of intuition that they are immediate awarenesses of these ordinary objects” (338). 25 Prauss 1971, 17. 26 I am here in agreement with Allison that Kant allows that there is a transcendentally realist stance that we can take even to the entities that form the domain for a classical idealist theory like Berkeley’s. See Allison 2004, 26–27. 24

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an ontological theory to something else.27 If we cannot determine whether an elliptical penny appearance is really disk shaped simply by seeing whether disk shape inheres in this appearance, how might we proceed? We could proceed by actually generating a series of other appearances by looking at the penny from different angles. (Perhaps I do not have to actually carry out these activities but can predict from the nature of the appearance and past experiences what such a series would be like.) This series of appearances could then confirm or disconfirm a judgment about the reality of disk shape using rules that connect various series of appearances with objective shape. These rules are empirical concepts. Now, connecting appearances together in this way is synthesizing appearances28—linking them, not constructing them—and on the present suggestion, it is through this process that empirical judgment occurs. The place where this new theory of judgment is first introduced is the Metaphysical Deduction (§§9–12, common to both editions, in the B edition numbering system).29 Interpreting it as I  have done helps us understand the claim made in a key passage in section 10 that the functions of synthesis and judgment are the same: “The same function that gives unity to the different representations in a judgment also gives unity to the mere synthesis of different representations in an intuition, which, expressed generally, is called the pure concept of the understanding” (A79/B104–105). Before turning to the task of Section 2 of this chapter, the theory of unified intuitions in section 15 of the B edition Deduction, it might be useful to ask how much of that task the doctrine of judgment and synthesis in section 10 has already accomplished. It has not, of course, taken us to the ultimate goal of the Deduction as I conceive it, the proof of Nomic Prescriptivism. But has it, for example, taken us as far as the conclusion of the first part of the B Deduction, section 20? But now the categories are nothing other than these very functions for judging, insofar as the manifold of a given intuition is determined with regard to them. (#13.) Thus the manifold in a given intuition also necessarily stands under the categories. (GW, 252; B143)

See Nussbaum 1990, 99, for a discussion of this turn. “By synthesis in the most general sense, however, I understand the action of putting different representations together with each other and comprehending their manifoldness in one cognition” (GW, 210; A77/B103). 29 Thus I agree with Melnick 2004:”The significance of this Deduction, I believe, is that Kant has set out an entirely new theory or account of intellectual cognition or thought in the transcendental deduction . . .” (54). I do not follow him in claiming that this new theory is that “cognitions are rules for the propriety of reacting.” 27 28



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It may seem as if it has. I have just been arguing that according to Kant’s theory of judgment as depicted in section 10, making a judgment about an appearance is just carrying out a synthesis guided by rules. Categories are the rules that operate at the highest level of abstraction within Transcendental Logic, the logical theory operating in section 10. The kind of judgment we have been considering above is subject-predicate judgment, but there are, according to Kant, twelve forms of judgment in all (see the Table of Judgments: GW, 206; A70/B95). Corresponding to each form of judgment will be a characteristic kind of synthesis. There are thus twelve categories as well (see the Table of Categories). So if empirical judging requires empirical concept–governed synthesis and if empirical concept–governed synthesis is a concrete level of synthesis requiring higher-level synthesis and if the “categories” is Kant’s name for the higher-level synthesis—and all of these conditions appear to be maintained by Kant by the end of section 10—then has not Kant proven by the end of section 1030 that “the manifold in a given intuition . . . necessarily stands under the categories”? Not quite. I see a difference between saying that the objects of intuitions are connected by synthetic activity (an “external operation of synthesis” as I call it) and saying that they are constituted by synthetic activity (an “internal operation of synthesis” as I call it).31 The former is the weaker claim and is compatible with the thesis that appearances are given independently of the operations of the understanding; the latter is a stronger claim and is not compatible with this thesis. In the paragraph preceding the “same function” sentence quoted earlier (A79/B104–105), Kant outlines three stages to cognition: the manifold of pure intuition, synthesis of the manifold, and the application of concepts. The third stage is described thus: “The concepts that give this pure synthesis unity, and that consist solely in the representation of this necessary synthetic unity, are the third thing necessary for cognition of an object that comes before us.” Compare this with the language from section 20 regarding what it is that receives unification by concepts: in section 10 it is the synthesis that receives unification, in section 20 it is the intuition that receives unification32, a point reinforced by Kant’s emphasis on the manifold “insofar as it is given in one empirical intuition” (“one” is here not only emphasized but capitalized in the German: Einer).33 Again, in

I set aside the fact that Kant references §13 rather than §10 in the passage just quoted. For some discussion of this, see GW, 727, n. 41. 31 In this I am in agreement with Aquila (see Aquila 1989, 107). 32 “The manifold that is given in a sensible intuition necessarily belongs under the original synthetic unity of apperception, since through this alone is the unity of the intuition possible” (this is the first sentence of §20). I am indebted to Robinson here. See Robinson 1984, 404–405. 33 A point made by Henrich 1968/69, 645. 30

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section 10 it is synthesis that is brought under concepts,34 in section 20 it is the manifold in a given intuition that stands under categories. I conclude, therefore, that the work of section 20 has not already been accomplished in section 10. In whatever way Kant reaches the conclusion of section 20 and whatever its ultimate significance for the position we have taken on appearances here, the journey begins in section 15 with the doctrine of unified intuitions. To this I now turn.

2.  Intuitions in General 2.1. Introduction There are two chief claims that Kant advances in section 15, the first section of what has come to be called “the first part” of the B edition Deduction, spanning sections 15–20 (the second part spans §§22–27). The first claim is that unity in intuitions is produced by mental activity (“combination”) not given by the senses; the second is that the kind of unity that intuitions have is the kind that judgments have. While the claims are perhaps clear enough, Kant’s reasons for holding them are not. My main purpose in this section is to offer a suggestion about what his reasons might be for the second claim, from which it will follow what his reasons are for the first. I intend to oppose my answer to one that has gained prominence among some recent commentators:35 when there is complexity in a unified representation it is a fundamental tenet of Kant’s theory of representation that it can come only from a judgment-like unity binding the elements governed by the categories. Successfully opposing this answer requires offering an interpretation of the doctrine of “combination” in section 15 that leaves room for intuitions unified by other means. My argument depends on a distinction Kant draws between two kinds of combination: composition and connection (nexus). My contention is that the kind of combination Kant is primarily thinking of in section 15 is connection synthesis, not composition synthesis. One of the immediate advantages of this reading is that it explains why Kant feels that it is obvious that intuitions unified by this type of synthesis have the form of judgments. If this is right, then there remains a form of synthesis not primarily under investigation in section 15:  composition synthesis. I  show in section 3.4 that this form of synthesis, while guided by the imagination, makes for another mode “Transcendental logic, however, teaches how to bring under concepts not the representations but the pure synthesis of representations” (A78/B104). 35 A clear version of this is proposed by Allison (2004, 175ff.). 34



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of unification—“aesthetic unification” I call it—of the elements that undergo composition synthesis. This shows that even if the results of section 15 are accepted for the kind of intuitions under discussion there—those unified by connection synthesis—Kant neither shows nor intends to show the validity of the general thesis that all unification of a manifold in a representation is category governed and judgment-like. To develop this case I proceed in four stages: 1. I give an account of the five main elements of section 15. 2. I  consider two alternative accounts of the problem, those of Dicker and Bennett, as a foil to develop my own interpretation. 3. I  explain the distinction between composition synthesis and connection synthesis. 4. I give reason to think that the basic form of combination in section 15 is connection synthesis rather than combination synthesis and draw some important implications from this for the interpretation of Kant’s intentions in the Deduction as a whole.

2.2.  Section 15: Synthesis, Intuitions, Judgments When Kant gives his account of synthesis “in its most general sense” in the Metaphysical Deduction, he says that it is “the action of putting different representations together with each other and comprehending their manifoldness in one cognition” (GW, 210; A77/B102) Guyer and Wood helpfully point out that in his own copy of the first edition Kant adds the words “Combination (conjunctio), composition (compositio) and nexus (nexus)” (GW, 210, n.  a). Kant draws the connection between synthesis and combination more explicitly in the first section of the B edition Deduction, section 15, explaining the difference between “composition” and “nexus” in relation to combination only later, in a note to the B edition Axioms of Intuition (GW, 286; B202–203). Section 15 contains five assertions: (1) The manifold of representations can be given in an intuition that is merely sensible, i.e., nothing but receptivity, and the form of this intuition can lie a priori in our faculty of representation without being anything other than the way in which the subject is affected. (2) Yet the combination of a manifold in general can never come to us through the senses . . . it is an action of the understanding, which we would designate with the general title synthesis . . . we can represent nothing as combined in the object without having previously combined it ourselves.

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(3)  . . . among all representations combination is the only one that is not given through objects (GW, 245; B129–130). (4) Combination is the representation of the synthetic unity of the manifold. (5) We must seek this unity . . . in that which contains the ground of the unity of different concepts in a judgment. It may appear from the first of these statements that Kant is endorsing some kind of sensory atomism (the “manifold of sense”) and from the second that he is saying that the complexity we find in our perceptions is a result of these atoms somehow being put together (“combined”) by the understanding. Kant then notes in the fifth statement that the principle of unification is conceptual, a form of unification also responsible for judgment. One version of this view is represented in Buroker’s recent book on Kant, where the sensory atoms are understood as data and data are read in accord with “Kant’s blindness thesis, according to which we are not conscious of the intuitive data prior to any intellectual processing.”36 Another version takes the manifold to be not some kind of behind-the-scenes raw data worked up into perception by the understanding but ordinary perceptual parts of ordinary complex perceptions; for example, the perception of the rung on the back of a chair as part of the perception of the chair as a whole. In his recent book, Dicker offers a particularly clear version of this account. According to Dicker,37 Kant’s problem is to explain what makes the multitude of perceptions (the perception of this rung, the perception of that rung, the perception of the seat, etc.) into the perception of the chair. “The answer given by Kant,” according to Dicker, is that representations are unified by referring to an object—by being representations of an object. To see this better, notice that being related to an object is certainly one way to unify a manifold of representations: the object serves, so to speak, as an anchor for them.38 But the anchor, of course, is not an anchor in itself: what is needed is an analysis of what it means for a representation to refer to an object that is consistent with Kant’s Transcendental Idealism. The view I  have been defending is that “reference to an object” is a primitive notion in Kant, the notion of an intuition, but Dicker takes the same view as Van Cleve, discussed previously:  “Kant’s answer . . . is that [representations] refer to an object by being related to each Buroker 2006, 46. I agree that consciousness of the sensory data depends on some kind of synthetic activity, but I argue in §3.4 that it need not be intellectual synthesis. 37 He in turn follows Wolff 1963, 116. 38 Dicker 2004, 98. 36



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other in a nonarbitrary or rule governed way, in accordance with the concept of an object.”39 I concluded in the previous section that in the “relation to an object” passages Kant is giving an account not of the general concept of an object or reference to same but rather of what objective property attribution to an object is. Objective property attribution to an object is a unification of some kind, and I presently argue that it is this kind of unification that constitutes the unification of intuitions at issue in section 15. What of the kind of unification that Dicker is concerned with? If we take the objects of ordinary empirical perception for Kant to be ordinary empirical appearances, these objects are certainly complex: the appearance of my bookcase has many parts. It is reasonable to suppose that the appearance acts as an “anchor” for the components of the intuition of the bookcase, the intuition of the individual back-of-book appearances. The unity of the appearance as a whole seems to come from spatial contiguity: one back-of-book appearance being next to another, all of them in a single local space. Where do these appearances come from, related as they are? The obvious answer is that they are simply given that way in sense experience, but that is not exactly Kant’s answer. It is close, however: appearances are intentional projections of an analogous structure of sense impressions whose structure is given. Is there anything in the doctrine of unified intuitions discussed to date from section 15 to cause trouble for this account? There may be if we reconstrue the problem of unifying perceptions not as the problem how a single perception of an object is formed out of perceptions of parts of the object but how we unify a perception of something that is X and a perception of something that is Y as a perception of an object that is both X and Y. For Bennett, this is the problem of unifying intuitions.40 This way of representing the problem assumes that the basic elements of the manifold of sense are perceptions of single properties bound to objects, not perceptions of multiple properties bound to objects. What is needed to effect the transition is the knowledge that the X object and the Y object are one and the same. It would seem that this transition is not something we can simply attribute to sensibility, and thus it would be a place where the operation of combination guided by the understanding would come in. But there is a problem for this reading. Kant’s criterion of the identity of ordinary objects, discussed, for example, in the Amphiboly section in connection with his critique of Leibniz (GW, 368; A263/B319), is spatiotemporal continuity. The latter is subject to the unity of space and time. In the well-known note to B160, Kant says that the unity of space and time is not due to sensibility, thus 39 40

Ibid., 103. Bennett 1966, 107–108.

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confirming our suspicions that sensibility could not provide an identity criterion for objects. But he also says that the unity of space and time is due to synthesis, adding: “For since through it (as the understanding determines the sensibility) space and time are first given as intuitions, the unity of this a priori intuition belongs to space and time, and not to the concept of the understanding (see #24)” (GW, 261; B161). In section 24 Kant distinguishes two kinds of synthesis: “figurative synthesis” (synthesis speciosa) is one kind; the other is “that which would be thought in the mere category in regard to the manifold of intuition in general, and which is called combination of the understanding (synthesis intellectualis) . . .” (GW, 256; B151). Figurative synthesis is the job of the productive imagination that is somehow under the guidance of the understanding but still distinct from the understanding. It is clear that the synthesis of the note to B160 is figurative synthesis, not intellectual synthesis. It is also clear that intellectual synthesis is the kind of synthesis at work in section 15, not the former.41 This is so because intellectual synthesis operates on the manifold of intuitions in general, and the implications of the unity of intuitions in general rather than empirical intuitions are the subject of the first half of the Deduction (§§15–20). As I argue,42 the whole point of the second half of the B edition Deduction is to extend the account of unity developed in the first part to empirical intuitions. Since Kant would need the resources of figurative synthesis to provide an account of the identity of individual objects and since this kind of synthesis A challenge to the reading of “intuition in general” as an autonomous way we have of thinking of objects when they are not sensuously present to us comes from the paragraph following the one just quoted from section 24. Here Kant discusses the role of imagination in representing such objects: 41

Imagination is the faculty for representing an object even without its presence in intuition. Now since all of our intuition is sensible, the imagination, on account of the subjective condition under which alone it can give a corresponding intuition to the concepts of understanding, belongs to sensibility. (GW, 256–257; B151) It would be natural to read Kant’s claim here to be that all representation of objects through intuition not actually perceived (affecting us through sensation) comes from the imagination, thus contradicting my contention that Kant allows that intuitions in general perform this function, too. But to read it this way is to take the passage out of context. In the previous paragraph Kant has been talking about intuitions in general, the unity of which he attributes to intellectual synthesis, not the synthesis of the imagination. So it seems as if we should take Kant’s statement here to be restricted to intuitions unified by the transcendental synthesis of the imagination. Two interpolations in Kant’s text would make this clearer. When Kant says that the imagination represents objects not present “in intuition,” I would have him say “in empirical intuition”; and when Kant says that the imagination gives “a corresponding intuition” (corresponding now to empirical intuition), I would have him say “a corresponding sensuous intuition.” This leaves room for singular representations of objects not empirically present and also not sensuous; that is, for intuitions in general. For an alternative reading of this passage, see Young 1988, 144. 42 See Ch. 7, Part II, §2.1.



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is not yet operating in section 15, we should not see the kind of unification that Bennett is interested in as the kind of unification Kant is interested in section 15. If at all, that would have to come later. We have seen what unification problems Kant is not solving in section 15, but we have not yet seen what problem he is solving. For this, we need to look further into Kant’s concept of “combination.” In a note added to the B edition Axioms of Intuition, he provides a taxonomy of kinds of combination, of which there are fundamentally two: composition and connection (nexus) (GW, 285–286; B201). The former is the synthesis of a manifold of what does not necessarily belong to each other . . . and of such a sort is the synthesis of the homogeneous in everything that can be considered mathematically. The second combination (nexus) is the synthesis of that which is manifold insofar as they necessarily belong to one another, as, e.g., an accident belongs to some substance, or the effect to the cause . . . (GW, 286; B202–203) We look at each kind in turn. Composition. Mathematics concerns magnitudes, of which there are two kinds in Kant: extensive and intensive. I call an extensive magnitude that in which the representation of the parts makes possible the representation of the whole . . . (GW 287; A162/B203) Composition aggregates elements into wholes. A  unified intuition would seem to be unified in the mereological sense: a whole intuition made out of parts. The idea seems clear, yet it is problematic to attribute it to Kant in section 15. To see this, notice, first, that Kant seems to directly contradict this doctrine in those texts where he says that the whole of space comes before the parts; for example, in the Metaphysical Exposition 3 (B edition): “And these parts cannot as it were precede the single all-encompassing space as its components (from which its composition would be possible) . . . the manifold in it . . . rests merely on limitation” (GW, 175– 176; A25/B39). This matter is somewhat resolved when Kant writes in the note to B160a (discussed earlier) that the unity of space and time is in fact given by the figurative synthesis of the imagination. So composition synthesis is governed by figurative synthesis. But Kant has distinguished figurative synthesis from intellectual synthesis, assigning only the latter to the discussion of intuitions in general, the kind of intuitions at issue in section 15. I conclude that in this section Kant is not including composition synthesis in his discussion of combination.

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Connection. One of the examples of connection (nexus) that Kant mentions is that of substance-accident. Thus nexus is the ontological version of subject-predicate judging, and so the connection between nexus and judgment is clear: nexus is precursor to explicit judgment—a kind of implicit judgment. What is less clear is what this has to do with the doctrine of unified intuitions in section 15. Here’s a suggestion from Sellars—the “Sellarsian story” as I call it.43 Pace the Platonists, we do not encounter properties by themselves. So any representation of a property is always of a property contained in an object; similarly, any representation of an object in general is a representation of an object as having a certain characteristic. For example, if I represent to myself the moon, I represent it as a round, silvery object in space, as a planet orbiting the earth, as a source of awe and wonder on a cloudless night in the forest. Intuitions in general are singular representations (A320/B377), and they too must be subject to this doctrine. Now objects-in-nexus-with-properties are what intuitions represent, and objects-in-nexus-with-properties are complex entities put together from elements. However, “synthesis alone is that which properly collects the elements for cognitions and unifies them into a certain content; it is therefore the first thing to which we have to attend if we wish to judge about the origin of our cognition” (GW, 211; A77–78/B103). So synthesis alone creates the complex from the elements it has gathered. But what kind of synthesis? It must be connection synthesis, a form of intellectual synthesis. A representation of an object in nexus with a property is a singular representation: the object is the subject and the property is the accident of the object, so it is in Kant’s sense an intuition, a synthesized intuition, not a judgment. Yet it is a very short step from a representation of a synthesized intuition to a representation of a subject-predicate proposition—just a matter of reconfiguring the elements. So synthesized intuitions are implicit judgments. Notice that when there is a nexus between object and property, the property is “in” the object; that is, the property is objectively predicated. This means that in section 15 Kant starts with objective predications. This gives us the explanation for Kant’s claim in section 21 that in the first part of the Deduction relatively little has been so far accomplished (only a “beginning” has occurred) (GW, 253; B144). We can go far in understanding Kant’s doctrine in the Deduction if we take Kant to be starting the B edition Deduction with intuitions in general that are intellectually unified as implicit judgments. (I also use the term “logically 43 I  base my reading immediately on an account of intuitions in Sellars 1978, esp. §§46–47. I should note that Sellars takes intuitions to be perceptions, contrary to my reading of intuitions in general, the kind of intuition of interest to Kant in §15 and throughout the first part of the Deduction. I adapt his idea to intuitions in general here. The main work in which Sellars explicitly develops his general reconstruction of Kant is Science and Metaphysics (1967), ch. 1. However, it is in Sellars 1953 [1963] that I find the clearest statement of the main idea that I exploit here in my reconstruction of the Sellarsian story I am about to tell. See esp. §7, 308–311.



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unified” to refer to the intellectual unifications of intuitions.) The last four of the five main doctrines we extracted from section 15, for example, are well accounted for on that supposition. If it is right, combination-as-connection, not combination-as-composition, is at issue in section 15. But what of the connection to sensibility that Kant affirms in the first of these? We need a bridge from the theory of judgment to the theory of sensibility. One such bridge is supplied by Sellars’s doctrine that all seeing is “seeing-as.” If this were, as Sellars believed, Kant’s own view, the argument that intuitions in general are logically unified would apply directly to perceptual intuitions, of which the latter are a special case. But this makes for a serious problem in interpreting the two-part structure of the B edition Deduction as a whole;44 for this reason alone we should be suspicious of the Sellarsian reading: it is more Sellars than Kant. This brings us to the end of our discussion of the first four of the five stages identified at the outset in the argument of section 15. The fifth stage seems to involve a claim to the effect that the unity of combination is a “unity which precedes a priori all concepts of combination” and that “we must therefore seek this unity . . . someplace higher, namely in that which itself contains the ground of the unity of different concepts in judgments, and hence of the possibility of the understanding, even in its logical use” (GW, 246; B131). This is the last sentence of section 15. Kant does not explicitly tell us where this source lies, but the first sentence of section 16 introduces the notion of apperception in the famous words “The ‘I think’ must be able accompany all my representations . . .” (ibid.). Guyer reasonably suggests45 that the “higher unity” mentioned in section 15 is that of the “I think” that must accompany all my representations of section 16; that is, a unity revealed by apperception. Chapter  7 contains a detailed discussion of that important concept in the B edition Deduction.46 In the remainder of this chapter I turn to the important issue of how to accommodate within CPR Kant’s theory of the distinction between judgments of perception and judgments of experience as drawn in the Prolegomena.

3.  Judgments of Perception, the Doctrine of Schematism, and Aesthetically Unified Intuitions 3.1.  Judgments of Perception in the Prolegomena In the Prolegomena Kant indicates that there are two kinds of judgments: judgments of experience and judgments of perception (§18:  Hat., 50; Ak 4, 298). In 44 45 46

I call this “the Triviality Problem” and discuss it at length in the next chapter. Guyer 1992, 149. See Ch. 7, Part I, §§1–3.

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section 20 Kant gives a short account of “experience in general.” It provides a lucid synopsis of Kant’s theory of experience (as he saw it at the time of writing the Prolegomena) and is worth quoting at length: At bottom lies the intuition of which I am conscious, i.e., perception (perceptio), which belongs solely to the senses. But, secondly, judging (which pertains solely to the understanding) also belongs here. Now this judging can be of two types: first, when I merely compare the perceptions and conjoin them in a consciousness of my state, or, second, when I conjoin them in a consciousness in general. The first judgment is merely a judgment of perception and has thus far only subjective validity; it is merely a connection of perceptions in my mental state, without reference to the object. Hence for [judgments of] experience it is not, as commonly imagined, sufficient to compare perceptions and to connect them in one consciousness by means of judging . . . (§20: Hat., 52; Ak 4, 300; my interpolation) What chiefly characterizes the difference between judgments of perception and judgments of experience is that the latter are objectively valid.47 If we allow ourselves a distinction between properties and objects of intuition for expository purposes, this means that the properties are somehow represented as in the objects (in the language of CPR familiar from our earlier discussion) rather than as just associated with the representation of the object in our subjective consciousness. In the former case Kant says that the objects of intuition are subsumed under the concept that expresses the property in question. He also says that the concept in this case determines the form of judgment with respect to the intuition. Kant adds to this account that “a judgment of experience arises from a judgment of perception,” adding a description of what is required for this to happen: “that the perception be subsumed under a concept of the understanding of this kind, e.g., the air belongs under the concept of cause, which determines the judgment about the air as hypothetical with respect to expansion” (§20: Hat., 53; Ak 4, 301). This point is significant for two reasons; first, it asserts that a more conceptually primitive form of judgment gives rise to a more conceptually sophisticated form; and second, it indicates that this happens through the work of the pure concepts of the understanding. The association between the categories and judgments about intuitions in general is also doctrine in CPR, but the first point seems to be a departure from CPR, in both its editions. This suggests that the doctrine of the two classes of perception is idiosyncratic to the Prolegomena, perhaps introduced to make a connection with those empiricist 47

Text quoted in this paragraph not from CPR is from §20, Hat., 52–53; Ak 4, 300–301.



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readers inclined to hold the “commonly imagined” account of judgment without actually endorsing such a theory in his more sophisticated account in CPR.

3.2.  Longuenesse and the Case for Finding a Doctrine of Judgments of Perception in the Critique of Pure Reason If Kant had simply dropped all reference to judgments of perception from his subsequent writings, this interpretation might be reasonable; but he does not. For example, judgments of perception are discussed and given roughly the same characterization as in the Prolegomena, in the Jäsche Logic (1792).48 Longuenesse49 has argued that judgments of perception do indeed have a role to play in CPR. It might be helpful if I orient my own account to five main stages of her argument. First, she notes that Kant develops an account of concept formation in the Jäsche Logic that involves a three-stage process:  comparison, reflection, and abstraction. Although much of CPR is devoted to a discussion of concepts assuming that they are somehow there, the question being to determine their kinds and how they function in judgment, Kant is clearly going to need to provide an account in CPR of how concepts arise. Longuenesse sees in the process of comparison and reflection at issue in the theory of concept formation (which she attributes to the imagination) the same process at issue in judgments of perception.50 In this way judgments of perception are prior to judgments of experience, “the subsumption of empirical objects under categories” (166). While I accept her account of empirical concept formation, I argue that judgments of perception occur subsequently to concept formation and involve a kind of “matching” of sense impression and concept. What makes judgments of perception prior to judgments of experience is that the latter employ metrically determinate concepts, whereas the former employ metrically indeterminate concepts. In a second stage she maintains that there is a symmetry in the relation of judgment to synthesis in the case of both judgments of perception and judgments of experience:  “ . . . if it is true that empirical judgments are formed by comparison/reflection/abstraction on the sensible given, it must also be added that in order for such reflection to be possible, the sensible given must be ‘run through and held together’ (A99) according to forms of synthesis that make it suitable for reflection under concepts combined in judgments . . .” (196). My account reflects this duality.

48 49 50

Young, 608; Ak 9, 114. Longuenesse 1998, ch. 7. Longuenesse 1998, ch. 5; see esp. 121–122 for a summary discussion.

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In a third stage she explains the transition from judgments of perception to judgments of experience by concentrating on what it takes to transform judgments of perception in hypothetical form into judgments of experience (173– 180). I accept her account in principle, though do not pursue the issue. Fourth, she notes that there are forms of perceptual judgment in the Prolegomena that are categorical in form but finds the examples (and the account of them offered there) not to be an adequate reflection Kant’s view (172–173). Instead she looks to forms offered in the Jäsche Logic where “we must resort to the form proper to subjective association, ‘I, who perceive x(s) as A also perceive it (them) as B’ ” (188–195; quoted text at 190). My own treatment of forms of judgments of perception formulates them in the style of the Logic, though my analysis is somewhat different from Longuenesse’s. Fifth and finally, Longuenesse argues for the compatibility of the doctrine of judgments of perception and doctrines in sections of the B edition Deduction (esp. §§18 and 19) that seem to preclude it. Her argument is that Kant’s conception of the forms of judgment in the Prolegomena (and Jäsche Logic) is broader than forms of judgments determined by the categories and that, appearances to the contrary, this broader notion of judgment is not collapsed in section 19 (194–195). Kant thus leaves room there for judgments of perception even if they are not mentioned by name. I accept this argument. Overall, Longuenesse makes a strong case for supposing that the doctrine of judgments of perception is not an aberration of the Prolegomena but is also operating, though not under that rubric, in CPR. I make my own case for this in three stages. In the first stage I show that Kant has a doctrine of what I call “schematic objects,” objects that are not determined by categories. In the second I  show how judgments about such objects are to be made, arguing that these judgments should count as “judgments of perception” in a broad sense: they are perceptual judgments that are not judgments of experience in the sense of the Prolegomena and they proceed by “comparison.” Section 3.3 presents these first two stages. The final stage, given in the next chapter,51 is a theory of the logical form of judgments of perception when that form is understood as it is in the Prolegomena and the Logic: as relations of appearances to the subject. I make the case for this in Section 3.4 of this chapter. The result is of importance to my argument because it is the main basis for my contention that there are for Kant in CPR intuitions that are aesthetically but not logically unified; hence not subject to the categories. This has significant consequences for later stages of my analysis of the argument structure of the Deduction in the B edition, especially part II.52

51 52

See Ch. 7, Part I, §3. See Ch. 7, Part II, §2.1.



