A COMPANION TO KANT'S CRITIQUE OF PURE REASON
Transcendental Aesthetic and Analytic Karl Aschenbrenner university of Ca...
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A COMPANION TO KANT'S CRITIQUE OF PURE REASON
Transcendental Aesthetic and Analytic Karl Aschenbrenner university of California, Berkeley
UNIVERSITY PRESS OF AMERICA
LANHAM • NEW YORK • LONDOM
Copyright © 1983 by University Press of America,"" Inc. 4720 Boston Way Lanham, MD 20706 3 Henrietta Street London WC2E 8LU England All rights reserved Printed in the United States of America ISBN (Perfect): 0-8191-3230-6 ISBN (Cloth): 0-8191-3229-2
What are meanings? or What is it for an expression to have a certain sense? Until fairly recently philosophers have not stepped back from their easels to consider what philosophy is, or how doing philosophy differs from doing science, or doing theology, or doing mathematics. Kant was the first modern thinker to see or try to answer this question--and a very good beginning of an answer he gave. Gilbert Ryle "The Theory of Meaning"
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Acknowledgements I acknowledge with thanks permission that has been granted to reprint excerpts from two papers published for the Mainz Kant Kongress by, respectively, Walter de Gruyter, Berlin, New York, 1974 ("The Derivation and Completeness of the Analogies of Experience"); and Bouvier Verlag, Herbert Grundmann, Bonn, 1981 ("Kant's Transcendental Deduction in A: A Newer Perspective") .
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Table of Contents Page
Introduction I.
The Difference Between Pure and Empirical Knowledge.
We are in Possession of Certain Forms of A Priori Knowledge and Even Common Understanding is Never Without Them. III. Philosophy Stands in Need of a Science Which Can Determine the Possibility, the Principles and the Extent of All Our A Priori Knowledge. IV. The Distinction Between Analytic and Synthetic Judgments. V. All Theoretical Sciences of Reason Contain Synthetic A Priori Judgment as Principles. VI. The General Task Which Confronts Pure Reason. VII. The Idea of and the Divisions Under a Special Science Bearing the Name of a Critique of Pure Reason.
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II.
Transcendental Doctrine of Elements First Part:
The Transcendental Aesthetic §1
Section I. Space Metaphysical Exposition of the Concept of Space §2 Transcendental Exposition of the Concept of Space §3 Conclusions from the Above Concepts Section II. Time Metaphysical Exposition of the Concept of Time §4 Transcendental Exposition of the Concept of Time §5
CKC Conclusions from These Concepts §6 Elucidation §7 General Observations on the Transcendental Aesthetic §8 Conclusion of the Transcendental Aesthetic Second Part:
The Transcendental Logic
Idea of a Transcendental Logic I. Logic in General II. Concerning Transcendental Logic III. The Division of General Logic into Analytic and Dialectic IV. The Division of Transcendental Logic into Transcendental Analytic and Dialectic First Division: Transcendental Analytic
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Introduction:
Book I:
Analytic of Concepts
Chapter I: The Clue to the Discovery of all Pure Concepts of the Understanding Section 1 : The Logical Employment of the Understanding Section 2 : The Logical Function of the Understanding in Judgments §9 Section 3 : The Pure Concepts of the Understanding or Categories §10-12 Chapter II: The Deduction of the Pure Concepts of the Understanding Section 1 : The Principles of Any Transcendental Deduction §13 Transition to the Transcendental Deduction of the Categories § 14
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The Relation of the Understanding to Objects in General, and the Possibility of Knowing These A Priori 158
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(Transcendental Deduction: Edition A) Section 2: On the A Priori Grounds of the Possibility of Experience Preliminary Reminder 1: Synthesis of Apprehension in Intuition 2: Synthesis of Reproduction in Imagination 3: Synthesis of Recognition in the Concept 4. Preliminary Explanation of the Possibility of the Categories as A Priori Knowledge Section 3:
Summary Representation of the Correctness of this Deduction of the Pure Concepts of the Understanding, and of its Being the Only Possible Deduction (Transcendental Deduction: Edition B) Section 2:
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Transcendental Deduction of the Pure Concepts of the Understanding On the Possibility of Combining in General §15
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Of the Original Synthetic Unity of Apperception §16
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All Sensate Intuitions are Subject to the Categories as Conditions Under Which Alone They in Their Multiplicity Can Enter into a Single Consciousness §20
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Supplementary Remark §21
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The Only Use of the Category Looking Toward Knowledge is its Application to Objects of Experience §22 -- §23
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The Application of the Categories to Objects of Senses in General §24
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The Fundamental Principles of the Synthetic Unity of Apperception is the Supreme Principle of All Employment of the Understanding §17 What Objective Unity of SelfConsciousness Is §18 The Logical Form of All Judgments Consists in the Objective Unity of the Apperception of the Concepts Contained Therein §19
Page -- § 25 The Transcendental Deduction of the Universally Possible Use in Experience of Pure Concepts of Understanding §26 Outcome of this Deduction of the Concepts of Understanding §27 Brief Formulation of This Deduction Book II:
Analytic of Principles
Transcendental Judgment in General Chapter I: The Schematism of the Pure Concepts of the Understanding Chapter II: System of All Principles of Understanding Section 1: The Highest Principle of all Analytic Judgments Section 2: The Highest Principle of all Synthetic Judgments Section 3: Systematic Representation of all Synthetic Principles of Pure Understanding
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Introduction:
1. 2. 3.
Axioms of Intuition Anticipations of Perception Analogies of Experience
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First Analogy: Substance Second Analogy: Causality Third Analogy: Community Postulates of Empirical Thought Possibility Actuality Refutation of Idealism Necessity
General Note on the System of Principles Chapter III. On the Ground of the Distinction of the Objects in General into Phenomena and Noumena Appendix:
The Amphiboly of the Concepts of Reflection
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Preface
The description 'Comment' is probably more appropriate to this effort than 'Commentary'. For this one may turn to the enormous literature on Kant. I have sought rather to emphasize the importance of Kant to us and his relevance to the place that philosophy has now reached. To ask about his value for us means to take him in a manner he himself could not have anticipated and thus in some degree to distort him. But Kant's historical place is far too secure for it to be injured by our effort to see what use he can be to us. I am inclined to think this is far greater than we may have supposed, even considering the recent revival of interest in Kant. Comment with this kind of emphasis may diverge from what may be deemed historically accurate. Resolute Kantians may be disappointed or offended. But Kant is truly only now coming into his own. It is a serious error to read Kant only as a precursor of the German idealist school. I believe he might have thought some of its famous figures often slightly mad. His problems are those of Leibniz and Hume, yes, and of Russell and Wittgenstein, more than those of Hegel and Fichte. Twentieth century philosophy really proceeds on from Kant without a break. It is a pity one must make allowance for Kant's passing before the great achievements of chemistry, physics, and mathematics in the nineteenth century, of logic and methodology in the twentieth were known to him, every one of which he would have followed with a voracious intellectual appetite. With Kant the modern intellect cuts every last link with the Middle Ages. That past had finally passed, and not without his help. He faces resolutely a limitless universe in space and time and possibility: it is what we make of it, intellectually and morally, no more, no less. Like Russell, Kant is a man for our season, a clear-headed realist, above all a philosopher of common sense, despite the apparatus of his architectonic, which must not distract us. The twentieth century philosophers are like Kant too in that they turned their backs on the Romantic age in all its forms: Kant never had to undergo the Romantic agony.
Since one must learn to divide the Critique in order to command it, we must ask how this is to be done. If we consider Kant to have undertaken some three tasks, analytical, dialectical and methodological, the Critique may be separated into three rather unequal parts. Analytical. First, the Prefaces may be detached in order to be read with the dialectic. This leaves us with the first part of the Critique running from the Introduction nearly to the end of the Analytic of Principles.The interest here is analytical, concerned with the nature, foundations and limits of empirical knowledge. Dialectical. Second, the Prefaces, having been written when Kant had the whole Critique before him, turn to its larger and final questions. Kant treated with a compassion unknown to Hume those desperate hopes of mankind and pretensions to transcendence that have been encoded in religion and moral systems. No one has more earnestly sought to do justice to them "within the bounds of reason alone" than Kant. The material in the Critique that bears the weight of this great concern begins with the two prefaces, resumes at the chapter on the distinction between phenomena and noumena and then occupies most of the Transcendental Dialectic. Methodological. The sequel to the foregoing, the Transcendental Methodology, concerns the manner in which the command of the system of knowledge may become operative. Kant retains this didactic feature of the baroque systems of thought of Wolff, Baumgarten, and others. The preceptors of the Enlightenment were all engagees and held it their duty to show how one could use what one had just learned. The methodological material in the Critique, however, is brief and uneven: what was needed was not more and more Erkenntnistheorie but a vast expansion of empirical knowledge, the very result that the nineteenth century produced. The present study provides comment on Kant's contribution in the Critique to the first of these great topics, the analytical. Every sectional and subsectional division of the Critique is carefully observed. I have hoped not merely to rehash the original, but rather to discuss it in such a way that it may be read with rather more ready profit than its difficult idiom usually affords the reader. But as for that,
there is really no such thing as reading Kant, only re-reading. This study of Kant's Critique is offered as a tribute to the late Professor Jacob Loewenberg who taught the Kant course at Berkeley for more than twenty-five years and was my teacher and an inspiration to me for years afterward. His lectures were models of organization and argument and made a pleasure of the hard work and careful thought required by him. I could not have believed that I was destined to be his chosen successor in teaching the Critique and other works of Kant. This Companion was prepared over some thirty years while teaching at Berkeley and is equally a tribute to Kant, Hume and the other masters of Eighteenth Century thought.
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Companion to Kant's Critique of Pure Reason: Transcendental Aesthetic and Analytic
INTRODUCTION The Introduction is undoubtedly the most lucid portion in all of the Critique and stands in little need of further exposition. This is not to say that it does not stimulate questions. One could wish that Kant had dwelt at even greater length and with the same clarity on its well-known topics : the terms 'analytic' and 'synthetic' in application to propositions, the nature of a priori knowledge and of synthetic a priori propositions, the need to determine the limits which knowledge obtained through pure reason may reach — and may seek to exceed. With great care he works up to the question which he thinks should be foremost in our thought in the investigation of pure reason: How are synthetic judgments possible a priori? The subject matter of the Critique from the Introduction through the Analytic of Principles covers Kant's answer to this question, and more besides. Thereafter, in the Dialectic, he turns to the pathology of pure reason: the penalties, and even in a way the rewards, that await pure reason in following its inherent bent to ask insoluble questions and demand answers to them. Its reach always exceeds its grasp and, Kant concludes with Browning, that's what a Heaven's for. The Introduction is considerably recast in B. There are several substitutions and additions in the earlier sections. The thought remains essentially the same, but B adds some turns of phrase that are memorably Kantian, for example, "All our knowledge begins with experience ... but it does not all arise out of experience." If the Critique can be reduced to an apothegm, it is this. I.
Of the Difference Between Pure and Empirical Knowledge
The difference which Kant describes is of course not a creation of his own since it goes back to ancient philosophy. Its mention prominently at the beginning of the Critierue does, however, underline a difference between himself and Locke and Hume, for example, especially the latter. Kant is taking pains to affirm the difference between two sources of our knowledge, whereas Locke sought from the outset to show that, although we might
be tempted to think otherwise, all our knowledge is derived from experience. Locke adds immediately that under experience there are two sources of our ideas: sensation and reflection. But the identification of the second source here does not at all serve to make the point Kant is making, for it is described as internal sense. Kant's reply to this would be that sense, whether internal or external (and a distinction bearing at least this name is also made by Kant) is but one source of our knowledge, one "place" where it begins, and that a second kind of knowledge and a second source must also be allowed for, that is, speaking generally, a priori knowledge and an appropriate source of this which the Critique proposes to lay bare. The response to Hume is similar. Hume regards imressions, of sensation and of reflection, as the ultimate source of all ideas in an even more radical fashion than Locke. His program is one either of denying that ideas have any validity if they cannot be traced to this source, or of saying that although we may often think we have ideas from some other source the fact is we do not have them at all in that case, and we are deluding ourselves. What Kant is saying on the other hand is that some ideas can be traced to intuitions, or as Hume would say, impressions, and some must be traced to an altogether different source. Kant's standpoint is one that in effect agrees with rationalism, however much of his explanation diverges from that of the supporters of innate ideas. He insists that a priori ideas are not innate at B 167 (in the Transcendental Deduction of the Categories). He has a different explanation of their inherence in the human mind. One should notice what powers Kant here attributes to objects, Gegenstande: they stir our sense into activity and produce, in some sense, .representations Vorstellungen; they set the understanding into motion to compare, connect and distinguish representations; and thus work them up into "that knowledge of objects which we call experience." At this point he has not yet made clear to us in what sense 'objects' is to be understood. Things themselves? Appearances? It is most likely he means the first of these; the second are in part a result of the activity of the first. The first two paragraphs are united by the contrast of "beginning with" and "arising out of experience."
The latter has of course important implications for what is to be said later in the Critique• We should not, however, read it altogether in the light of what follows. All that Kant is saying here is that we must be prepared to find experience to be a much more complex affair than the empiricists supposed. Of course all knowledge begins with experience, but it is a thing of such complexity that there may very well be elements in it that do not arise from the impressions of sense and that we may not be able at a glance, and without skill and practice in analysis, to trace to their origins. This is, in fact, the very contingency we had better prepare ourselves for. If there is an ingredient in our empirical knowledge that does not owe its presence solely to impressions of the senses we may call it a priori. It is not yet taken as established that there is such a component: the proof of this is to come in the very next section, as we see from its title, "We are in possession of certain kinds of a priori knowledge, and even common understanding is never without them." The remainder of the section is meant to make the idea 'a priori1 clear, distinguishing it from mere predictions about phenomenal trains of events, such as what is said to be bound to happen if one undermines the foundations of a house. The a priori knowledge which the Critique is investigating is to be understood as knowledge in which there is no appeal to experience but is such as to apply to the world of experience, and indeed to make it possible. These are uniquely Kantian theses that we do well to have in mind from the very outset. It should be noted that the sections marked I and II in B were added in that edition replacing the two paragraphs with which section I of A began. As noted, B adds the phrases about the Anfang and the Entsprung, that is, beginning with and arising out of experience, and it contributes a welcome, but still insufficient exposition of the notion of necessity as applied particularly to propositions such as causal laws. II. We are in possession of certain kinds of a priori knowledge and even common understanding is never without them.
We learn presently that the task of a critique of pure reason is to show how synthetic judgments are possible a priori. If we overhear someone asking how it is possible for someone to steal the gold in Fort Knox, having just entered the conversation at that point, our first or prior question is likely to be: What? Has someone stolen the gold? So here before we ask how it is possible for there to be so and so we need to know that there are examples of so and so. What then is pure or a priori knowledge and how is it recognized or1acquired? It is not to be acquired through experience, which can at most tell us what is the case as a matter of fact but not that it must be as it is. As we have already noted, we also use the term 'a priori1 in a relative sense of the future when we say that if we undermine a house we know a priori , that is in advance, that it will fall. But this rests merely on previously confirmed empirical knowledge. What then characterizes a judgment that is absolutely a priori? The first mark of such a judgment is that it is necessary. Kant adds that if the judgment is not only necessary but itself deducible from a necessary judgment then it is valid absolutely a priori. But it is not clear what this can add to its simply being a priori. The second mark of an a priori judgment is that it is universal in its range. Again, we must look beyond mere experience. In the sense of an inductive accumulation of positive instances, experience can never lend the character of strict universality to any proposition, for this is merely to know that there have been no exceptions hitherto. A proposition that is strictly universal, says Kant, is one to which no exceptions will be permitted (dass gar keine Ausnahme als möglich verstattet wird!. This clause should be carefully stored in memory, since it is relevant to Kant's view of the peculiar necessity attaching to synthetic a priori principles of science, considered in the Analytic of Principles, but of course also much in view before then. We shall recur to it. Examples of these judgments are now brought forward. The propositions of mathematics and the causal law are mentioned prominentlyNecessity and unlimited universality have been treated as practically synonymous in this section though Kant has not given a real explanation of necessity as yet. Indeed one of the major shortcomings of the Critique is Kant's failure to give an adequate
explanation of what he means by the necessity of the principles which it is the main purpose of the Critique to enunciate and prove. So far we have been told that they are of unrestricted universality and that we will not permit exceptions to them. He now adds a kind of third property that pertains to them, that they are jjrii spensable(unentbehrlich) for the possibility of experience and therefore, he says (or it might be better to say "in that sense" instead of "therefore") a priori. The question he has not yet addressed himself to is how they differ from analytic a priori propositions. Once this has been done we shall have to return to the question as to what he means by saying that certain _^nnnepts are a priori. At the end of the present section he devotes a paragraph to exemplifying such concepts. It is no accident that he here uses almost the very same notion and procedure that Descartes resorted to with the ball of wax and also arrives at the same result. If we think away the color, weight, impenetrability and other properties of a body we inevitably arrive at an irreducible minimum, namely the space occupied by the body. And, says Kant, the same process should lead us to the notion that there is a support of all the qualities of a body in a substratum or substance. This is also characteristic of Locke's approach to the idea of substance. Many more such echoes from the past are to be discerned in the Critique, but as we shall see, Kant renovates radically the notions he borrows. The two sections just finished thus first make the distinction between pure and empirical knowledge and then assert that pure or a priori knowledge is not a mere abstract possibility but that we do in fact possess such knowledge. III. Philosophy stands in need of a science which can determine the possibility, the principles and the extent of all our a priori knowledge. The next question then is where these a priori propositions are to be found. Kant points out that certain metaphysical propositions are particularly to be numbered among them and that they go beyond everything empirical. Up to now Kant has taken examples of "transempirical" propositions only from mathematics and the causal law. In a paragraph added to the text in the second edition (paragraph 3 in III) Kant
particularly identifies the subject matter of metaphysics as the ideas of God, freedom and immortality. He has not yet pointed out that metaphysics has several senses for him. The sense in which God, freedom and immortality are the subject matter of metaphysics is quite different from that in which causality is. Ideas such as the former in his view inevitably lead to illusion and confusion though they have some redeeming features in the end; causality on the other hand is an absolutely indispensable notion for both science and common experience. Nothing in Kant's critical philosophy is more important than the line he draws between these two different sets of notions. Both of them readily lead us beyond experience, but the needs they serve are utterly different. Our success in mathematics in seeming to leave experience behind us emboldens us, says Kant, to undertake even bolder transempirical researches. We tend to overlook the fact that the notions of mathematics must in principle be illustrable or exemplifiable in intuition, but we confuse this kind of intuition with conceptual thought. The metaphysician is like a dove that feels the resistance and pressure of the atmosphere upon its wings and supposes that its flight may be easier in a space wholly devoid of air. Just so Plato left the world of the senses and took flight with the wings of ideas into the inane atmosphere of the pure understanding. He failed to notice that the understanding can really advance nowhere in such a flight: to transcend is necessarily to go beyond snmpt-.h i ng and to measure one's distance from it. The inclination of human reason is to ignore this, to give no thought to the foundations of its speculative structures. The source of the illusion that palpable progress is being made in metaphysical researches lies in misunderstanding the nature of the propositions being formulated, particularly those that are a priori. The mere analysis of what is contained in concepts is useful and informative, but it actually does not materially advance our thought, although it may falsely be construed to do so. We must distinguish a priori knowledge which expounds what is already implicit in our thought from a priori knowledge which does in fact advance to new truths. To understand the difference, Kant deems it necessary to undertake a study of the form of propositions which express our various kinds of knowledge . 8
IV.
The distinction between analytic and synthetic judgments.
We now arrive at the acknowledged locus classicus of this celebrated distinction. Two pairs of distinctions are put forward in the Critique: analyticsynthetic, and a priori-a posteriori, but only the first of these receives any extensive discussion here. The second has in effect already been taken up in the earlier sections. Kant first explains the distinction between analytic and synthetic judgments offering examples of each, and then discusses an example of judgments that are both synthetic and a priori. The analytic-synthetic distinction is based upon formal considerations and is regarded as exhaustive. In an analytic(judgment the predicate is said to be ;fintained in the subject, and in a hidden or covert fashion (versteckterweise). In a synthetic judgment the predicate is not contained in the subject but is connected with the subject, since in fact we have said that A _i_s B. An explanation of defining phrase is added by Kant to the effect that the two kinds of propositions are "thought through identity" and "without identity," respectively. He also calls them explicative and augmentative judgments (Erlauterungsurteile and Erweiterunqsurteile) . All judgments of experience are synthetic. The predicate is not to be discovered or confirmed by confining ourselves to an analysis of the subject, as in the analytic judgment. We must look beyond the subject, acquaint ourselves with its relations toward other things. If such judgments are confirmed by experience we have extended our knowledge. Although the predicate is not contained in the subject, the two do form a unity which Kant characterizes as a "whole of experience itself a synthetic unity of intuitions." But although all judgments of experience are synthetic, the reverse is not the case. There are also synthetic judgments which are a priori. In these there is a necessary connection between subject and predicate, but not by virtue of the fact that the predicate is contained in the subject or logically related to it. The best example is "everything that happens has a cause." This illustrates our a priori speculative knowledge. Propositions of this sort are at the very center of the concerns of the Critique.
In order that we may be as faithful as possible to what Kant actually thought and said about the analyticsynthetic distinction it may be well to quote the text. In doing so, I shall also suggest a possible way of distinguishing what seem to be several strands of Kant's thought on the subject. I suggest that there are some four rather different but overlapping ways that Kant tries to make the distinction. (I shall quote almost verbatim from Kemp Smith's translation, so that the English-speaking reader can readily locate these passages particularly in IV and V of Kant's Introduction.)
(1) Containment. The first and most apparent way Kant makes the distinction is to say that in an analytic proposition the predicate is contained in the subject. There are various ways he expresses this. The concept of the predicate is covertly contained in the subject. We need merely analyze the subject through the predicate. We add nothing to the subject through the predicate. In the analytic proposition our knowledge is not extended. Appropriate modifications or negations are made for the synthetic proposition in these and the other quotations. (2)
Dependence on the principle of contradiction or of identity. We can extract the predicate from the subject in accordance with the principle of contradiction . The judgment is thought through identity. We proceed in accordance with the principle of contradiction. The predicate is bound up with the subject. The predicate belongs to the subject. In these expressions nothing is said that literally requires the containment of the predicate in the subject. Rather, there is said to be a necessary connection between the two that may be revealed or demonstrated through appeal to logic or the "laws of thought." (3)
Psychological connection between subject and predicate. I must be careful to explain this style of connection. I think it is doubtful that Kant actually intended to interpret the connection as psychological in nature. One may, however, come to the 10
conclusion that what Kant says about the relation may in the end come down to, amount to a psychological explanation of the connection. Certainly his prima facie characterization of the relationship sounds psychological: I must become conscious to myself of the manifold which I always think in the subject. In the analytic proposition, the question is whether I actually think the predicate in the representation of the subject (Axioms of Intuition, A164/B205). The question is not what we ought to join in thought to the given concept but what we actually think in it, even if only obscurely (Kant's emphasis). There is still more that suggests that Kant was close to a psychological version in the Introduction, as we have already noted. If we think it a little implausible to regard 7 + 5=1.2 as synthetic, Kant asks us to think of large numbers, e.g., 104,787,223 + 888,926,415 + 688,923,147 = 1,682,636,785, Of course, for most persons the sum here will be a "psychological novelty" arrived at through careful arithmetical calculation. But we also believe there is a right and a wrong about addition regardless of how perfectly or imperfectly individual calculators may add, regardless of their thought processes. It should be apparent that Kant might have been willing to correct the impression that the analytic relation was only psychological. If so we are thrown back on (1) or (2). There is, however, a revision of (3) that suggests itself: (4) Relationship of concepts. This we might call Kant's conceptualism, since Kant from the outset commits himself to the distinction between concepts and intuitions. What enters into the subjects and predicates of judgments such as appear in the theoretical generalizations of science is concepts (particularly in predicates). It is quite possible to interpret judgment and thought in Kant as being the work of a wholly different part of the human Geist from intuitions. Intuition is what confronts us in inner sense, in introspection ,• and is the subject-matter of psychology. But thought must in some way be exempted from the jurisdiction of psychology, although of course, thinking has to be done with intuitional aids. If one can accept this division of labor, the 11
reduction of the connection between subject and predicate to something psychological becomes less inevitable. I am not certain that it is wholly set aside inasmuch as Kant in V once more insists that the question is not one of how we ought to relate predicates to concepts but how we actually think (B17). But I think we must not equate "how we actually think" with what we have called "psychological reduction", even though it is tempting. The emphasis should be on think or thought, on what actually is included in the thought of the subject, and we should remember that thought is never in Kant reducible to intuition. With this in mind we may now reflect on the following passages which present the relation in "conceptualistic" terms: The concept of the predicate is contained in the subject. We must go outside the concept of the subject in the synthetic judgment (but not in the analytic). All the conditions for the (analytic) judgment are present in the concept of the subject. I must analyze the subject to reveal the predicate. I must become conscious to myself of the manifold which I always think in the subject. It will be noted that we repeat the last of these from (3) above, thus underscoring the problem of whether we are to regard it as psychological or conceptualistic in character. Of course the passages we have quoted under (1) and (2) also lend themselves indirectly to interpretation under (4). The issue must ultimately come down to what we are to understand by 'thought' and 'concept'. I do not think Kant has anything original to< say on this matter or to help us solve the puzzles that have been endemic to it since Plato. We may in the end exonerate Kant of the charge of psychologizing logical matters but it is not so clear how we are to understand his "ontology of thought". Our impression of Kant's "psychologizing" may stem from his tendency to think not in terms of propositions and sentences but of judgments. It is easy to regard the former as objects or "objectives" of some sort and it is a wrench to think of them as acts of mind. This characterization, however, suits judgment and Urteil perfectly and the objective style is correspondingly alien. Possibly the "content" of 12
every judgment could be regarded as a kind of adverb, that is, "A judges thus: snow is white." A judgment is a kind of performance characterized by what we think of as the assertion. Seen in this way, as an act of mind, it is natural in using the idiom of judgment and Urteil to speak of it in those terms which, under (3) above, sound psychological or psychologistic. The discussion introducing the synthetic a priori judgment in the last paragraph of IV briefly defines and illustrates this judgment. In Section V Kant asserts that there actually are such judgments and locates them in the several fields of knowledge. An exemplary synthetic a priori judgment is, "whatever happens has its cause". This cannot be known on the evidence of experience; it is to be thought of as a necessary truth; and yet it is not true because it is analytic. It is well to note the phraseology which Kant uses of this type of judgment. In it the predicate is joined to the subject completely a priori " on the basis of mere concepts" (aus blossen Begriffen). Usually Kant says that logical or analytic a priori judgments join their predicates to their subjects on the basis of blosse Begriffe, for without going either to experience or to any fundamental preconditions for experience we can decide their truth simply by the inspection of concepts alone. Since that is Kant's customary and even emphatic phrase to characterize analytic judgments and procedures, the present wording may be construed as the result of an oversight or inadvertence. If Kant is certain of anything, it is that the causal principle is not analytic. I believe that Kant's view of the role of analytic a priori judgments is altogether modern, or at least compatible with typical thought of our century on the subject. Kant in principle regards the conditionals corresponding to the valid forms of the syllogism as analytic and regards other logical operations in a similar light. Of course premises and conclusions may themselves be synthetic, but the principles guiding the inference are analytic. "Pure logic," he remarks a t A54/B68 "is a body of demonstrated doctrine, and everything in it must be entirely a priori." It is also worthy of remark as early as possible that Kant cer tainly intends to separate logic from psychology ]ust a g fundamentally as Frege, Peirce, or Russell 13
have done, in spite of the fact that, as noted above, his analysis of judgment is not altogether free of a psychologizing tendency. He parts company with one of the major current viewpoints when it comes to the homogeneity of mathematics and logic, since he regards mathematical propositions as synthetic and a priori. Hence they could not be derived from logic. V.