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3.3.  Judgments of Perception, Empirical Schemata, and Empirical Concepts One clue to the general orientation of Kant’s theorizing on the topic of judgment lies in his remarks in the Logic about Locke: Leibniz and Locke are to be reckoned among the greatest and most meritorious reformers of philosophy in our times. The latter sought to analyze the human understanding and to show which powers of the soul and which of its operations belonged to this or that cognition. But he did not complete the work of his investigation, and also his procedure is very dogmatic, although we did gain from him, in that we began to study the nature of the soul better and more thoroughly. (Young, 543–544; Ak 9, 32) For Locke, perceptual judgment is a matter of the mind’s comparing a sense impression of an object perceived with a library of general ideas already generated by abstraction, catalogued and labeled as to type: This is called Abstraction, whereby ideas taken from particular beings become general representatives of all of the same kind; and their names general names, applicable to whatever exists conformable to such abstract ideas . . . Such precise, naked appearances in the mind . . . the understanding lays up (with names commonly annexed to them) as the standards to rank real existences into sorts, as they agree with these patterns, and to denominate them accordingly. (Essay II, xi, 9) Kant’s account of the generation of concepts in the Main Doctrine of Elements of the Logic reflects Lockean theory to a remarkable degree, appealing, for example, to operations of reflection, comparison, and abstraction in the generation of concepts, all operations that figure in Locke’s theory. One notorious difficulty in Locke’s theory is his account of abstract ideas, suggesting in places that they are abstract particulars of some kind. One of Kant’s major contributions to the theory of general ideas is his replacement of Locke’s problematic notion of an abstract idea with the notion of a concept. His clearest application of this notion is with mathematical concepts understood as rules for constructing mathematical objects in intuition: Thus I construct a triangle . . . The individual drawn figure is empirical, and nevertheless serves to express the concept without damage to its

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universality for in the case of this empirical intuition we have taken account only of the action of constructing the concept . . . to which many determinations, e.g., those of the magnitude of the sides and the angles, are entirely indifferent . . . (GW, 630; A713/B741) This same doctrine is present in Kant’s discussion of empirical schemata: In fact it is not images of objects but schemata that ground our pure sensible concepts. No image of a triangle would ever be adequate to the concept of it. For it would not attain the generality of the concept, which makes this valid for all triangles, right or acute, etc., but would always be limited to one part of this sphere. The schema of the triangle can never exist anywhere except in thought, and signifies a rule of the synthesis of imagination with regard to pure shapes in space. Kant then extends the idea of mathematical schemata to empirical concepts: The concept of a dog signifies a rule in accordance with which my imagination can specify the shape of a four-footed animal in general, without being restricted to any particular shape that experience offers me or any possible image that I can construct in concreto. (Both passages are from GW, 273; A140–141/B180) There is of course a difference between an actual dog, something satisfying the concept of a dog, and an image of a dog, something generated by the schema of a dog. Since it is not entirely clear what the relation between empirical concepts and empirical schemata might be for Kant, let’s begin with a simple question: How would we tell empirically that something is a dog? We would see how it looks to us. Notice that we can identify most empirical objects simply by their shapes and movements: if it looks like a dog, and walks like a dog, it probably is a dog. So for identification purposes, we are as well off with images of dogs (especially moving images) as with their real correlates. Once we have recognized a certain kind of image in a judgment, we can then use that judgment to make a judgment about the determinate object corresponding to it. But how do we make the first kind of judgment? Kant does not specifically tell us this in the section on empirical schemata, but there is a text from the Postulates of Empirical Thought that gives the answer. We have seen this passage before, in Chapter 4, where I discussed it in relation to an objection from Friedman to the claim that pure images provide a model for geometry,



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but its main thrust is to give Kant’s account of how we determine the shapes of objects given empirically. Here is that passage again: It may look, to be sure, as if the possibility of a triangle could be cognized from its concept in itself . . . for in fact we can give it an object [Gegenstand] entirely a priori, i.e., construct it. But since this is only the form of an object it would still always remain the product of the imagination, the possibility of whose object would still remain doubtful, as requiring something more, namely that such a figure be thought solely under those conditions on which all objects of experience rest. Now that space is a formal a priori condition of outer experiences, that this very same formative synthesis by means of which we construct a figure in imagination is entirely identical with that which we exercise in the apprehension of an appearance in order to make a concept of the experience of it—it is this alone that connects with this concept the representation of the possibility of such a thing. (GW 324–325; A223/B271; my underlining) I propose the following reconstruction of the doctrine in this passage. First, there is the reception in sensibility of a particular sensation of some kind, becoming a “sense impression” in my terminology when its spatial form in taken into account. Sense impressions are intuitions that project their structure onto their objects, appearances; thus sense impressions are what Kant is calling here “the experience” of an appearance. (Sometimes “experience” [Erfahrung] refers to a conceptualized intuition, as at GW, 255; B147, but here the sense of the passage requires that we take it to make reference to a preconceptual item.) I shall initially call whatever kind of unification may apply to sense impressions “sensory unification,” leaving it open whether sensory unification is the same kind of unification at issue with the unified intuitions of section 15 just discussed. The task of the understanding is to determine what kind of object is represented by that impression. On Locke’s view, the mind would somehow compare the particular impression (“idea”) with its catalogue of abstract ideas, noting when a match occurs and then “denominating” the object of the perception with the term associated with the matching abstract idea in the catalogue. For Locke this procedure is perceptual judgment. However, Kant would find this account unacceptable since it depends on what he would (plausibly) regard as a problematic notion of abstract idea. On Kant’s own account, as I read it, the process begins with a sense impression, as with Locke’s, but then diverges from the latter when the imagination attempts to produce a match for the sense impression by spontaneously applying various image-constructing rules. The result of this activity is an image with

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its corresponding object. (This is a schematic object.) The imagination does so, let us suppose, initially by trial and error: it works through its catalogue of empirical rules,53 applying each until it produces an image that is an exact match for the sense impression in question. The production of an image is an act of synthesis—specifically composition synthesis, not connection synthesis, hence not shown by the argument of section 15 to be a form of potential judging. So we still need a way of connecting this kind of synthesis to the doctrine that the same function that gives unity to intuitions gives unity to judgments. The connection is close at hand. Once an image has been productively generated, the operations of comparison and recognition are applied to determine an exact match54 between sense impression and generated image.55 We can further suppose that the understanding keeps track of which rules are used in constructing the matching image and that each rule has a cognitive label associated with it just as, with Locke, each abstract idea has a name associated with it. Judging, then, is an act of recognition that the procedure P1 used to produce an image matching a given sense impression x and the procedure P2 constructing an image of an S-type object in general (a schema of S) are one and the same procedure. I take this to be the sense of the underlined

53 The question of how this catalogue is produced is the question of empirical concept acquisition, one that Kant does not specifically address in CPR. However, in light of the theory of empirical concept acquisition in the Jäsche Logic (Young, 589–593; Ak 9, 91–96), we may find in the account offered here the materials for an answer. Since concepts are what are in common to several representations, concepts as schematic rules are the common schemata used to produce images of schematic objects. See also Longuenesse 1998, 116–17, and Ch. 2, §5, of this book. 54 One may ask how the subject knows that there is an exact match. One possible answer for Kant is that some things are candidates for immediate knowledge; determining geometrical matches is one of them. Another is that the matching procedure is operating behind the scenes of conscious experience. The following passage from the Schematism chapter suggests that the latter is Kant’s position: “The schematism of our understanding with regard to appearances and their mere form is a hidden art in the depths of the human soul, whose true operations we can divine from nature and lay unveiled before our eyes only with difficulty” (GW, 273; A141/B180–181). 55 Young 1988 is quite disparaging of the idea that Kant’s theory of imagination is a theory of images; “If we suppose that Kant conceives of imagination as the capacity for mental imaging . . . the task [of making sense of Kant’s theory] is not even worth undertaking” (140). This harsh judgment is rendered against the supposition that Kant’s theory of geometry is dependent on image construction—we have had something to say about that role above—but it also applies to the role of imagination understood as a faculty of image construction in the theory of perceptual judgment. The link between imagination and the power of judgment “remains puzzling so long as we suppose that he conceives of imagination as the capacity for mental imaging.” However, according to Young, if we accept his account of imagination, the puzzle disappears:

Since we can represent particulars only though sensible intuition, the identification of a particular as falling under a concept or rule requires that we be capable of construing or interpreting sensible awareness as the awareness of something conforming to a certain



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portion of the passage quoted earlier from A224/B271, with the words “formative synthesis” corresponding to the second procedure, P2, and “that which we exercise in the apprehension of an appearance in order to make a concept of the experience of it” corresponding to the first, P1. This description involves a comparison of sense impressions with rules for producing sense impressions. The generality of concepts lies in the generality of rules, and the generality problem for concepts is solved by this model since only those concepts associated with rules actually activated in the construction of features of the sense impression are counted. While this is not precisely the kind of comparison Kant seems to be describing in the Prolegomena account of judgments of perception, it shares two central features with that account: (1) on both accounts a comparison between sense impressions and other things is at issue (see the passage from Prol. §20: Hat., 52; Ak 4, 300, quoted earlier); (2) in neither case are categories employed in the process of judgment. These are added in later to produce determined objects of empirical intuition, the logically unified intuitions of section 15 of the B edition Deduction. There is some further, indirect, evidence that Kant’s doctrine of judgments made by the application of empirical schemata corresponds to the doctrine of judgments of perception in the Prolegomena. In that work Kant does not have a section corresponding to the Schematism section in CPR, although he does discuss schemata of pure concepts of the understanding in the course of discussing the “universal principles of natural science” (§§24–26). What is lacking is a discussion of empirical schemata. However, what has been present in the preceding three sections (§§18–20) is the doctrine of judgments of perception and the distinction between judgments of perception and judgments of experience. We shall see that the material of this discussion corresponds to a considerable degree with aspects of the doctrine of empirical schematism in CPR. One final point. On the Lockean reading the role of the synthesis of apprehension is to produce an image to match a sense impression. This explains something that may seem to give rise to a puzzle in Kant’s theory of empirical judgment:  Kant says both that the synthesis of apprehension is an act of the productive imagination—thus, in the language of the doctrine of mathematical method (GW, 630; A713/B741), it is an a priori construction—and that rule. Such construal or interpretation, as I have argued, is the characteristic of imagination. (151) Unfortunately, Young does not explain how the imagination carries out this act of “construal” for Kant: if my interpretation in the body of the chapter is on the right track, Kant’s answer involves the use of an image-constructing capability. Young also draws here an important distinction between “construal” and “judgment,” the former operation assigned to the imagination. This distinction is reflected in a distinction I am about to draw between implicit and explicit judgment, respectively.

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it synthesizes sense impressions, the objects of empirical intuition. The latter would seem to make it a posteriori. The “Lockean” reading I have given to Kant resolves the tension by accepting that the construction is indeed a priori but that the match, when it occurs, is with a sense impression, thus contributing the a posteriori aspect of empirical judgment. So we now have Kant’s account of how we tell whether something is a dog: we infer that it is from the relevant features of a sensory image of a dog; and we now also have an account of what a sensory image of a dog is and how we tell what its shape is:  it is a sense impression that has been matched by an image constructed by following the rule for constructing images of dogs, the schema of a dog. Now, the “relevant features” discussed so far involve only shape and movement. What about size? How big is the sensory image of the dog? The question is difficult to answer. Suppose we mentally picture a dog. How big is the picture? How big is the dog? We can perhaps say various things about relative size of the parts of the picture; the head image is about a quarter the size of the body image, but suppose we wonder what metric the image has: how many feet long is the image of the dog or the dog itself? These are questions that seem to have no good answers. Images are not things with a metric. Yet intuitively they are spatiotemporal things, and they do have definite shapes and colors. I now argue that this intuitive aspect of images transfers to Kant’s theoretical account of images. As mentioned previously, Brittan has argued that the space Kant is describing in the Aesthetic is a metrically amorphous space: For Kant, space and time do not have an intrinsic metric. Rather, a metric is “brought to” space and time by the understanding—that is, they are conceptualized in certain ways. The activity of the understanding thus makes measurements of objects with respect to their spatial and temporal properties possible . . . the understanding thereby makes determinate space and time possible.56 Let’s accept this suggestion for now. Are there also metrically amorphous objects for Kant? The answer to this is yes, since the objects of intuition are appearances (on my view) in Kant’s technical sense; that is, they are undetermined objects of empirical intuition, and they are, in the first instance, undetermined metrically. This is so because conceptual determination of an empirical object must include determination of the magnitude of an object. Real objects of course do have a particular size and are moving at a particular speed (etc.). In this sense they are determinate objects. Now, the notion of particular sizes and speeds is the notion of magnitude, and magnitude is one of the schematized categories of 56

Brittan 1978, 99.



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quantity. Kant’s idea of how magnitude is determined involves the notion of a unit of measurement. This is also one of the schematized categories of quantity. The unit can be something we observe “at a glance,” like a ruler, or it can be a larger item we use as a unit. A magnitude arises from a unit of measurement by counting the number of times we have to apply the unit to gain the total extent of the object (or event.) When we abstract from this process, we arrive at the concept of a number. Kant tells this story quite clearly in various sections of the Critique of Judgment57 but also in the Schematism chapter of CPR (GW, 274; A142/B182). Does Kant leave room in his account for the concept of a metrically amorphous object? If so and if it is to play a role in the construction of real empirical objects and of our recognition of them in perceptual contexts, there will have to be rules for synthesizing them. Does Kant’s account countenance such rules? Meerbote58 has argued that Kant countenances two kinds of mathematical ideas: geometrical-formal schemata and abstract concepts. The former construct metrically determinate figures, the kind needed for geometry, but the latter do not involve metric determination. Kant’s example is of the concept of a line. Meerbote finds Kant saying (B16) that the idea of a line is a “concept” because “my concept of the straight line contains nothing of quantity, only quality.” If we compare this passage with those quoted, first, from the doctrine of mathematical method (GW, 630; A714/B742) and, second, from the doctrine of schematism explaining the concept of a dog (GW, 273; A140–141/B180), we find that in both cases abstraction has been made from the magnitude of figures constructed by the rules postulated in these passages. Here, I suggest, is the place where Kant makes a home for rules for constructing metrically amorphous images.59

See esp. §26 (Plu., 107; Ak 5, 251), first paragraph, and comment 1 to §57 (Plu., 214–216; Ak 5, 341–343). 58 Meerbote 1981. 59 As noted, Meerbote 1981 discusses the role of schematism in the determination of a metric for objects but does not specifically endorse the distinction I draw between rules for constructing metrically amorphous images and schematization of images that assigns a metric to them. As we shall see, the latter involve the schematized category of quantity; the former do not involve schematized categories at all. He does of course allow for the possibility of nonmetrically determinate rules in line with his endorsement of the idea of “geometrically non-determining properties” but does not associate these with the schemata of pure sensible concepts (219). Meerbote explains the metric-determining role of schematizing as follows: “units are stipulatively introduced, but both stipulation and iteration require imaginative exhibition simply because, in geometrical a priori determination properties are assigned to non-abstract, non-sense perceptible properties” (218). It is the role of the unit of measurement that brings this operation into the realm of schematized concepts, and that role is essential to the determination of magnitude. But it is not clear why the process of drawing a line itself requires that a unit be “stipulated.” This is especially true if drawing a line is understood on the analogy with “connecting the dots,” as I argue it should be. The basic process of image construction seems to me therefore to lack an essential characteristic of a magnitude-introducing schematism. 57

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I am going to call the metrically amorphous objects that result from the application of empirical concepts “schematic objects.” When objective synthesis is applied to schematic objects we get determinate objects of empirical intuition. These constitute not a new class of objects but a new kind of cognition Kant calls experiences (Erfahrungen): “ . . . the categories do not afford us cognition of things by means of intuition except through their possible application to empirical intuition, i.e., they serve only for the possibility of empirical cognition. This, however, is called experience” (GW, 255; B147–148). When categories are applied to empirical intuitions understood as intuitions of schematic objects, the immediate result is a logically unified intuition. The logically unified intuitions in turn potentiate judgments of experience. To summarize:  The construction of the experience of a real dog proceeds in stages. First there is the metrically amorphous image constructed by the metrically indeterminate empirical concept of a dog. This is a function of the imagination guided by concepts. In the case of this function being applied to ascertain the properties of a perceived object, this rule is constrained by a sense impression in the way indicated above. The immediate result of this activity is a metrically amorphous image having shape, relative size of components of the shape, and movement. (A corollary of this is that a sense impression itself is a metrically amorphous item corresponding to the image tracing it.) A schematic object is the projection of a sense impression or perhaps of the image of a sense impression (I leave the matter ambiguous for now). Both images and objects are entities with a perspectival character: a schematic dog image is an image of a dog “viewed” from a particular perspective: the front, top, rear (etc.), as is the schematic object projected from this image. In other words, a schematic dog is an ordinary empirical appearance in my sense. A schematic dog has no particular size in units, nor is it moving at any particular speed in units. It is, in this sense, an indeterminate object. We have already decided that a schematic dog is an ordinary empirical appearance and are now saying that it is an indeterminate ordinary empirical appearance. Since we concluded in section 1 that “appearances” in Kant’s sense are indeterminate ordinary empirical appearances, are we in a position to conclude that Kantian appearances are schematic objects? Not quite, as we are about to see in the next paragraph but one. To move closer to the experience of a real dog the mind now needs to add the schemata of the categories of the understanding, specifically quantity, to the operations of metrically indeterminate empirical concepts, transforming an indeterminate “image” of a dog into a determinate, categorially schematized “experience” of a dog. (The problem of adding the other schematized categories to complete the determination of the dog, especially the categories of substance and causality, remains, but Kant leaves the details of how this happens to the Analogies of Experience, where we shall not follow him.)



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As mentioned, there is an ambiguity in the account just offered of schematic objects that I now wish to address. There are really two candidates for it: one is the sense impression itself, a metrically amorphous spatial array of sensory items given by sensibility; the other is the sensory image, the object that results from the “connecting of the dots” afforded by the application of the concept of a dog to the sense impression. Both are items that are sensory in whole or in part, are given in whole or in part, and are indeterminate with respect to schematized categories. In the next subsection I take up this question. On the way to answering it we shall discover the existence of a new class of intuitions, aesthetically unified intuitions. The existence of this class of intuitions is critical to an understanding of the two-part structure of the B edition Deduction and to the central problem that the second part is to resolve.

3.4.  Aesthetically Unified Intuitions The following passage, taken from the “argument from beneath” in the A edition Deduction, may help resolve this question. The first thing that is given to us is appearance, which, if it is combined with consciousness, is called perception (without the relation to an at least possible consciousness appearance could never become an object of cognition for us, and therefore would be nothing for us . . . it would be nothing at all). But since every appearance contains a manifold, thus different perceptions by themselves are encountered dispersed and separate in the mind, a combination of them, which they cannot have in sense itself, is therefore necessary. There is, thus, an active faculty of the synthesis of this imagination in us, which we call imagination, and whose action exercised immediately upon perceptions I call apprehension. For the imagination is to bring the manifold of intuition into an image; it must therefore antecedently take up the impressions into its activities. (GW, 238–239; A119–120; my underlining) I ask that we first focus on the account of appearance. Appearances are said to contain a manifold; that is, a multiplicity of elements described as “dispersed and separate in the mind.” Kant then says that it is therefore “necessary” that these elements be combined, an operation that cannot be carried out by sense. (Kant calls these elements “perceptions”—appearances combined with consciousness. This suggests that the elements serving as inputs into synthesis are conscious elements. Since this seems contrary to fundamental Kantian doctrine, I ignore this part of Kant’s text and assume the elements are not already endowed with

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consciousness.) Kant says very clearly that these elements are “dispersed and separate in the mind,” “put together” by an act of the imagination, rather than given by sensibility. If these elements constitute a sense impression, then this is certainly, as it stands, a contrary text for my interpretation. The difficulty with taking this text at face value is that it makes the account of the imagination, in its capacity to draw images, difficult to make sense of. Kant says that the imagination is “exercised immediately on perceptions” (sensory elements) to “bring them into an image.” The elements are already there—the image that is produced does not create these elements—yet it somehow draws them. How? One possibility is that it rearranges them, as if we had a quantity of beads strewn all over the floor that we now arrange in a line. Alternatively, drawing on an analogy from Falkenstein, we might liken the process to “connecting the dots” in a child’s exercise book.60 Although perhaps the former analogy fits the words more naturally here, the second is not unnatural and makes for an account that fits better the account of empirical schematism already developed. So I shall understand the work of the imagination in this passage in line with Falkenstein’s analogy. This suggests that appearances, at least as the term is used here, are sense impressions, the subjects of the dot-connecting, image-producing syntheses but not the images themselves. However, since Kant also calls appearances the objects of intuition, I shall modify this description by saying that appearances are the intentional objects of sense impressions. What happens when an existing impression is acted upon by the imagination and an image of it is produced? The dots are connected by the application of a rule derived from the concept of a certain type of object. When the dots are connected, we can say that they are combined, combined by composition synthesis, not connection synthesis. (Such a synthesis is of homogeneous elements that do not necessarily go together; GW, 286–287; B201.) But all combination creates unity of the elements that are thus combined. So connecting the dots creates a unity out of the sense impression whose elements are thus connected. But because the combination is not by connection, the unification is not logical unification. I shall call it “aesthetic unification.” Intuitions in general are logically unified. What of sense impressions? When they are synthesized, they are aesthetically unified. Must they be synthesized? Kant’s answer, I  think, is not “necessarily unconditionally” but necessarily if I am to be conscious of them. Otherwise they “are nothing to me.” Let’s follow Sellars in supposing that if an appearance is “something to me,” then I see it as something, as a table-shaped appearance in this case. Now “seeing as” is not explicitly judging on the basis of vision—in that case we would say “seeing that.” We have already supposed that thinking of something as something 60

Falkenstein 2004, 98–99.



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is an implicit judgment, and logically unified intuitions in general are the ways we think of something as something in general; hence logically unified intuitions in general are implicit judgments. I shall argue61 that intuitions in general are not sensory representations; they are thought-like rather than sensation-like. I now suggest that something parallel is going on for Kant with sense impressions of which we are conscious. Because there are two layers of perceptual objects, schematic objects and categorially schematized objects, there are two levels of explicit judgments to be made about their properties. Judgments made about schematic objects correspond to perceptual judgments because schematic objects are undetermined by the schematized categories, including magnitude; judgments about categorially schematized objects are judgments of experience. However, when I  see a dog, I  am not attending to my perceptual experience, isolating what is due to sensibility and what is contributed by categories, and then saying to myself, “This is a dog-shaped figure in space.” So the imaginative synthesis that constructs indeterminate images is not an explicit judgment of perception, but as a completed synthesis of the manifold, it contains the results that determine how the judgment (match) will turn out and therefore potentiates an explicit judgment of perception. It seems reasonable to call the completed synthesis an implicit perceptual judgment. So now we have a fully developed symmetry between logically unified intuitions and aesthetically unified intuitions: both are implicit judgments due to synthesis, the one implicitly a judgment of experience, the other implicitly a judgment of perception. In Section 1 of this chapter I considered a text from section 13 of the Analytic, where Kant says that there can be appearances that are not subject to the rules of the understanding. I argued on methodological grounds that these texts should be taken at face value and claimed that good readings of central Kantian arguments, including the Deduction, could be found that are compatible with so taking them. We are partway there. The doctrine of empirical concepts shows that Kant countenances a layer of ordinary perceptual consciousness consisting of schematic objects that are subject to a nonmetrically determining synthesis. The latter amounts to an implicit judgment of perception. One set of conditions under which there would be appearances not subject to the rules of the understanding would occur when no synthetic operations at any level are carried out. But in this case the appearances “would be nothing to me,” since I would have no awareness of them. That there could be, for Kant, appearances that are not under the rules of the understanding that we are not conscious of is perhaps not very controversial. What is much more controversial is the possibility of appearances not under the rules of the understanding that we are conscious of. Yet on our model this is quite possible; all that is needed is for the synthesis 61

See Ch. 7, Part II, §2.1.

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of indeterminate empirical concepts to occur while the categorially schematizing synthesis does not. The preconceptual synthesis potentiates explicit perceptual judgments. These judgments are limited to the properties of schematic objects—relative size, shape, color perhaps—they would not extend to a metric and other conceptually determined properties of these objects. What I have argued for so far in this subsection can be summarized as follows. For Kant there are two classes of unified intuitions, logically unified intuitions in general and aesthetically unified intuitions, and the members of both these classes are unified in a way that potentiates judgments, judgments of experience and judgments of perception, respectively. Furthermore, these unifications are both accomplished by synthesis, and it is synthesis that also makes these intuitions objects of our consciousness. Evidence for these conclusions can be found in a text from section 18 in the B edition Deduction,62 where Kant characterizes two kinds of unities of a manifold, both unities of consciousness. The first is the famous transcendental unity of apperception, and the second is the subjective unity of consciousness. Both are synthetic unities of a manifold, both are accompanied by consciousness.63 But there is a difference, Kant says: the kind of unification afforded the manifold by the former is an “objective” unity; that afforded by the latter is a “subjective unity of consciousness, which is a determination of inner sense, through which that manifold of intuition is empirically given for such a combination.” I postpone further discussion of the subjective unity of consciousness to Chapter 7.64 In the next and final subsection, I take up a vexed question in Kant scholarship expressed in Lewis’s exasperated question, “Does the sage of Königsberg have no dreams?”65

3.5.  The Problem of Sensory Illusion for Kant Our question is, How does Kant solve the problem of sensory illusions, dreams, hallucinations and similar objects. The model provides a simple solution: sensory illusions are schematic objects whose construction is driven not by a need to match sense impressions but by the unguided spontaneity of the imagination. For example, when I hallucinate a pink elephant I have an intuition of a schematic pink elephant, one generated by internal rather than external causes. By

Quotations are taken from B139–140 (GW, 250). Kant says this explicitly in §18 for the subjective unity of consciousness, but for the transcendental unity of apperception he says it when first introducing the concept in §16 (GW, 247; B132). There it is consciousness as self-consciousness. 64 See Ch. 7, §3. 65 Lewis 1929, 221. 62 63



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and large this solution fits the texts in which Kant discusses illusions. There is, for example, this text in the Prolegomena (discussed in Ch. 3): The difference between truth and dream, however, is not decided through the quality of the representations that are referred to objects, for they are the same in both, but through their connection according to the rules that determine the connection of representations in the concept of an object . . . (Hat., 42; Ak 4, 290) Kant says of these representations that they are “referred to objects”: one is the dream representation, the other is the true representation, and they are qualitatively similar. Our model fits this text exactly: the true representation is an intuition of a schematic object generated by a rule but guided by a sense impression; the dream representation is a schematic object generated by a rule not guided by a sense impression but due to internal factors.66 Since schematic objects are objects with metrically indeterminate spatiotemporal properties, our model also easily accommodates in the obvious way the claim of qualitative similarity. But not only is there qualitative similarity between the representations, there is the clear implication that we know that there is. Descartes is astonished that he cannot tell the difference between waking and dreaming. Kant too thinks we can make judgments just about the qualitative character of the appearances: that is how the confusion between truth and illusion comes about (“And then it is not the fault of the appearances at all, if our cognition takes illusion for truth . . .” (Hat., 42; Ak 4, 290). Again, our model accounts for this possibility nicely though the possibility of making judgments of perception directed to the schematic objects present in each case; in each case we judge them to have the same nonmetrically determinate properties. 66 The present analysis treats illusions as states whose content comes via intentional objects. An alternative is to treat illusions as nonintentional states with content ascribed adverbially. Thus, dreaming of sugar-plums on the first reading has schematic sugar-plums as objects of a dream intuition but on the second alternative dreaming of sugar-plums is a matter of dreaming in a sugar-plum manner. (See Van Cleve 1998, 9) The textual evidence seems generally to support the first reading. The attraction of the second reading seems to lie in its ability to avoid an absurd consequence, viz., that Kant did not acknowledge the existence of dreams or illusions given a certain reading of the Deduction when the goal of that reading is understood to account for dreams by means of objective judgments only. Thus Beck writes; “But I say “Last night I dreamt I saw a three-headed monster,” and my judgment about that event is as objective as the judgment that I slept in my bed . . .” (Beck 1978, 54.) This is true, of course, but it leaves the question of what analysis Beck thinks Kant gives to the difference between dreaming and truth since they both involve a representation which is “referred to an object.” But on Beck’s own account “referral to an object” (relation to an object) happens only when an objectively determining synthesis has occurred, just what Kant denies in this passage is the case with dreams.