All theoretical sciences of reason contain synthetic a priori judgment as principles.
Although the nature of synthetic a priori judgments has been as yet only sketched out by Kant, he now affirms that there are such judgments. He has cited a few examples but said little about the domains in which these examples, and others of their kind, are to be found. We now learn that three domains contain such judgments: all mathematical judgments are synthetic; natural science , and in particular physics, contains synthetic a priori judgments as principles,- and at least in intent (ihrem Zwecke nach), all propositions of transcendent metaphysics, are synthetic and a priori. Even in this section we must permit Kant a considerable latitude: he will not in a matter of moments be able to show us that there are synthetic a priori judgments, nor that those of mathematics, pure natural science, and metaphysics are of this kind. We may therefore regard the present section as enunciating his principal thesis rather than proving it. The Critique as a whole must be appealed to for proof, if it is forthcoming. In the next section (VI), we learn that the question to which the Critique addresses itself is: How are synthetic a priori judgments possible?
2
We have already remarked that we need to ask the question, how p can be true (or possible), only if we already know that indeed p, or p is true. Kant did not in practice separate clearly the two questions whether there are such propositions, and how they are possible, although he explicitly recognizes in VI a difference that is close to it: we may properly ask how there can be pure mathematics and pure natural science, for that there are such enterprises is shown by their actually existing (B20-21). When one scans the whole expanse of the Critique in detail there is probably as much of an answer to each question as one may hope to find. 14
One must not dismiss the whole program of the Critique by saying, there are in fact no synthetic a priori truths and therefore a campaign to discover how they are possible is doomed from the beginning. The real questions are such as these: how can there be necessary truths in geometry and arithmetic; what is the basis of our (assertedly unshakeable) belief that every event has a cause; are we compelled to believe that there must be a first cause if we believe that every event has a cause? Kant believes his predecessors have given inadequate answers to such questions, and his own answers to them deserve serious consideration even if it could be shown that the key propositions involved are not synthetic and a priori in nature. The first area that Kant identified as containing synthetic a priori judgments is judgments of mathematics.^ He says that it was erroneously supposed that the Grundsätze (axioms) of mathematics were analytically true because the proof of them proceeded by means of principles that were analytically true. We can also find support among earlier thinkers for the view that mathematical propositions are true on the ground that they are instantiations of the law of contradiction and are thus analytic. Kant offers but two examples in support of his view about mathematical propositions. The first is the arithmetical truth that 7+5=12. This Kant declares to be synthetic on the ground that it cannot be regarded as analytic. Why then may it not be thought to be analytic? The reason he cites sounds even more explicitly "psychological" than was the account given of the nature of analytical propositions in IV. He is arguing that if thinking of whatever is thought in 7+5 were somehow identical with thinking 12, or if one could not think the one without thinking the other, then the statement would be necessarily and analytically true. If on the other hand one can think of one without the other the statement of their equality is synthetic. It is now said that the concept of the sum of 7 and 5 contains nothing more than the combination (or rather the combining) of the two numbers but that it does not contain what issues from the process of combining, that is, 12. The term Vereinigung (unification, combination) is just as tolerant of being interpreted as an act in process as it is as the product of an a ct completed. The English term 'combination' on the 15
other hand leans heavily in the second direction. He may therefore be saying that we must not identify the act of combining 7 and 5 with the result of the act, 12. Would it be compatible with what Kant says to regard 7+5 as a kind of command, thus: "Combine 7 and 5"? This would not at the outset reveal the outcome, which might in principle be novel or surprising. Only the carrying out of the task would reveal the result. Unfortunately, this interpretation, while seeming to account for the difference of the two members, (7+5) and 12, would be useless, since obeying an imperative yields nothing one can judge to be true. The rest of the exposition may in fact be psychological, but it also lends itself to the kind of conceptualistic interpretation developed above. The difficulty with this is that it would require more of a theory of concepts and conceptual thought than Kant offers. But more importantly, it is incompatible with Kant's firm conviction that the necessity of mathematical judgments is based on a priori intuitions and not concepts. So far as the psychological aspect of mathematical operations is concerned, one may readily concede that a sum may not be readily recognizable in a series of addends. But the mere fact that a sum turns out to be a psychological novelty is an inadequate ground for regarding the judgment as not analytic. We must also remember that any psychological process takes place in time. When we interpret the left hand member of an arithmetical formula as an operation to be carried out, the result will not be "inevitable" until the operation is carried out. Kant does in fact rather courageously consider an intimate connection between arithmetic and time, for example in the Prolegomena• But it can scarcely be thought to lead to anything except unwelcome results. Kant's second mathematical example is of course drawn from geometry: the straight line is the shortest distance between two points. What Kant says on this subject is altogether insufficient to prove that the proposition is synthetic. It rests on the assertion that 'straight' is a qualitative and 'shortest' is a quantitative term. But how this yields the conclusion in question is not explained. If we consider a near equivalent of this proposiiton, namely Theorem 20 in the first book of Euclid, we find a demonstration that makes no appeal to a distinction of quantity and 16
quality. Euclid's proposition reads: "Any two sides of a triangle are greater than the third side." This is proved solely by appeal to the equality of the base angles of an isosceles triangle, to Axiom 9 which states that a whole is greater than its part, and to previous Theorem 19 which states that if one angle of a triangle is greater than another then the side opposite the greater angle is greater than the side opposite the lesser. To prove: AB+AC > BC Produce AB to D Join D, C Let AD=AC ißDC < IBCD
BD > BC, etc. Without reference to a concrete case such as this Kant simply states that intuition must be called to our aid to effect the synthesis, between the key notions in the subject and predicate (straight and shorte st) . Kant emphasizes what we may speak of as our thoughtprocesses in geometry and presumably our mathematical thinking in general. We must, he says, attend to how we actually do think, and when we do, we shall see that we must appeal to intuition to effect a connection between subject and predicate. He does not explain why in fact intuition, even pure intuition, should yield an unassailable result. In any appeal to empirical intuition one would certainly be wise to draw conclusions with caution. Yet pure intuition is credited with yielding infallible results. One should remark finally that the notion of syntheticity touches not only the form of certain propositions, but is generally taken in the explicit sense that whenever a proposition is synthetic, there must occur a process of synthesis and an agent who performs the process of synthesis. This agent cannot, however, simply be said to be you or I, or Smith or Jones: we must look to something which we may designate the Paradigmatic self. With this phrase we may draw attention to the "we" to whom Kant assigns such momentous tasks as devising or applying the categories, 17
among several others. For example, speaking of the categories he says, "we ourselves introduce into appearances the order and regularity we call nature" (A125) and countless similar things. It is paradigmatic in the sense that it is not the local you or I that is doing any of this. (We shall explain the identity and function of this self in more detail as we proceed.) One should now observe that attributing the process of synthesis in 7+5=12 to a paradigmatic self would effectively remove the operation from being subject to the criticism in terms of psychologism. It would however do so at the expense of our trying to understand this operation in any familiar terms, since it would be, as it were, taking place "behind the scene." The second area that contains synthetic a priori judgments is natural science. The development of the concepts and the demonstration of the principles underlying science is referred to by Kant as metaphysics in a certain sense, what we can call natural metaphysics. True synthetic a priori judgments of natural metaphysics are necessary but unlike analytic propositions they are not necessarily true because their contradictories are self-contradictory. Neither are they highly probable or highly confirmed synthetic truths, to which there are no known exceptions. To say of them that they are necessarily true is to say that, come what may, we will not under any circumstances permit ourselves in speaking of this world the thought of their falsity, dass gar deine Ausnahme als mö'glich verstattet wird (Introduction II, and elsewhere). This suggests that we have adopted some kind of rule, one that inherently rules out the falsity of the rule. Kant has in fact, in the Transcendental Deduction and elsewhere, and very prominently, referred to these synthetic a priori propositions as rules. But, rules! Are we not seeking to find the truth about the world and how _i_t is? How can we prescribe rules to the order of nature? Does not nature go its own way in spite of us? Kant's answer is a radical revision of the received doctrines of empiricist philosophers. If we ask, how can VT£ prescribe to nature, Kant's answer is, because the order of things that we are ruling and ordering is a world partly of our own creation, the world of appearances, and must therefore tolerate our regulistic venturesomeness. This is the world we confront in perception and in all our scientific efforts to wring 18
the truth from nature. It is not a world of things themselves but as he says, appearances or phenomena (Erscheinungen). This then is what is at the bottom of the claim that there can be, and indeed there are, necessary truths about the world around us: because in fact it is, _iri its formal aspect, a world of our own creation. The fundamental truths about or the laws of this world are in fact rules governing it. It might seem to be a rather arbitrary and capricious state of affairs where we can make our own world. Kant's answer is that the "creation" which we here speak of is not yours or mine. The "creative agent" is the paradigmatic self. We must seek to lay bare the efforts and achievements of such a self, and the Critique is the record of doing just this. We should be prepared in reading the Critique for a shift in the "mode" of such a statement as the causal law. At the outset we are invited to rethink our "sentential categories," allowing for synthetic as well as analytic a priori propositions, and we are asked to regard these propositions, or at least certain of them, as necessarily true. In the Deduction we learn that they must be treated as rules: of course this is a wrench to our thought since we generally do not speak of a rule (nor does a German speak of a Regel) as true or false. As we go on to the farther reaches of the Critique, to the sections that follow upon the statement of the Antinomies of Pure Reason, we detect a reinterpretation of the rules in pragmatistic terms: the causal law is to be followed because it is scientifically good advice, because it leads us to material truths about the world which we would not know how to search for, or to find, if we proceeded without it. The third area containing synthetic a priori propositions or principles is that of transcendent metaphysics. It remains to be seen, however, whether they are true or even meaningful at all or whether they are merely so in the intention of the propounders of such principles. Their domain comprises rational Psychology, cosmology, and theology. It may be well to remark again that neither the theses of natural nor those of transcendent metaphysics are provable by appeal to experience, nor to concepts alone (that is, they are not analytically true). What 19
distinguishes them is that the theses of natural, but not those of transcendent metaphysics apply to experience and are needful to make experience possible. The proof of such principles can only be, as Kant says, transcendental. The defense of these contentions makes up the content of the transcendental analytic and dialectic . VI.