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The account just offered explains how, when we are aware that a certain representation is an illusion, we are still able to see that it shares properties with its veridical doppelgänger. But how do we account for judgments we make when we are taken in by the illusion? I wake up and think that I see my cousin standing at the foot of the bed. Unfortunately, he is dead and so this is an illusion. This is a good-faith judgment with objective content: I believe on the basis of my perceptual experience that there really is a man standing at the foot of my bed. From what we know of Kant’s theory of judgment, this state must contain an objective synthesis, no different in content from that occurring when it happens that my perceptual representation is veridical. This would be a problem if the objective synthesis were a constituting synthesis, the kind of synthesis that produces logically unified intuitions in general. But we saw in section 1 that there is another application of objective synthesis, synthesis that connects but does not construct intuitions—“external synthesis” I call it. My proposal is that good-faith objective judgments made about illusory objects do indeed involve objective synthesis but external rather than constituting objective synthesis. This allows us to go between the horns of a dilemma posed by Thöle: “either to understand objective unity in so weak a sense that even dreams and hallucinations can be taken validly as objective unities or to attribute to Kant the nonsensical position that dreams and hallucinations cannot exist at all.”67 Dreams and hallucinations are not objective unities since they are not unified constitutively by categories, but they are appearances that can be determined by objective judgments since they are subject to external applications of synthesis guided by the categories. (An external application of synthesis in my sense is a connecting of intuitions that are already unified by means of rules. An internal application of synthesis is the connecting of the elements of a manifold into a unified intuition. The former thus depends on the latter.) With both external and constituting synthesis there are implicit judgments applied to appearances, but the difference lies in the modality of these judgments. If I simply apply an objective rule to an actual ordinary empirical appearance, I may well find that it satisfies it, but there is no necessity in this. Even if as a matter of fact all actual ordinary empirical appearances turn out to satisfy the rule, this is still a contingent generalization. But Kant thinks that there is necessity in our experience of finding actual objects to be in accord with this rule, which necessity requires explanation; the doctrine that empirical intuitions are subject to a constituting synthesis provides the requisite necessity. As we see in

“ . . . die objektive Einheit entweder in einem so schwächen Sinn zu verstehen, daß auch Träume und Einbildungen als objektive Einheiten gelten können, oder Kant die unsinnige Position zuzuschreiben, daß es Träume und Einbildungen gar nicht geben kann” (Thöle 1991, 287). 67



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Chapter 7,68 this is one of the central results Kant needs to demonstrate in the second part of the Deduction (B edition). There is one remaining problem with this model of illusions. It amounts to a problem of consistency of the model with other elements of Kant’s doctrine. The issue concerns the doctrine of Nomic Prescriptivism in the case of the rule of the unity of space and time. This doctrine holds that we construct the properties of appearances to be in accord with this principle; that is, that all objects of empirical intuition are in unified space and time. As Quinton has argued in a well-known paper, “Spaces and Times,” it is reasonable to suppose that failing to occur in spatiotemporal connectivity with all other objects is a criterion of nonactuality, a position he attributes to Kant.69 He maintains that for Kant this principle is a necessary principle,70 one that in our terms would count as an “intellectual condition.”71 This is the position I also attribute to Kant. Since on the doctrine of Nomic Prescriptivism the understanding prescribes intellectual conditions to the world, would it not then follow that the existence of schematic objects unsynthesized by the rule of topological unity are ruled out a priori? Is this not, indeed, the very point of the argument of section 26? This is a significant challenge to the present reading that I defer to the next chapter, where I deal with the argument of section 26 in the second part of the B edition Deduction.72 We are now ready—as ready as we will ever be—to tackle the complexities of the B edition Deduction itself. This is the topic of the next, and final, chapter.

See Ch. 7, Part II, §2.2.4. Quinton 1962, 138. 70 For Kant of course, the necessity is not analytic but necessary in the special sense Kant gives to the a priori synthetic. Quinton’s own discussion seems to me to muddy the water on this point (ibid., 138–140). 71 Quinton goes on in the paper to dispute this position, arguing that we can imagine assigning actuality to objects that occur in distinct spatial domains not topologically connected to one another (ibid., 141–144), though he does not think that this is possible for topologically disconnected times (144–47). 72 See Ch. 7, Part II, §2.2. 68 69

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Transcendental Deduction II: The B Edition Transcendental Deduction

I.  The First Half of Kant’s B Edition Transcendental Deduction of the Categories 1. Introduction The new theoretical concepts introduced in the Deductions are the notions of apperception and the unity of apperception. Although these notions appear in both editions, Kant’s accounts differ somewhat in characterization of these notions and the role they play in the argument. Here I focus only on the account in the B edition. In the last sentence of section 15 Kant indicates interest in the question of what gives unity to judgments. But how is Kant understanding the scope of the question? Is he interested in understanding what all judgments in all their variety in the Table of Judgments have in common, what makes them a kind of thing? An affirmative answer is suggested most directly in the rewritten version of the Paralogisms at B406: “Now since the proposition I think (taken problematically) contains the form of every judgment of understanding whatever . . .” (GW, 445; B406). Towards the end of the fourth sentence of section 16, Kant also calls the unity of the I think “the unity of self-consciousness” (GW, 246–247; B132). So it may be in section 16 that Kant means to establish a connection between the unity of the class of all judgments of all twelve types enumerated in the Table of Judgments and the unity of self-consciousness. However, this project, if Kant indeed is embarked on it, is not one that directly affects the outcome of the argument of the Deduction, and so I shall not attend to it here.1

I have done so elsewhere, in an unpublished MS entitled “Kant’s Two Projects of Apperception in the B-Edition Deduction.” 1

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Another possibility is that in his discussion of the unity of apperception Kant is mainly interested in what gives unity to the elements in a judgment; not all judgments whatsoever but subject-predicate judgments in particular. I  argue that this project is in the foreground of Kant’s development of the overall argument of the Deduction, especially in sections 15–20, and it is this project that I  shall try to explain here. I  argue that apperception is to be understood as a power—the power of apperception as I call it. This power is a second-order power, the power to be aware of our representations. In being aware of our representations we are, of course, aware of ourselves2 and of the unity that our representations have in virtue of being ours. So, there is an intimate connection here, too, between apperception and the self. We shall see that this second-order awareness is an analytical power to reveal structure in our representations, which structure can have got there only by synthesis. But synthesis relies on the same kind of mental function as judgment (A79/B105), and once Kant has decided this, the judgments are potentially of two kinds: judgments of perception and judgments of experience.3 However, in an argument spanning sections 17–19 of CPR, Kant appears to leave room only for judgments of experience. These judgments are then connected with the categories in section 20, when Kant declares the first phase of the Deduction complete. The unity of apperception plays a key role in this argument, making its appearance in section 18, where Kant declares: The transcendental unity of apperception is that unity through which all of the manifold given in an intuition is united in the concept of an object. It is called objective on that account . . .(GW, 250; B139) It is from this starting point that Kant proceeds to his final conclusion in section 20. So it is crucial to understand what this starting point is. I argue that it is not, in itself, a reference to the unity of the self or to self-consciousness but to the kind of unity that the elements of subject-predicate judgments—“copula judgments” as I called them earlier,4 “judgments of experience” as Kant calls them in the Prolegomena5—possess. Once Kant has decided that he is working with

At GW, 189 (B68), Kant says,” Consciousness of itself (apperception) is the simple representation of the I  . . .” Here apperception is an act of consciousness, so I would take the sense of Kant’s words to be that apperception is a second-order act directed in a first-person way to the states of the self; e.g., I am aware that I am having an empirical intuition of an apple. 3 This assumes of course, that the argument of the previous chapter, that judgments of perception are allowed for, though not under that name, in the doctrine of CPR, is accepted. 4 See Ch. 6, §3.4. 5 See Prolegomena, part II, §18, at Hat., 50; Ak 4, 298. 2

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objective unities of apperception, thus understood, it is a fairly easy jog to the finish line in section 20. We can summarize the distinction between the two projects by saying that, in the first project, the I think designates the unity of a system of judgments, whereas in the second, the I think is a power of second-order awareness (not a representation) that reveals the proposition-like structure of intuitions, and the unity of apperception is the kind of unity that binds together the elements of copula judgments and it is not identified by Kant with the self or its unity. The effect of these distinct treatments of apperception has created confusion in Kant’s own exposition, and the tendency for commentators to see “the unity of apperception” as a Kantian synonym for “the unity of self-consciousness” has compounded the confusion. I attempt to dispel both difficulties in the following discussion. To clarify for the reader my understanding of Kant’s doctrine of apperception in the second project, I offer a paraphrase of the following critical selection of text from the first paragraph of section 16. This is the original text: The I think must be able to accompany all my representations . . . Thus all manifold of intuition has a necessary relation to the I think . . . But this representation is an act of spontaneity, i.e., it cannot be regarded as belonging to sensibility. I call it the pure apperception in order to distinguish it from the empirical one, or also the original apperception, since it is that self-consciousness which, because it produces the representation I  think, which must accompany all others . . . I  also call its unity the transcendental unity of self-consciousness in order to designate the possibility of a priori cognition from it. (GW, 246–247; B131–132) (The italic text is the text subject to paraphrase, the text in boldface represents, as usual, Kant’s own emphasis.) This is the paraphrase: The analytical power of apperception must be able to accompany all my representations . . . Thus all manifold of intuition has a necessary relation to the analytical power of apperception . . . But the term “I think” represents an act of spontaneity, i.e., it cannot be regarded as belonging to sensibility. I call this act6 the pure analytical power of apperception In making Kant’s pronoun “it”—sie in the German text—refer to “this act” I am taking a liberty with the grammar of Kant’s German, since sie is a feminine pronoun that would have to refer to a feminine noun, Diese Vorstellung (“this representation”) being the closest one available. For the pronoun in Kant’s text to refer grammatically to ein Actus (“an act”), the pronoun would have to be neuter, es. 6



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in order to distinguish it from ordinary first order perception, or also the original apperception, since it is a second-order awareness which reveals an implicit propositional structure—the “I think” structure as I call it . . . I also call the unity of the states of the self upon which this power is exercised the transcendental unity of self-consciousness in order to designate the possibility of a priori cognition from it. (GW, 246–247; B131–132) In the last section of the passage just quoted and paraphrased from section 16, Kant introduces a new idea, that the unity of self-consciousness (the unity of the self) has implications for a priori cognition. I maintain that this idea is developed by Kant in a separate argument given near the end of both sections 16 and 17. Its distinctive role is to fill in an apparently missing step between the end of section 17 and the beginning of section 18: namely, by what right does Kant help himself to an objective unity of apperception at the outset of section 18, having not mentioned it before? Kant’s answer centers on what he calls the “principle of the necessary unity of apperception,” which he declares to be “an analytic proposition” in section 16 (GW, 248; B135). This analytic proposition has major consequences for Kant; I argue that it serves as a bridge from judgments about our own states that are not objective to judgments that are objective, thus justifying a claim that there are some examples of true, objective judgments. It should be noted that because of the content of this principle, the subject of these judgments is the self, and that subject is carried forward by implication as the subject of the judgments having the objective unity of apperception in section 18. But again, the unity of apperception is not, per se, the unity of the self. The arguments that I lay out here form a continuous sequence of arguments beginning in section 15 and ending in the declaration in the last sentence of section 20: “Thus the manifold in a given intuition also necessarily stands under categories.” But is this not the conclusion of the deduction as a whole? What then is there left for Kant to accomplish? Plenty, says Kant! In section 21 Kant explains that what remains to be shown is that “empirical intuitions” are also subject to the categories; only then the aim of the Deduction “will first be fully attained” (GW, 253; B145). But if section 20 shows that all intuitions are subject to the categories, it is a trivial matter to show that one particular kind of intuition—for example, an empirical kind—is subject to the categories, contrary to Kant’s claim that the major part of the Deduction is to come after section 20. I call this the Triviality Problem and devote a section of Part II of this chapter to solving it. Finally, we come to the second half of the Deduction, the half in which I take this liberty because doing so seems to make the most philosophical sense of the passage and involves only a single grammatical adjustment regarding gender in the pronoun.

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Kant attains his final goal. Discussion of this half occurs in the final section of Part II. Part I consists of the sections dealing with the apperception project.

2.  The Analytical Power of Apperception Consider a first-order perceptual representation; for example, seeing an apple that is red. I come to be aware of this representation. In so doing I can come to be aware of several things this representation implies: that it is mine, that it is a seeing (rather than a hearing, smelling, thinking), that it entails the existence of an apple, that the apple is red. Notice that this awareness is now expressed propositionally: that it entails the existence of an apple, that the apple is red. This awareness is directed to a single intuition revealing its propositional implications. To reveal these implications is a power of apperception (GW, 249; B137).7 Accordingly, I call this the analytical power of apperception. This power can similarly be directed to intuitions in general: the thought of an apple that is red. This power is an analytical application of the understanding, and it requires an explanation: what makes it possible for the mind to examine its representations and break them down into propositional parts like this? The answer, for Kant, is that the parts, suitably related, were already there to begin with, present not explicitly as judgments, as is the case with the propositional formulations just given, but as implicit judgments, as elements combined in a way that permits the power of apperception to unlock their implicit structure: “where the understanding has not previously combined anything, neither can it dissolve anything, for only through it can something have been given to the power of

Howell 1992 provides an extensive and searching discussion of the principle of apperception in §16, of which he considers two chief variants, 7

(S) All of the elements of the manifold of i (where i is some arbitrary intuition) are such that H is or can become conscious, in thought, that all of those elements, taken together, are accompanied by the I think, and (W) Each element of the manifold of i is such that H is or can become conscious, in thought, that the I think accompanies that element (161). Howell then argues that even if (W) is something Kant can perhaps prove (he does not concede this), (S) is what needs to be proven, and unfortunately, all Kant’s attempts to do so fail. (W) is more or less what the analytical power of apperception accomplishes as I have formulated it; it separates and propositionalizes (this is the force of saying that the I think accompanies that element) the elements of the intuition. (S), on the other hand, is not something that the analytical power of apperception accomplishes. It is something that arises from paying attention to the fact that all representations subject to the power of apperception are mine. This formulation is relevant to the first apperception project, not the second. The second project is the main line of argument in §§15– 20. So the failure to prove (S), if indeed it is a failure, does not undermine that line of argument.



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representation as combined” (§15: GW, 246; B131). It is the power of synthesis that carries out the combination:  . . . The synthesis of a manifold, however, (whether it be given empirically or a priori) first brings forth a cognition, which to be sure may initially be raw and confused, and thus in need of analysis; yet synthesis alone is that which properly collects the elements for cognitions and unifies them into a certain content; it is therefore the first thing to which we must attend if we wish to judge about the first origin of our cognition. (§10: GW, 211; A77–78/B102) These two sides of mental activity are both ultimately due to the understanding; the apperceptive side corresponds to the analytical function of the understanding, the ground of the apperceptive side corresponds to synthetic activity of the understanding operating under the rubric of the imagination:8 The same function that gives unity to the different representations in a judgment also gives unity to the mere synthesis of different representations in an intuition, which, expressed generally, is called the pure concept of the understanding. (GW, 211; A79/B105) Dickerson has argued that the unity of apperception is not a second-order unity for Kant, an act of self-awareness of ourselves and our states, but is the primary unity that holds the elements of intuition together and confers on us the ability to represent a multiplicity of elements of sense as part of an objective unitary cognition.9 This is the conception of the unity of apperception in the second apperception project. I note that an act of second-order awareness is crucial to the discovery of this unity in all representations. This second-order act of awareness is the analytical power of apperception that expresses itself in second-order judgments possessing the form of an objective cognition; that is, possessing the unity of apperception as it is being understood in the second apperception project. Many texts in sections 15–18 do indeed read this way, leading Dickerson to put the texts that lend themselves to the second-order reading in the background. Now, Kant introduces in section 16 a distinction between the “analytical unity of “Synthesis in general is, as we shall subsequently see, the mere effect of the imagination . . .” (GW, 211; A78/B103). 9 “I argue that Kant’s notion of apperception, despite initial appearances, should not be assimilated to modern notions of ‘self-awareness’, ‘self-consciousness’, ‘self-knowledge’ or ‘self-reference.’ Rather, apperception is the reflexive act whereby the mind grasps its own representations as representing and is thus an essential part of all thought and cognition” (Dickerson 2004, 81). Also see Brook 1994, 37. 8

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apperception” and the “synthetic unity of apperception” (GW, 247; B133–134). The synthetic unity of apperception is the mirror of the analytic unity of apperception: the former is the kind of unity of elements in an intuition in general and the latter is the kind of unity that the products of the analytic power possess when applied to intuitions in general; namely, the unity characteristic of individual judgments. Because the analytical power of apperception is what reveals the existence of synthetic unity in intuitions in general, we could say that the analytic power is primary in the order of discovery but posterior in the order of production. If, as Kant maintains, all representations—at least all that count—are subject to the power of apperception (whether carried out or not), then all representations are subject to the analytical power of the understanding; that is, some propositional structure is revealed for all representations in the act of apperception. This structure must have been created by a prior synthesis of the elements of an intuition. In the specific case of connection synthesis (nexus), the elements are unified in an implicitly judgmental way: judgment is just a way of making explicit what is already inherent in the intuition. It is not, for example, a matter of comparing perceptions with one another. I mention the latter possibility because it is the procedure that Kant ascribes to judgments of perception.10 This class of judgments raises the question whether they too fall under the doctrine of the priority of synthesis over judgment just described and, if they do, whether they involve unification of intuitions in the same sense, as implicit judgments. I considered this important question previously11 and concluded that even judgments of perception require a prior synthesis, but it is not a synthesis that produces logically (intellectually) unified intuitions. So even aesthetically unified intuitions are structured so as to potentiate judgments, judgments of perception. I am about to argue that the analytical power of apperception also operates on aesthetically unified intuitions to produce second-order judgments in explicitly propositional form but not in the objective propositional form characteristic of judgments of experience. In Section 3, I make a proposal about how Kant understood the propositional form of judgments of perception.

3.  The Propositional Form of Judgments of Perception I intend to proceed in this section from the assumption that the analytical power of apperception generates propositionalized forms of all intuitions, aesthetically 10 11

See Prolegomena, part II, §20, at Hat., 52; Ak 4, 300. See Ch. 6, §3.4.



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unified and logically unified alike. The forms are, respectively, judgments of perception and judgments of experience.12 What is crucial for original apperception is the propositionalizing of intuitional content not initially in propositional form. It is not crucial that the propositions be those involved in judgments of experience; judgments of perception are also possible.13 However, by the time Kant reaches section 18 and the objective unity of apperception, only propositions of experience are revealed by the power of apperception. Of special note is the first-person proposition of experience of the form “I am in state S.” This is a judgment of experience because it employs the copula “am”. Let’s now look more closely at how the original power of apperception generates a judgment of perception from an aesthetically unified intuition. In a judgment of perception, Kant says in the Prolegomena, I express “a relation of two sensations to the same subject” or “I relate two sensations in my senses only to one another” (Hat., 52: Ak 4, 299). This relation occurs in an intuition having what Kant calls in section 18 of the Analytic a “subjective unity of consciousness” rather than the objective unity of consciousness when the relationship can be expressed in a judgment of experience (a “copula judgment” as I call it).14 We might ask what two sensations? In his example given there—“the room is warm, the sugar sweet, the wormwood repugnant”—it may not be clear what two sensations Kant is speaking of nor what kind of relation they bear to one another.

This provides an answer to an objection from Guyer that any attempt to attribute to Kant a doctrine of judgments of perception in CPR is bound to fail: 12

How can judgments of perception express any form of self-consciousness, yet not use the categories? . . . the obvious answer is that the notion of judgments of perception cannot be reconciled with the assumption that categories figure in any form of self-consciousness at all precisely because this notion is an expression of Kant’s type I premise that there is a fundamental contrast between self-consciousness and objective experience, rather than of his distinct type II premise that the use of the categories is ultimately a necessary condition of self-consciousness itself. (Guyer 1987, 100–101) The answer has two parts. The first is that what I call “the power of apperception” is an analytic power that reveals propositional structures hidden in representations, whether that structure be propositions expressing perceptual associations in the subject or propositions expressing determinate objective experiences. One kind of proposition revealed is a second-order proposition regarding the attribution of perceptual states to subjects. If all of these had to be in the form of a predication with a potential substance as subject, “I am in perceptual state S,” then that would rule out judgments of perception, which are not in that form. But because in original apperception—the kind at issue in §16 where the power of apperception is exercised—we do not attribute states to ourselves in that form but rather in a form where the subject is not a potential substance (“perceptual states S is mine”), then the problem does not arise. This is the second part of the answer. 13 Meerbote concurs in this possibility. See Meerbote 1981, 216. 14 See Ch. 6, §3.4 for further discussion.

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In a later example (“If the sun shines on the stone, it becomes warm”; Hat., 54 n.*; Ak 4, 301),15 Kant seems to suggest that the relation is a temporal sequence rather than a causal sequence, but in another important discussion, this in the Jäsche Logic, Kant clarifies his meaning: A judgment from mere perception is really not possible, except through the fact that I express my representation as perception; I, who perceive a tower, perceive in it the color red. But I cannot say: it is red. For this would not be merely an empirical judgment, but a judgment of experience, i.e., an empirical judgment through which I get a concept of the object. E.g., In touching the stone I sense warmth, is a judgment of perception: but on the other hand, The stone is warm, is a judgment of experience. It pertains to the latter that I do not reckon to the object what is merely in my subject, for a judgment of experience is perception from which a concept of the object arises; e.g., whether points of light move on the moon or in the air or in my eye. (§40: Young, 608–609; Ak 9, 114) This passage, which I take to be more perspicuously formulated than the corresponding passage in the Prolegomena, indicates that there are two sensations (“perceptions”) in every judgment of perception. In the first example they are that which represents the tower and that which represents the color red. In my judgment I perceive the one somehow in the other. This passage also makes clear that the relation indicated by “in” here is not objective inherence, as in the case of judgments of experience, but something else: I suggest co-occurrence in subjective space and time. Similarly, the other example in this passage indicates that what makes the judgment “In touching the stone I sense warmth” a judgment of perception is not that it is a temporal rather than a causal sequence but that it is not a relation of the objective inherence of a property in an object. It is simply the sequence of perceptions: a stone-touching perception is succeeded by a perception of warmth. Since the warmth/stone examples are so similar, I suggest that we read this account into the Prolegomena passages. Thus, when Kant says (in language from the Prolegomena) that “I relate two sensations in my senses only to one another,” for the first example from the Logic he would mean that I judge that the location of the appearance of the tower and that of the color red co-occur in subjective space and time and, for the second, that I judge that the sensations of the sun shining and of warmth are temporally adjacent. The German is Wenn. Whether translated as “if ” or “when” there is still a sequence implied by the becoming warm of the stone upon being shined upon by the sun. However, in general I do not rely on the examples from the Prolegomena to illustrate Kant’s doctrine of judgments of perception, but instead on those in the Logic. 15



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It is not easy to say into which of the twelve forms of judgments a relational judgment like this would fall. But this is not a difficulty specific to judgments of perception, formulated canonically as relational judgments, but a problem in general for the ability of Kant to deal with relations within the system of classification of the Table of Judgments.16 There are two main possibilities here. One is that judgments of relation in the modern sense (those expressed by multiplace predicates) are forms of judgment that are additional to the twelve forms Kant presents in the Table of Judgments17 or at least that this is true of a subclass of relational judgments; namely, spatiotemporal relations of the precategorial sort. Perhaps Kant is treating them as falling under the doctrine of the Aesthetic rather than the Analytic, where the Table of Judgments occurs. Since judgments of perception express spatiotemporal relations of the precategorial type, we would not, on this view, expect to find a place for them in that table. The second possibility is that Kant may be trying to place these judgments within one of the existing twelve types of judgment understood precategorially. (This appears to be his approach in the Prolegomena.) In any case I do not attempt to further resolve this question here. The main point I have been defending, in this chapter and the preceding one, is that a doctrine of judgments of perceptions does not violate any of the substantive, philosophical doctrines that Kant either relies on or attempts to establish in the Deduction. In original apperception, the undetermined objects of intuition (a representation of the tower appearance and of the color in this case) are propositionalized. But they must be propositionalized in a way that is not objective; that is, they are not objects to which any property is objectively ascribed. This requires that we formulate the propositionalized version of the appearances carefully so as not to contain a determined empirical object, including the self. We could not, for example, allow for a propositionalized formulation in the tower perception / red color perception example of the form “I have a perception of a tower, I have a sensation of the color red and the perception and sensation co-occur in the spatiotemporal form of my sensibility,” because in saying that I have a certain state we are saying that I am in a certain state and that is a judgment of experience—it objectively assigns a property to an object; in this case myself. This occurs only as a late-stage application of apperception: nonoriginal apperception. However,

Friedman (1985) has argued that another manifestation of problems that Kant has with relations is the lack of a modern theory of the logic of relations, something Kant has sought to overcome, Friedman claims, in his theory of the construction of mathematical objects in pure intuition. 17 In CPR Kant offers no justification for introducing just these twelve forms of judgment other than the following remark, “If we abstract from all content of a judgment in general and attend only to the mere form of the understanding in it, we find that the function of thinking in that can be brought under four titles, each of which contains under itself three moments” (A70/B95). 16

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we are currently looking at original apperception, an early-stage application of the apperceptive power. To give us the formulation we are seeking let us first suppose that we are dealing with judgments in the form of an appearance relation (not a predication) between an object and myself; for example, “The stone feels warm to me.” I propose to analyze this statement as a judgment of perception in two stages: D1. The stone feels warm to me iff there is an S such that S is a qualitative sensation of warmth and there is an I such that I is a singular sensory intuition of the stone and S and I are associated in my sensibility. D2: S and I are associated in my sensibility iff S and I are co-located in the spatial and temporal forms of my sensibility. I submit that by avoiding a subject-predicate formulation with “I” as the subject term, we have a nonobjective propositional content revealed by the power of apperception. If this account of the distinction between two forms of apperception is accepted, then the way is clear to offering a conservative reading of the argument of the first part of the Deduction. In section 18 Kant is specifying a late-stage application of apperception, yielding propositional formulations that are all objective. Whether the subject terms designate representations of objects distinct from myself or not, in both cases they are the objects of intuitions determined by objective judgment. This is what Kant asserts in Section 19: “I find that a judgment is nothing other than the way to bring given cognitions to the objective unity of apperception” (GW, 251; B142). It may be thought that section 19 offers an independent argument against the possibility of judgments of perception in the words: “ . . . I find that a judgment is nothing other than the way to bring given cognitions to the objective unity of apperception” (GW, 251; B141). Taken just by itself this declaration is entirely general and would therefore be inconsistent with the doctrine of judgments of perception. However in the next sentence Kant in effect restricts the scope of “judgments” to subject-predicate judgments:  “That is the aim of the copula is in them:  to distinguish the objective unity of given representations from the subjective.” As long as we find a formulation not using the copula, as we have done above, the door is left open to a doctrine of judgments of perception.18 Ultimately, the question whether a doctrine of judgments of perceptions should be accommodated within the teachings of the Deduction is settled only after we decide whether a doctrine of aesthetically unified intuitions needs to 18

Also see the note on this issue in Ch. 6, §3.4.



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be accommodated within those teachings, something we investigate in detail in Part II, Section 2.1.19 In section 20, Kant draws his conclusion, a first and intermediate conclusion as it will turn out:20 Therefore, all manifold, insofar as it is given in one empirical intuition, is determined in regard to one of the logical functions for judgment . . . But now the categories are nothing other than these very functions for judging . . . Thus the manifold in a given intuition also necessarily stands under the categories.” (GW, 252; B143) Kant is able to use this analysis to establish that the manifold of intuition is subject to the categories (his §20 conclusion) only because he is working with a conception of intuitions that connects them essentially to a set of objective properties. These are the logically unified intuitions with which Kant is primarily concerned in sections 15–20, the kind of intuitions to which late-stage applications of the power of apperception apply—that is why it has been relatively easy for Kant to show that unified intuitions are subject to the categories.

4.  Problems from Sections 17 and 18 The Unity of Apperception is the kind of unity that judgments have, and I have just been arguing that Kant allows for two kinds of judgments in CPR, judgments of experience and judgments of perception. Both are revealed by the power of apperception to have propositional contents. Propositions have a unity and Kant’s term for it is “the unity of apperception.” Sometimes, however, Kant distinguishes between “the analytical unity of apperception” and the “synthetic unity of apperception”; for example, in the phrase “the analytical unity of apperception is possible only under the presupposition of some synthetic one” from section 16 (GW, 247; B133–134). So there is an analytical unity of apperception that is the mirror of the synthetic unity of apperception; the former presents to consciousness a propositionalized form of the elements synthetically unified in the intuitions to which the power of apperception is directed, the latter constitutes the synthetic unification itself.

A similar conclusion is drawn by Allison 2004, 181, specifically with respect to how the argument of §26 should be read. My view is that the matter is settled there affirmatively. Allison thinks that it is settled there negatively. 20 See §21. 19

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The present issue is whether portions of the texts of sections 17 and 18 allow for both kinds of judgment—many scholars think that they do not. I now argue that in fact these sections do not rule out this possibility.

Section 17 Although Kant does not specifically use the term “synthetic unity of apperception” in the body of the passage quoted—he uses “unity of consciousness”—he uses it elsewhere in the passage, and I take these two terms to be used as equivalents here. This is the passage from section 17: Understanding is, generally, the faculty of cognitions. These consist in the determinate relation of given representations to an object. An object, however, is that in the concept of which the manifold of a given intuition is united. Now, however, all unification of representations requires a unity of consciousness in the synthesis of them. Consequently, the unity of consciousness is that which alone constitutes the relation of representations to an object, thus their objective validity . . . (GW, 249; B137) It is possible to read Kant’s doctrine in section 17 as saying, absolutely, that the synthetic unity of consciousness allows only for logical unification (relation to an object–type unification), but it also possible to read the passage as saying that the kind of relation that representations have when they are in “relation to an object” constitutes a certain kind of relation; namely, a conceptual relation between representations. On this reading, Kant would here be announcing (or reannouncing)21 his new theory of judgment, not insisting that all forms of judgment or synthetic unity are objective. So this passage need not be taken to say that there can be absolutely no nonobjective synthetic unities of consciousness/ apperception.

Section 18 Section 18 may seem to close—and bolt—the door against this possibility: The transcendental unity of apperception is that unity through which all of the manifold given in an intuition is united in a concept of an object. It is called objective on that account and must be distinguished from the subjective unity of consciousness, which is a determination 21

See Ch. 5, §1, for a discussion of the initial introduction of this idea in §10.



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of inner sense, through which that manifold of intuition is empirically given for such a combination . . . (GW, 250; B139; my emphasis) We have considered this text before and concluded22 that it is overall quite helpful to the case for finding in Kant a distinction between two types of unified intuitions: those that are logically unified and potentiate copula judgments, which are objective, and those that are aesthetically unified and potentiate judgments of perception, which are not objective. Is not Kant saying here that what this power reveals is always an objective structure, even in the case of aesthetically unified intuitions, thus contradicting one of the central tenets of this book? Not necessarily. I  suggest that Kant could be saying that the kind of unity of apperception that is transcendental is restricted to those that are objective— the transcendental unity of apperception alone is objective. The point would be clearer if Kant had emphasized only the word “transcendental” rather than both “transcendental” and “unity.”23 This is of course a crucial point to be made for the purposes of a deduction of the categories, and he makes it here for the first time.24 This leaves room for the existence of other kinds of unities of apperception. When Kant applies the term “transcendental” to something, I  take him to mean that a proper understanding of the thing will show that it has a key role to play in the project of establishing the existence of a priori cognition, typically by means of a transcendental argument or by means of Nomic Prescriptivism. So Kant might simply be saying in that first sentence of section 18 that those unities of apperception that have transcendental significance are restricted to those that are also objective. As mentioned, this does not exclude the existence of another type of apperceptive unity. On my view, of course, there is another type. It is that revealed by the power of apperception applied to aesthetically unified intuitions, which, as I have argued,25 are the kind of intuitions having what Kant calls here (in the very next sentence) a “subjective unity of consciousness.” To make the connection to this power clearer, Kant should have added that the subjective unity is also a synthetic apperceptive unity; that is, a synthetic unity potentiating propositional affirmations, in the form not of the copula judgments to be introduced in section 19 but of noncopula judgments: judgments of perception. Ch. 6, §3.4. I observe that in the corresponding passage in §16 dealing with the unity of self-consciousness, Kant emphasizes only the word “transcendental”: “I also call its unity the transcendental unity of self-consciousness . . .” (GW, 247; B 132). If my interpretation is accepted, Kant should also have done the same in the corresponding phrase in §18. 24 The term “transcendental” has already been applied to the unity of self-consciousness (see n. 23); Kant is now, for the first time in the B edition Deduction, applying it to the unity of apperception. 25 Ch. 6, §3.4. 22 23

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Unfortunately, he does not say this. Nevertheless, the main point is that the subjective unity of consciousness does not play a key role in the argument for a priori cognition; that is, it is not a unity with transcendental significance. And that Kant does say. My conclusion is that in the texts of sections 17 and 18 Kant did not intend to exclude the possibility that logically unified intuitions and those that are merely aesthetically unified are both subject to the I think as long as it is taken in its sense as the analytical power of apperception.26 This is not to deny, of course, that in the text at the beginning of section 18 Kant does intend to be focusing his remarks on an objective version of the synthetic unity of apperception, using that version as the basis for the arguments of sections 19 and 20. But if that is so, what justification is there for introducing that version in the first place? Kant’s answer is to be found in his discussion of a new principle, the Analytical Principle of Apperception.

5.  The Analytical Principle of Apperception In the last paragraph of section 16 (B135) Kant introduces an apparently new idea: that the principle of apperception is an analytic proposition that somehow implies a “synthesis of the manifold of intuition.” (This and the next few quotations are taken from §16:  GW, 248; B135, unless otherwise indicated.) In order to assess this claim and its relevance to the synthesis of intuitions, it would be requisite to know what the principle is. One suggestion27 is that it is the I think formulation that expresses the analytical power of apperception: If something is my representation then I am aware that it is (or can so become). This is a second-order statement that Kant certainly thought was necessarily true. Perhaps he thought this because he thought that it was a conceptual truth, a point reinforced when we consider that Kant adds a proviso to the initial formulation, that the principle applies to only those representations “that are something to me” (GW, 246; B132). Perhaps the just-given formulation is definitive of what “is something to me” means, hence is analytic. However, although there

There is a further difficulty for my position coming from the fact that Kant seems to restrict the application of the term “judgments” in the Critique (§§19–20) to copula judgments, leaving out altogether the application of that term to the affirmation of the propositional contents potentiated by aesthetically unified intuitions.* In the Prolegomena, as noted, Kant pursues a more liberal policy, allowing the term “perceptual judgments” to apply to affirmations of this kind. I take this to be at most a terminological inconsistency between the two works rather than a doctrinal distinction. (For further discussion see Ch. 7, Part I, §3.2.) 27 Made by Allison 1983, 137. 26



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is some difficulty in pinpointing exactly what proposition Kant is taking to be analytic at B135 here, it does not appear to be this one. Kant reiterates at B138 that there is an analytic principle of apperception and now specifically states that “it says nothing more than that all my representations in any given intuition must stand under the condition under which alone I can ascribe them to the identical self as my representations, and thus can grasp them together, as synthetically combined in an apperception, through the general expression I think” (GW, 249–250). This is the principle Howell identifies as Kant’s analytic principle of apperception. He says that the principle is “trivial” and that “Kant does not use this principle as a premise in the further argument of the Deduction.” Its sole point is to remind readers that “that condition is that the relevant representations must be synthesized or held together by the mind.”28 The impression that the principle is trivial is given by the emphasis that Kant gives to two occurrences of “my,” suggesting that Kant is simply saying that all representations that are mine are mine or, less tautologically but no less trivially, that all representations that are mine are so in virtue of whatever conditions are necessary for them to be so. This is why Howell declares the principle to be of no further use in the argument of the Deduction. But it is hard to accept that this is Kant’s intention. Kant spends much effort developing the principle and his discussion of it is the last major philosophical idea before the assertion made in the first sentence of section 18: the transcendental unity of apperception is an objective unity. This is a strong claim, one that certainly is a premise in the later stages of the Deduction, and it seems to me desirable to find a role for the analytic principle at the end of section 17 as well as a justification for assigning transcendental status to the objective unity at the beginning of section 18. I now offer a suggestion of how both of these things can be accomplished simultaneously. What Kant has in mind, I suggest, is a proposition that links the nonobjective formulation of the subject of an I think proposition revealed by the power of apperception, a certain representation r is mine, with an objective formulation, I am in representational state r. Kant gives just such a proposition following his initial identification of an analytic form of the principle of the necessary unity of apperception at B135 in section 16: (Kant’s formulation of the analytic proposition) [1]‌I  am therefore conscious of the identical self in regard to the manifold of the representations that are given to me in an intuition because [2] I call them all together my representations, which constitute one. (GW, 248; B135; my interpolated numbers) 28

Howell 1992, 158; n. 6, 370–371.

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Note that the inference here is from [2]‌to [1], and as in my proposed formulation, this is an inference from a formulation in which the term “my representations” is the subject of the assertion (that they are mine) to one in which “I” is the subject of the assertion (that I  have them), just what is required if my interpretation of Kant’s intentions are correct here. The principle in question is this: “if my representations are indeed mine, then I indeed have them.” I call this the Analytic Bridging Principle for Apperception. Since it is an analytic principle, it is available as a premise in any proof for which it might be useful. The “I” form of the consequent of this principle is a genuine subject-predicate statement that must eventually meet the condition for an objective judgment that Kant will go on to define in section 19. The condition is that the subject of a genuine subject-predicate sentence must conform to the category associated with that judgment type; namely, it must conform to the category of substance. By this condition, the form with “my representations” as a subject is not a genuine subject-predicate statement because my representations will never be shown to be a substance. This means that the intuitions underlying this form of judgment will have only a subjective unity, an association of representations like that between the representation of a tower and the perception of the color red in the example of perceptual judgment Kant gives in the passage from Young, 608609, Ak9, 114, quoted above from the Logic. In other words, Kant is here making a deductive inference from judgments based on subjectively unified intuitions, what might more generally be called “associative judgments,” to those based on objectively unified intuitions, what Kant calls “judgments of experience.” This account may seem inconsistent with Kant’s general doctrine that no transition from associative judgments (judgments of perception) to judgments of experience can be made without the addition of categories. However, the case of the self is special for Kant. It is the one case where the inference can be made without an actual, prior application of the categories to the subject—it anticipates that determination but does not require that it be in place first. This is possible only because of the analyticity of the statement that formulates this inference.29 If I  have Kant right here, the statement of the Analytic Bridging Principle marks the transition from one kind of apperception to the other: from an original form of apperception that takes the “my representation” form, “If I am in a certain representational state r then I am aware that r is mine,” to an objective form of apperception, “If I am in a certain representation state r then I am aware that I am in that state.” As some support for this contention I note that in the sentence immediately following the sentence in which Kant states the bridging principle, he calls the form of synthesis explaining what makes my representations mine

29

This very long footnote is placed at the end of the chapter as Note A.



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the “original synthetic unity of apperception” (GW, 248; B135–136; emphasis added). This interpretation is not, as far as I know, represented among existing interpretations of the role of Kant’s doctrine of apperception in the argument of the first part of the B edition Deduction. Nevertheless, it has some advantages in preserving Kant’s argument against charges that it suffers from egregious philosophical defects. Consider, for example, Guyer’s rendering of the argument of sections 16–18 in his 1992 article in the Cambridge Companion to Kant.30 According to Guyer, in section 16, “Kant reiterates the basic claims of the first-edition argument about apperception.” Guyer represents these claims as follows: 1. All representations, whatever their empirical status, are recognized to belong to a single self. (The I think principle implies an analytic unity.) (B131–132) 2. Analytic unity of apperception implies a synthetic unity. (B133) 3. The synthetic unity of apperception implies an a priori synthesis:  mental activity. (B133) 4. A priori synthesis is an affair of the understanding. (B135) According to Guyer, the categories are now introduced, not directly after step 4 (as in the A edition) but only after the argument of sections 17–19. The problems begin in section 17. When Kant says there that “the unity of consciousness is that which alone constitutes the relation of representations to an object, thus their objective validity,” according to Guyer, “Kant would now be defining an object as constituted by any conceptual connection of the manifold of intuition whatever,” thereby espousing a “deflationary” definition of an object (151). But for Kant to show that there are objects that are distinct from the self, “Kant’s original task” in the Deduction, then “at this point in the argument he should be arguing only that the conditions for the unity of apperception—which still remain to be discovered—are necessary conditions for knowledge of objects, not, as he seems to be suggesting, sufficient conditions.” The problems only get worse in section 18, where Kant now identifies the original unity of apperception with the deflationary account of an object (“The transcendental unity of apperception is that unity through which everything in a given manifold is united in a concept of the object” [B139].) There is no progress here from the kind of unity of mental activity that characterizes the self to the kind of unity that objects must have thence to the applicability of the categories: “ . . . because the unity of apperception has just been identified with cognition of objects, this still seems to base his argument on a controversial definition of knowledge of an object.”

30

Guyer 1992. The following quotations from Guyer’s text are from 150–152.

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The complaint that no progress has been made is inevitable if the transcendental unity of apperception mentioned at the outset of section 18 is simply the original unity of apperception mentioned at the outset of section 16. If, however, there are two conceptions of the (propositional) unity revealed by apperception, one original and nonobjective, the other objective, then at least the possibility of real progress exists. If we now take the account of “relation to an object” of section 17 as asserting not a deflationary definition of the concept of an object in general but a more general claim about the kind of thing into which the concept of objectivity falls—it falls into the unities-of-consciousness kind (unities given by rules applied to representations in some fashion), section 18 now makes its assertion that the transcendental unity of apperception is of this kind. I have suggested that the emphasis here should be on the word “transcendental” alone—as it has been in the corresponding reference to the transcendental unity of self-consciousness (at GW, 247; B32, in §16), thus making the point that unities of apperception that have transcendental significance are objective unities. But what is Kant’s interest in making this claim here? What example of such a claim does he have in mind? And, what justifies the claim? In general terms I see Kant’s problem to be getting from the subjective unity of the manifold of self-consciousness (what makes all of my states mine) to a proposition that has transcendental significance; that is, that has a key role to play in furtherance of the project of the Deduction, especially its prescriptivism. Kant’s position in section 18 is that this will be an objective proposition that can somehow be derived from the subjective unity of self-consciousness. What is the proposition and how is it derived? My suggestion is that this is where the Analytic Bridging Principle for Apperception comes into play for Kant: it allows us to infer from the original unity that my states have when they are mine, asserted in section 16, to the unity of the self as object of logically unified intuition (the objective unity of apperception), asserted in section 18. This is Kant’s only example to date of a genuine subject-predicate statement that he is in a position to prove from the original apperception of the unity of self-consciousness, an example, moreover, that he believes has great significance for the furtherance of the project of the Deduction. It remains somewhat problematic exactly how the doctrine that the objective unity of apperception, understood as genuine subject-predicate statements with the self as subject, can help with the further steps in the argument, those in sections 19 and 20. Perhaps the point is simply to show there is at least one case of an object that meets Kant’s transcendental conditions for objectivity, thus showing the real possibility for an extension of these conditions to all appearances.31 Perhaps—Kant doesn’t really say. Another suggestion comes in Pereboom 2001, 96–98. He also denies that the discussion of “relation to an object” in §17 is intended to provide a sufficient condition for objectivity. 31



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6.  Synopsis of the First Part of the B Edition Deduction This synopsis presents a summary of the line of argument in the first part of the B edition Deduction, beginning with the doctrine of unified intuitions in section 15 and leading to the conclusion in section 20 that intuitions are subject to the categories. The principle of the power of apperception introduced in section 16 yields the doctrine that the unity of the kind of intuitions under discussion in section 15, intuitions in general, is due to synthesis guided by the understanding. Kant develops the idea of an objective unification—the unification of the representation of properties with the representation of objects when those objects really possess the properties—in section 17 and asserts in section 18 that the unity of transcendental apperception is objective. In terms of Kant’s doctrine of the original power of apperception to propositionalize and decompose the elements of intuitions, I take this to mean that the propositions composing the apperceived elements of intuitions in general are objective propositions—the apple really is red—and that the corresponding syntheses are objectivizing syntheses and the unity they possess (or the unity of the intuitions that they give rise to) is the objective synthetic unity of apperception. In section 19 Kant says judgments just are the way in which the objective synthetic unity of apperception is revealed. In section 20 Kant says that the functions of judgment are the categories. Drawing on the Same-Function Doctrine of section 10 (Kant does not actually mention it in §20) allows Kant to reverse direction and read the categories back into the functions that explain the ability of the mind to carry out the activity needed to produce unified intuitions of the type at issue in section 15. Since, as noted, that type is intuition in general (Anschauung überhaupt), a species of sensible intuition, Kant concludes that sensible intuitions, subclass überhaupt, are subject to the categories. QED. What remains to be shown is that sensible intuitions, subclass empirische, are as well. This is the ultimate objective of section 26 and the main subject of Part II of this chapter, the concluding part of my account.

7.  Conclusion of Part I and Transition to Part II In Part I, I  take myself to have removed the major impediment arising from Kant’s doctrine of apperception to accepting that Kant countenances a class of intuitions that are aesthetically unified. These intuitions are not constituted by synthesis, though they are made an object of conscious awareness by synthesis, in contrast to intuitions in general, intuitions both constituted by synthesis and

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made an object of awareness by synthesis. Moreover, the synthesis that operates in the case of aesthetically unified intuitions is not category governed; the synthesis that operates in the case of intuitions in general is category governed. The existence of aesthetically unified intuitions, now that it has been established and shown to be compatible with the tenets of the first part of the B edition Deduction, serves as the main problem the argument of the second part of the Deduction is designed to solve. What is the problem? Pollok suggests that it is because there still remains after the first part the possibility of a Humean theory of experience.32 By leaving alive the possibility of aesthetically unified intuitions and perceptual judgments, an empiricist like Hume might be content to say that despite all that went on in sections 15–20, aesthetic unification is still all that there is to the unity of sense perception. Appeal to categories and other such devices might have some subjective validity, but no proof of their objective validity has yet been provided. I agree with this hypothetical empiricist—my arguments to date in this chapter have been devoted to establishing this point. So the problem that remains is to prove a priori that empirical intuitions (the perception of empirical objects) are not just aesthetically unified, they are also logically unified; that is, they possess the same kind of unification as intuitions in general. Since judgments of perception are correlated with aesthetically unified intuitions and judgments of experience with logically unified intuitions, the problem is at the same time to show that while there still remains the possibility of making judgments of perception about a given empirical object, there is the necessity of also making judgments of experience about it.33

II.  The Second Half of Kant’s B Edition Transcendental Deduction of the Categories 1.  Why the Deduction in the B Edition Needs a Second Part By Kant’s own account the B edition Transcendental Deduction divides into two parts: the first part being sections 15–20 and the second, sections 22–27.34 Pollok 2008, 333. This description of the problematic of the second part of the deduction may be contrasted with Pollok’s own: “With [the] argument of the second proof step, the aim of which is to show ‘how experience is [. . .] possible by means of these categories’ (IV, 475) the distinction between judgments of perception and judgments of experience consequently vanishes from Kant’s thinking” (ibid., 335). 34 Some of this material has appeared previously in Vinci 2013. 32 33



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The explanation of the relation between the two parts is given in section 21. He says that in the first part: In the above proposition, therefore, the beginning of a Deduction of the pure concepts of the understanding has been made [. . .]. In the sequel (#26) it will be shown from the way in which the empirical intuition is given in sensibility that its unity can be none other than the one the category prescribes to the manifold of a given intuition in general according to the preceding #20; thus by the explanation of its a priori validity in regard to all objects of the senses the aim of the Deduction will first be fully attained. (GW, 253; B144–145) From this passage it appears that the first part deals with one kind of representation, “intuition in general,” showing that it has a certain of unity (“the one the category prescribes”); but there is a second kind of representation, “empirical intuition.” Empirical intuition apparently also possesses a unity, but of what kind remains to be determined even after the argument of the first part has been concluded. This is what the second part is to show; what it shows is that the kind of unity empirical intuitions possess is the same as the kind intuition in general possesses; that is, the one prescribed by the category. Thus, “in regard to all the objects of our senses the aim of the Deduction will first be fully attained.” This is Kant’s own characterization of the relation between the two parts of the Deduction, and if taken at face value, it indicates that there are two disjoint classes of representations, both intuitions, both unified, the first class designated by the term “intuitions in general,” the second by the term “empirical intuitions.” The language of empirical intuition (empirische Anschauung) appears throughout CPR and means, roughly “sensory perception of an object.” The language of “intuition in general” (Anschauung überhaupt) is more localized. It makes its first significant appearance in the “Metaphysical Deduction” at A79/B105 (GW, 211–212): “The same understanding . . ..brings transcendental content into its representations by means of the manifold of intuition in general, on account of which they are called pure concepts of the understanding that pertain to objects a priori; this can never be accomplished by general logic” (my italics). One might think that Kant is just talking generally here about intuitions as they have been understood in the Aesthetic, but if we compare this passage with passages from the discussion of the difference between General and Transcendental Logic, Kant indicates that intuitions in general are a special class of intuitions distinct from empirical intuitions. In one passage, Kant says that Transcendental Logic itself has been introduced: “in the expectation, therefore, that there can perhaps be concepts that may be related to objects a priori, not as pure or sensible intuitions but rather merely as acts of pure thinking . . .” (GW, 196; A57/B81). What

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are the objects of these “acts of pure thinking”?35 They are not empirical objects, for “there would be a logic [Transcendental Logic] in which one did not abstract from all content of cognition; for that logic that contained merely the rules of the pure thinking of an object would exclude all those cognitions that were of empirical origin” (GW, 196; A55/B80; my emphasis). Later (in the chapter on phenomena and noumena) Kant says that they (the objects of “pure thinking”) are not objects of intellectual intuition understood as intuition that takes a noumenon but rather “[t]‌he object to which I relate appearance in general is the transcendental object . . . I have no concept of it except merely as the object of a sensible intuition in general . . .” (GW, 349; A253/B308; my emphasis). (In line with the context and the sense of the passage, I would read “thinking in general” for “appearance in general” in the above passage.) The term “sensible intuition in general” is Kant’s language for the representation by means of which concepts are related to objects, not as intellectual intuitions but nevertheless still as acts of pure thinking” (from the earlier quoted passage GW, 196; A57/B81). I contend that this means that a sensible intuition in general is an intuition (it is the means by which we relate concepts to objects) with the form but not the matter of empirical intuitions (that is how the class of intuitions in general “excludes” empirical intuitions) providing immediate cognitive access to physical, rather than pure (“not as pure intuitions”), objects in space and time. Consistent with this contention is Kant’s account of intuition in the so-called classification passage: We are not so lacking in terms properly suited to each species of representation that we have need for one to encroach on the property of another. Here is their progression: The genus is representation in general (representatio). Under it stands representation with consciousness (perceptio). A perception that refers to the subject as a modification of its state is a sensation (sensatio); an objective perception is a cognition (cognitio). The latter is either an intuition or a concept (intuitus vel conceptus). (GW, 398–399; A319–320/B376–377) This passage asserts that perception is representation with consciousness, only a subspecies of which is representation as sensation. Distinct from representations as sensation are “objective representations,” and a subspecies of these are It seems that these pure acts of thinking are different from the acts of thinking Kant discusses in §22 (GW, 254; B147) of the B edition. The former are characterized as intuitions (in general), things that relate our concepts directly to objects, the latter as not being intuitions, as what you get when you subtract intuitions from judgments. 35



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intuitions. This passage is consistent with the reading of intuitions in general just proposed; it is also consistent with the passage in the Jäsche Logic in which Kant classifies representations, an account that omits sensation altogether as a property relevant to objective representation (Young, 569–570; Ak 9, 64–65). I conclude from these considerations taken together that “sensible intuitions in general” or just “intuitions in general” are items separate from sensations and from the pure intuitions of space and time. Because all sensible intuitions have a sensible form—in the case of human sensible intuitions, the form is space and time—all sensible intuitions in general have the form but not the matter of sensation, and in the case of human sensible intuitions in general, they have the form of space and time but not the matter of human sensation.36 In section 26, the “sequel” to section 20, Kant confirms that the purpose of the second part is to show that the kind of unity present in intuitions in general is present in a second class of intuitions, “sensible intuitions” as they are called there: But this synthetic unity can be none other than that of the combination of the manifold of a given intuition in general in an original consciousness, in agreement with the categories, only applied to our *sensible intuition*. (§26: GW, 262; B161; my asterisks) The synthetic unity in question is achieved by an act of synthesis Kant calls “the synthesis of apprehension,” an act that constructs empirical intuitions. So here too it seems fair to read “sensible intuition” in this passage as equivalent to “empirical intuition” in the passage from section 21. Here too there are two classes of intuition, the kind of unity of the first of which has been shown to apply to the second. So we should not treat intuitions in general as referring to all intuitions in general, as we might naturally be disposed to do, but treat it as This taxonomy is apparently inconsistent with one given in §22: “Sensible intuition is either pure intuition (space and time) or empirical intuition of that which, through sensation, is immediately represented as real in space and time” (GW, 254; B 146–147). This classification does not leave room for a class of intuitions that are sensible in form but not in matter. (Thanks to Jeff Edwards here.) If we understand the parenthetical remark “pure intuition (space and time)” to refer to pure intuitions of space and time, I think it must be accepted that this is a contrary text. However, Kant’s account of perception given here (representations accompanied by sensation) is itself inconsistent with his account of perception in the so-called classification passage. As just noted, this passage asserts that distinct from sensations are “objective representations,” and a subspecies of these are intuitions. So Kant has collapsed the distinction between objective perceptions and perceptions somehow involving sensation in §22. This is significant, since a sensible intuition in general in my sense is an objective intuition without sensation, something that is allowed for in the classification passage but not in §22. Despite its proximity to §§15–20, I do not take the account there to govern but rather the account of the classification passage, which I take to be canonical. 36

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referring to a special class of representations distinct from empirical representations. Only in this way can the Triviality Problem be avoided. I call this the Bifurcation Interpretation.37 Of course, this also assumes that we can take Kant’s words at face value here. Is there reason not to? Unfortunately, yes:  the text of section 20 contradicts the Bifurcation Interpretation in at least two ways. The heading of the section, “All *sensible intuitions* stand under the categories, as conditions under which alone their manifold can come together in one consciousness” (GW, 252; B143; my asterisks), asserts a universal claim about sensible intuitions: they all “stand under the categories.” But if empirical intuitions are sensible intuitions, it is a simple syllogistic inference to conclude that empirical intuitions fall under the categories as well, as Kant does later in this section: Therefore all manifold, insofar as it is given in one *empirical intuition*, is determined in regard to one of the logical functions for judgment . . . But now the categories are nothing other than these very functions for judging . . . (§20: GW, 252; B143; my asterisks) This is hardly the beginning of the argument; it is the end, contrary to Kant’s avowals in section 21. This is the Triviality Problem. So there is a contradiction between section 20 on the one hand and sections 21 and 26 on the other. My strategy for resolving the contradiction assumes the correctness of the Bifurcation Interpretation. There are three adjustments I  propose to make to achieve consistency with the Bifurcation Interpretation. (1) Replace the occurrence of “empirical intuition” in asterisks in the last passage from section 20 (just quoted) with “sensible intuition in general.” (2) Replace the occurrence of “sensible intuition” in asterisks in the heading of section 20 with the same locution, “sensible intuition in general.” (3) Take the occurrence of “sensible intuition” in asterisks in the passage from section 26 quoted above (GW, 262; B161) in the narrow sense, equivalent to “empirical intuition.” I thus would read the following passage from section 21 in the way indicated in square brackets, where the “above proposition” is that derived as the conclusion of section 20: In the above proposition . . . I must abstract from the way in which the manifold for an empirical intuition is given [that is, by means of actual sensation] . . . In the sequel (Section 26) it will be shown from the way Here there is a lengthy note on which views among those of recent commentators on the B edition Deduction should be classified as holding a “bifurcation” reading in my sense. It appears at the end of the chapter as Note B. 37



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in which the empirical intuition is given in sensibility [that is, by means of actual sensation] . . . (GW, 253; B144–145; my interpolations) There are, however, problems with this interpretation that come from texts in the second part of the Deduction that we have yet to consider.38 These are texts that occur in sections 23 and 24 in which Kant says that intuitions in general embody an abstract conception of intuition that applies to intuitions possible for all beings with sensible faculties: “The pure concepts of the understanding are free from this limitation [space and time] and extend to objects of intuition in general, whether the latter be similar to our own or not, as long as it is sensible and not intellectual” (§23: GW, 255; B148; my interpolation). This abstract notion of intuition provides an object that may be thought about but not “cognized”: “The pure concepts of the understanding are related through the mere understanding to objects of intuition in general, without it being determined whether this intuition is our own or some other but still sensible one, but they are on this account mere forms of thought, through which no determinate object is yet cognized” (§24: GW, 256; B150). If we understand intuitions in general as they occur in sections 21 and 26 in this abstract sense, the intuitions in general are not, as we have been contending, intuitions in spatiotemporal form without the matter of sensation but are, simply, intuitions in some sensuous form or other, and the “way in which the manifold for an empirical intuition is given” (language from the passage just quoted from §21) becomes “in spatiotemporal form” rather than “by means of sensation.” Some interpreters39 have understood the occurrence of “intuitions in general” in sections 21 and 26 in just this way and have therefore postulated that the first part of the Deduction shows that all possible forms of sensible intuition, including nonhuman forms, are subject to categorical determination and that the second part shows that intuitions in the particular form of human sensible intuition, spatiotemporal form, are subject to categorical determination. While there are attractions to this reading, there are three problems that suggest it should be rejected. The first is that it gives rise to the Triviality Problem in the usual way: intuitions in spatiotemporal form are a species of sensible intuitions, and all of the latter have been shown by the first part of the Deduction to be determined by the categories. It is a trivial matter to infer that the species has this same characteristic. The second difficulty for the alternative reading is that the abstract account of intuitions in general, that introduced in section 23, seems not to Thanks to Michael Hymers here. Thus Howell, “About this arbitrary intuition in general, the only assumption that the B-Deduction makes is that i [an intuition] is passively given to H [a subject] in the form of a manifold, through H’s sensibility” (Howell 1992, 127). 38 39

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have objects sufficiently robust to give objective validity to the categories that determine them: But this further extension of concepts beyond our sensible intuition does not get us anywhere. For they are then merely empty concepts of objects . . . mere forms of thoughts without objective reality . . . Our sensible and empirical intuition alone can provide them with sense and significance. (GW, 255; B148–149) But the first part of the Deduction, said in section 21 to concern intuitions in general, surely does get us somewhere (even if it is only the beginning of getting us there), and it does so by proving the objective validity of the pure concepts of the understanding. This is accomplished by showing that sensible intuitions in general have objective unity (§§17 and 18) and that this kind of unity is achieved by an objective synthesis made possible by the functions of the understanding; that is, the categories (§§19 and 20). This results in kinds of judgment that possess “objective validity” (§19: GW, 252; B142). I am therefore going to propose, contrary to some of Kant’s official pronouncements, that we treat the sensible intuitions in general that are referred to in sections 21 and 26, thus the kind of intuitions in general whose unity is the subject of the argument of the first part, as being human sensible intuitions in general. They alone are able to provide objective validity to the categories. Third and finally, although intuitions in general are understood in section 23 as applying in principle beyond the range of human intuitions to all intuitions given in sensibility and intuitions in general are the topic of the first part of the Deduction, in section 17 Kant seems to be interested only in human sensible intuitions:  “All the manifold representations of intuition stand under the first principle insofar as they are given to us . . .” where the “first principle” is that “all the manifold of sensibility stand[s]‌under the formal conditions of space and time” (B136).40 The contrast they have with human empirical intuition is then best conceived to reside in the difference between intuitions that have the form but not the matter of sensation and those that have both, respectively. To summarize: If this interpretation is accepted and we also allow for the substitutions in sections 20 and 26 as indicated, the contradiction between these sections can be resolved, and the Triviality Problem solved straightforwardly, as follows. When Kant says that “[a]‌ll sensible intuitions stand under the categories,” in section 20, I  would have him mean that all sensible intuitions in general stand under the categories; that is, all intuitions in general stand under the categories. This same meaning holds throughout section 20, including for 40

See Evans 1990, 557.