The general task which confronts pure reason
Having explained the nature of judgments, analytic and synthetic, and shown that certain sciences contain judgments that are not only synthetic but a priori, Kant now sets himself the task of setting forth explicitly a momentous problem that arises about them. We must ask the question how such judgments are possible, and this necessitates an undertaking that we may call a critique of pure reason. The examination of the pretensions of pure reason to knowledge outside or beyond experience, to a priori knowledge in short, comes down to just this question about the possibility of synthetic a priori judgments. We may make this clearer to ourselves if we raise similar questions about other judgments; Kant did not explicitly raise these questions since they answer themselves in the framework of the Critique. The questions are: How are synthetic a posteriori judgments possible? How are analytic a priori judgments possible? Whereas the comparable question ,about the possibility of synthetic a priori judgments occupies a book of nearly 900 pages (in B ) , one would think that these questions should be less difficult to answer. Synthetic a posteriori propositions are the day in and day out reports of our experience, inner or outer, accumulations of information, and generalizations about the world, both the most problematic and the most unexceptionable. If we ask how this knowledge, or at least information, is possible we must first say that it is because it is based upon experience. The rest of our task will be to offer interpretations of this as it applies to various areas of experience: the past, present, and future; the remote and the accessible; 20
the abstract and the concrete; the general and the particular; the theoretical and the actual; and so on. The task should not be as arduous as the one we have uncovered for synthetic a priori propositions. In fact, however, even a moment's reflection on the philosophical effort that has been expended on the question of the nature of truth should show us that the question is no less difficult than the one Kant puts at the center of the Critique. What is even more important is the involvement of the two questions with one another. Take a simple Kantian example of a judgment of experience , the sun warms the stone. Kant's point is that this and all such judgments of experience are possible only because certain synthetic a priori propositions are antecedently true. If we ask how analytic a priori propositions or judgments are possible, the answer Kant would propound is, they are possible because in some judgments predicates are already contained in their subjects. We can be a priori certain of whatever is asserted of these subjects whenever we know or can show that indeed the predicates are so contained. But can we be and, if so, how can we be a priori certain of any assertion when we find that its predicate is not contained in its subject, and that no accumulation of experience bears on the truth of it? The prior question is, are there any such .propositions. Though Kant has put forth no great effort to show this, he has satisfied himself that there are three areas in which they are found. These propositions are either mathematical or they set forth the basic propositions of natural science (call this natural metaphysics) or of transcendent metaphysics. This is the framework for the inquiry called the critique of pure reason. Kant says that metaphysics, whether natural or transcendent would not have fared as ill as it has in his time, if the problem of the synthetic a priori had been broached. Hume failed to do so with regard to natural metaphysics, in particular the causal axiom (every event has a cause), and in a sense rejected it along with the whole apparatus of "divinity or school metaphysics." Kant says that if Hume had hit on the problem he himself has uncovered about the synthetic a priori, he would have seen that his conclusions would equally invalidate or "liquidate" all of mathematics, a result Hume would certainly have abhorred. 21
We are thus said to be confronted by an unavoidable and most arduous bask, to see how we can justify necessary truths that are not analytic. If we fail» not only will school metaphysics collapse, but science and mathematics as well. Such a serious outcome must be avoided. Kant was ever a man to embrace his duty when he saw it, but he came to the realization of it only slowly. At a time when many men think of retiring from their labors, Kant had just begun the enormous labor of producing the Critique , and to this he found it necessary to add two others. The task he found to be that of providing a foundation for all knowledge and in the end he found this would have to include even that pretension of knowledge, metaphysics. It cannot be ignored as the sceptics have done. Its roots, Kant found, are far deeper than one might suppose. As he explains in this section, although metaphysics cannot claim to have arrived at any knowledge hitherto, we cannot doubt that there are certain deep-seated drives in man that insistently issue in questions of a metaphysical character. Hence we must try to discover how metaphysics as a natural human disposition is possible. This should enable us to learn whether metaphysics as science is possible. In this way we can answer the basic questions that must be addressed to pure reason, regarding mathematics, science, and metaphysics. Since this is an investigation of something entirely within our grasp, the powers of the human mind, and not of a subject matter that stretches on through inaccessible reaches of time and space, we can hope to complete the investigation, definitively. But we shall succeed only if we keep our eye on the question how, whether, and in what domains pure reason can hope to extend its knowledge materially.
VII. The idea of and the divisions under a special science bearing the name of a critique of pure reason The final section of the introduction presents little that is essential to the total economy of the critique that is now to unfold. It proposes to present a general summation of the tasks to be undertaken by such a critique but actually offers a rather confusing picture of it, hesitating between terms to characterize it such as organon, doctrine, and canon, all of them dear to the system-loving Kant. The principal 22
result, looking to what Kant has said here and elsewhere, is that a critique of pure reason is not coextensive with a system of pure reason, but "an examination of the faculty of reason in general in respect of all knowledge toward which it may strive independently of all experience? (A xii). Kant seems to have contemplated at one time the construction of the entire system of pure reason, but this proved to be a more ambitious program than he was ever able to carry out. We have, however, a fragment or sample of it in the Metaphysical Foundations of Natural Science and in certain ethical writings. Although it does not present the system of pure reason thus contemplated, the Critique presents both more and less of it than we may expect. The principles in the Transcendental Analytic go a considerable way toward supplying a knowledge of the content of such a system. Thus we learn in considerable detail how the ideas of substance and causality are supplied by it. Yet if we look for a consequent analysis of these notions we are disappointed. We learn, for example, that a cause is said to be a materially necessary and sufficient condition of its effect, much in the manner of Hume's positive doctrine on the subject (Treatise I-IV-XV) but the many vexing questions which it occurred to Hume to raise are not raised by Kant. This cannot be because he had no appreciation of their reality and gravity, but because in a critique he thought himself justified in hastening on to all the other problems that a propaedeutic of pure reason must address itself to. The Critique proved to be an even more formidable and arduous task than he may have conceived it to be at the outset.
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TRANSCENDENTAL DOCTRINE OF ELEMENTS We proceed now to the body, though not yet the heart of the Critique, a term we must reserve for the doctrine of the categories and the categorial principles. It should be said at once that we cannot even mention all of the most important issues that have arisen about the Transcendental Aesthetic or Logic. We must restrict ourselves to a brief exposition and elucidation with such suggestions about further problems as can readily be exhibited within this framework. It is very well-known that Kant thought himself obliged to follow an expository plan that would suit a treatise on logic. Here we must think of logic both in a very general sort of way which applies to the Critique as a whole, and also in a more particular way that is illustrated in the distinction between Transcendental Aesthetic and Transcendental Logic and in the divisions within the latter. Kant follows the general organization of logic prevailing in his day, the division of the subject into a Transcendental Doctrine of Elements (Elementarlehre) and a Transcendental Methodology (Methodenlehre), a distinction that he found precedents for in the ontologies and logics of the Leibniz-Wolff school which he himself had studied and which he used in his lecture courses. We may say that the Doctrine of Elements is intended to answer the question through what means synthetic a priori judgments are possible and the Methodology, through what methods they can be realized. If the model of logic is followed in further detail, the traditional divisions would be ConceptsJudgments-Inferences. In the transcendental doctrine of elements we ask about the possibility and authority of a priori concepts, judgments, and inferences. Here one must first pause over the term 'transcendental,1 and even more must be said of this by and by. Kant is saying that there are certain conceptions and principles of an a priori nature which are absolutely indispensable for human experience and for the larger and more formal extensions of such experience in science and theoretical endeavor in general. These conceptions and principles are limited, however, in that they must apply to experience and that they are not only irrelevant when applied beyond experience but in fact generate a peculiar set of intellectual errors when 25
they are so applied. Since they do not arise experience, they may be said to transcend it in a limited sense; the transcendence is not absolute. In order to make just this distinction, Kant uses 'transcendental' for concepts that do not arise from but yet apply to experience and make experience and science possible, and 'transcendent' for concepts that neither arise from experience nor are necessary as presuppositions of experience (Cf. A296/B352). With this definition, we must now look for the body of a priori conceptions, judgments (or principles), and reasonings. The conceptions comprise two broad areas that are essentially distinct from one another: first, space and time, and tuen,the twelve categories. It is best to employ the somewhat vague term 'conception' rather than 'concept' to cover these two families, because Kant holds that our representations of space and time are not concepts. It is true that he occasionally refers to them in this way, but only after he has driven home the distinction. What it means to say that they are not concepts is specifically explained in the Transcendental Aesthetic. Following this model of logic further we find a priori i udgments or principles considered in the second book of the Analytic, namely the Analytic of Principles. The clue to these is supposed to be provided by the four classes of categories, although the derivation is somewhat forced in several important respects, as we shall see. Finally the reasonings or inferences of an a priori nature that we engage in, or that we are likely to engage in, are to be found in the second large division under Transcendental Logic, called Transcendental Dialectic. The articulation of topics here has also been the subject of criticism, but Kant's intent is perfectly clear. Ordinarily, human beings are probably inclined to consult experience in their discourse about their affairs. But quite often they confront what is inaccessible, at least for the time being, to experience. They must make predictions about the future and hypotheses about the past. They must invent theories and explanations for what they have not experienced, and so on. The outcome is often readily introduced by the phrase "it stands to reason that." Reason, pursuing its ordinary tasks, is what we must rely on in such instances; it goes beyond the present into one or another more or less unknown area, but not 26
unknowable in principle. We are also inclined, or we may yield to the temptation to employ concepts and principles that are established in relation to experience in areas which lie beyond experience. The issue now is about the phrase 'beyond experience.' In the previous case this could mean unknown areas of space or time that we have never traversed but that are not in principle unknowable: there is no error in applying concepts of experience in these areas. But if 'beyond experience' means beyond all possibility of experience then reason is guilty of a most serious fallacy if it now employs concepts specifically devised to deal with experience. It has exceeded the proper limits within which the intellect in general may operate. Its reasoning now becomes dialectical. Of the many uses of this term Kant selects the one that equates it with a "logic of illusion." These are not ordinary illusions. They are the errors that underlie pseudo-sciences such as Rational Psychology (the doctrine about the immortal soul, its origin and destiny in a hereafter, its relation to a body and a physical world of space and time), Rational Cosmology (the doctrine that affirms an absolute origin of the causal series, a ground of freedom beyond determinism, and several other doctrines) and Rational Theology (the demonstration of the existence of a divine being from his concept or possibility alone). The last of these perhaps typifies the logic of illusion best, for it seeks to demonstrate a reality or fact of existence from concepts alone without even the most tenuous connection to experience. It is exemplified in St. Anselm's ontological argument for the existence of God. We may now offer a glance at the whole territory to be surveyed. There is no better way to do this than to reproduce the Table of Contents that appeared in the first edition of the Critique in 1781. (The second edition presents all or most of the many often minute sectional divisions but makes a perspicuous view much more difficult.)
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I.
Transcendental Doctrine of Elements Part I
Part II
Transcendental Aesthetic Section 1
Space
Section 2
Time
Transcendental Logic Division I Book I
Analytic of Concepts
Book II
Analytic of Principles
Division II
II.
Transcendental Analytic
Transcendental Dialectic
Book I
The Concepts of Pure Reason
Book II
The Dialectical Inferences of Pure Reason
The Transcendental Methodology Chapter I
The Discipline of Pure Reason
Chapter II
The Canon of Pure Reason
Chapter III
The Architectonic of Pure Reason
Chapter IV
The History of Pure Reason
Part I and Part II through Book I supply the concepts or conceptions to be considered. Bpok II supplies the judgments or principles. Division II expounds the inferences of pure reason. In this way the general model of the divisions of formal logic has been followed. The Methodology at the end is supposed to show us how all of these "Elements" can now be put into operation to accomplish the task of gaining knowledge worthy of the name. As we shall have many occasions to observe, this "architectonic" often supplies Kant with rather poor justification for taking up certain subjects, but the subjects are almost invariably of momentous importance even when the justification appears faulty.