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the occurrence of “sensible intuition” that I propose to substitute for “empirical intuition.” His conclusion in section 20 is now that all intuitions in general are subject to the categories. On the other hand, when Kant uses “sensible intuition” in section 26, it means sensible intuitions in the narrow sense; that is, empirical intuitions. Here his conclusion is that empirical intuitions have the same kind of unity, category-governed unity, that sensible intuitions in general possess. The reason that “only a beginning” to the Deduction is made by the end of section 20 is that it is easier to show that intuitions in general are subject to the categories than to do this for empirical intuitions. On this proposal, Kant’s argument in the B edition is now rendered consistent with what he himself says it is in his clearest statement of it: his statements in sections 21 and 26. This seems to me to be the best outcome for Kant and the most plausible and simplest outcome for his interpreters. It is worth emphasizing that when I say that Kant takes intuitions in general (as well as their objects) to be spatial in form, I intend this literally. In Chapter 3 I try to make this intelligible by means of an analogy between intuitional representational systems and geographical maps. Symbols on a map are entities in spatial form representing spatial objects, the location of which in the map can be occasioned but is not constituted by the sense experience of the mapmaker. I also argue in Chapter 3 that the form of intuitions is responsible for the capability of intuitions to represent a world of spatial objects. Let’s say that this account is accepted. This means that Kant’s task in the second part of the B edition Deduction is to show that empirical intuitions (sense-perceptual representations) have the same kind of unity as intuitions in general; that is, unification by means of categories. For this to be an interesting project there has to be an alternative that Kant means to exclude by his argument, an alternative that allows for the unification of empirical intuitions by other means. What other means are possible? I have previously argued that Kant allows for a distinction between logical unification and aesthetic unification such that appearances we are conscious of are always aesthetically unified but can, in principle, fail to be logically unified.41 Kant’s main tasks in the second part of the B edition Deduction is to show that when appearances constitute actual empirical objects, they must possess logical unification in addition to aesthetic unification. Most commentators are not prepared to allow that, for Kant, there can be intuitions that are not logically unified, so they must have other ways of dealing with the Triviality Problem. I consider how Allison deals with it. The role of the unity of apperception is crucial to Allison’s analysis of the problem. The Apperception Principle is initially formulated in section 16 by 41

See Ch. 6, §3.4.

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Kant as the principle “[t]‌he ‘I think’ must be able to accompany all my representations . . .” (GW, 246; B131), later as the principle that I must be able to become aware of all of my representations (even if I am not actually so aware in given cases), the principle of self-consciousness:  “For the manifold representations that are given in a certain intuition would not all together be my representations if they did not all together belong to a self-consciousness; i.e. as my representations (even if I am not conscious of them as such) . . . (GW, 247; B132).42 Allison takes the initial formulation as fundamental and argues that the principle directly assures that the unity of intuitions is the unity of a judgment about the object of the intuition.43 This is so because the term “I think” represents for Kant what all judgments have in common: it is the form of judgment, and when Kant says that all my representations must have this term accompany them, he means that all my representations have the form of judgments. They are, in a word, “thoughts.” Allison thus takes the unified intuitions of the first part of the B edition Deduction to be thoughts, items whose unification is that of judgment, thus governed by the pure concepts of the understanding. As he notes,44 taking things in this way provides one half of a solution to the Triviality Problem; the other consists in taking the representations of the second part to be perceptions. Since it is an open question whether perceptions are subject to the same kind of unity as thoughts, a major task remains to Kant for the second part of the Deduction to accomplish. One of the very strong points in favor of this interpretation of the Apperception Principle is the clean resolution it seems to yield for the Triviality Problem. However, there is a big difficulty with the interpretation: the Triviality Problem, expelled through the front door, marches in through the back. This is so because of the universality of the principle of apperception (all representations “that mean something to me” are subject to it [§16]) and Allison’s claim that the principle of apperception entails that all objects to which it applies are thoughts. We thus have the following syllogism: Syllogism A 1. All objects to which the principle of apperception applies are thoughts. 2. All thoughts are subject to the categories. A third reading of apperception holds that apperception is the first-order relation that binds the various elements of an intuition into a basic cognitive unity, whatever that turns out to be. See Dickerson 2004 for a recent reading of this kind. Although it does justice to some of Kant’s texts on apperception, it does not do so to others. Moreover, it severs any essential connection between the second-order character of the principle of apperception in those texts where it occurs and the role of these texts in the argument of the Deduction. 43 Allison 2004, 162, 163ff. 44 Ibid., 162. 42



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3. Empirical intuitions (“perceptions”) are items to which the principle of apperception applies. Thus, 4. Empirical intuitions are subject to the categories. This syllogism owes its first three premises to the first part of the Deduction: all that remains to reach the conclusion of the second part is to draw the inference from line 3 to line 4. Doing so, of course, is trivial, and so the Triviality Problem reappears. The only premise that does not certainly represent Kantian doctrine is line 1; to solve the Triviality Problem this line must be rejected. However, line 1 is justified by Allison’s underlying reading of the meaning of the “I think” in the “I think” formulation of the Apperception Principle. It is this interpretation that we must therefore reject. Unfortunately, there is potential a version of the Triviality Problem even for my own reconstruction of the argument. This reconstruction depends on two main points: (1) the possibility that there are aesthetically but not logically unified intuitions; and (2) Kant’s doctrine subjects all representations, including those only aesthetically unified, to the power of apperception. But then there is again the familiar syllogism leading to the Triviality Problem: Syllogism B (1) All intuitions are subject to the original power of apperception. (2) All intuitions subject to the original power of apperception are unified by a category-governed synthesis. (3) Empirical intuitions are intuitions. Thus, (4) Empirical intuitions are unified by category-governed synthesis. Here, line 2 is a potential candidate for rejection as Kantian doctrine, and I reject it; the Triviality problem does not arise for my interpretation.45 45 My account, like Henrich’s (Henrich 1968/69, 640–59), sees part I of the B edition Deduction starting with intuitions assumed to be unified and proceeding, in Part II, to a discussion of intuitions not assumed to be unified. But Henrich’s account runs into difficulties with his claim that “if all given representations are ‘mine’ in the sense indicated that means that they can be taken up into the unity of consciousness in accordance with the categories” (654). The difficulties can be put into the form of a dilemma. Either all representations are accessible to the unity of consciousness in accordance with the categories, or some are not. If the former, the triviality problem recurs; if the latter, we still have to account for the apparent universality of Kant’s claim that the “I think” must accompany all my representations. On my solution all representations are subject to the original synthetic unity of apperception (if they are something to me) but denies that this shows by itself that all representations are subject to the categories. Henrich’s solution is to say that Kant allows for the possibility that some representations are not taken up into the unity of consciousness in accordance with the categories but that he didn’t take this possibility seriously (654). If he didn’t take it seriously, why did

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Nevertheless, it is still true that all logically unified intuitions are unified by a category-governed synthesis, thus giving rise to a further syllogism: Syllogism C 1. All logically unified intuitions are synthesized by a category-governed synthesis. 2. Empirical intuitions are logically unified. Thus, 3. Empirical intuitions are unified by category-governed synthesis. Here, both premises do represent Kantian doctrine. What prevents triviality is that the truth of the second premise is unproven before the second part of the B edition Deduction; because of the existence of the possibility of unlogically unified intuitions it is epistemically possible prior to the second part that empirical intuitions are of this kind. The task of the second part is to show that they are not, in fact, of this kind. Only when this is done can the syllogism be applied and the objective of the Deduction finally accomplished. It is now time to consider how Kant carries out that task.

2.  The Second Part of the B Edition Deduction 2.1. Introduction I argued previously46 that for Kant there are two ways in which synthetic activity can potentially involve an intuition for Kant—internally vs. externally. When embodied in activity made about already unified intuitions or about un-unified intuitions, synthetic activity is “external” to the intuition; when the role of synthetic activity is to create the unity of intuitions (hence constitutive of the descriptive representational capability of the intuition), that activity is “internal” to the intuitions. Combination in its two forms performs this role. I argue that, for Kant, the class of intuitions at issue in the second part of the Deduction in particular, empirical intuitions, are not only potential subjects of recognition, an external application of synthesis (judgment), but are unified by internal applications of intellectual synthesis. Showing this is of vital importance to Kant’s

Kant devote the greater part of the Deduction to replying to it? Henrich’s solution does not offer a satisfactory explanation. (See also Evans 1990, 558: “I think that it can be shown that Kant did take [this possibility] seriously and that this is crucial to an understanding to the proof structure of the Transcendental Deduction.”) 46

See Ch. 6, §3.1.



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objective in the Deduction since it is a necessary (but not sufficient) condition of Nomic Prescriptivism that all relevant empirical intuitions (those of empirical objects and empirical appearances alike) be unified by a constituting (internal) intellectual synthesis. We will now see how Kant proposed to show in section 26 that this condition is true.

2.2.  The Argument of Section 26 2.2.1. Introduction

When we turn to the text of section 26, we can discern four main themes in the first three paragraphs (those coming before the first break) that progressively move Kant to his conclusion. (All passages are from GW, 261–262; B159–161.) The first is the theme of Nomic Prescriptivism, a form of Transcendental Idealism: Now the possibility of cognizing a priori through the categories whatever objects may come before our senses, not as far as the form of their intuition but rather as far as the laws of their combination are concerned, thus the possibility of as it were prescribing laws to nature and even making the latter possible, are to be explained. The second theme has two parts. Part A, making up the second paragraph, is a discussion of the synthesis of apprehension: [B]‌y the synthesis of apprehension I  understand the composition of the manifold in an empirical intuition, through which perception, i.e., empirical consciousness of it (as appearance), becomes possible. Part B, occurring in the first third of the final paragraph, is the claim that the synthesis associated with Part A must conform to the unity of space and time. The synthesis of the apprehension of the manifold must always be in agreement with the [unity of space and time], since it can only occur in accordance with this form. The third theme, already discussed and occurring in the middle of the final paragraph, is the claim that the kind of unity present in intuitions in general is transferred to empirical intuitions. How and why this is to be done is one of the main arguments to be reconstructed here.

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The fourth theme, making up the last third of the final paragraph is the conclusion: Consequently, all synthesis, through which even perception itself becomes possible, stands under the categories, and since experience is cognition through connected perceptions, the categories are conditions of the possibility of experience . . . The transition from theme 2B to theme 4 is the transition from the spatial unity that all objects of intuition must meet to the applicability of the categories to perception. The argument of theme 3 is accomplished through this transition. In a passage after the conclusion of the main argument of section 26 consisting of the four themes we have identified, Kant uses an example to show how this transition is accomplished: Thus, if, e.g. I  make the empirical intuition of a house into perception through apprehension of its manifold, my ground is the necessary unity of space and of outer intuition in general, and I as it were draw its shape in agreement with this synthetic unity of the manifold in space . . . (GW: 262; B162) Kant’s answer turns on what is needed for drawing the outline of a house “as it were.” What is needed is that the points of the house represented in our perception be topologically connected. Kant does not say exactly why this is needed or for what, but a literal reading of this example can connect topological connectedness with the account of perceptual judgment developed in the last chapter as follows. According to that reading, perceptual judgment is a process whereby (1) a sense impression of an object is “apprehended”; (2) an exact match for the impression is produced by the productive imagination following certain rules; (3) the object of the impression is “recognized” as falling under the rules used in producing the matching image. In order for these images (the impression and the produced image) to have stability for purposes of comparison, the points composing each need to be in a unified space, and to be compared they both must be in a single space. If this is Kant’s ultimate explanation of the role of the unity of space in the process by which we make perceptual judgment, then, as a conclusion to the Deduction, it is a considerable disappointment, because it does not show that the unity of space as a whole is needed to think about reality as a whole, for the spatial unities in question are local, occurring, perhaps, merely inside the sense organs of perceivers. A second suggestion is that since (1) the synthesis of apprehension is constructing a representation of a metrically determinate object, in this case a house,



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(2) a metrically determinate object must be subject to the laws of geometry, and (3) the laws of geometry apply only to objects in a topologically unified space (“Space, represented as object as is really required in geometry . . . [B160n.]), it follows that (4) the synthesis of apprehension must be subject to the synthesis that produces the representation of topologically unified space. But where do the categories come in? Kant’s answer is that the “categories” come in as the category of magnitude (die Kategorie der Größe [B162]).47 But if this is Kant’s argument, it is puzzling, because the role of the representation of the global unity of space, on Kant’s own account, is as a necessary condition for the representation of magnitude, not a sufficient condition, as his argument would seem to require. His argument requires this because it is supposed to prove, not just assume, that all objects of empirical intuition are subject to categories, in this case the schematized category of magnitude, by deriving this result from the necessity (that is assumed) that all objects of empirical intuition are subject to the global unity of space and time. This proof is a non sequitur unless the unity of space and time is sufficient for all objects contained therein to have a determinate magnitude. This is just what Kant does not seem to prove. If, on the other hand, Kant simply assumes a metrically determinate class of empirical objects (a class of objects with a magnitude) ab initio and then argues that this is possible only if they occur in a globally unified space, there is of course no non sequitur, but now it is trivial that the representation of this class of objects must be constructed in accord with the rules for constructing objects with magnitude. This fails to achieve the promise of section 26 as advertised in section 21. Do we do any better if we consider how the applicability of the other categories might be derivable from the applicability of the unity of space and time? Of special interest are the relational categories of causality, substance, and community. This problem is compounded by a note (B160) wherein Kant describes the synthesis responsible for producing the representation of a unified space and time as both due to the understanding and “preceding all concepts.” But how can a synthesis that is described as “preceding all concepts” also be described as governed by the categories of relation? What is especially at stake here, aside from terminological consistency, is the issue of causality: has Kant shown that bringing objects under the topological unity of space and time thereby brings them under the category of cause? Here I think that interpreters have three main options, none of which are entirely satisfactory. 47 Guyer and Wood translate die Kategorie der Größe as “the category of quantity,” but Größe means “magnitude” and appears only in the list of schematized categories at A142/B182, not in the list of categories proper at A80/B106, and only in parentheses after Vielheit in the list of categories proper in the Prolegomena, §20 (Ak 4, 303). The only occurrence of a term in the Tafel der Kategorien that would translate into English as “quantity” is Quantität, the heading for the three categories, Einheit (unity), Vielheit (plurality), and Allheit (totality).

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The first, Option A, requires filling in a gap in Kant’s own reasoning in the text of section 26 (perhaps finding inspiration from the Second Analogy) and saying that the grounds we have for assigning a determinate location to a particular object in space and time involve assumptions about the causal processes in which that object participates in relation to ourselves as perceivers and in relation to other objects. In the discussion of examples just following the proof, at B163, Kant says explicitly that the location of particular events in time in relation to other events is determined by us as a result of applying the category of cause and effect. On Option A it uses the category of cause and effect to determine particular locations of objects (and events) in time and space that constitute the role of categories in the synthesis of apprehension.48 Unfortunately, in the text of the proof itself Kant seems to locate the place where the categories enter the argument wholly otherwise than in the determination of specific spatial and temporal locations for empirical objects, maintaining that the synthesis creating the unity of the formal intuitions of space and time (space and time as topologically unified universal containers of objects) is carried out “in accordance with the categories,” from which Kant derives his conclusion: “All synthesis, therefore, even that which renders perception possible, is subject to the categories . . .” (B161). If we assume that “the categories” includes the relational categories of causality, then we have a second option, Option B. Option B sees Kant arguing that the rules we use to construct our representation of topologically unified space and time contain or, somehow, constitute causal rules. For example, drawing on arguments from the Second Analogy, we might treat temporal relations as causal relations, thus treat the connectedness of temporally ordered events as the connectedness of causal relations. A suggestion along these lines has been made by Brittan.49 Moreover, this reading seems to fit Kant’s own example of freezing water, where he says of the category of cause that by its means “I determine everything that happens in time in general as far as its relation is concerned” (GW, 262–263; B163). Unfortunately this option suffers from a number of serious difficulties of its own. For one, if causality were a governing category, it would seem that the category of causality should be embodied in a principle constitutive of space and time, a claim explicitly rejected by Kant in the Analytic of Principles (A178– 180/B221–223). For another, in the note just mentioned (B160), Kant asserts that the unity of space and time as formal intuitions is due to synthetic activity (contrary to what one might have inferred from the Aesthetic) but that the unity “precedes any concept.” Whatever this might mean, it certainly seems to rule out A position of this sort underlies Strawson’s discussion of cause in the Second Analogy. See Strawson 1966, 133–146. 49 Brittan 1978, ch. 7. 48



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the possibility that the unities of space and time are constructed by synthetic activity subordinate to the category of cause and effect. If Option B can be described as inflating what look like nonrelational categories (the unity of space and time) into relational categories, the next option I consider, Option C, embodies the reverse idea: deflating the relational categories into spatiotemporal properties. Kant’s schematized categories are deflated categories in this sense. Option C is the suggestion that when Kant says intuitions are governed by the relational categories, he means the schematized relational categories. Option C comes in two versions. Version 1 has it that the schematized categories are derived from the unities of space and time but are not themselves these unities. The second version holds that the schematized version of the relational categories, that is, their schemata, just are the unities of space and time.50 Support for Option C (in either version) comes indirectly from the discussion of the general category of quantity in Kant’s house example. The category there is not any of the concepts listed in the Table of Categories under “Quantity” but is in fact the schematized category, magnitude, corresponding to but not identical with the category proper of plurality.51 In his official account of the schematized categories (at GW, 274ff.; A142/B182ff.), Kant gives the schematized category of causality as “the succession of the manifold insofar as it is subject to a rule.” This would fit Kant’s account of cause in the freezing-water example as a concept that is “abstract[ed] from the constant form of my inner intuition, time . . . through which, if I apply it to my sensibility, I determine everything that happens in time in general as far as its relation is concerned” (Kant’s emphasis). There is additional support for Option C (both versions) from Kant’s general discussion of the Analogies of Experience. First, the general principle of the Analogies is stated in the A edition in terms of the unity of time: “Their general principle is: As regards their existence, all appearances stand a priori under rules of the determination of their relation to each other in one time” (GW, 295; A176/B218). Second, when it comes to “compounding the appearances,” this happens “only in accord with an analogy with the logical and general unity of concepts, and hence in the principle itself we make use of the category, but in its execution (its application to appearances) we set its schema in its place, as the key to its use or rather we set the latter alongside the former, as its restricting condition . . .” (GW, 298; A181/B224). (The “principles” that Kant has in mind are synthetic principles.) The function of “compounding appearances” is the synthesis of apprehension, and the latter is the central focus of the argument of 50 51

For an interpretation along these lines, see Melnick 2004. See the earlier note discussing this.

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section 26, so there is a connection between the two passages, making for an at least indirect case that it is the schematized relational categories that are shown to be necessarily applicable to empirical intuition by means of the necessary applicability of the unity of space and time to all objects of empirical intuition. But there are difficulties with Option C (in both versions) similar to those discussed in connection with the case for quantity. In the note to B160, Kant says of space as a formal intuition (as an object) that it is “required in geometry” (GW, 261; B160n.). This is presumably because geometry applies to objects that have a metric. The objects in question have a metric because they have been schematized; that is, they are subject to a synthesis that assigns a magnitude to the lines and angles and shapes of these objects. Apparently Kant takes the topological unity of space to be a precondition of this; this is perhaps why he says that the synthesis that constructs unified space “precedes all concepts” (ibid.), where “concepts” are understood primarily as magnitude, one of the schematized concepts of quantity. If this is indeed Kant’s doctrine, it makes trouble for Option C, since Option C would require that the topological unity of space proves that objects are subject at least to the schematized category of quantity, whereas Kant’s doctrine in the note requires the converse: that the unity of space and time is necessary, not sufficient, for the applicability of this category. I believe, indeed, that no argument is available in section 26 showing directly that any intuition subject to the synthesis that constructs representations of unified space and time is necessarily subject to the relational categories. I do, however, suggest an indirect argument. But first I shall complete the exegetical case that Nomic Prescriptivism is one of Kant’s primary objectives in the argument of section 26. We have just been discussing the fourth theme in section 26, the establishment of a connection between the logical unity of empirical intuitions and the categories:  “Consequently, all synthesis, through which even perception itself becomes possible, stands under the categories . . .” But this is not quite the end of the argument, for Kant adds an additional point: “ . . . and since experience is cognition through connected perceptions, the categories are conditions of the possibility of experience . . .” (GW, 262; B161). Depending on how it is understood, the phrase “the categories are conditions of the possibility of experience” may or may not add an additional theme. If we understand “experience” to be something like a judgment or an objective representation of a world of spatiotemporal objects, there is nothing new added here: the categories are needed for a unified sensible and objective representation of a world of spatiotemporal objects, and the latter is needed for experience. Call this the subjective reading of this phrase. But if we remember Theme 1, the theme of Nomic Prescriptivism in general, we may see the claim that categories are conditions of possible experience in a stronger sense: that the categories are rules by means of which we



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create an objective world itself. The contrast here is between the role of the categories in constructing representations of a world and the role of the categories in constructing the (phenomenal) world itself.52 If read in this stronger way, this counts as a possible fifth theme:  the role of the categories in Nomic Prescriptivism. Call this the “objective reading” of the phrase. In the language of the passage quoted for Theme 1 from section 26, Kant gives some indication that he sees an objective argument as part of his project: not only do we “prescribe laws to nature,” but it may even be a question of “making the latter possible.” Making nature possible seems to be a clear statement of the objective reading of Nomic Prescriptivism, and that is how I shall take it. My conclusion after discussion of the fourth theme has been that there is no completely satisfactory way to show that the unity of space and time can be employed to prove that the concepts on Kant’s list of categories necessarily govern the objects perception gives to us—at least not directly. But I think there is an argument form showing this indirectly. My proposal for an indirect proof rests on two elements. The first is that the principle of the unity of space and time comes to be an intellectual condition for Kant in the B edition; that is, a condition such that any coherent description of a world of objects that does not collapse into solipsism must meet it. Kant officially holds that there are exactly twelve categories, that these categories exhaust the set of intellectual conditions, and that the unity of space and time is not among the categories. The second element is that Kant can resolve the tension by separating the concept of an intellectual condition from the concept of a category, thus allowing that some things that are not categories are a necessary part of coherent thinking about the world. I present some reasons for holding this view and for holding that Kant held it in the next section. For now I simply assert it. Categories explain how the twelve forms of judgments can be made in light of Kant’s noninherentist theory of judgment: they can be made by synthetic acts connecting appearances in the appropriate ways. The appropriate ways are provided by the categories. Why should all of these forms of judgment be necessary to a coherent understanding of the world? Kant’s answer seems to be that they are all necessary to a comprehensive theory of logical inference: that is the “clue” Kant uses to identify the right set of categories.53 But logical inference is a hypothetical business: it tells us what has to be true if something else is true. It doesn’t tell us what is absolutely necessary to a coherent view of the world. Kant’s

Allison also identifies these two senses of making experience possible. In the first sense Kant’s “goal is arguably accomplished”; in the second it is not (Allison 2004, 197). I shall argue that for the relational categories at least, the first goal is achieved only if the second is. 53 See Melnick 2004. 52

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argument, as I understand it, is that the categories also provide absolute intellectual conditions: absolute conditions on how we have to think of the world. The problem is that we have not so far uncovered a strategy, one that might directly accomplish this, emerging from his argument in section 26. My suggestion is Kant can accomplish this objective indirectly. He can argue for Nomic Prescriptivism based on the correspondence between the unity of space and time understood as an intellectual condition and the unity of space and time we inevitably find in the world of experience. Once this doctrine is in place Kant can then argue that since the world is constructed by us and is a rather complex place, there needs to be a complex set of rules for constructing it, some of which will have a priori status. He can further argue that the categories fit this requirement. My task in the next section is to show that the unity of space is indeed an intellectual condition for Kant, at least in the B edition. 2.2.2.  Proving That the Unity of Space Is an Intellectual Condition: The Subjective Phase of the Deduction in the B Edition

We are working on the assumption that Kant was guided in his construction of the Transcendental Deduction of the Categories in both editions by an analogy with the argument-structure of the Transcendental Exposition of the Concept of Space. This structure has two main stages, a proof of the validity of geometrical concepts and an argument for idealism (the Second Geometrical Argument for Transcendental Idealism) based on this proof. The first stage itself has two phases: a subjective phase, in which the applicability of geometry to objects of pure intuition (pure geometry) is established, and an empirical phase, in which the applicability of geometry to the objects of empirical intuition (applied geometry) is established. We begin with consideration of the subjective phase of the first stage. I argue that although the subjective phase of the Transcendental Deduction in the A edition Affinity Argument fits Kant’s definition of a subjective deduction in the A edition Preface (GW, 103; Axvi–xvii), the subjective phase of the Deduction in the B edition, in the version that I am reconstructing, fits Kant’s definition of an objective deduction. As maintained in Chapter 5, the Affinity Argument was Kant’s paradigm example of an argument for attributing the category of causality to the set of subjective conditions necessary for thinking about a world of objective objects. This argument was an inference to the only possible explanation for our ability to imaginatively generate a counterfactual series of experiences of an actual object that do not simply reproduce a series of experiences already had. My example was that I seem to be able to imaginatively and reliably produce the experiences I would have if I were to walk around my house at second-story level, having never done so before. We infer that I could not do this reliably unless I had something like a theory of my



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house; this in turn relied on the assumption that all events stood in causal connection with other events. Because this is an inference to what conceptual resources are necessary in order to carry out certain cognitive operations that I actually engage in and because the inference is a kind of hypothetical inference, Kant seems to call this argument a “subjective deduction.” An objective deduction, on the other hand, seeks to establish necessities in thought by a more conceptual route (hence, according to Kant, by a more certain route) by means of analyzing the nature of objectivity in its various forms and seeking the conditions necessary for the representation of objectivity in its various forms. Section 17 of the B edition Deduction is a largely objective deduction in this sense, as are parts of the A edition Deduction. In these texts Kant’s major preoccupation is explaining what distinguishes those representations that are part of the objective properties of objects from those that are not. Kant does so by classifying as objective that class of possible perceptions that would occur in certain lawlike patterns under various manipulations of our environment. The distinction that Kant draws here is between subjective representations that are merely subjective and subjective representations that also are part of the objective properties of spatiotemporal objects “outside us.” Now, this is not the distinction between reality and appearance, in the ordinary sense; for example, the distinction between dreaming in the ordinary sense and waking or between something merely seeming to have a certain physical property and something else actually having it. Nevertheless, any account of perceptual epistemology needs to explain this distinction as well, and there is evidence from the Prolegomena54 that Kant became increasingly convinced in the period between the two editions that he needed to give such an account. In the A edition Deduction, Kant draws an analogy between what our cognitions would be like if they were not subject to lawlikeness and a dream: Thus the concept of a cause is nothing other than a synthesis (of that which follows in the temporal series with other appearances) in accordance with concepts; and without that sort of unity . . . the manifold of perceptions . . . would then belong to no experience, and would consequently be without an object, and would be nothing but a blind play of representations, less than a dream. (GW, 235; A112) It would have been doctrinally possible for Kant to have expanded his objectives in the B edition Deduction to include an account of the conditions necessary to account for the distinction between illusion and reality in the ordinary sense—the sense that figures centrally in Cartesian skepticism and the responses to it in the post-Cartesian early modern period. Let’s explore the 54

N. 2 to part I, A4, 288–291; Hat., 40–41.

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possibility that he did so. The question Kant would then be addressing is not whether Cartesian skepticism is right—he does that elsewhere55—but rather what presuppositions are needed for us to draw the ordinary illusion-reality distinction in the first place? This makes for a transcendental argument. Of course, Kant was aware when he wrote the A edition of the existence of the ordinary illusion-reality distinction and of the skeptical issue that philosophy had made of that distinction, but he was not aware that his readers might have thought that in proposing a metaphysical system with an idealist dimension, he had reduced the world to mere illusion. Yet in one of the first reviews of CPR, that is just the reaction he received;56 so he incorporated into subsequent developments of his theoretical philosophy a number of new arguments designed to correct this impression. I think that it is reasonable to expect that in the extensively revised B edition Deduction, the main theoretical argument of CPR, he would also have incorporated some means of addressing this concern. My suggestion is that he might have done so by bringing the distinction between reality and illusion under the umbrella of the transcendental method. What this would mean is that Kant takes this distinction now to be of fundamental importance to the possibility of our having cognitions about an objective world to begin with; that is, that he would have elevated the conditions needed for this distinction to be coherently formulated to the level of intellectual conditions. At the same time, I surmise that Kant saw that the distinction between illusion and reality (at whatever level in the transcendental hierarchy that distinction is to be drawn) depends on the localization of objects in a topologically unified space and time. Thus, it is our inability to coherently integrate the space and time in which the objects of our dream intuitions occur into the space and time of the world we represent as real that constitutes the criterion by means of which we classify dream worlds as unreal. It also seems to give us one of the conditions needed for us to distinguish hallucinations from real objects. For example, what makes something a hallucination of pink elephants dancing on the sidewalk in front us rather than the real thing is the fact that the set of properties composing the elephants is not located in the real three-dimensional world that makes up our environment. However, for there to be publicly available means of verification/disproof that this is so it is necessary that there be spatial and temporal pathways connecting other events we experience and have experienced; unless there is a spatial pathway between the putative location of the apparition in front of me and other people nearby, the fact that others nearby cannot see the elephants (assuming that they cannot) is not grounds for

55 56

Especially in the B edition, in the Refutation of Idealism (GW, 326–328; B274–279). Garve 2000.