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TRANSCENDENTAL DOCTRINE OF ELEMENTS First Part §1
Transcendental Aesthetic^
Kant introduces the Transcendental Aesthetic with a preliminary section that amounts to a glossary of terms, among them the following: intuition (Anschauung) sensibility (Sinnlichkeit) , concept (Begriff) , sensation (Empfindung) , appearance (Erscheinung) , and matter and form. We may take these us in order somewhat different form his, not to improve upon it, but to proceed rather more plainly from the general to the particular. The most general terms are probably matter and form. This ancient Aristotelian distinction is frequently adverted to both here and in what follows. In one sense it cuts across the lines of the intuitiveconceptual. It cannot be simply equated with intuition and concept because of something which emerges from a further division that emerges particularly in § 8 of the present series of subsections:
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The pure concepts (of the understanding) are the categories, to which we shall come in due time. The pure intuitions, also called a priori intuitions, are space and time. The empirical concepts are classes and relations such as man, table, fire, to strike, drowning, magnetism. The empirical intuitions include the apprehension of what Kant's predecessors called the secondary qualities: color, sound, taste, feel, smell. -> But the conceptual and intuitive are not coextensive with the formal and the material, for Kant regards anything that is a source or domain of relations as formal. This puts the pure intuitions, space and time, among the formal notions. In general it is "we" who are responsible for the form of the objects and processes in our experience, for ordering them in the manner that they are. The empirical matter is a kind of brute reality which we cannot attribute to the activity of ourselves, of the paradigmatic self. Kant's account of this varies, but it is usually attributed in some manner to things themselves. When we ask after this "manner" one cannot help but think that Kant's answer owes more than a little to Locke : things-we-know-not-what leave effects upon us that we come to speak of in the language of empirical intuitions, color, sound, etc. These are given to us, he says in the present section; they are attributed to sensation, and we may speak of the capacity to receive them as sensibility. The whole complex of an experienced object or process comprises all of the four factors, conceptual and intuitive, empirical and pure. Organized in these terms, the ordinary object of our attention is what we may call an appearance or phenomenon (Erscheinung). In the Preface to B (B xxvii), Kant makes a hazardous inference to the effect that such an appearance justifies us in affirming that something appears, which is of course a thing in itself. It is hazardous, if not worse, since it is an empty inference based solely on the fact that we have called it an appearance. (Since x is an appearance, something must appear in it.) It is also a somewhat half-hearted inference, since we can only infer a thing itself as something that may be thought, rather than as anything known. We shall of course have to recur many times to this problem of the thing itself. An even more general term than any of the foregoing is representation (Vorstellung). This term 30
refers to anything whatever that may come before the mind, or of which we may be aware: intuition, concept, perception, category, etc. The distinctions Kant is working out in these early pages should be supplemented at once by reference to other terms that he employs from time to time. Thus the present section introducing the Transcendental Aesthetic should be compared with a parallel section that introduces the Transcendental Logic at A50/B74 and with a section that opens the so-called Metaphysical Deduction, A66/B91 ff. In the first passage he speaks of two sources of our knowledge: receptivity, which is of course the capacity of receiving impressions and is essentially co-extensive with sensibility in the Aesthetic; and spontaneity which is the power of conceptual thought. Intuitions and concepts are specifically identified as the two elements jointly indispensable to knowledge. Matter and form, terms which have appeared earlier, are alternative ways of speaking of receptivity and spontaneity . Another way of characterizing the same distinctions appears at A66/B91 where he speaks of intuitions resting upon affections, concepts upon functions. That is, in intuitions we are receptive, or affected by something other than ourselves. With concepts, the mind is itself active or spontaneous. If the term 'functor1 had been more readily to hand, Kant might well have employed it since to speak of a concept as a function seems to our ears a slight mixture of types. (I shall in fact later on speak of the categories, that is the pure concepts of the understanding, as functors• A functor may be understood as a kind of instrument or agent in the hands of the paradigmatic self performing a certain epistemic task.) Throughout we see a variety of terms employed, yet Kant is on the whole consistent. Problems of course arise when he comes to speak of narrower epistemological problems. What must particularly be remembered in the foregoing is that sensation must not be identified with intuition, since some intuitions are formal or pure while others are empirical, directed toward sensation. As Kant conceives of his problem in the last paragraph, in order to arrive at the pure or transcendental elements in knowledge we must look both toward intuition and conception. The Critique will be concerned very little with specific empirical concepts 31
and even less with empirical intuitions. In the Aesthetic Kant abstracts from all concern with such concepts and all concern with intuition narrowly construed as sensation. He confines his interest to Space and Time, that is, to non-empirical or pure intuitions. In accordance with Kant's own divisions, I shall in the course of this study treat the analytical portion of the Critique (the Aesthetic and Analytic) as a kind of effort to analyze experience, to "unpack" the object of experience of its various "contents" and to track them down to their sources. But when we put the matter so .we seem to need to say that one of the sources of experience ^LJJ experience. How can we divest this of its apparent vacuity? To answer this we need to observe a most important distinction which is nearly always perfectly clear in Kant (once we are made aware of it). Two different, though related, things are intended in the Critique by the term 'experience' in different circumstances. The two senses may be distinguished in the following manner. In the first sense, the term 'experience' is used to designate the having of empirical intuitions, whether of inner or outer sense. As functional parts of the total object of experience we should not properly say that we are aware of these in seeing, hearing and so on. What we see and hear are whole appearances: persons, houses, bells and dogs. Empirical intuitions are more nearly sense data, or perhaps the simple impressions Hume spoke of. We are perhaps sometimes aware of these by themselves: normally what philosophers such as Kant are speaking about as intuitions present themselves only after an effort to analyze the familiar objects of experience -- namely houses, dogs,;: etc. Intuitions are objects of experience in a narrow' sense and our apprehension of them as ingredients of appearances may be designated intuitional experience,
In the second and more familiar, pre-analytical, sense of experience, Kant means our apprehensions of what we are referring to with the familiar language of things and process, that is, appearances: persons, trees, houses, hats, planets, walking, flying, building. This we may call apparent or phenomenal experience , E2•
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The first sense is almost invariably present when Kant speaks in negative terms. When for example, he warns us of the penalties of attempting to employ the categories without reference to experience it is intuitional expereince that he has in mind, or E-j. It would not be E2, since apparent or phenomenal experience, or appearances themselves inherently involve the organization of the categories, and also space and time. Kant's analytical method, the method of "unpacking" is to subject what is present in E2 to analysis, to bring to light what it involves, contains or presupposes, that is, the pure concepts or categories, the pure intuitions, space and time, but before all of these, E.J , the data of empirical intuition. The order of our encounter with these is different in the two cases. In point of the order of time as ordinarily experienced, E2 precedes E-| : we do not first have sense data and then build rocks and trees of them nor does Kant think so. Rather, in this sense, we first find ourselves in a familiar world of phenomenal objects and processes and then by a process of analysis uncover various "ingredients" such as sense data. But in point of the order of ground, E. precedes E2. This is the order that the deduction of the categories lays bare : the order of the construction of the appearances in E2 proceeds from component,or ingredient intuitions through the processes of synthesis to objects and processes familiar to the light of day. I believe Kant adheres strictly to this division of senses of the term. Its most significant instances come to light after he proceeds to the Analytic of Concepts and Principles and it is central to the doctrine of the Dialectic. The purpose of the aptly named Analytic is to analyze phenomenal experience and its objects; the purpose of the Dialectic is to warn us of the disastrous consequences of proceeding without recursibility to intuitional experience. It is well also to have this distinction in mind in the Aesthetic.
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Transcendental Aesthetic Section I Space §2
Metaphysical Exposition of the Concept of Space
A high degree of modernity, meaning relevance to our philosophical affairs and our way of going about them, can be attributed to Kant from the fact that he is the first of the great philosophers who couches his problems in something approaching the so-called formal mode of speech. He asks about judgments (sometimes he says Satze, propositions or sentences), what they refer to, how we verify them, how they are possible. The failure of Hume to do so explicitly is one of the serious weaknesses of his approach. After Kant one must wait until the twentieth century to find philosophers who take hold of their problems in this manner. The material mode of speech asks how we acquire ideas, what ideas and objects are, how "we" build up complex ideas out of simple ones, and so on. Kant is a transitional figure and employs now the formal, and now the material mode. The point is, the new mode has been discovered and used. The general question of the Critique is, how are synthetic a priori judgments possible, and that of the Aesthetic is, how are the synthetic propositions of geometry and arithmetic or in general of mathematics possible. This question is not, however, precisely the question considered in the two sections of the aesthetic as a whole. Rather it is the question which is particularly raised by what, in B, is called the Transcendental Exposition, in both sections on space and on time. The Exposition for space raises the basic question in somewhat the following form: since geometry is concerned with space, what must our conception of space be to account for geometrical propositions being both necessary and synthetic. Kant is not concerned now with geometry itself, but what our notion of space must be to square with the fact that the propositions of geometry are of a certain sort. The Metaphysical Exposition has provided the answer: space is not an empirical concept; it is a necessary and a priori representation, and so on. (Time is treated in similar fashion.) Thus the Metaphysical Exposition is a kind 35
of "lemma" for the Transcendental: since, according to the Metaphysical Exposition, our conception of space is so and so, we can explain how the propositions of geometry can be such and such. The character of our geometry is determined by our view of space — a reasonable view if geometry i_s_ concerned with space. The term 'transcendental' may by now appear to be a fairly well-chosen term for what is said in § 3 (and in §5). The term 'metaphysical' is perhaps a little more obscure in application. It may be thought that the term is chosen because it is the nature of space or of time that is, in a very special sense, being expounded. But the question Kant asks in § 3 is what our representation of space must be if we are to explain how geometry is possible. Thus it is more nearly the conception (Begriff) of space, rather than space, that is being examined. Kant's own explanation in §3 is that "an exposition is metaphysical when it contains that which presents a concept as given a priori" ; but this is not far from what elsewhere he seems to mean by 'transcendental'. It is interesting to speculate on the analogy which Kant no doubt has in mind between the subsequent metaphysical deduction of the categories and the present metaphysical expositions of space and time, but we shall not pursue the matter further. It should be noted that in B Kant modified the sentence at the beginning of B38 from, "In order to enlighten ourselves on this matter, we shall first examine space," to "...first give an exposition of the concept of space." The term "concept" (Begriff) is only to be understood with qualifications. In the body of the four arguments about space, and this is re-affirmed later, we learn that our notion of space is precisely not a concept; 'space,' is not a class name. Space is in fact a kind of "individual" or "particular" for there is only one space (and one time). Our representation of space is emphatically an intuition and thus fully antithetical to a concept, but it is of a unique kind, an "a priori" or "formal" or "pure" intuition.^ 1. Turning now to the arguments themselves, Kant's exposition begins with the observation that space is not an empirical concept, where the emphasis is clearly on 'empirical'. The denial that it is a concept is taken up in §3. We cannot derive the representation of space from anything outside ourselves. Here 'experience' means empirical intuition. Thus 36
Kant means to say that the representation of space is not based upon visual and tactile sensations, since these are unthinkable without already presupposing some grasp of space. The issue is over 'outside' and 'based upon'. Kant's terms are ausser mir (outside m e ) , abgezogen (derived from),and bezogen (referred or related to). As to the first, if he means outside in a literal sense, the argument is not trivial. If he does not, it is indeterminate. The same must be said of bezogen , and of abgezogen, the first of which is the vague and abstract 'related to' and the second is built on the figure 'drawn from', again inviting speculation as to what is intended. But here another consideration must be introduced for which we should refer to the opening sections of the Transcendental Deduction, of the categories A85/B117 ff,(just prior to the section referred to in the footnote a moment ago). Here Kant makes a most important distinction, if not indeed, a concession. He says we must not confuse the process by means of which in actual psychological fact we learn or come to possess notions such as either space and time or the categories with their ground or, as he says, the principle of their possibility. The explanation of the first could be called an empirical deduction or an "explanation of possession," the second a transcendental deduction. This distinction is relevant here and will remove some of the doubts we have about Kant's first argument. He himself would have said, and did, that Locke and Hume provided for the first adequately (at least in intent) but never faced the second squarely. Let us suppose then that an empirical deduction, an explanation of possession, has been provided (in our day we might call for Piaget's aid, and perhaps that of the "cognitive psychologists") and let it give a functionally adequate psychological account of how we acquire the concept of space. What more are we entitled to ask? What falls outside it? For this we must see what enters into our conception of space and we need only point to the spatial infinite and infinitesimal to see that these involve us in concerns beyond psychology, because psychology at most may succeed in giving an account of our imagery (of the infinite) but scarcely whether our idea of it is true or false, clear or confused. 37
This expansion of Kant1s thought with the means he himself has provided serves to show that there is "more" to space and time than can be explained by any empirical deduction. What is needed in addition to such a deduction is to show that what we think under space and time must have objective validity (Gültigkeit). Similar considerations hold for the categories: an empirical account cannot answer philosophical questions. Kant wants to provide reasons why we may extend the notion of space beyond our personal and local imagery in the unrestricted manner that is necessary for geometry, as he conceives it. An analogous procedure will be followed in the deduction of the categories. If the deduction of the categories or a justification for the employment of the notions of space and time can be given in one sentence, it will be this, "The categories and space and time must be presupposed because otherwise knowledge and experience are impossible; since however, these are real, we may affirm the validity of the categories and space and time." It will now be said that this simply comes down to saying that we are justified in applying the categories and space and time to experience because without them there would be no experience, and that accordingly the whole argument is, as C.I. Lewis and others have said, question-begging. But there is another way to construe Kant's effort and we arrive at this when we see that his whole effort in the Critique was one of taking the limitlessly rich notions of "experience" and "knowledge" and progressively unpacking them of their contents, a process that would reveal not only the contents but in what circumstances they could be used. Looked at in this way, Kant's method may be spoken of as diremptive. "Presuppositions" such as the pure intuitions and concepts are progressively revealed in the Critique, enabling us to give an account of experience. Of course one first needs to know what counts as knowledge or as experience and what makes a mere pretense at it. Thereafter one needs a skillful philosopher to manage the analytical effort of "unpacking." This effort is already present in the Aesthetic. 2. in the second argument we learn that space is an a priori representation, that it underlies all outer intuitions. In a sense this simply reaffirms 38
what appeared in 1. In 1 the emphasis1 is on denying that our representation of space is empirical. In 2 it is on affirming the alternative to this, namely, that space is a priori. The two statements are essentially equivalent. If in 1 Kant could argue that space must be presupposed if we talk of anything outside us, this must also include what is said in 2 to the effect that if we have outer intuitions, space is a necessary condition of them. 2 goes on to say that objects presuppose space, but not vice versa. Since one can conceive of space from which objects have been removed, empty space is not nothing. in our thoughts about the world we inhabit, the world of appearance, space can never be absent. This may readily be granted, but it is far less convincing to be told that our representation of space is a priori (and not just that sentences about it are a priori) considering the consequences Kant will draw from this in the Transcendental Exposition: that only on the condition that our representation of space is a priori can we explain how synthetic a priori geometrical prepositions about space are possible. One of the serious omissions of the Critique is its failure to explain to us how we are to construe 'a priori' in two such different contexts as when we say first of our representations of space or time that they are a priori and then when we say this of propositions or judgments. Of course Kant wishes to have the phrase construed in such a way that space , or time, is logically, not temporally, prior to objects or events in it. But how can the representation of any thing or existent be a priori? There are alternative phrases such as zum Grunde liegen , that space or time must lie at the foundations, or must be presupposed, but what precisely are we to understand by such phrases? It should also be observed that what is meant by being able to conceive of is not made clear. Here he says one cannot think of what it may be like to think away space: Man kann sich niemals eine Vorstellung davon machen, dass kein Raum sei. If it means something like "one cannot picture to oneself..." the remark is trivially true since pictures are spatial. It cannot mean that one cannot make sense of "space does not exist" or that one cannot draw any consequences from such a proposition.