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denying that the elephants are real. This is so because public verification conditions depend on the following inference: (1) If there were real pink elephants dancing on the sidewalk, others would see them (if they were looking in the right direction, were not blind, etc.). (2) Others do not see them. Thus, (3) There are no real pink elephants dancing on the sidewalk. The main premise, (1), would itself not be true if the putative location of the hallucinatory elephants and the location of the observers were not connected spatially.57 That is how the topology of space becomes part of the public conditions necessary for us to distinguish illusion from reality. Similarly, unless there was a temporal pathway connecting this part of time with events an hour hence, the fact that I  see no elephant traces on the sidewalk in that location an hour hence would not be evidence of the absence of elephants in that location an hour before. Indeed, if the spatial and temporal One thing that would make (1) true is that causal processes are propagated linearly over continuous space and time paths. This is the modern view of nonquantum causality and was probably Kant’s view of causality in general. So there is an important connection between the topological properties of space and time and a notion of causal propagation defined at the level of scientific theory in Kant’s theory of science. I shall not explore that connection further here. However, this raises an important question for the Deduction. If the modern conception of causality is right, then isn’t it, too, an intellectual condition for distinguishing illusion from reality, along with the topological unification of space (and time)? Perhaps it is even more fundamental than the latter? The answer to the second question is negative because Kant allows for the possibility that there might be a world that is not subject to the law of causality. He does this twice in the space of two paragraphs at GW, 222–223; A90–91/B122–123. Kant does not say that in this world there would be no distinction between illusion and reality—and, if there is, there would still need to be a criterion to allow us to tell the one from the other. Perhaps the criterion still involves some kind of causal or quasi-causal linkage operating in enough situations to make the appropriate instances (or enough of the appropriate instances) of (1) true, but there would be no universal law of causality operating everywhere all the time. In this case, the existence of some causality would be an intellectual condition but not universal causality. Yet the universal connectedness of all parts of space could still be a universal fact. It might, for example, be possible to establish this by an independent mathematical-type argument, a possibility still to be discussed. So even in this case, though the presence of some causality in nature is an intellectual condition, the topological laws for space and time are more fundamental than the causal law. The answer to the first question is also (perhaps) no. The first, key premise is formulated as a counterfactual necessity, not explicitly as a causal relation. There may be ways in which (1) could be true even if there were no causality at all—a position allowed by Kant—yet it might be that the truth of (1) still depends on the truth of the topological laws. 57

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regions in which we observed events were disconnected from other spatiotemporal regions, the very possibility of public verification conditions for the veridicality of our experiences would be eliminated. Without the possibility of public verification of the veridicality of our experiences, we lose the possibility of having a coherent understanding of an objective world containing ourselves and things distinct from ourselves. This is why thinking of the world as topologically unified is an intellectual requirement. I call the argument for this The Objective Deduction of the Unity of Space in the B Edition. I conclude this section with a second line of argument, this one more directly textually based: that the unity of space and time are intellectual conditions for Kant. In Part II of the B edition Deduction, Kant also addresses the issue of what makes it possible for us to have cognitive thoughts of objects (cognitio) in sections 22 and 23. This provides material for a second objective deduction: that the unity of space and time is one of the intellectual conditions governing the way we must think about an objective world. In order to cognize objects, the objects must be empirical objects, that is, the objects of empirical intuition; in order for something to be an object of empirical intuition, it must be given in the form of space and time. “Things in space and time, however, are only given insofar as they are perceptions (representations accompanied by sensation), hence through empirical representation” (GW, 254; B147). Here there is a chain of conditions, starting with the possibility of having cognition and ending with sense perception, that represent Kant’s considered and most explicit account of the “boundaries of the [cognitive] use of the pure concepts of the understanding” (GW, 255; B148; my interpolation); that is, intellectual conditions on cognition. The unity of space and time has not appeared in this list so far. But there is a gap in this account that these unities might fill. Reasonably enough, Kant does not say that all possible representations of objects require that we actually perceive the objects. In the Antinomies (§6) Kant considers a case of the moon where, of course, no actual perception has occurred: but this means only that in the possible progress of experience we could encounter them; for everything is actual that stands in one context with a perception in accordance with the laws of the empirical progression. Thus they are real when they stand in an empirical connection with my real consciousness . . . Nothing is really given to us except perception and the empirical progress from this perception to other possible perceptions. (GW, 512; A493; B521) It must be admitted that this sounds very much like analytical phenomenalism, but Allison has argued, correctly in my view, that the resemblance is



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“superficial” and “masks the distinctive feature of the Kantian analysis, namely, the role given to a priori laws or principles.” These laws “are nothing other than the Analogies of Experience.”58 The connection between the progression of perceptions and the Analogies of Experience is indeed made by Kant in a corresponding passage from the Postulates of Empirical Thought: The postulate for cognizing the actuality of things requires perception, thus sensation of which one is conscious—not immediate perception of the object itself the existence of which is to be cognized, but still its connection with some actual perception in accordance with the analogies of experience . . . (GW, 325; A225/B272) As mentioned in connection with my discussion of Option C, Kant connects the principle of the Analogies with the unity of time: “Their general principle is: As regards their existence, all appearances stand a priori under rules of the determination of their relation to each other in one time” (GW, 295; A176/B218). Kant says “one time” not “one space,” but I think we can see that extending the principle in this way to the unity of space would be natural in light of the reasoning given above that spatial continuity is an essential presupposition of our ability to distinguish the actual from the illusory. Suppose, to return to our distant planet example, that it is simply too hot for humans to survive there. Modern analytic phenomenalists might be tempted to give empirical content to such assertions by relying on certain counterfactual propositions: if humans could survive in such conditions they would perceive such and so. But such counterfactuals are unknowable and unempirical—how could we know what human perceptual capabilities would be if humans could survive there? Fortunately, we have seen that Kant does not import empirical content into representations of environments not perceived or perceivable by humans by this device (phenomenalism). Rather, Kant makes the connection between empirical content and sensory experience through the intermediary of spatiotemporality: empirical content requires spatiotemporality; spatiotemporality is the form of the sensory part of perception. Kant need not even require that all representations with empirical content be directly connected to actual perception (although he says this in the passages quoted above), but they must be connected to the perceivable world somehow. Conceptually, this gap can be filled by the requirement that space be topologically unified. Thus, in our too-hot-distant-planet example, Kant would require our assertions to have empirical content wherein a spatial path connects the planet with human perceivers. This requirement places additional spatiotemporal constraints on what is cognizable –thus adding 58

Allison 2004, 40.

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further depth to his conception of empirical content—and the mandated existence of a spatial path ensures that in principle there is always the possibility of a chain of causes traveling from the planet to our eyes, either directly or through effects of some intermediary object that we can directly perceive, thus ensuring the empirical nature of our access to all objects of meaningful cognition. This is another reason for treating the assumption that the world is a spatiotemporal whole as an intellectual requirement of the idea of an objective world of empirical objects. 2.2.3.  The Proof That the Unity of Space Has Empirical Objective Validity; the Proof of Nomic Prescriptivism; and the Proof That the Unity of Empirical Intuitions Is the Unity of the Categories

The status of the unity of space as an intellectual condition provides the first phase of the B edition Deduction: a proof that our conception of space as topologically unified makes it possible for us to think about a world that has objective content, an intentionalized form of objective validity. The other phase of the Deduction establishes that the topological principle has empirically objective validity.59 This latter kind of objective validity is established by demonstrating the truth of the necessary counterfactual that all objects in our experience are connected in space in a way precisely analogous to that in which the theorems of applied geometry were demonstrated.60 Once this is established, a necessary correspondence between the subjective and objective domains is proven. It is this correspondence that allows for the final stage of the Deduction in the B edition, the argument that this correlation can be explained only by the Copernican revolution in metaphysics: the doctrine that we prescribe laws to nature. This stage corresponds to the Second Geometrical Argument for Transcendental Idealism, and I call it “The Transcendental Proof of Nomic Prescriptivism in the B-edition Deduction.”61 Since I hope to have already made the structure of that

The reader may wish to revisit the discussion of the notions of intentionally objective validity and empirically objective validity in Ch. 5, §2. 60 See Ch. 4, §2. 61 There is an alternative construal of the subjective stage of this argument that makes it a closer analogy to the Second Geometrical Argument. Rather than treat the necessity of the unity of space and time as established by transcendental argument, it is treated as established by mathematical method applied to pure objects. In this case, there would be a tight analogy between the two proofs; in one case Kant would prove the theorems of pure geometry, in the other he would prove the theorems of pure spatial topology. There would then be the correlation between the truths of pure topology and the truths of applied topology to be explained, and the explanation would go as described. There are advantages to reading Kant’s argument this way, it is a precise analogue of the Second Geometrical Argument for Transcendental Idealism, and the strength of that argument would then 59



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argument clear—it is an inference to the only possible explanation for a correlation between a thought domain and an empirical domain—I need not further explain that form of argument here. Thus Kant accomplishes the Copernican revolution in metaphysics. A reader that is keeping track of things accomplished in the chapter to date will have noticed that though much has been promised, nothing has so far been accomplished in showing that empirical intuitions have the same unity as intuitions in general; that is, the unity of the categories. Since this is supposed to be the major result of the Deduction, to be achieved in section 26, clearly work remains. Briefly, I take Kant’s answer to the question to be as follows. With the Copernican revolution now accomplished, he next reflects on the question whether empirical intuitions—perceptual representations of physical objects in space—are logically or aesthetically unified. Suppose that they are only aesthetically unified. In this case there would be no way to explain how we know a priori that every object that would be presented to us in sense experience must agree with the intellectual condition that all objects reside in a topologically unified space. So we can eliminate that possibility. What remains is the other possibility; namely, that empirical intuitions are logically unified—that is, their unity is the unity of the categories. With this conclusion Kant achieves the final purpose of the Transcendental Deduction. So his work is complete but ours is not—not quite yet. This is so because we do not yet see how the logical unification of empirical intuitions shows that they must agree with the intellectual condition that all objects reside in a topologically unified space. 2.2.4.  Kant’s Explanation of How Logically Unified Empirical Intuitions Come to Be in Accord with the Unity of Space and Time 2.2.4.1.  The Scope of the Explanation

Since the correlation at the heart of the Transcendental Proof of Nomic Prescriptivism in the B edition Deduction is between our experience of empirical transfer almost undiminished to the corresponding argument in the Deduction of the categories, which we might call the Argument from Topology for Nomic Prescriptivism. But what would the mathematical argument be and is there any inkling that Kant makes one? In fact, I think there is. I have elsewhere* developed a reconstruction of that argument, based on ideas in the CPR, that begins with the assumption that time is topologically unified and moves there to the conclusion that space is, too. This might count as a mathematical argument in the required sense. But this argument would not depend on demonstrating that the unity of space is an intellectual condition and would thus sever any role for intellectual conditions from the Transcendental Deduction of the Categories. This would seem to me to make Kant’s greatest metaphysical argument decidedly un-Kantian. (*In an unpublished MS, “A Reconstruction of Kant’s Arguments for the Unity of Space and Time.”)

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objects in unified space and time and the corresponding intellectual condition, it will be helpful to remind ourselves of what makes empirical objects empirical. Empirical objects are appearances, objects of sensory processes that begin with the affection of our faculty of sensibility by things external to the mind. Kant’s account of the reality of the objects of our representations is also provided in terms of the externality of the source of the representations. The correlation in question is between objects we take to be real, on the basis of the usual empirical cues as to the external source of representation, and the counterfactual necessity62 in our experience of finding them subsequently to be in a space or time not disconnected from those in which any other real objects are to be found. There are, of course, objects that we experience that are not real:  dream objects, hallucinatory objects, and the like. We do not find in experience that these objects are connected in space and time to all other actual objects. But these cases do not constitute a counterexample to Kant’s argument because it is an explanatory argument, the scope of which is determined by the scope of the explanandum; if only intuitions of real objects figure in the latter, then only intuitions of real objects figure in the explanans. And I propose it is only intuitions of real objects that are in the scope of the explanandum for Kant. Thus only real empirical objects are in the scope of the explanans. The effect of this is that Kant allows that the objects of some intuitions fall outside the scope of the argument of section 26–these would be the schematic objects of Chapter 6— and thus allows that some intuitions have not been shown by that argument to possess logical unification.63 This is no problem for an account (like mine) that recognizes the existence of appearances whose unity is aesthetic rather than logical, but it is seen as a deep problem for accounts that maintain that all intuitions for Kant are logically unified. That puzzlement of this sort is so widely felt about Kant’s treatment of dreams and illusory objects may be a symptom of a similarly widespread misunderstanding of the structure of Kant’s argument for the logical unification of empirical intuitions. But there may still seem to be a problem for this account:  if the principle of the topological connectedness of space and time is an intellectual requirement on the construction of a coherent world of objects and the understanding has a mission to construct such a world, why are there illusory objects to begin with? Would not the existence of schematic objects unschematized by the rule of topological unity be ruled out a priori? Is this not, indeed, the very point of the argument of section 26? I say “counterfactual necessity” and not “analytic necessity,” since we will see that the principle that real objects are in topologically unified space is not an analytic principle. This is a good thing, of course, since otherwise the procedure described here would be circular. 63 A point also made by Thöle 1991, 288. 62



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The reply, for real objects, is that their contained schematic objects (appearances prior to metric determination)64 must indeed be subject to a synthesis that insures their incorporation into a unified spatiotemporal world. That is the consequence of Nomic Prescriptivism and makes the topological principle an a priori synthetic proposition. Unreal objects, however, are schematic objects whose cause lies not in external stimulation of the faculty of sensibility but in internal influence on the faculty of imagination. The faculty of imagination knows this, as it were, and thus responds with a synthesis that does not deploy the resources of schematizing, transcendental synthesis. (“Transcendental” means “objectivity-producing” here.)65 When I  say that the faculty of imagination “knows this,” I do not mean that we know this, at least not consciously. Rather I mean that the imagination responds differentially to inputs that originate externally from those that originate internally. So there is a contrast here between an account of what the real consists in and an account of how we can know when something is real. This contrast seems to be in play in the difference between Kant’s discussion of the real in the Anticipations of Perception and his discussion of actuality in the Postulates of Empirical Thought. Consider the following passage from the latter: The postulate for cognizing the actuality of things requires perception, thus sensation of which one is conscious—not immediate perception of the object itself the existence of which is to be cognized, but still its connection with some actual perception in accordance with the analogies of experience, which exhibit all real connection in an experience in general. (GW, 325, A225/B272)

See Ch. 6, §3.3. This solution may be compared with one that Thöle 1991 proposes. Thöle agrees that not all empirical intuitions fall under the categories: “only those perceptual contents that are represented as determined in space and time”(288). Arguing later that while some illusions (like afterimages) may be localized in global space by reference to actual objects (the afterimage appears over there next to the wall), with dreams this is not possible, yet “all given spatial representations must allow themselves to be interpreted as parts of a comprehensive, objective space” (292). Since this is not the case with dreams, “we can be satisfied with the weaker assertion, R2, To each spatial representation there must be a comprehensive space of which the given representation represents a part” (292). A consequence of embracing the weaker principle is that “we can allow next to ‘actual’ space also a ‘dream space’.” These “representational contents” (Vorstellungsgehalte) also “stand under the categories” (292). But there is a difference between saying we think objects are integrable in a global space (as we do in a dream) and saying they are integrable in a unified space, as they are in reality but not in a dream. Both are in a sense “standing under the categories” on my account: in the dream case they stand “externally” under the categories, in the reality case they stand “constituted by” the categories. It is not clear how these two cases are to be distinguished on Thöle’s account. 64 65

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I have already argued that the requirement for a connection of an object with “some actual perception in accordance with the analogies of experience” should be read as an intellectual condition itself depending on a requirement of the unity of space and time. The definition of the category of the Real in the Anticipations of Perception, on the other hand, makes no reference to conscious perception or intellectual conditions. This means that we can mistakenly believe that an illusory object is a real object because we mistakenly think that this intellectual requirement is met. But just because we can make this mistake does not mean that the faculty of transcendental synthesis can make this mistake: its response to sensory affection is to make it true that the requirement is met for the object which this affection stimulates this faculty to produce, regardless of what we may consciously think.66 This may seem to be too large a dose of empirical psychology, offered without the benefit of empirical evidence, that I  am asking the reader to swallow on Kant’s behalf. This would be true if this proposal were offered from the stance of transcendental realism, for then we start off with very few constraints on what is possible. So in this case lots of empirical evidence would be needed to cut the possibilities down to a manageable number of plausible hypotheses. But that is not the stance Kant is taking: he believes that he has proven by the Transcendental Argument for Nomic Prescriptivism that we prescribe reality to nature. The facts going in for Kant are these: we already know how we have to think about the world, we know that we have sensory experience of objects in space and time, and we know that we have to make appearances be in accordance with how we have to think about the world and with its spatiotemporality. These facts place considerable constraints on what kind of mechanisms it will be possible for transcendental psychology to employ. Figuring out which among the remaining possibilities are the plausible ones may very well be something we can do from the armchair.67

This distinction may help with a problem posed by Baum 1987: “If you rely on the idealistic model of the maker’s view of his product . . .[h]‌ow can it ever happen that our perception does not properly fill in the intuitive (space and time) and other intellectual (categories) framework that conditions them in one way or another?” (101). The answer is that we, insofar as we are the legislative function of transcendental synthesis, cannot make mistakes of this kind, but we, insofar as we are epistemic agents operating with incomplete information and a perhaps inadequate grasp of intellectual conditions, can. 67 A version of the “armchair science” objection is made by Young 1994. He says that Kant’s “talk about mental manufacture sounds to the contemporary ear like a caricature.” He acknowledges that “much in the text suggests this picture,” but “If Kant’s aim were to propound such a theory, however—more generally, if his theory of synthesis were meant to be a theory as to how experience gets produced—his efforts would be sadly misdirected.” This is so because Kant faces an “unwelcome dilemma”: 66



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2.2.4.2.  The Explanation

The task of Section 2.2.4 is to provide an account of the psychological mechanism Kant postulates to explain how it is that the objects of logically unified empirical intuitions would have to be in accord with the unity of space and time, an accordance that counts as an intellectual condition for Kant. Part of the mechanism is already afforded by Kant’s projectionism for intuitions:  properties of the structure of intuitions themselves are projected onto the intentional objects of intuitions, as discussed in Chapter 3. So Kant does not have to come up with a separate argument connecting the results of operations on the structure of intuitions with objects in the outside world. Notice, however, that we have developed the theory of the projection of cognitive structure only in its application to the kind of empirical intuitions Kant is dealing with in the Aesthetic, which are empirical intuitions taking undetermined objects— appearances in Kant’s sense (GW, 155; A20/B34) and, as I argued previously68, also in the ordinary sense. But in this section we are considering how the postulation of a different class of intuitions, logically unified intuitions, might explain something, and I  attribute to Kant the same projectionist doctrine:  whatever structure they have is also projected onto their intentional objects.69 If it were meant to be empirical, his theory would be superficial at best, providing merely an armchair account . . . If it were meant, on the other hand, to describe activities and faculties which are not themselves empirically accessible, Kant’s theory would violate his own strictures against speculating beyond the bounds of possible experience.” (332) There certainly is in Kant a problem about where in the two worlds (phenomenal vs. things in themselves) the experience-constructing self is to be located; there are problems with each possibility. If this problem is, indeed, what the second horn amounts to, it is a problem for Kant but not a methodological problem; Kant may need another pigeonhole in his Transcendental Psychology. But if the complaint is that Kant is violating his own method, the charge is unfair. Kant’s method requires that metaphysical conclusions not be derived either from premises that depend on an illegitimate source beyond sense experience, like intellectual intuition, or by an illegitimate inference from premises that are available from sense experience. In the reasoning that I attribute to Kant in the Copernican revolution, neither of these things is the case. Young’s final complaint is this, “How could Kant claim to know that unobservable processes necessarily impose the categories throughout all experience” (ibid.). It must be admitted that there is an element of contingency in any argument Kant makes from subjective forms, forms either of sensible intuition or of thought; these are how humans’ subjectivity is constituted, and it cannot be ruled out as logically impossible that something we would count as sensible intuition or thinking could occur in different forms. Nevertheless, for humans, there is an answer to this worry. Because the subjective side constitutes intellectual conditions, ways that we have to think if we are to be thinking about an actual world at all, as long as nomic prescription is actively undertaken, no part of experience that is part of the actual world can fail to fall under these conditions. 68 See Ch. 6, §1. 69 Here I follow Aquila not only in projecting our representations onto intentional correlates but in projecting conceptual aspects of our representations (the “noetic” side) onto their intentional correlates (the “noematic” side). See Aquila 1989, 95.

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When an intuition is logically unified, the elements unified are a singular representation and a property-like representation, and the unification is accomplished by a connection synthesis rather than a composition synthesis.70 A connection synthesis is a constituting application—an “internal application”—of synthesis rather than an “external application” of synthesis—as in the case of explicit judging,71 but the products of connection synthesis are still judgment potentiating (implicit judgments), and the kind of synthesis is intellectual rather than imaginative.72 When the understanding comes to “prescribe laws to nature,” in this case the law that all physical objects are in a topologically connected space, I suggest that it does so in stages. First, it applies a connection synthesis that logically fuses together an intuition of an appearance (an undetermined object) meeting the actuality condition with the category of actuality itself, thus yielding the logically unified intuition, this (actual) empirical object’s being actual. As I argued in the previous subsection, meeting the actuality condition is not a conscious application of the criterion of actuality but is the state affairs wherein the sensuous matter associated with the appearance is in fact being produced in the faculty of sensibility by an external source. This unified intuition now potentiates a judgment: (1) This empirical object is actual. However, this by itself does not yield the desired result, which is to demonstrate that the structure of the unified intuition necessarily potentiates a judgment that this empirical object is in a topologically unified space. (Projection then carries this result to the object of the intuition.) To achieve the desired result, two additional judgments are needed, this time judgments in the form of general principles sufficient to complete a syllogism with the proposition This empirical object is in a topologically unified space as its conclusion. These principles are: (2) All actual empirical objects are spatial objects. (3) All spatial objects are in a topologically unified space. Fortunately, Kant has already shown that both of these principles are justified by showing that they are intellectual conditions on our ability to coherently represent an objective world. The justification for (3) is accomplished in the Objective Deduction of the Unity of Space in the B edition, as presented in 70 71 72

See Ch. 6, §2. See Ch. 6, §1. See Ch. 6, §2.



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Section 2.2.2 of this chapter; the justification for (2) is given in the preamble to the Metaphysical Exposition in the famous words, “By means of outer sense (a property of our minds) we represent to ourselves objects as outside of us, and all in space” (GW, 157; A22/B37), as discussed previously.73 From (1), (2), and (3) we can infer, (4) This empirical object is in a topologically unified space. Since this argument applies to all appearances meeting the actuality condition, we can say, (5) All objects of empirical intuition meeting the actuality condition exist in topologically unified space. Since being in a topologically unified space is an intellectual condition, we can conclude that (6) All objects of empirical intuition meeting the actuality condition meet at least one intellectual condition. Finally, we need to exploit the principle of section 10 in the Analytic, that the underlying procedures for synthesis and judgment are the same,74 to read this result back into the judgment-potentiating structure of the intuition, which structure consists in the synthesis of the property-like elements of spatiality and topologically unified spatiality in (2) and (3), respectively, with the object-referring element in a single logically unified intuition. In other words, empirical intuitions are subject to at least one intellectual condition. Now, this is what I have set out to prove on Kant’s behalf, but Kant, of course, has wanted to prove more; namely, that all objects of empirical intuition meet some or all of the official set of twelve categories. I do not have a direct proof of this to offer, nor do I see one in Kant’s texts, but I do have an indirect proof, already sketched out in Section 2.1. There the proof was that if (1), it is already shown to be the case that we prescribe laws to nature on account of what I have since called the Transcendental Proof of Nomic Prescriptivism in the B edition; and if (ii), it is a consequence of this proof that all empirical objects meeting the actuality condition do so because they are the objects of intuitions logically unified by applications of the rule for topological unity—that is, (3); and if (iii), there is much more to a physical object than just See Ch. 2, §2. See Ch. 6, §1.2, and also the synopsis of the first part of the B edition Deduction, Part I, §6, of this chapter. 73 74

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its schema in unified space; then (iv) there must be many more rules operating in the synthesis of empirical intuitions. What are they? Well, a clue is to be found in the kind of judgments we make about such objects, a clue that Kant himself gives in section 10 in the Analytic, in the so-called Metaphysical Deduction. (Recall that Kant refers to the Metaphysical Deduction by name in the first sentence of section 26, just before introducing the doctrine of Nomic Prescriptivism. Could this be why? [GW, 261; B159].) This is a clue to what the list of categories should be. This list scratches where Kant itches, and the cause of the itch is Nomic Prescriptivism. If this suggestion is right, then the only intellectual condition of which Kant really needs to directly prove that it holds of empirical intuitions (meeting the actuality condition) is the one we have just directly proved: the need for actual empirical objects to occur in a topologically unified space. 2.2.5.  Some Final Thoughts on the Strength of Kant’s Argument

If we return to the ur-form of the Deduction of the Categories in the B edition— namely, the Transcendental Exposition of the Concept of Space—I have argued that the latter argument is a strong one and that it derives its strength from the structure of its final part, the Second Geometrical Argument for Transcendental Idealism.75 It does so because the structure of the final part has two correlated sides, each of which is independently established by applications of the same method, Kant’s mathematical method. This allows us to set up a dilemma to answer the question why there should be such a correlation: Is it due to chance or to some other cause? Once we allow Kant this dilemma, he makes an overwhelmingly convincing argument that it is the second option and (in my opinion) makes a fairly strong argument for his own idealist version of it. The structure of the final part of the Transcendental Deduction of the Categories in the B edition—namely, the Transcendental Proof of Nomic Prescriptivism—has the same correlated structure, established, similarly, by independent applications of Kant’s method. But in this case there is a difference with the geometrical argument: while the method applied to the empirical side is of a piece with Kant’s mathematical method—establishing experimentally the truth of counterfactual necessities—the method applied to the intellectual side is quite different. It is a version of transcendental argument, Kant’s philosophical method, which, of course, contrasts with his experimental method for mathematics. This is an important difference, one on which Kant significantly comments in section 13 in the Analytic.76 Nevertheless, the point relevant to the See Ch. 4, §3. At GW, 221 (A87/B120), Kant says, “Geometry nevertheless follows its secure course through strict a priori cognitions without having to beg philosophy for any certification of the pure and lawful 75 76



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strength of the argument is the same with the Deduction as with the Exposition. There is the same dilemma: Is the correlation due to chance or to some other cause? Kant, of course, chooses the second option and makes the argument that the cause is to be found in nomic prescription by the intellect to the world of appearances. How strong is that argument on an independent assessment? My view is that it is quite strong—though not as strong as the Topological Proof discussed earlier—given the following proviso: that indeed there is a counterfactual necessity for us to find that all actual physical objects occur in topologically unified space. We should not allow this necessity to become an analytic necessity. If we do not and there is indeed such a necessity, then we need to explain why it should be a condition of our thinking about an objective world that we assume the same principle that is true of the empirical world. In addition to chance, there are only two options here (as Kant notes in §27 at GW, 264; B166): (a) the empirical side causes the intellectual side to be the way it is, and (b) the intellectual side causes the empirical side to be the way it is. How could the second possibly be true? For it to be true, somehow the fact that all the objects in the actual and counterfactually accessible universes occur in a topologically unified empirical space must transmit itself into our cognitive faculties, therein somehow producing a conceptual condition on how we have to think if those thoughts are to have objective content. Kant couldn’t see how that was possible, and neither can I.

Note A Arguing against McCann (1985, 78), Keller (1998) also sees that Kant retains a commitment to precategorial knowledge of the self, contrary to McCann (92; see also the section “Self-knowledge and the subject-object theory,” 103–107). Eventually, of course, we come to have knowledge of the empirical self, categorial knowledge that must include knowledge of our subjective states. But, he argues, this is still apparently problematic after the first part of the Deduction: It seems to be specifically the problem of self-knowledge that leads Kant to divide the argument of the B-Deduction into two steps. Since pedigree of its fundamental concept of space.” Also at GW, 22 (A89/B122), he says, “Thus a difficulty is revealed here that we did not encounter in the field of sensibility, namely how subjective conditions of thinking should have objective validity, i.e. yield cognitions of the possibility of all cognition of objects . . .” Recall from Ch. 5, §2, that “objective validity” here means intentionally objective validity, not empirically objective validity, thus making the difficulty fall solely on the intellectual side, to be solved by applications of philosophical method—the method of transcendental argument.

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he defines knowledge in terms of judgment in the B-Deduction, and judgments have an objective force that the so-called perceptual judgments of the Prolegomena do not, the implication of Kant’s new theory of judgment appears to be that no knowledge of inner states is possible. For inner states seem to be precisely states that are inherently subjective. (92) Keller goes on to claim that this explains why a second step is needed in the B-Deduction: Kant needs to show how all sensible representational contents can be candidates for judgments requiring categories. In this way Kant can sustain the claim of judgment to objectivity and still provide room for subjective experiences. (93) Keller will argue that Kant accomplishes this through his argument that all objects are subject to the unity of time and that this latter derives from the unity of self-consciousness, not of the idiosyncratic self, but of a kind of impersonal self-consciousness that Keller claims to find in the first part of the Deduction (107–111). I do not myself find such a notion in the first part of the B-Deduction and so part company with Keller on the details of his interpretation of the second part. But I also have to object to his account of the general problem that the second part is to resolve for Kant. According to Keller, the problem is that the first part rules out the possibility of judgments of perception. But I have argued in Chapter 6, Section 3.3, that this is not so* and that it is not so because of the difference between the nonobjective access we have to the states of the self in an original apperception and the access we have to the empirical self in a later-stage apperception. If I have interpreted Kant’s texts in sections 16–18 correctly, Kant makes the transition via the Analytic Bridging Principle, not via the doctrine of the unity of space and time in section 26. This principle establishes the existence of an objective self—that there is such a self, not how in particular it can be subject to the categories. This latter is indeed the work of the second part, in developing the theory of time determination in sections 24 and 25. But this theory makes sense as explaining how the objective self is objectively constructed only if we already know that it actually exists. This, I submit, is work already accomplished in the first part by means of the Analytic Bridging Principle. According to Keller, we make the transition from (primitive) “self-knowledge” to knowledge of the empirical self by introspection:  . . . I represent myself as the formal subject of thought. I can, however, enrich this formal notion of subject through introspection and more



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indirect empirical evidence (included in the term “self-intuition”). This empirical self-consciousness differs from self-knowledge. (106) That this crucial transition for Kant’s argument would be left to introspection seems quite un-Kantian to me. (*Whether they are or not is, in any case, irrelevant, since even if allowed, judgments of perception would not be the means of providing objective predication of subjective states to the self.)

Note B In this note I  consider a sampling of recent interpretations of the B edition Deduction with an eye to which count as Bifurcation Interpretations in this sense. One that clearly does is Allison’s interpretation in the second edition of his Transcendental Idealism (2004, ch. 7). Since I  discuss Allison’s reading in the body of this chapter, I do not further discuss it here. In the first edition of Transcendental Idealism (1983, ch. 7), Allison takes a difference in terminology between Object and Gegenstand—the first occurs characteristically in the first part of the Deduction, the second characteristically in section 26—to mark a distinction between two kinds of objectivity, intentional objectivity and real existence, also marked by a difference in Kantian terminology between objektive Gültigkeit and objektive Realität, respectively. There is a bifurcation here, but it is a bifurcation of the concept of objectivity into two kinds rather than two kinds of intuition. This is at least a difference of sufficient significance, in emphasis if not substance, from the position advocated in the second edition that I do not regard the 1983 interpretation as a bifurcation interpretation in my sense. Somewhat in the spirit of Allison’s 1983 treatment, Aquila also sees Kant dividing the labor of the B edition Deduction between attention to the representational (“noetic”) side in part I and to the objective (“noematic”) side in part II. However, because of Aquila’s projectionism, having begun the Deduction in part I, Aquila feels compelled to observe: “Obviously, Kant does not suppose that . . . any considerable effort will in fact be required for finally completing the Deduction, that is, from moving from the structure of cognition to the structure of correlative ‘reality’ ” (Aquila 1989, 144). So Aquila’s reading of the two-part structure of the B edition Deduction is also not bifurcationist in my sense. (Also see the note to Aquila, Ch. 5, §3, on a further difference between Aquila’s reading and mine re the correlation between the subjective and objective sides.) We also need to consider this question in connection with Henrich’s proposal for the structure of the B edition Deduction in his famous paper “The Proof

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Structure of Kant’s Transcendental Deduction” (Henrich 1968/69). Henrich maintains that the first part of the B edition Deduction “is . . . valid only for those intuitions which already contain unity. That is: wherever there is unity, there is a relation which can be thought according to the categories” (645). Henrich now adds: “This statement, however, does not yet clarify for us the range within which unitary intuitions can be found” (645). That is, it is unknown in §20 whether there is a class of un-unified intuitions, thus the result of §20 is restricted to a possible subclass of the full set of intuitions, which restriction “will be overcome in the paragraphs of section 26, i.e., the second part of the deduction will show that the categories are valid for all objects of our senses” (646). This way of putting things may in turn suggest that Henrich thinks there is a class of un-unified intuitions, in addition to the class of unified intuitions, subject to a different argument revealing that they all are subject to the categories. This then would make his interpretation a version of the bifurcation reading, but in a later article Henrich denies that he intended this (Henrich 1984, 43–44), and I think a careful reading of the earlier article will confirm this. (For a thorough discussion of Henrich’s argument in that paper and some criticisms in previous secondary literature thereof to which I am much indebted, see Evans 1990, 553–570.) Evans’s own interpretation is very close to my own with respect to its acknowledgment of the existence of a kind of unity that is not conceptual unity; e.g., “the unity of Gestalt contexture” (Evans 1990, 562). In light of this possibility Evans then proposes: “The second step of the B-deduction has the task of showing that while there may be nonunified intuitions, an in principle nonunifiable manifold of intuition is impossible . . . the core of the second step is to be found in the first section of #26” (565). My own position, though close to this, argues that even though there can be nonlogically (nonconceptually) unified intuitions— that’s what appearances are in the official sense of the Aesthetic—those that are of actual objects must be logically unified. My account does not trade on the notion of the possibility of unification. Nevertheless, Evans’s account is a version of the Bifurcation Thesis. Baum (1987) argues not that there are two classes of intuitions whose subjection to the categories is under discussion in the first and second parts, respectively, but that there are two aspects of one kind of intuition that are under discussion in the two parts, respectively. In the first part it is shown that for any intuition to have an object (have “objective validity”) category-governed intellectual operations are required; in the second part it is asked, “How, in a word, can objective validity be reached through perceptions which are quite independent of the understanding?” (100). This account is similar to that of Allison 2004 in this respect, but since it does not bifurcate intuitions, it does not count as a Bifurcation Thesis theory.



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The Bifurcation Thesis, as I employ it, states that there are two kinds of intuition, that the first part of the Deduction demonstrates of the first kind that it is subject to the categories, and that the second part demonstrates that the second kind is subject to the categories. But there is a negative version of this thesis that agrees with the positive version that there are in principle two kinds of intuitions in play in Kant’s arguments, that the first kind is shown by the first part to be subject to the categories but that the second part maintains some kind of negative thesis about the second kind of intuition—for example, that there are none of this kind or that there can be none of this kind. I take the treatment in Robinson 1984 (discussed in Ch. 6) to be of this kind. If we take the possibility of nonlogically unified intuitions for Kant and the possibility of judgments of perception for Kant to be mutually dependent (as I do), then the account in Pollok 2008 (discussed earlier, in §7) counts as a negative Bifurcation Thesis as well, since he argues that in the first part of the Deduction room is still left for judgments of perception, whereas in the second part they “vanish” (335). However, in my discussion of the Bifurcation Thesis I talk only about the thesis in its positive version. Some accounts treat the first part as showing that all intuitions are subject to the categories and the second part as explaining how this happens for the objects specifically of human intuition (objects in space and time), e.g., Howell 1992, n. 49 to ch. 6, 367; and Henrich 1969, 650–653. I take these to be paradigm examples of nonbifurcation interpretations. Other accounts that treat the arguments of the first and second parts as different attempts to reach the same conclusion, e.g., Guyer 1992, are of course also not instances of the Bifurcation Thesis. For another analysis of responses in the recent secondary literature to the problem of the two-part structure of the B edition Deduction, see Keller 1998, 89–92. His own view is stated in summary form on 92, and I discuss it in Note A here in Ch. 7. *  * *

REFERENCES

Primary Sources of Kant’s Writings Kants gesammelte Schriften, ed. Deutschen Akademie der Wissenschaften, 29 vols. Berlin:  De Gruyter, 1902–1983; 2nd ed. for vols. I–IX, 1968. Immanuel Kants Werke, vols. III–IV, eds. A. Buchenau und E. Cassirer. Hildesheim: Gerstenberg, 1973.

Translations of Kant’s Writings into English “Concerning the Ultimate Ground of the Differentiation of Directions in Space,” in Theoretical Philosophy, ed. and trans. D. Walford with R. Meerbote. Cambridge: Cambridge University Press, 1992. Critique of Judgment, trans. and ed. W. Pluhar, foreword by M. J. Gregor. Indianapolis: Hackett, 1987. Critique of Pure Reason, trans. N. K. Smith. London: Macmillan, 1929. Critique of Pure Reason, abr. ed., trans. N. K. Smith. London: Macmillan, 1934. Critique of Pure Reason, ed. and trans. P. Guyer and A. W. Wood. Cambridge: Cambridge University Press, 1998. Lectures on Logic, ed. and trans. J. M. Young. Cambridge: Cambridge University Press, 2004. Prolegomena to Any Future Metaphysics, ed. and trans. G. Hatfield. Cambridge:  Cambridge University Press, 2004.

References to Secondary Literature Allais, L. (2009). “Kant, Non-conceptual Content and the Representation of Space.” Journal of the History of Philosophy 47, 383–413. Allais, L. (2010). “Kant’s Argument for Transcendental Idealism in the Transcendental Aesthetic.” Proceedings of the Aristotelian Society CX, part I, 47–75. Allison, H. (1983). Kant’s Transcendental Idealism. New Haven, CT: Yale University Press. Allison, H. (2004). Kant’s Transcendental Idealism, rev. ed. New Haven, CT: Yale University Press. Ameriks, K. (1978). “Kant’s Transcendental Deduction as a Regressive Argument.” Kant-Studien 69: 272–292. Angell, R. (1974). “The Geometry of Visibles.” Nous 8, 87–117. Aquila, R. (1983). Representational Mind. Bloomington: Indiana University Press. Aquila, R. (1989). Matter in Mind. Bloomington and Indianapolis: Indiana University Press. Aquila, R. (2003). “Hans Vaihinger and Some Recent Intentionalist Readings of Kant.” Journal of the History of Philosophy 41, 2: 231–250.

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Bauer, N. (2005). “A New Reading of Kant’s Subjective Deduction.” Eastern Study Group of the North American Kant Society, University of Pennsylvania. Bauer, N. (2008). “Kant’s Transcendental Deductions of the Categories.” PhD diss., University of Chicago. Baum, M. (1987). “The B-Deduction and the Refutation of Idealism.” Supplement, Southern Journal of Philosophy 25: 89–114. Beck, L. (1978). “Did the Sage of Königsberg Have No Dreams?” In L. Beck, ed., Essays on Kant and Hume (38–60). New Haven, CT: Yale University Press. Bennett, J. (1966). Kant’s Analytic. Cambridge: Cambridge University Press. Berkeley, G. (2002 [1732]). An Essay towards a New Theory of Vision, 4th ed. D. Wilkins, ed. Dublin. Brentano, F. (1874). Psychologie vom empirische Standpunkt. Leipzig. Brittan, G. (1978). Kant’s Theory of Science. Princeton, NJ: Princeton University Press. Brittan, G. (1986). “Kant’s Two Grand Hypotheses.” In R. Butts, ed., Kant’s Philosophy of Physical Science (61–94). Dordrecht: Reidel. Broad, C. (1941). Kant’s Theory of Mathematical and Philosophical Reasoning. Proceedings of the Aristotelian Society 42: 1–24. Buroker, J. (1981). Space and Incongruence. Dordrecht: Reidel. Buroker, J. (2006). Kant’s Critique of Pure Reason:  An Introduction. Cambridge:  Cambridge University Press. Butts, R. (1969). “Kant’s Schemata as Semantical Rules.” In L. Beck, ed., Kant Studies Today (290– 300). LaSalle, IL: Open Court. Carnap, R. (1949). “Geometry and Empirical Science.” In H. A. Feigl, ed., Readings in Philosophical Analysis (238–249). New York: Appleton-Crofts. Descartes, R. (1984 [1641]). Meditations on First Philosophy. In J. Cottingham, R. Stoothoff, D. Murdoch, eds., The Philosophical Writings of Descartes, vol. 2. Cambridge:  Cambridge University Press. De Vleeschauer, H.-J. (1962). The Development of Kantian Thought, trans. A. Duncan. London: Nelson. Dicker, G. (2004). Kant’s Theory of Knowledge. Oxford and New York: Oxford University Press. Dickerson, A. (2004). Kant on Representation and Objectivity. Cambridge: Cambridge University Press. Dryer, D. (1966). Kant’s Solution for Verification in Metaphysics. Toronto: University of Toronto Press. Dyck, C. (2008). “The Subjective Deduction and the Search for a Fundamental Force. Kant Studien 99: 152–179. Evans, J. (1990). “Two-Steps-in-One-Proof: The Structure of the Transcendental Deduction of the Categories.” Journal of the History of Philosophy 28, 4: 553–570. Falkenstein, L. (1995 [2004]). Kant’s Intuitionism. Toronto: University of Toronto Press. Friedman, M. (1985). “Kant’s Theory of Geometry.” Philosophical Review 94: 455–506. Friedman, M. (1992). Kant and the Exact Sciences. Cambridge, MA: Harvard University Press. Garve, C. (2000 [1782]). “Review of Critique of Pure Reason by Immanuel Kant.” In B. Sassen, ed., Kant’s Early Critics. The Empiricist Critique of the Theoretical Philosophy (53–58). Cambridge: Cambridge University Press. George, R. (1981). “Kant’s Sensationism.” Synthese 47, 2: 229–255. Goodman, N. (1968). Languages of Art. Cambridge, MA: Harvard University Press. Guyer, P. (1987). Kant and the Claims to Knowledge. Cambridge: Cambridge University Press. Guyer, P. (1992). “The Transcendental Deduction of the Categories.” In P. Guyer, ed., The Cambridge Companion to Kant (123–160). Cambridge: Cambridge University Press. Hagar, A. (2008). “Kant and Non-Euclidean Geometry.” Kant-Studien 99: 80–98. Hatfield, G. (1990). The Natural and the Normative. Cambridge, MA: MIT Press. Hatfield, G. (2003). “What Were Kant’s Aims in the Deduction?” Philosophical Topics 31, 1–2: 165–198. Henrich, D. (1968/69). “The Proof Structure of Kant’s Transcendental Deduction.” Review of Metaphysics 22: 640–659.

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Henrich, D. (1981). “ ‘Die Beweisstruktur der Transzendentalen Deduktion der reinen Verstandesbegriffe’—eine Diskussion mit Dieter Henrich.” In Burkhard Tuschling, ed., Probleme der “Kritik der reinen Vernunft”. Berlin and New York: De Gruyter. Howell, R. (1992). Kant’s Transcendental Deduction. Dordrecht: Kluwer. Hume, D. (1955 [1748]). An Inquiry concerning Human Nature. C. Hendel, ed. Indianapolis: Bobbs Merrill. Hume, D. (1967 [1740]). A Treatise of Human Nature. L. Selby-Bigge, ed. Oxford:  Oxford University Press. Keller, P. (1998). Kant and the Demands of Self-Consciousness. Cambridge: Cambridge University Press. Kitcher, Patricia. (1987). “Discovering the Forms of Intuition.” Philosophical Review 96, 2, 205–248. Kitcher, Patricia. (1990). Kant’s Transcendental Psychology. New York: Oxford University Press. Kitcher, Philip. (1975). “Kant and the Foundations of Mathematics.” Philosophical Review 84, 1, 23–50. Lewis, C. (1929). Mind and the World Order. New York: Dover. Locke, J. (1959 [1690]). An Essay Concerning Human Understanding, vol. I. A. Fraser, ed. New York: Dover. Longuenesse, B. (1998). Kant and the Capacity to Judge. Princeton, NJ: Princeton University Press. MacKenzie, A. (1990). “Descartes on Sensory Representation:  A  Study of the Dioptrics.” Canadian Journal of Philosophy, suppl. vol. 16, 109–147. Mattey, G. (1988). “Comments on Tom Vinci: A Kantian Theory of Representation.” APA Central Division Annual Meetings, Cincinnati. McCann, E. (1985). “Skepticism and Kant’s B Deduction.” History of Philosophy Quarterly 2: 71–89. Meerbote, R. (1981). “Kant on Intuitivity.” Synthese 47: 203–228. Melnick, A. (2004). Themes in Kant’s Metaphysics and Ethics. Washington, DC: Catholic University Press. Mittelstaedt, P. (1976). Philosophical Problems of Modern Physics. Dordrecht: Reidel. Moore, G. (1962). Some Main Problems of Philosophy. New York: Collier. Nussbaum, C. (1990). “Concepts, Judgments, and Unity in Kant’s Metaphysical Deduction of the Relational Categories. Journal of the History of Philosophy 28, 1: 89–103. O’Keefe, J. A. (1978). The Hippocampus as a Cognitive Map. Oxford: Oxford University Press. Palmquist, S. (1987). “A Priori Knowledge in Perspective:  Mathematics, Method and Pure Intuition.” Review of Metaphysics 41, 3–22. Pereboom, D. (1988). “Kant on Intentionality.” Synthese 77: 321–352. Pereboom, D. (2001). “Assessing Kant’s Master Argument.” Review of Howell 1992. Kantian Review 5: 90–102. Pollok, K. (2008). “ ‘An Almost Single Inference’—Kant’s Deduction of the Categories Reconsidered.” Archiv f. Gesch. d. Philosophie 90: 323–345. Prauss, G. (1971). Erscheinung bei Kant. Berlin: De Gruyter. Quinton, A. (1962). “Spaces and Times.” Philosophy 37, 140: 130–147. Reid, T. (1997 [1785]). An Inquiry into the Human Mind on the Principles of Common Sense. Edinburgh: University of Edinburgh. Richards, P. (1974). “Kant’s Geography and Mental Maps.” Transactions of the Institute of British Geographers 61: 1–16. Robinson, H. (1984). “Intuition and Manifold in the Transcendental Deduction.” Southern Journal of Philosophy 22, 3: 403–412. Russell, B. (1912). The Problems of Philosophy. London: Oxford University Press. Salmon, W. (1980). Space, Time and Motion. Minneapolis: University of Minnesota Press. Sellars, W. (1963 [1956]). “Empiricism and the Philosophy of Mind.” In W. Sellars, ed., Science, Perception and Reality (127–196). London: Routledge and Kegan Paul. Sellars, W. (1963 [1953]). “Is There a Synthetic A Priori?” In W. Sellars, ed., Science, Perception and Reality (298–320). London: Routledge and Kegan Paul. Sellars, W. (1967). Science and Metaphysics: Variations on Kantian Themes. London: Routledge and Kegan Paul.

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Sellars, W. (1978). “The Role of Imagination in Kant’s Theory of Experience.” In H. Johnstone, Categories: A Colloquium (321–345). University Park: Pennsylvania State University Press. Shabel, L. (2006). “Kant’s Philosophy of Mathematics.” In P. Guyer, ed., Kant and Modern Philosophy (94–129). Cambridge: Cambridge University Press. Smith, N. (1962 [1923]). A Commentary to Kant’s “Critique of Pure Reason”. New York: Humanities Press. Strawson, P. (1966). Bounds of Sense. London: Methuen. Stroud, B. (2000). Understanding Human Knowledge. Oxford: Oxford University Press. Thöle, B. (1991). Kant und das Problem der Gesetzmäßigkeit der Natur. Berlin: De Gruyter. Van Cleve, J. (1999). Problems from Kant. Oxford and New York: Oxford University Press. Vinci, T. (1988). “A Kantian Theory of Representation.” APA Central Division Annual Meetings, Cincinnati. Vinci, T. (2006). “Review of Wayne Waxman’s Kant and the Empiricists.” Notre Dame Philosophical Reviews ( June 8). Vinci, T. (2013). “Solving the Triviality Problem in the B-Edition Transcendental Deduction.” Proceedings of the XIth International Kant Congress. Berlin: De Gruyter. Warren, D. (1998). “Kant and the Apriority of Space.” Philosophical Review 197, 2: 179–224. Waxman, W. (2005). Kant and the Empiricists. Oxford and New York: Oxford University Press. Westphal, K. (2004). Kant’s Transcendental Proof of Realism. Cambridge: Cambridge University Press. Willaschek, M. (1997). Der transzendentale Idealismus und die Idealität von Raum und Zeit. Zeitschrift für philosophische Forschung, Band 51, , 537–64. Wilson, M. (1978). Descartes. London: Routledge. Wolff, R. (1963). Kant’s Theory of Mental Activity. Cambridge, MA: Harvard University Press. Young, J. (1988). “Kant’s View of Imagination.” Kant-Studien 79, 2: 140–164. Young, J. (1994). “Synthesis and the Content of Pure Concepts in Kant’s First Critique.” Journal of the History of Philosophy 32, 2: 331–357.

NAME INDEX

Allais, L., 24, 26–28, 30–35, 30n12–35n19, 135n1 Allison, H., 24–26, 25n6, 37, 37n21, 115, 116n21, 121n25, 143n20, 147n26, 150n35, 187n19, 190n27, 203–205, 213n52, 218, 231 Ameriks, K., 22, 102–103, 102n3, 138 Angell, R., 97 Aquila, R., 5, 47, 127n28, 135n1, 149n31, 225n69, 231

Austin, J. L., 47n6 Bauer, N., 114, 114n18–19 Baum, M., 224n66, 232 Beck, L., 135–136, 139–140, 140n15, 173n66 Bennett, J., 102n2, 121n25 Berkeley, G., 20, 20n27 Brentano, F., 46–62 passim, 141 Brittan, G., 75n12, 76n13, 87, 166, 210 Broad, C., 75n12 Buroker, J., 99–100, 152, 152n36 Butts, R., 75n12 Carnap, R., 75n12 Descartes, R., 49, 74, 91, 173 De Vleeschauer, H.-J., 135n3 Dicker, G., 152–153 Dickerson, A., 120n24, 181, 181n9, 204n42 Dryer, D., 25, 25n6, 79–80 Dyck, C., 114n19 Edwards, J., 199n36 Evans, J., 206n45, 232 Falkenstein, L., 11–12, 11n5, 16–19, 18n18, 20n26– 27, 22n28, 61n22, 96, 170 Friedman, M., 67n1, 75n12, 80–81n20, 80–83, 162, 185n16 George, R., 19, 51–52n10

Goodman, N., 57–60 Guyer, P., 9n1, 51n9, 137n7, 138, 138n10, 151, 157, 183n12, 193, 209n47, 233 Hagar, A., 75n12, 96–97 Hatfield, G., 9n1, 67n2, 73, 105, 105n9, 110n13, 111n14 Henrich, D., 149n33, 205–206n45, 231–233 Howell, R., 180n7, 191, 201n39, 233 Hume, D., 20, 112, 117–118, 124, 196 Hymers, M., 201n38 Keller, P., 229–230, 233 Kitcher, Patricia, 11n5, 15n13, 20n27 Kitcher, Philip, 5, 22, 67–73, 67n1, 67n4, 71n9 Leibniz, G. W., 1–4, 2n2, 6–7, 153, 161 Lewis, C. I., 123n26, 141, 172 Locke, J., 134, 161–166 passim Longuenesse, B., 13n9, 41–42, 52n11, 112n15, 120n24, 125n27, 159–160, 164n53 MacKenzie, A., 46 Mattey, G. J., 15n13 McCann, E., 229 Meerbote, R., 87, 167, 167n59, 183n13 Melnick, A., 76n13, 148n29, 211n50 Mittelstaedt, P., 98 Moore, G., 76n13 Nadel, L., 15n13 O’Keefe, J. A., 15n13 Palmquist, S., 71n9 Paul, R., 59n20 Payette, G., 59n20 Pereboom, D., 135n1, 147, 147n24, 193n13 Pluhar, W. S., 9n1

240

Name Index

Pollok, K., 146n23, 196, 196n33, 233 Prauss, G., 147 Quinton, A., 175, 175n70–71 Reid, T., 97 Richards, P., 15n13 Robinson, H., 149n32, 233 Russell, B., 76n13 Salmon, W., 97n35 Sellars, W., 41, 41n26, 128, 156–157, 156n43 Shabel, L., 67n2 Smith, N. K., 11, 16–17, 125n27 Strawson, P., 75n12, 92, 96, 102n2, 210n48 Stroud, B., 47n6

Thöle, B., 174, 174n67, 222n63, 223n65 Van Cleve, J., 76n13, 77–79, 77n16, 121n25, 140–142, 152, 173n66 Vinci, T., 15n13, 20n25, 196n34 Warren, D., 24, 26, 28, 37, 37n21, 38n23 Waxman, W., 76n13, 80, 83–88 Westphal, K., 117–118, 124 Willaschek, M., 30n12 Wolff, R., 102n2, 152n37 Wood, A., 9n1, 51n9, 151, 209n47 Young, J. M., 9n1, 154n41, 164–165n55, 224–225n67

SUBJECT INDE X

Note: Page numbers for definitions are in bold type. absolute being, 24 absolute space, 24 abstract concepts, 167; of space, 39 actuality itself, category of, 226 actual object, 226 A edition Deduction: Affinity Argument and, 114, 116–131, 119–120, 214; objective deduction in, 215; subjective conditions of thought and, 113; transition to B edition and, 131–133

aesthetically unified intuitions, 6, 8, 55, 169–172 Aesthetic, Transcendental Idealism in, 23, 36–39 aesthetic unification, 151, 170 affinity: as functional concept, 118; transcendental, 129 Affinity Argument, 114, 116–131, 119–120, 214 Analogies of Experience, 211 analytical power of apperception, 180, 180–187 analytical unity of consciousness, 44 Analytic Bridging Principle, 192–194, 230 analytic definitions, 42. see also definitions; geometric propositions and, 68 Analytic of Principles, 210 analytic phenomenalism, 121–122 Analytic Principle of Apperception, 190–194, 203–205

analytic-synthetic distinction, 67 analytic unity of apperception, 182 a posteriori vs. a priori cognition, 4–5, 76–77 appearances, 145–150; L. Beck on, 135–140; empirical intuitions and, 135–150; as empirical objects, 146–147; experience and, 135; form of, 11, 13; illusion and, 144; matter of, 11; Nomic Prescriptivism and, 85, 99, 137; object and, 142; ordinary empirical, 145–146; as ordinary empirical objects, 146–147; reality and, 215– 218; rules and, 140; J. Van Cleve on, 140–142

apperception, 7, 176. see also the "I think"; thought; analytical power of, 180, 180–187; Analytic Principle of, 190–194, 203–205; analytic unity of, 182; intuition and, 205–206; objective unity of, 186; power of (see power of apperception); synthetic unity of, 182, 188; thought and, 204–205; transcendental unity of, 172, 188–190, 194; unity of (see unity of apperception) applied geometry, 90; imagination and, 64 applied mathematics. see geometrical argument apprehension, synthesis of, 207–208 a priori cognition, 130–131; vs. a posteriori cognition, 4–5, 76–77 a priori construction (in mathematics), 66–67, 73–74

a priori form of intuition, 9, 28. see also intuition; L. Allais on, 24, 26, 30–35, 31n16–35n19; H. Allison on, 24–26; geometrical arguments for, 28–36; nongeometrical argument for, 36–39; D. Warren on, 24, 26 a priori form of representation, 5; pure representation vs., 9–22 a priori reasoning, 4; empirical reasoning vs., 2–4 Argument from Topology for Nomic Prescriptivism, 221n61 associations, causality and, 117 awareness, power of, 177 B edition Deduction, 150–157, 176–233, 230. see also Transcendental Deduction; objective deduction of the unity of space in, 218–220; subjective phase of, 214–220; transcendental proof of Nomic Prescriptivism in, 220–221; transition from A edition and, 131–133 Berkeley, G., 20 Bifurcation Interpretation, 200, 231–233 Brentano intentionality, 46–63 passim, 47, 141