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More important, one is throughout advised that space and time and other a priori representations pertain only to the world of appearance. This certainly has the consequence that we are thought "to be able to conceive of" a world of things themsleves which do not lie in any space or time. How then does our not being able to think away space and time in the world of appearance relate to our being able to think them away in a "world" of things-themselves? The conceiva-. bility of that world is never adequately explained, although we are told several times in the Critique that we must be able to think it even if we cannot know it. Finally, a serious issue about time must be anticipated in the present argument. We will be told in 5, argument 2, that time (like space) can be thought void of events. But the first premise of the First Analogy is that time cannot be perceived in itself (kann für sich nicht wahrgenommen werden). We must be prepared for some differences in the problems of empty space and empty time. 3. The third and fourth arguments are also closely linked and in part overlapping. Both of them assert that the representation of space is one, and is not a concept. A concept is a representation (an object of thought or attention) that may have other concepts of lesser generality subsumed under it (unter sich). It is not a representation that holds within it (_in sich) these subordinates or that contains the individuals that may be classified under concepts. This amounts for Kant to saying that the representation of space must be an intuition rather than a concept — the division is exhaustive. May there be more than one space? Our thought of space is not of a multitude of spaces somehow sewn or joined together but of one seamless "particular" within which divisions can be made. If it were not such a seamless whole we would be able to say of it, as we do of other aggregates, that the whole of it is a summation of its parts. (One should read this section in conjunction with the Axioms of Intuition at A162/B202 ff.) We cannot think of space in terms of aggregates as if one might add encompassing shells bounded not by more space but by nothing. Rather we see that "spaces" must be encompassed by more "spaces" and thus we are merely subdividing one space with every advance in the exploration of it. I think this 40
j_s the trend of Kant's somewhat confusing line of thought here. If the representation of space by some such argument can be declared an intuition, since it is not a class concept that comprises a great many members, Kant thinks it must also be regarded as a priori since we see (intuitively, in a sense less technical than Kant's) that we grasp the whole of it without building What we grasp, u p our view through piecemeal research. what we lay hold of, in our intuition of infinite space, or space as infinite, is not just a generalization about "all space" from the spaces we are acquainted with. We suppose that this grasp of it may accomplish what piecemeal inspection and generalization cannot hope to do. We are not prepared to have to revise our view of it because of some future finding that may force us to alter our view. (Perhaps we could confidently think so at least until the twentieth century. But the interpretation of the "new physics" and of "bounded space" is by no means complete as yet.) 4. Kant's principal point is given in the last line, namely that the representation of space must be regarded as intuition not concept. His reason is that while the range of instances subsumable under a concept is potentially infinite a given space contains or is divisible into an infinite number of spaces. Since no concept contains its instances and space does contain them space is not a concept. The only alternative is to regard it as some kind of intuition. What is essentially new in 4 is that space is infinite, an "infinite given magnitude," (eine unendliche gegebene Grosse). I believe this interpretation may be given. To come to know what space is, as we emerge from infancy, is to see that there can be no end of it, for any alleged end would be a bound, and a bound would imply further space. Space cannot be bounded by nothing unless the nothing is itself space; but if it is, then it is simply a contiguous part of one space. And so on, and on. Common sense grasps something that it intuitively sees cannot be limited, cannot extend merely so far, and no farther. We are in command of something boundless, infinite when we grasp what space is; anything less than this would not be space. And since we cannot ordinarily conceive of any new fact" that would compel us to revise our notion and nothing that would nullify it, Kant feels justified in speaking of it as a priori. 41
These then are the arguments that are meant to establish that the notion of space is a priori, that it is an intuition, that it is not "based upon" experience although we come to "possess" it through experience, that it is not a concept of a "commodity" like tigers, windows, right hands, or grains of sand. This would not be too far from affording a notion of space that common sense could recognize as a clarification of its own thought on the matter and not a revision or correction of it except for the fundamental unclarity of what it means to say that space, not propositions about space, as in geometry, is a priori, that it somehow inhabits the soul as an original, not derived, possession. But if we could satisfy ourselves on this matter, the next question would be whether the notion of space so expounded could serve to demonstrate what Kant says it will in the next section, namely, the a priori and synthetic nature of the propositions of Euclidean geometry. §3
Transcendental Exposition of the Concept of Space
We have already alluded to the approach Kant adopts in the Transcendental Exposition. Its purpose is to explain how geometrical propositions can be synthetic and known a priori. We can explain how we can have such a priori knowledge only if the conception of space is understood in the terms of the foregoing Metaphysical Exposition as an intuition that can precede objects and determine the concept of them a priori. Space can be regarded as a priori because it is an aspect of the form of the object of appearance. The paradigmatic self is the author of the object of appearance insofar as its form is concerned, and this means first of all relations of space. The Aesthetic is meant to be the first fruits of Kant's "Copernican Revolution".9 Why are "outer" objects as they are? Because the observer is as he is and because the object is itself but an appearance, not a thing itself. When Kant's argument in the expositions, together with an assumption, is plainly stated we can see where current thought diverges from it. The propositions of geometry are a priori (1) The propositions of geometry are synthetic (2) 42
In addition Kant assumes, Geometry is descriptive of space or spatial figures. (3) The question is, what must be true if all of these are true? The answer is given in the Metaphysical Exposition : Space is an a priori represenation, not learned from experience. (4) Space is an intuition, not a concept. (5) These two say that space is a formal or a priori intuition. They may not be so much proved (or deduced) as expounded (hence, their exposition). We are also to understand, as we see in the next subsection, that the a priori nature of space means that: Space is the form of appearance, not a property of things themselves. (6) What now is the source of modern divergence from Kant? The challenge is to (2) and (3). The fact is, I think, that Kant did not offer adequate grounds for (2), and for rejecting the antithesis of (2), that they are analytic or true by virtue of their concepts alone. The two propositions seemed to him to go together. But the present-day repudiation of (2) has made (3) unnecessary. Since the alternative to (2) is that the propositions are analytic, (1) would of course immediately follow. It seems to me therefore, that what we have in the Aesthetic is a fairly clear account that simply begins from premises that are no longer acceptable. It is not confused or otherwise impossible. The situation in mathematics currently as it affects these matters is that geometry is not inherently about space, not even Euclidean geometry, that several other enterprises have asgood a claim to be known as geometries, and that in their current formulation the propositions of geometry deserve to be regarded an analytic. What made the Aesthetic appear necessary to Kant was that the propositions of geometry had to be interpreted as synthetic (this was to be explained by an appeal to some kind of intuition) and that they were nevertheless necessary truths, or as Kant said, a priori (this was to be explained by the fact that 43
they were about space , and that space was an a priori representation). It is not surprising that the Aesthetic is now thought to be superfluous, at least in respect to space. The concept of space must be considered in the light of three possible interpretations of the propositions of geometry: (a)
If geometrical propositions express and conform themselves to our visual intuition, then, for example, the postulate of parallels and its consequences, (if not the whole of Euclidean geometry) become at most merely probable; whether the described lines as extended do or do not meet in a point is a matter of probability only and subject to experience.
(b)
If geometrical propositions need not conform to visual intuition, they express only the logical consequences of the original ideas and the axioms expressed with their aid; neither the choice of these ideas nor of the axioms or their consequences reflect our notions of visual space.
(c)
Geometrical propositions are neither the consequences of arbitrary axioms nor are they empirical, conforming to visual intuition, but conform to an a priori intuition of space and of flgural relations in space.
Kant in effect proposes (c) as an alternative to either of the preceding alternatives. The points and lines spoken of in geometry are neither tubelets of ink on paper nor do 'line' and 'plane' merely signify sets of elements defined in a certain arbitrary manner. For Kant a geometrical line has no palpable breadth or weight as does the ink of a line drawing, but it is not a mere conceptual entity. The geometrical imagination is capable of grasping "perfect" and "abstract" notions though usually not without the rough stimulus to the imagination afforded by actual visual depiction. No eye of sense can grasp a line without breadth or a perfect solid, but the geometrical imagination, or as Kant calls it, a priori intuition can do so. That is how Kant sees the matter.
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But Kant's proposal of a third way between the empirical and the conceptual has the consequence that the a priori intuition proposed as the foundation of geometrical knowledge cannot serve to support geometry either as an empirical or as a theoretical science. The a priori intuition he supposes relies in effect upon our commonsense visual perceptions of space but then he hopes to be able to refine upon the visual meaning we attach to 'line', 'triangle', 'plane' and the like, and to divest them of crudity and inaccuracy. Such an intuition is impossible to identify either in experience or imagination and it is unnecessary to presuppose it for our gross commonsense use of geometrical notions. To demand "perfect" points, lines, planes in order to have a reference for geometry is like demanding a perfect horse or elephant to provide a perfect exemplification of the species type depicted in zoology. This would make the species preeminent and the individual specimens derivative instead of basing the species on the specimens. It thus pleases Platonists but no one else. Such a hypothesis of geometry would remove it from the area of scientific concern; its alleged perfection would be irrelevant to the development of empirical geometry and unduly restrict theoretical. If geometry is empirical (or in the respect in which it is), restrictions other than those imposed by the methods of inquiry employed are artificial. If it is theoretical, the constraints normally imposed by experience are irrelevent. Kant's a priori intuition offends in both senses: even if there were such intuitions, empirical and theoretical geometry would proceed without their aid. But we must not leave this matter under the impression that Kant has simply made a few blunders. Before we leave the discussion of space we must consider two further topics. The first is why Kant feels it necessary to propose the kind of solutions he did and thus why he gets into the situation just described, the second is just what he had in mind under "pure intuition." The questions that are agitating Kant are how this marvel of perfect science, geometry, is possible and how it can be provided with a sounder philosophical basis than those of the Platonists, Leibnizians, and Empiricists.
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We must call to mind the unusual position which geometry had come to occupy in men's thoughts. Here was a science that appeared to be empirically relevant to the world around us, that enjoyed in architecture, engineering, astronomy, and many other subject matters the most explicit practicality and confirmability conceivable, and that at the same time appeared to consist of nothing but the most self-evident and necessary truths conceivable. By the seventeenth century its triumph was so evident that it became the model of all truth: significant and relevant, not "empty" as logic appeared to be, and yet demonstrable in the most rigorous manner. It was celebrated for itself and the truth it contained and also for the method it used and exemplified. The method in particular came to be generalized and made a model for the presentation of all thought and possibly even for its discovery: the mos qeometricus was made even more famous by two celebrated practitioners, Spinoza and Leibniz. Suspicion of the Achilles' heel of Euclid's geometry, the postulate of parallels, had not yet raised any searching questions about its method or meaning although in Kant's own lifetime Saccheri had really raised such issues without knowing how serious their consequences would be. It is not surprising that Kant should wish to provide a firm ground for geometry. Its truths were indeed necessary, as everyone thought, but he thought they were not true solely from their concepts and definitions. They were moreover significant truths, relevant to the real world. Kant thought, and rightly, that there would be bound to be serious consequences unless an explanation were forthcoming for both purported facts about geometry: necessity and material truth. His uncovering, if not discovery, of the analytic-synthetic distinction appeared to him to explain the second, the doctrine of the a priori nature of space, already affirmed in the Inaugural Dissertation of 1770, contributed much of what was needed for the first. But it was only with his invention of the a_ priori or pure intuition that he felt that all the parts of the explanation fell into place. This raises the second topic we need to discuss here before continuing, namely what Kant means by pure intuition. First of all, pure intuitions must be distinguished from empirical intuitions. The latter would be what we would experience in using our eyes where visual contrasts of color, or light and shade, together 46
with other knowledge enable us to identify, let us say, a rectangle, a house, a table,a sheet of paper. We are not being entreated to turn up empirical intuitions of this sort, nor to make measurements upon round or square physical bodies when we are told by Kant that in mathematics one must go beyond mere concepts and their necessary relations to intuitions to clinch our insights and proofs. But if it is not to these fully concrete intuitions then what are we being asked to turn to? It should be noted that for much the same reasons as those Plato appealed to, Kant would say that empirical intuition could afford us examples of points, lines, planes, volumes, edges and so on only in a crude sense as visual aids. But what would they be aids to? It can only be supposed that it would be the imagination in one sense or another. Thus, what the imagination makes a n effort to grasp is the line with but one dimension and without the breadth or thickness that anything in the visible world possesses if it is at all visible; or the plane, or volume with similar perfections. The imagination may succeed in its effort but only under the stimulus of visible objects that are in themselves crude replicas of perfect lines, planes, and volumes. Hume had followed Berkeley in the rejection of the notion of abstract general ideas. " ' T I S usual with mathematicians to pretend, that those ideas, which are their objects, are of so refin'd and spiritual a nature, that they fall not under the conception o r the fancy, but must be comprehended by a pure and intellectual view, of which the superior faculties of the soul are alone capable. The same notion runs thro1 most parts of philosophy, and is principally made use of to explain our abstract ideas, and to show how we can form an idea of a triangle, for instance, which shall neither be an isosceles, nor scalenum, nor be confin'd to any particular length and proportion of sides." (Treatise I-III-I) Although in general Kant rarely echoes Plato's view, in this instance he is certainly closer to him than to Hume. What he is defending as pure or a priori intuition is in a sense a re-affirmation of the abstract ideas which Hume and Berkeley thought mathematicians 47
were in the habit of claiming to have, with the provision that they are to be regarded as intuitive, anschaulich, and not conceptual or "intellectual." Kant could not have foreseen that the requirement of the corroboration of some sort of inner vision would in the course of the development of mathematics be unnecessary or impossible to meet. But even so he might well have offered a direct response to the views of the British philosophers (assuming that he was acquainted with Berkeley's Principles and Hume's Treatise). His requirement of intuition to support mathematical demonstrations neither brings it closer to "experience" nor shows in consequent fashion why proof that resorts to concepts alone must be insufficient or invalid. There are better ways than Kant's to account for the empirical relevance and the necessity of geometrical propositions. But it is the development of mathematics rather than some inherent error on Kant's part that has shown this.
Conclusions from the Above Concepts Kant now draws a number of consequences from the foregoing exposition and places the idea of space in a larger framework. (a) Given that appearances and things themselves are exhaustive alternatives, if our representation of space must be declared a priori (in order for there to be, as is alleged, truths of a synthetic a priori nature in geometry), then space can be neither a thing itself nor any determination of such things, because we cannot assert anything a priori about things in themselves. (b) When Kant now says that "space is but the form of all appearances of outer sense," this is permitted by his "matter-form" terminology, since space, as well as time, falls to the side of form. He goes on to say that just as we must suppose that the subject's receptivity for intuitions must be presupposed for his having them so also must the form precede all appearances of outer sense. Whatever he can count to the side of form, of relation, is to be numbered among the stock of what we already possess — although who or what the "we" or " I " is in this connection is not, at this point at least, made clear. 48
The schools of Descartes and Leibniz are here unmistakable. Not only is Kant speaking in the manner of Leibniz of an original endowment of the mind, the process relating and forming that with which we are affected (afficiert), but we are also repeatedly reminded of Descartes' procedure with the ball of wax when he finds that only extension cannot be removed by doubt. And yet when Kant confronts himself with the doctrine we may call innatism, as at B167f., he rejects it out of hand. The term he uses there is "implanted" (eingepflanzt) and he argues that if categories were simply implanted dispositions to thought they would be robbed of their necessity. "I would not then be able to say, the effect is (necessarily) tied up in the object with the cause, but that I am so organized that I can only think this representation as so connected." But Kant does not think through the consequences of what he has here admitted, and he never fully clarifies the numerous phrases he uses throughout the Critique to describe our original posession of the categories and pure intuitions nor distinguishes this from innate or implanted posession. In the passage in the Aesthetic we are discussing the phraseology is vague: only from "the human standpoint" (Standpunkt eines Menschen) can we speak of space. The constant use of outer intuition and "receptivity" in contexts where things-themselves are the "givers" is never clarified, yet conclusions are as constantly drawn from assertions involving them. Until such clarification is forthcoming many sentences such as those in the early paragraphs of this section will appear to be question-begging, and there are many more of this kind elsewhere. Kant now introduces a distinction to which he adheres throughout the Critique, between the empirical reality of space (later also of time) or we might say its empirical reference, and its transcendental ideality. This is the coup of a master philosophical strategist. For he lays claim to the term 'real' ( a valuable piece of metaphysical property) and applies it to the object of appearance or experience which, as so far "unpacked" , contains empirical and formal intuitions and will later also prove to involve empirical and pure concepts. The supplemental phrase "transcendental ideality" adds the further provision that the class of assertions these four classes of representations make possible not only applies to human experience but is restricted to it. Elsewhere Kant allows that it is only a cautionary, not a necessary restriction.
49
50
Transcendental Aesthetic Section II Time §4
Metaphysical Exposition of the Concept of Time
There is no concept that permeates the fabric of Critique quite in the manner that time does. At the very outset one should learn that the Aesthetic is but one place where it occupies the center of the discussion. The other places are the Schematism (A137/B176 ff.), the Analogies of Experience (A176/B218), and the First Antinomy (A426/B454), not to mention important encounters of lesser scope elsewhere. Moreover, these later references often seem to revise or even to conflict with what was said earlier. Not only does the Critique recur to the topic of time but it is also an emphatic part of its whole subject matter. Kant more than any philosopher before him including Leibniz and the empiricists placed natural scientific knowledge about a world generally in space, but invariably in time, at the center of the cognitive enterprise. His standpoint involves what George Boas in his Howison Lecture so aptly termed "the acceptance of time."1" But while Kant does not present a picture of the universe in the eternal and immutable terms that Plato, Leibniz and the rationalists used, neither does he exalt time, change, or process in the manner of Hegel, Marx, and others in the nineteenth century. He simply sees time as central to all cognitive concern with man's existing universe. Kant is moreover scrupulous in what he regards as outside the scope of time, notably logic. Even if his view of what logic is or does is traditional, he seeks to exclude from it all temporal, psychological, and rhetorical involvement. He has a clear view of the line between these two which emerges in his frequent and careful segregation of logical from temporal priority or sequence. This may be shown by referring to the form of judgment Kant adverts to in his derivation of the concept and principle of causality. Logically, an if-p-then-q proposition connotes nothing about the temporal priority or order of p in relation to q. But when we use this form to express a process in nature, 51
what p expresses may be a cause and q an effect where the one may report an earlier and the other a later event. Thus, unlike some rationalists, Kant sees clearly that causal relations differ from logical implication precisely because of the factor of time. In a similar manner a subject-predicate sentence is a mere form. When it is employed to express the fact that something has a certain property time enters the picture. We are now thinking in terms of a temporal series, a set of passing conditions or states (expressible as predicates) possessed by a permanent substance continuant in time (expressible by the subject). Kant sees that if we are talking about the world we attend to in daily experience and in science then we are dealing in time-suffused concepts. "Time," he says, "is the formal a priori condition of all appearances whatsoever." (A34/B50) We should be aware at the outset that while the principal concern of the Aesthetic is to establish the a priori character of space in order to explain the asserted synthetic a priori character of the propositions of geometry, the concern with time is not precisely parallel and indeed may even appear to diverge widely from it. There is no science of time comparable to geometry that one might call, let us say, 'chronometry' or perhaps 'chrononomy', and that must be explained by supposing or presupposing the a priori nature of time. Kant succeeds, however, in turning up two propositions about time: it has only one dimension; different times are not simultaneous but successive. In fact, however, it is not necessary that propositions be derived from a science about time. All that is required is that there be propositions of some sort that are synthetic and a priori that owe this character solely to the fact that time is an a priori representation. The propositions just mentioned are found in the third argument of the Metaphysical Exposition of the Concept of Time. In the Transcendental Exposition Kant argues also that certain concepts such as alteration and motion presuppose an a priori notion of time. The proposition about alteration that must be explained is that "only in time can two contradictorily opposed determinations be found in one thing, that is, by one of them succeeding the other." This would be a proposition of metaphysics, one would suppose. 52
In the Prolegomena (|10) Kant asserts a connection between time and arithmetic, virtually as a parallel to that between space and geometry, and in the Schematism he says that "the pure image (Bild) of all magnitudes for outer sense is space, that of all objects of the senses as such is time. The pure schema of magnitude as a concept of understanding is number which is a representation that gathers together the successive addition one to one of homogeneous elements." And in the Introduction he has said that in performing the operation of addition one must go beyond the mere concepts of the addends to call in the aid of intuition by referring successively in time to fingers or points. This is said in support of the notion that intuition must be called in to support our understanding of arithmetical operations. Presumably, as Kant says elsewhere, if we encounter larger numbers we can proceed in "decadic" fashion: we refer first to the ten fingers to make one decade, then again to the same source, if necessary to make further decades, and then a decade of decades to make a hundred, and so on. He does not elaborate but in the discussion later on of the antimonies he affirms the notion that quantities must be conceived of through a process of "successive synthesis." (e.g. A433/B461). It is not clear how Kant would think we proceed with irrational numbers such as t. On the whole one must agree with Kemp Smith's view that "in regard to the nature of arithmetical and algebraic construction he had never really attempted to arrive at any precision of view" (Commentary, p. 131). And he may further be right in saying that Kant probably omitted because of further reflection any effort in the second edition to define the intuitions that arithmetic is said to rest upon in terms of time (Commentary, p. 133). We may now turn to the arguments of the Metaphysical Exposition. In this exposition Kant undertakes to show that our representation of time is a priori not empirical, that it is an intuition not a concept, that it is a necessary, that is, an absolutely indispensable notion, that time is infinite, and that it is in some grand sense one, a kind of transcendental particular or individual. We turn now to the arguments. 1. The representation of space was said not to be derived from observation or from anything "outside me" (ausser mir) for this notion already necessarily involves space. In the present section we learn that the representation of time could not arise from any 53
source in experience for it would then either succeed or coexist with such a source: but either of these relations would itself be temporal, one of the "modi of time", as Kant calls them, and thus presuppose time. It is hard to see that such an argument deserves very much attention. What should we understand by such a phrase as 'derived from1 (abgezogen) as applied to time? If it means simply learned from~experience we should remind ourselves that Kant has generally allowed that even a priori notions must in some sense be learned or acquired although this process of learning cannot show us on what their a priori authority rests. Neither of course can the fact that they have to be learned rob them of such authority. What Kant in this connection calls empirical deduction is a psychological or as he puts it at B119, a "physiological" enterprise that may, as he later says, reveal to us how we acquire concepts and categories even though it may not provide evidence such as one may hope to attain in a transcendental deduction. (It is interesting to note that the characteristic Wittgensteinian gambit, "how do we learn...?" would not have seemed philosophically adequate to Kant; at least he rejected all of Hume's and Locke's efforts.of this sort -- not because their derivation of the ideas was false but because it could not also explain their a priori character.) Kant offered no examples of what a mere empirical deduction would be like, except to say it was what we have Locke to thank for. It would be particularly interesting to know what he would have had in mind as an empirical deduction of space and time. The corresponding point is made by Hume with an almost impudent brevity: "The table before me is alone sufficient by its view to give me the idea of extension" (Treatise, I-II-III). 2. Time is a necessary or indispensable condition for having any intuitions, says Kant. If we accept the ultimate difference between concepts and intuitions, between thought and sensation, as we are everywhere in the Critique asked to do, and if simultaneity is a modus of time, this proposition is acceptable. It would seem to say that two or more intuitions or parts of intuitions are always either successive or simultaneous. It also says much more than this. Time permeates all of what in a narrow sense is experienced. Would it also exist even if there were no intuitions? Is it prior or fundamental in that sense? This appears to be what Kant says, yet I think he does not mean that 54
there can be empty time. Kemp Smith's translation is very misleading here if not flatly wrong. What Kant says is, Man kann in Ansehung der Erscheinungen überhaupt die Zei~selbst nicht aTIflTeBen, ob man zwar ganz wohl die Erscheinungen aus der Zeit wegnehmen TTann: "Although one can quite well remove appearances "from time, one cannot eliminate time from appearances themselves." The dependent clause does not say "though we can quite well think time void of appearances" as Kemp Smith translates it. Kant does not mean that time may be empty, or that appearances a_s a_ whole may be removed from time, leaving an empty receptacle, but rather that any given appearance can be removed, in thought, from time. Of any given event we may say that its non-occurrence is conceivable. If it is asked, can one then conceive of all events as obliterated, leaving empty time, or is it a necessary truth that there be at least one event, or possibly, at least two, I think we must say that the supposition is void of significance: no one knows how to interpret the phrase 1 all events' . The degree to which time permeates all our thought about the material world is scarcely to be questioned. Rather, one must ask what Kant means in saying that time apart from our experience is nothing. We will return to this theme in connection with the empirical reality and transcendental ideality of time at the end of the Aesthetic. An even more difficult question i,s what we are to understand by the phrase 'time itself' which, as we have seen, is crucial in the Analogies, where it is said we cannot perceive (wahrnehmen) time in itself. To this theme we shall of course recur. One thing I believe we must say is that 'time itself' does not mean empty time. 3. As we have explained in the Metaphysical Exposition of Space (p.36 n.7) and as Kant himself concedes on the following page, argument 3 belongs in the Transcendental Exposition of Time and adds nothing not to be found there except examples of axioms of time, such as that time has but one dimension. We may therefore postpone discussion until we reach the Transcendental Exposition. 4. The fourth argument parallels argument 3 regarding space (in B ) . Its essential point is to say that time is a kind of particular or individual, not a class or a class concept. Our representation of this individual is an intuition. The one-ness of time 55
will scarcely need much argument if we confine our attention to events and processes in a world of things seen and felt. It is obvious that 4 is incompatible with what we must now think about time. The special theory of relativity led to a drastic revision of our views of space, time, and motion. "Before the advent of the theory of relativity," said Einstein, "it had always been assumed that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference." The anomalies resulting from the empirical confirmation of the constancy of the speed of light independent of the motion of its source led Einstein to abandon the fundamental tenet of classical mechanics that the "time-interval (and the space-interval) between two events (or two points on a rigid body) is independent of the condition of motion of the body of reference." One can no longer use the terms 'succession', 'simultaneity' and the rest of the time vocabulary in any absolute sense: there may be different times that are not part of one and the same time. According to classical mechanics if we have two uniformly moving coordinate systems devoid of rotation, then natural phenomena run their course in both of them in accordance with the same general laws. But if we are dealling with bodies that are moving with velocities much closer to the speed of light than those of terrestrial or even planetary bodies, then times and distances will be significantly different for them than for ourselves. At most then the Kantian doctrines of space and time can retain their significance only for a confined, although important, area of physical science. But this is incompatible with their absolute or transcendental character for experience as a whole. 5. The final argument asserts that the infinitude of time signifies that all determinate times are but limitations of one such infinite time. Time is an intuition and it is not constructed by the successive addition of parts in the way we progressively probe with ever more powerful telescopes the depths of the world in space to expand the cognitive empire. It is important to distinguish between space and time themselves, each seen to be infinite, and the physical world in space and time. Kant is here speaking only of the former. Even a fairly young child early comes to see that what he thinks of as space 56
and as time can inherently have no limits, either in large or small, for space can only be bounded by space, and time by time. But the world in space and time is something else again. When Kant comes to the solution of the antinomies, the difference becomes more apparent. We cannot speak a priori of the limitless extent in either space or time of the universe, and can neither affirm it nor deny it, for to do so is to go beyond the limits of application of space, time, and the categories, that is, perception or intuitive experience. Here we must work for every meter we advance into the unknown. This world is not an already-given, that is, gegeben, it is assigned to us (by ourselves of course) ü"s i task, aufgegeben. At no point is Kant asking whether time has a beginning — we already grasp its limitless character, if we grasp it at all. Nor does he ask whether space has an outer edge — even a child sees this to be senseless. What he asks is what notions are necessary to facilitate our progressive advance into the unknown reaches of the world, into the remote and the minute. Two such necessities are the notions of limitless space and time, and then also categories and principles.