242

subject Index

Cartesian theory of ideas, 49 categories, 5, 8, 101–133. see also Transcendental Deduction; of actuality itself, 226; Affinity Argument and, 114, 116–131; K. Ameriks on, 102–103; judgment and, 111–112; principles of, 101–108; schematized, 167n59, 209, 211; Second Geometrical Argument and, 65; Table of Categories, 111, 213; thought and, 204–205; unity of the, 7–8 category-governed synthesis, 6, 208 causality: associations and, 117; subjective conditions of thought and, 109 causal rules, 124 circumstance, experimentally possible, 72 cognition: of objective world, 26; of space, 18; synthetic a priori, 68 combination, 150 composition synthesis, 151, 155 comprehension, 13 conception, 44; concept vs., 5; linguistic, 44 concept of space, 18–19, 38–39, 44, 88–96 passim; abstraction and, 39; general, 40–45 concept of three-dimensional space, 19–21 concept of time, 88–96 passim concepts: abstract, 167; conception vs., 5; construction of, 66; empirical, 161–169; experience and, 135; innate, 20; intuition and, 135; matter and, 40; pure sensible, 43; synthetic-conception ground and, 43; theory of, 40–45 “Concerning the Ultimate Ground of the Differentiation of Directions in Space” (Kant), 69

connection synthesis, 150, 155 consciousness, 139; analytical unity of, 44; objective unity of, 183; power of awareness and, 177; subjective unity of, 172, 183, 188– 190; synthetic unity of, 44; unity of (see unity of consciousness) construction: of concept, 66; geometrical method and, 77 Container View, 4, 11–19; L. Falkenstein on, 16–19, 18n18; geometrical method and, 22; grounds for, 20–21n27, 20–22; a priori form of intuition and, 9–10; N. K. Smith on, 16–17 coordination component of map analogy, 58–61, 61n21 Copernican dichotomy, 106 Copernican inference, 106 Copernican revolution in metaphysics, 4, 107,

definitions, 42–43; analytic, 42; deflationary, 194; empirical concept and, 43; geometric propositions and, 68; synthetic, 42–43; types of, 42 deflationary definition, 194 Descartes, R., 49, 74, 91, 173 determined objects of empirical intuition, 165–166

Doctrine of Method, 133 dreams, 172; representation and, 49; schematic objects and, 173; truth vs., 49 (see also illusion) empirical appearances, 145–146 empirical application of Euclidean geometry, 75 empirical concepts, 161–169; representation of space and, 38–39; synthetic definitions and, 43 empirical domain, form of objects in, 93 empirical intuitions, 7, 34, 55, 168, 197–201, 205–206, 207; appearances and, 135–150; determined objects of, 165–166; as distinct from objects of, 34; objects of, 165–166; undetermined objects of, 166; unity of space and time and, 221–228 empirically objective validity, 116 empirical objects, 55; appearances as, 146–147; Euclidean geometry and, 34–35, 34–35n19, 65; unified intuition and, 226–228 empirical psychology, 224 empirical reasoning: intuition and, 5; a priori reasoning vs., 2–4 empirical representation, 29–30 empirical rules, 124–125, 164 empirical schemata, 161–169 Euclidean geometry, 10, 64. see also geometrical method; in CPR, 66–77; empirical application of, 75; empirical intuitions and, 34–35, 34–35n19; empirical objects and, 65; object geometry type of, 74–75; pure application of, 75, 75n12; pure objects and, 65; space geometry type of, 75; spatial order of sensation and, 12 experience, 128–129; Analogies of, 211; appearances and, 135; concept and, 135; judgments of, 6–7 experimentally possible circumstance, 72 external application of synthesis, 174, 206

copula judgments, 177 counterfactual necessity, of geometry, 69–77

figurative synthesis, 154 First Geometrical Argument for Transcendental Idealism, 5–6, 34–36, 65, 88–94 passim; regressive nature of, 103 First Metaphysical Expositions, 19, 20–21n27, 53, 55 First Reading of the Metaphysical Expositions,

deduction. see A edition Deduction; B edition Deduction; objective deduction; subjective deduction; Transcendental Deduction

formal intuition, 13; map analogy and, 61; pure form of intuition vs., 11–19; pure intuition and, 13

128

36–38



Subjec t Ind e x

formative synthesis, 82, 165 form of appearance, 11; form of intuition and, 13 form of intuition, 13, 23; form of appearance and, 13; form of sensation and, 22; outer, 9; a priori, 9, 9–22; pure, 11–19 form of objects: in empirical domain, 93; in pure domain, 93 form of outer intuition, 9 form of representations, 10 form of sensation, 9, 11; form of intuition and, 22 form of sensibility, 21, 29–30 form of thought, 201 forms: as mechanisms, 11–12; as orders of intuited matters, 12; as representations, 11 form-space, 68–94 passim, 76n13; geometrical, 85; topological, 85 generalizations, 72 geometrical argument, 26; in CPR, 66–77; imagination and, 64; mathematical method to, 65; for a priori form of intuition, 28–36; in Prolegomena, 27–36; Transcendental Idealism and, 64–100 geometrical-formal schemata, 167 geometrical form-space, 68–94 passim, 76n13, 85 geometrical method, 5, 22. see also Euclidean geometry; KV (Kitcher-Vinci) account; mathematical method; construction and, 77; Container View and, 22; counterfactual necessity of, 69–77; physics and, 96–99 global space, 14; intuition and, 15–16; pure intuition and, 14 hallucinations, 48–49, 172–175, 216–218. see also dreams; illusion "heap thesis," 11–12 Hume, D., 20, 112, 117–118, 124, 193 idea: of an intuition, 139; of an object, 139; Cartesian theory of, 49; object of, 49 idealism. see Transcendental Idealism illusions, 6, 172–175. see also dreams; hallucination; appearances and, 144; reality and, 216–218 images, 164; metric of, 167, 167n59 imagination: applied geometry and, 64; faculty of, 114, 223; imitative, 125; objects in domain of, 29; productive, 125; pure geometry and, 64; reproductive, 125–128 imitative imagination, 125 implicit judgments, 180 impressions. see sense impressions Influx Theory, 32 innate concepts, 20 intellectual conditions, 3, 113, 213. see also subjective conditions; unity of space as, 214–220 intellectual synthesis, 154

243

intentionality, 46, 46–63, 139. see also Brentano intentionality; applying map analogy to, 60–63; intuition and, 47; sensation and, 55 intentionally objective validity, 116 Intentional Map Model, 61 intentional object, 48 internal application of synthesis, 174, 206 intuited matters, forms as orders of, 12 intuitional representations, projectionism and, 5, 30 intuitions, 4, 151–157; aesthetically unified, 6, 8, 55, 169–172; apperception and, 205–206; concepts and, 135; determined objects of empirical, 165–166; empirical (see empirical intuitions); empirical reasoning and, 5; formal (see formal intuition); form of, 23; in general (see intuitions in general); global space and, 15–16; idea of, 139; intentionality and, 47; judgment and, 6; local space and, 15–16; logically unified, 6, 55, 165; nonsensory, 13; outer, form of, 9; a priori form of (see a priori form of intuition); projection principle and, 56; pure form of, 11–19, 23, 28; pure representation and, 9–22; representational capacity of, 55–63; rule for connecting, 16; sensation and, 22; sensible, 195; synthesis and, 6, 212; synthetic activity and, 6, 149–150; synthetic unity of, 182; undetermined objects of empirical, 166; unified (see unified intuitions); unity of (see unity of intuitions) intuitions in general, 7, 55, 150–157, 197–200. see also unified intuition; sensible, 198–204 intuitive representation, 13 isomorphism argument, 54 the "I think," 7, 25, 136, 157, 176–179, 180n7, 190–193, 204–205, 205–206n45 judgments, 151–157; categories and, 111–112; copula, 177; implicit, 180; intuition and, 6; subject-predicate, 147, 177; Table of Judgments, 109, 111–112, 185; unity of, 7 judgments of experience, 6–7 judgments of perception, 6, 157–169; CPR and, 159–160; empirical concepts and, 161–169; empirical schemata and, 161–169; B. Longuenesse on, 159–160; Prolegomena and, 157–159; propositional form of, 182–187 Kästner, A. G., 84–86 Kitcher-Vinci account. see KV (Kitcher-Vinci) account KV (Kitcher-Vinci) account, 5, 69–77, 73. see also geometrical method; pure mathematics and, 90 laws. see also rules: governing the structure of space, 68; lawlikeness of geometrical propositions, 69; Nomic Prescriptivism and, 85; of reproduction, 118–119

244

subject Index

Leibniz, G. W., 1–4, 2n2, 6–7, 153, 161 linguistic conception, 44 local space, 14, 14–15; intuition and, 14–16; pure intuition and, 14; unity and, 15 Locke, J., 134, 161–166 passim logic, psychology and, 110 logically unified intuitions, 6, 55, 165; unity of space and time and, 221–228 logical unification, 170 magnitude, 166–167 map analogy, 15–16, 55–63; application of, to intentionality, 60–63; coordination component of, 58–61, 61n21; formal intuition and, 61; sensation and, 61; transformation component of, 57–59; transparent point of, 59–61, 59n20, 61n21; veridicality feature of, 58–59 mathematical method, 65. see also geometrical method; in CPR, 66–77; M. Friedman on, 80–81n20, 80–83; W. Waxman on, 83–88 mathematics, 83 matter: of appearance, 11; concept and, 40 mechanisms, forms as, 11–12 Metaphysical and Transcendental Expositions (Kant), 10 Metaphysical Deduction, 151 Metaphysical Expositions, 10; First, 19, 20–21n27, 53, 55; First Reading of the, 36–38; Second Reading of (see Second Reading of the non-geometrical Metaphysical Expositions); Transcendental Idealism and, 23–45 metrically amorphous images, 167, 167n59 metrically amorphous objects, 167 metrically amorphous space, 166 metrically determinate object, 208 mind-dependent object, 6, 30–35, 31n16–35n19; of representation, 49 modern physics, non-Euclidean geometry and, 96–99

nature, creation of, 129 necessity: counterfactual, 69–77; of geometry, 69–77; to geometry of sense impression, 34–35n19 "A New Reading of Kant's Subjective Deduction" (Bauer), 114n18 Newtonian absolute space, 24 Nomic Prescriptivism, 4; appearances and, 85, 99, 137; argument from topology for, 221n61; laws and, 85; Transcendental Deduction and, 148, 207; Transcendental Idealism and, 99, 107, 133, 207; transcendental proof of, 220–221 non-Euclidean geometry, 97; modern physics and, 96–99 Nongeometrical Expositions, 36–39 nonsensory intuition, 13

object geometry, 74–75 objective deduction, 8, 214–215; of unity of space, 218–220 The Objective Deduction of the Unity of Space in the B Edition, 218–220 objective predication, 146 objective reality of pure geometry, proof of, 94 objective structure, 23–24; projection and, 30 objective unity of apperception, 186 objective unity of consciousness, 183 objective validity, 82; empirically, 116; intentionally, 116; Second Geometrical Argument for Transcendental Idealism and, 103; subjective conditions and, 3–4, 6, 115 objectivity, 116 objects: actual, 226; appearances and, 142; determined objects of empirical intuition, 165–166; in domain of imagination, 29; empirical (see empirical objects); form of, 93; of idea, 49; idea of, 139; intentional, 48; metric of, 167, 208; mind-dependent, 6, 30–35, 31n16– 35n19; perception of, 53; a priori intuition of, 28–36; pure (see pure objects); real, 216; schematic (see schematic objects); space represented as, 13; spatial (see spatial objects); transcendental, 142; undetermined objects of empirical intuition, 166 optimization theory, 1–3 ordinary empirical appearances, 145–146 ordinary empirical objects, appearances as, 146–147

outer intuition, form of, 9 perception, 158; judgments of (see judgments of perception); of spatial objects, 53; topologically connected, 208 phenomenal geometry, 96–97 phenomenalism, 121–122 physics, non-Euclidean geometry and, 96–99 power of apperception, 177; analytical, 180, 180–187

power of awareness, 177 predication, objective, 146 productive imagination, 125 projectionism, 52–54, 225; and intuitional representations, 5, 30 projection principle, 53–54; intuition and, 56; spatial objects and, 53–54, 54n12–14 proof of objective reality of pure geometry, 94 propositions: analytic, 190–194; judgments of perception and, 182–187; transcendental significance of, 194 psychology: empirical, 224; logic and, 110; transcendental, 224 pure application of Euclidean geometry, 75, 75n12 pure domain, form of objects in, 93



Subjec t Ind e x

pure form of intuition, 28; formal intuition vs., 11–19, 23 pure geometry, 90; imagination and, 64; proof of objective reality of, 94 pure intuition, 99; formal intuition and, 13; global space and, 14; local space and, 14; of space, 35n19 pure mathematics, 27–29, 90 pure objects: Euclidean geometry and, 65; representation of, 5 pure representation, a priori form vs., 9–22 pure sensible concept, 43 pure structure, 10 pure thinking, 198 realism, transcendental, 147 reality: appearances and, 215–218; illusion and, 216–218

real objects, 216–218 referral of sensation, 51, 51n9–52n10 Refutation of Idealism, 122, 137–138, 229–333 representational capacity of intuition, 55–63 representations, 157, 212–213; dreams and, 49; empirical, 29–30; empirical concept and, 38–39; form of, 10; forms as, 11, 15; intuitive, 5, 13; mind-dependent object of, 49; a priori form of (see a priori form of representation); projectionism and, 30; of pure objects, 5, 9–22; of space, 36–39; theory of, 50–52; truth and, 49 reproduction, 125–128; law of, 118–119 reproductive imagination, 125–128 rules. see also laws; schemata/ schematism: appearances and, 140; causal, 124; for connecting intuitions, 16; empirical, 124–125, 164; guidance from, 122; schemata as, 42; of unity, 111–112; unity of, 121 schemata/schematism, 42. see also rules; categories and, 167n59, 209, 211; empirical, 161–169; geometrical-formal, 167 schematic objects, 168; dreams and, 173 Science and Metaphysics (Sellars), 156n43 Second Geometrical Argument for Transcendental Idealism, 6, 30–35, 31n16–35n19, 65, 85, 95–96; objectivity and, 103; subjectivity and, 103; Transcendental Deduction and, 65 Second Reading of the non-geometrical Metaphysical Expositions, 38–39, 39; defense of, 40–45 self, unity of, 7, 177 self-consciousness, unity of, 138, 177 sensation, 183–184; from external sources, 83; form of, 9, 11; intentionality and, 55; intuition and, 22; map analogy and, 61; matter of appearance and, 11; referral of, 51, 51n9– 52n10; spatial order of, 11

245

sensationism, 19 sense, 172 sense impressions, 33, 163; necessity to geometry of, 34–35n19 sensibility, 154; form of, 21, 29–30; pure form of, 12 sensible intuitions, 195 sensible intuitions in general, 198–204 sensory illusions. see illusions sensory unification, 163 shape of space, 42 space. see also global space; local space; three dimensionality: absolute, 24; abstraction and, 39; cognition of, 18; concept of (see concept of space); empirical concept and, 38–39; laws governing structure of, 68; local, 14–15; metric of, 166; pure intuition of, 35n19; representations of, 36–39; shape of, 42; structure of, 68; subjective conditions and, 75–76, 76n13; universals and, 41 space geometry, 75 space represented as object, 13 spatial form, 55–63 spatial objects, 21; perception of, 53; projection principle and, 53–54, 54n12–14 spatial order of sensation, 11 spatiotemporal container, 11–12. see also Container View subjective conditions. see also intellectual conditions: causality and, 109; objective validity and, 3–4, 6, 115; Second Geometrical Argument for Transcendental Idealism and, 103; space and, 75–76, 76n13; of thought, 108–116, 115, 132–133 subjective deduction, 8, 214–215 Subjective Phase of the Deduction in the B Edition, 214–220 subjective structure, 23–24; projection and, 30 subjective unity of consciousness, 172, 183, 188–190

subjective validity, 196 subject-predicate judgments, 147, 177 Syllogism A, 204–205 Syllogism B, 205–206 Syllogism C, 206 synthesis, 151–157; of apprehension, 207–208; category-governed, 6, 208; composition, 151, 155; connection, 150, 155; external application of, 174; figurative, 154; formative, 82, 165; intellectual, 154; internal application of, 174; intuition and, 6, 212; transcendental, 223–224 synthetic activity, 123, 206; intuition and, 6, 149–150; unity and, 13 synthetic a priori cognition (mathematics), 66–77 synthetic-conception ground, 43 synthetic definitions, 42–43. see also definitions; empirical concept and, 43; geometric propositions and, 68

246

subject Index

synthetic unity of apperception, 182, 188 synthetic unity of consciousness, 44 synthetic unity of intuitions, 182 thought: apperception and, 204–205; categories and, 204–205; causality and, 109; form of, 201; the "I think," 7, 25, 136, 157, 176–179, 180n7, 190–193, 204–205, 205–206n45; pure, 198; subjective conditions of, 6, 108–116, 115, 132–133

three dimensionality: concept of, 19–21; pure intuition and, 88 time, concept of, 88–96 passim. see also unity of space (and time) topological form-space, 85 topologically connected perception, 208 topological unity of space, 209 Transcendental Aesthetic, 4, 11, 12, 144 transcendental affinity, 129 Transcendental Deduction, 5, 8, 101–133, 177, 179. see also A edition Deduction; B edition Deduction; categories; Affinity Argument and, 114, 116–131, 119–120; K. Ameriks on, 102–103; appearances and, 135–150; Nomic Prescriptivism and, 148, 207; principles of, 101–108; Second Geometrical Argument and, 65

Transcendental Exposition of the Concept of Space, 5, 22, 88–96, 103, 214 Transcendental Idealism, 4, 23–45; J. Buroker on, 71, 99–100; D. Dryer on, 79–80; First Geometrical Argument for (see First Geometrical Argument for Transcendental Idealism); geometrical argument and, 64–100; Nomic Prescriptivism and, 99, 107, 133, 207; in Prolegomena, 27–36; Second Geometrical Argument for (see Second Geometrical Argument for Transcendental Idealism); J. Van Cleve on, 77–79 Transcendental Logic, 149 transcendental object, 142 transcendental philosophy, 21 The Transcendental Proof of Nomic Prescriptivism in the B edition Deduction, 220–221

transcendental psychology, 224 transcendental realism, 147 transcendental synthesis, 223–224 transcendental unity of apperception, 172, 188–190, 194 transformation component of map analogy, 57–59

transparent point of map analogy, 59–61, 59n20, 61n21 Triviality Problem, 179, 200, 200–201 truth: dreams vs., 49; representation and, 49 "the understanding," 138, 180 undetermined objects of empirical intuition, 166 unified intuitions, 150. see also intuitions in general; aesthetically, 169–172; empirical objects and, 226–228; logically, 165 unity of apperception, 7, 120, 120n24, 138, 176, 181; analytic, 182; objective, 186; synthetic, 182, 188; transcendental, 172, 188–190, 194 unity of categories, 7–8 unity of consciousness, 143, 188; analytical, 44; objective, 183; subjective, 172, 183, 188–190; synthetic, 44 unity of intuitions, 55, 85–86, 206, 207; synthetic, 182

unity of judgments, 7 unity of rule, 121 unity of self, 7, 177 unity of self-consciousness, 138, 177 unity of space (and time), 8, 132–133, 175, 208; empirical intuition and, 221–228; as intellectual condition, 214–220; logically unified intuition and, 221–228; objective deduction of, 218–220; topological, 209 unity/unification, 7; aesthetic, 151, 170; local space and, 15; logical, 170; revelation of, 7; rules of, 111–112; sensory, 163; synthetic activity and, 13 universals, space and, 41 validity. see objective validity; subjective validity veridicality feature, of map analogy, 58–59 verification, 216 virtual transformation, 59

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LO CORUM INDE X

“Concerning the Ultimate Ground of the Differentiation of Directions in Space” Ak edition volume 2 283…70 WM edition 361–372…69n7 371…70 Critique of Judgment Ak edition volume 5 251…14, 167n57 254…15 341–343…167n57 Plu. edition 107…14, 167n57 110–111…15 214–216…167n57 Critique of Pure Reason A edition (Ak edition volume 4) xvi-xvii…8, 105, 113, 214 xvii…114 xvii-xviii…129 1…73 1–4…68 19…14, 47, 77 20…11, 13, 16, 140, 145, 225 22…25, 50, 54n12, 132n31, 227 23…20n27, 37 25…38, 132n31, 155 27…50 29…146 41…35n19 46–49…77 52…109 55…198 57…197, 198 70…109n11, 111, 149, 185n17 77…20, 148n28, 151 77–78…156, 181 78…111, 112, 150n34, 181n8

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79…123, 136, 148, 149, 177, 181, 197 80…209n47 84…104, 104n8 85…104, 130 87…67n2, 91, 103, 228n76 87–88…104 88…105 89…115, 229n76 89–90…3, 101, 104, 109, 135 90…104, 115, 121 90–91…217n57 92…115 98ff…132 99…159 100–102…118 104…121 105…121, 126 108–109…142, 143 109…142 111–115…114, 119 112…120n24, 215 112–114…118 114…107, 114 119–120…169 120–126…114 121…126 121–128…118 123…125 125…107, 130 127…114 140…42, 82 140–141…162, 167 141…81, 164n54 142…167, 209n47, 211 144…120 162…155 165…33 176…211, 219 178–180…210

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248

locorum Index

Critique of Pure Reason (Cont.) 181…211 191…136, 140 197…121, 141 221–222…86 223…163 224…81, 165 225…219, 223 239…81, 83 240…83 247…140n15 253…140n15, 198 263…153 319–320…198 320…22, 56n18, 156 342–367…25n5 367ff…91n27 373…12n8, 13 429…14n11 429…n18 493…218 713…28, 29, 33, 33n18, 35n19, 73, 77, 80, 83, 93, 162, 165 713–714…66 714…167 741…71n9 766–767…117 767…124, 133 B edition (Ak edition volume 3) xi-xii…71n9 xvi…105 xviff…105 xvi-xvii…4 xvi-xviii…35 xvii…51n9, 106 xvii-xix…4 3–4…72 4…73 4–5…68 16…167 19…66 32…194 33…13, 47, 51n9, 77 34…11, 13, 16, 140, 145, 225 35…25 36…132n31 37…50, 54n12, 227 38…20n27, 37, 50 39…38, 132n31, 155 40…88, 94–95 41–42…24 45…146 58…35n19 64–66…77 68…177n2 70…144 76…109

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79…111 80…198 81…197, 198 95…149, 185n17 96…109n11 102…151, 181 103…148n28, 156, 181n8 103–104…20 104…111, 150n34 104–105…123, 148, 149 105…181, 197 106…209n47 108…112 116…104 116–117…104n8 117…104, 130 119…91, 103 119–121…104 120…67n2, 228n76 120–121…105 121…115 122…3, 101, 104, 109, 115, 135, 229n76 122–123…101, 121, 217n57 125…115 129–130…152 129–131…86 130…136 130ff…15 131…157, 181, 204 131–132…25n4, 178, 179, 193 132…172n63, 176, 189n23, 190, 204 133…112n15, 193 133–134…41, 44, 182, 187 135…179, 190, 191 135–136…193 136…43, 44, 202 137…122, 143, 180, 188 138…67n1, 191 139…177, 189, 193 139–140…172n62 141…136, 186 142…143, 186, 202 143…7, 148, 187, 200 144…156 144–145…197, 201 145…179 146–147…199n36 147…163, 198n35, 218 147–148…168 148…201, 218 148–149…202 150…201 151…154, 154n41 152…126 154…20, 21n27 157…60 159…228

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L ocor um Ind e x 159–160…107 159–161…207 159–162…132 160…13, 16–17, 52, 62, 153, 154, 210 160–161…13 160–161n…13 160n…209, 212 160n. a…155 161…154, 199, 200, 210, 212 162…208, 209 163…210 166…229 166–167…107 180…42, 81, 82, 162, 167 180–181…164n54 182…167, 209n47 182ff…211 183…120 201…155, 170 202–203…151, 155 208…33 218…211, 219 221–223…210 224…211 233…35n19, 137n304 236…136 242…121, 141 268…86 271…81, 163, 165 272…219, 223 274–279…122, 216n55 275–278…91n27 276…21n27 276–277…137 277–278…138 298–299…81, 83 299…83 304…140n15 308…198 309…140n15 319…153 336…140 367–377…22 376…56n18 376–377…198 377…156 406…176 406–423…25n5 457…14n11 457n…18 521…218 741…29, 33n18, 71n9, 77, 80, 83, 162, 165 741–742…66, 73 742…33, 167 742ff…93 794–795…117 795…124, 133

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249

GW edition xvi-xvii…123 22…229n76 102…8 102–103…129 103…105, 113, 114, 123, 214 110…4, 51n9, 106 110–111…4, 35 110–112…105 146…66 155…51n9, 225 155–156…11, 16 157…37, 50, 51n9, 54n12, 227 159…38 172…47 175…51n9 175–176…155 176…88 184…35n19 189…177n2 190…144 194…109 196…197, 198 206…109n11, 111, 149 210…20, 148n28 210n. a…151 211…111, 112, 123, 156, 181, 181n8 211–212…197 220…104, 104n8, 130 221…67n2, 91, 103, 228n76 221–222…104, 105 222…3, 101, 104, 109, 115, 135 222–223…101, 121, 217n57 224…115 228…132 229–239…118 231…121 231–232…121, 126 233…142 234–236…114, 119 235…120n24, 215 235–236…118 236…107 238–239…169 238–241…114 239…126 239–242…118 240…125 241…107, 130 245…152 245–246…86 246…157, 181, 190, 204 246–247…176, 178, 179 246ff…15 247…25n4, 41, 44, 172n63, 182, 187, 189n23, 194, 204 248…179, 190, 191, 193

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250

locorum Index

Critique of Pure Reason (Cont.) 248–249…43 249…122, 143, 180, 188 249–250…191 250…172n62, 177, 189 251…186 252…7, 143, 148, 187, 200, 202 253…156, 179, 197, 201 254…198n35, 199n36, 218 255…163, 168, 201, 202, 218 256…154, 201 256–257…154n41 257…126 258…20, 21n27 259…60 261…13, 107, 154, 212, 228 261–262…132, 207 261n…13 262…199, 200, 208, 212 262–263…210 264…107, 229 273…42, 81, 82, 162, 164n54, 167 274…167 274ff…211 275…120 285–286…155 286…151, 155 286–287…170 287…155 290…33 295…211, 219 298…211 304…35n19, 137n304 309…121 323…86 324–325…81, 163 325…219, 223 326–328…216n55 326–329…122 327…21n27 327–328…138 327–328nn. 1–2…138 327–329…91n27 328…137 340–341…81, 83 341…83 349…198 368…153 398…56n18 398–399…22, 198 411–425…25n5 425ff…91n27 428…12n8, 13 445…176 445–453…25n5 471–473…14n11 512…218

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630…29, 66, 80, 162, 165, 167 657…124 727n. 41…149n30 Kemp Smith edition 83…125n27 Entdeckung Ak edition 8…20n26 221–222…20n26 Lectures on Logic Ak edition volume…9 11…110 14…110 16…110 18…110 20…109n12 32…161 34…50, 122 64–65…199 70–72…67n2 91–96…40, 164n53 95…41 114…159n48, 184, 192 142…42n27, 43 564…40 Young edition 527…110 529…110 531…110 532–533…111 535…50, 109n12 543–544…161 545…122 564…40 569–570…199 574–575…67n2 589–593…40, 164n53 592…41 608…159n48 608–609…184, 192 632–633…42n27 633…43 Lectures on Metaphysics Ak edition volume…28 235…51n10 Prolegomena to Any Future Metaphysics Ak edition volume…4 276…50 280…66 281…28 281–283…28 281n…66 282…32, 33 283–284…89

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L ocor um Ind e x 284–285…72, 89 287…29, 90, 91 288…95 288–291…215n54 290…49, 173 298…157, 177n5 299…183 300…158, 165, 182n10 300–301…158n47 301…158, 184 303…112, 209n47 321–322…76, 84 Hat. edition 27…49–50 32…66 32–34…28

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251

33…28, 66 34…32, 33 35…89 36…72, 89 38…90 39…29, 91, 95 40–41…215n54 42…49, 173 50…157, 177n5 52…158, 165, 182n10, 183

52–53…158n47 53…158 54n…184 55…112 73…76, 84

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