§5
Transcendental Exposition of the Concept of Time
The term or concept 'time' by itself seems nearly as baffling as 'eternity' so that one scarcely knows what he is being asked with the questions what he thinks time is or whether it is real or illusory. The prior question should rather be whether one understands the time vocabulary: 'duration', 'period', 'interval', 'while', 'before', 'after', 'hitherto', etc. One must know the "modi of time" and must be able to employ the vocabulary in the most specific manner. Only when we approach time so, may we be said to know what time is in the primary sense, though of course not exhaustively. If we do, we know for example that if t precedes u and u precedes v, then t precedes v. This proposition is evidently synthetic, certainly not merely conventional. Its necessity rests upon a grasp of a whole scalar system and not merely upon "the meaning of the word 'precede'." If this is so I would conclude that in this particular the Transcendental Exposition is correct: this theorem of chrononomy, if we may so call it, is synthetic and its syntheticity rests upon something one might wish to call an a priori intuition, as Kant does. To this extent his contentions are Plausible. 57
The purpose of the Transcendental Exposition'3 is to show that only if the generalizations about time in the Metaphysical Exposition are accepted can we explain the truth of the following propositions, which are presumed to be synthetic and a priori: Time has only one dimension.(1) Different times are successive not coexistent.(2) In addition it is said: (3) that only presupposing an a priori notion of time is it possible to explain how alteration in the state and the properties of anything is possible. Propositions (1) and (2) are merely cited as examples. Offering one or two examples in the foregoing sections on space is sufficient for the purpose, since we may be referred to Euclidean geometry for many more examples if we demand them. But the examples for time are altogether too few since there is no body of propositions known as a science of time to which we may be referred for the purpose. If we produce more examples it is at our own risk if we assert that they are synthetic and a priori. Here as elsewhere Kant's procedure is probably to be explained by saying that he was in some haste to compose the Critique and was therefore concerned to abbreviate examples and expositions wherever he thought the reader might be spared them. But one might well prefer to have more time devoted to the elucidation of concepts such as time or the categories and less to other matters such as the Amphiboly or the Transcendental Methodology at the end of the Critique. (At A82/B108 we are told that "in this treatise, I purposely omit the definitions of the categories, although I may be in possession of them." The want of a true analysis of such notions is itself one of the severest obstacles to our acceptance of the deduction of the categories.) In the present section the want of examples is a serious matter: we are being asked to grant the a priori character of time not because there is a whole science such as geometry that cannot be accounted for without it but merely a few propositions that may well have other explanations. It is one of the ostensible purposes of the Transcendental Exposition to account for the concept of alteration. But this is scarcely in order, since the exposition is originally said to have been necessitated by the fact that there are synthetic a priori judgments (or propositions) . At the beginning of § 3 we are told that a certain kind of knowledge is what ; 58
necessitates the Transcendental Exposition. Of course the mere concepts of alteration and motion are scarcely knowledge. As it stands, all that §5 contributes on this subject is that time is an analytic component of alteration and of motion. This is plausible no doubt but it is not apparent why the notion of time that is necessitated must be an a priori representation characterized in the manner just shown in the Metaphysical Exposition of time. It should be noted that Kant does cite a body of knowledge as that which necessitates the Transcendental Exposition namely general phoronomy (allgemeine Bewegungslehre). It is not clear, however, what he has in mind here: mechanics, Newton's Principia, or theses such as those of the Metaphysical Foundations of Natural Science. Mechanics is an empirical not an a priori science and thus not in need of a transcendental exposition (by §3). Parts of the Principia may well deserve such an exposition (as well as the deduction that the conservation, causality and reciprocity principles receive in the Analogies) but it is not apparent why the notion of time as expounded in § 4 is necessitated. One of the most interesting consequences of this section is perhaps the stimulus it affords to present our knowledge of time in a systematic fashion. But we may concede that the Transcendental Exposition of Time is not a very potent portion of the Critique, considering what an important role time plays later on. §6
Conclusions from these Concepts
The intended outcome of the foregoing exposition of time is that time is to be considered as an a priori representation. Clarification of this assertion is the purpose of the present subsection. It is safe to say that no philosopher before Kant had said (or denied) precisely this before and so the need to expand upon it is apparent. It had been said, and denied, that notions like time were innate, but Kant's view of time and space is more subtle and complex than this. What then are we to understand by his characterizing space and time, not only propositions about them, as a priori? (a) Time is not something which might exist of itself or as an attribute or relation of things in 59
themselves. It is in fact not objective but subjective, a feature of our apparatus of thought about ourselves and the world. This is sufficiently startling in itself but the manner of expressing it is more startling. Time (or space) is said to be not simply a subjective representation but an a priori representation, and the two expressions are intended to make the very same statement. Why then is the characterization 'a priori1 preferred? For the reason that Kant wishes to be entirely sure that no one understands him to mean by the representation time only a psychological entity -subjective in that sense. Time and space and certain other notions are presented by Hume as such constructs and an elaborate apparatus of their psychological origin and functioning is worked out. But for Kant this could never enable us to see how, for example, each of these is a system that is necessarily infinite in scope. The "laws of chrononomy" are in that event merely contingent generalizations about how "time passes" in our subjective world: but then the use of either space or time for intellectual or scientific purposes is destroyed. This Kant meant to avoid at all costs. The cost was to present time as many things at once: subjective but not psychological, real but not transcendent, abstract but not intellectual, intuitive but not sensate, and so on. It is the subjective framework for all our empirical intuitions, it is the form of inner intuition. The emphasis here is upon "form." These are the traits of time that Kant tries to pack into the assertion that it is an a priori intuition. (b) Kant now endeavors to combine these several near-paradoxes into a consistent picture of time itself. Time is the form of inner sense, a set of relations that holds together in one system our mental life, abstracting from all content. But introspection suggests no kind of shape for them -- Kant says Gestalt. We are forced to resort to analogy. We hit on the device of a line extending without limit fore and aft. It is easy to forget that all our intellectual devices have had to be invented. The idea of time on the analogy of a divisible, extendable line, so trite to ourselves, was likewise one of man's triumphs of discovery, possibly as significant as counting itself. 60
The aptness of a good analogy is not only that it codifies what we already know but facilitates intellectual venturesomeness and leads us reliably to new truths. This is the consequence of the line analogy for time. As soon as we grasp it we find an application for the fact that a line is extendable without limit, divisible without limit, that we may pass smoothly from one "point" to the "next", that we may number the points, grouping them at will as we proceed. The projection of one line upon another also has a useful application to time. Thus,
A B for every point in A' B1 there is a corresponding point in. A B, so that if A B is a segment of the time series representing a set of experiences (A B ) , then some other longer line A' B' may represent a "richer" experience (A' B 1 ) concurrent with it and be coordinated to it. Any further sets of events or experiences (e.g., M N) can be coordinated in the same manner, so that A B , A1 B', M N, and so on, are not different times but coordinated to one time (as Kant says, "different times are not simultaneous times but successive", and thus simultaneous times are not different, 4 ) . There is, however, one exception, says Kant. The points of the line are simultaneous, whereas the moments of time are successive. This reminds us of a fundamental and unsolved mystery in time: how we can "hold experience together" without the arrest of time. But such an arrest must be meaningless. Strictly speaking, all that is real in time is the present moment, but if we are forever hovering on this moment (it is of course not an identical "this") we do not have the time experience. The completely irreducible intuitive component of the experience of time is what we grasp as the Passage of time, ranging from the few seconds of the specious present William James spoke of to the "ein-mein" experience of a whole lifetime (B132). In order to analyze fully this feature of time we must go beyond the one-dimensional figure. In the Analogies Kant seeks to show that permanence,
61
succession, and simultaneity presuppose three intellectual (as against intuitive) constructs, the categories of relation. As he there shows, we must try to do what is strictly impossible, that is, grasp "time itself" and we can do this only by taking a step beyond intuition. Hence, the need for categories or their principles. The Aesthetic must be supplemented by the Analytic. Kant has drawn an interesting picture of our view of time. Physics has not revised it. Our experience of time has in no sense undergone any alteration, and experience is what Kant is analyzing. (c) The third generalization Kant permits himself is that time is the formal condition of all appearances, inner or outer. We cannot fail to notice the apparent conflict between statements in (b) and (c) that "time cannot be the determination (Bestimmung) of outer appearances" and that time is "the immediate condition (Bedingung) of inner and the mediate condition also of outer appearances." The statements are equally obscure. If the first one is taken to mean that events in space cannot be ordered in time, the statement seems certainly false even if space has only the qualified "objectivity" Kant accords it. We may then suppose that it is Kant's intention to see time as determining only inner sense. Then if outer events are mediately inner events, as may be asserted by (c), they too are conditioned by time. This would be to take time in a very "subjective" sense, something like an "experience of duration" which we do doubtless have. But it is to seriously weaken, if not destroy, the idea of equably flowing time that Newtonian physics presupposes. We shall recur to these themes of "inner" and- "outer" below. The emphasis upon time as the condition of all appearances (c) makes explicit Kant's "acceptance of time". All things in heaven or earth are ultimately subject to human "interpretation" and thus to formal determinants in our experience. The most pervasive of these Kant now declares to be time. This seemingly innocent statement may, and I for my part think that it does, contain the seeds of disaster in the Kantian system. We shall see this emerge even more clearly as we proceed to the doctrine of synthesis later on. Kant here states explicitly that the time experience is the fundamental framework of all experience. 62
All representations are inner before they are anything else. There is a want of any definition of 'inner' and 'outer': obviously their one- or threedimensionality is insufficient for this purpose. We are left with the bare assertion that all experience is inner experience -- including outer experience. The inner is inner and the outer is inner too! We cannot here employ the ordinary naive use of these terms : only an extra-ordinary use and definition would obviate the paradox, and this is nowhere proposed. Kant's purpose is to make a broad generalization about experience. We commonly suppose ourselves able to distinguish between experience about ourselves, our aches, pains, sensations and do on, and about the things around us, trees, houses, chairs, hats, and shoes. Kant is pointing out that the latter are first of all sensations, or intuitions, before they receive the more complex organization of causal laws afforded through the categories and are experienced in a broader sense of the term. This distinction is incidentally of the utmost importance in Kant. Experience in a kind of rudimentary sense, we may call it experience^ (E. ) , is simply having sensations, sense data, more or less what Kant calls empirical intuitions. Experience of objects and processes regarded as and treated as objective and fully organized by the categories is experience in the more familiar sense; we may designate it experience, (E2). Kant's point now is that we have E-j in either the inner (subjective) or the outer (objective) sense only within the framework of time. Thus as he says, "Time is an a priori condition of all appearance whatsoever." Notice that he says a condition (eine Bedingung) , for there are others, such as empirical concepts and also the categories. (Appearances are objects and processes fully organized by pure and empirical intuitions and pure and empirical concepts.) But not only is time, as a pure intuition, a necessary condition of intuitions, but the reverse is also true: if we abstract from intuitions time is nothing at all. If we try to think of time outside the framework of an organized active and receptive mind it vanishes. "Time is solely a subjective condition of human intuition." If we now recall that things themselves are purported entities totally other than appearances, it follows that we cannot ascribe temporal attributes 63
to them. The phrase transcendental ideality of time is meant to convey just this. Time is an indefeasible aspect of the world of phenomena. Kant does not claim that a world of things themselves would be one of "nontime" or "anti-time." He merely warns us that time cannot be ascribed except where conditions of inner or outer intuition are met. At the same time, by a bold stroke, as we remarked earlier, he claims the fullest right to speak of the empirical reality of time. He throws out a challenge to anyone who, like Berkeley's Hylas, locates the truly real in an inaccessible substratum, mental or physical. The first question to be addressed to such a philosopher would be what warrant of experience enables him to attribute meaningfulness to assertions about substrata. None of course. By this, the foremost relevant test, time is certainly real. First, as Berkeley himself (or Philonous) has reason to speak of himself as a realist (had he chosen to do so), so Kant may claim to be a realist and in a closely similar sense, although his misreading of Berkeley made him think; Berkeley an "idealist", a confusion that continued through the nineteenth into our own century. There is also a further interpretation that brings Kant even closer to ourselves. The transcendental ideality of space and time is meant first of all to exclude the substratum metaphysicians for whom reality is everywhere except in our experience. But in a less metaphysical sense it also liberates as well as restricts. There is no reason why physical research which finds itself forced to speak in such terms as curved space, reversible time, and converging parallel lines must be regarded by the Kantian as uttering nonsense. "Apart from experience, space and time are nothing"; this means, if the conditions of ordinary "terrestrial" intuition cannot be met, then the absolute coordinates of space and time are no longer applicable. The metaphysician may here fall into paradox and confusion. But the theoretical physicist is no metaphysician who reaches into a world of things-themselves when he employs his bizarre concepts: he is simply compelled to resort to a more complex language which appears to defy geometry but is in fact only something other than familiar geometry. No one experiences anything that is denoted by 'curved space' and 'reversible time 1 ; hence space and time are in this sense "nothing."
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What Kant wishes to exclude is metaphysical nonsense, not theoretical novelty. It is inconceivable that with his lifelong enthusiasm for and unusual competence in science, he could have wished to set metaphysical bounds to physical explanation. We must expand our knowledge by the orderly progressive development of the laws of nature, provided that we can always recur to an experienced world of space and time. The Kantian view is hospitable to the progressive expansion of the scientific view of the world. But we cannot ignore the authority of naive space and time. What is the world in total abstraction from them? Kant does not say with more recent positivists that the question is meaningless. He merely answers that it can be nothing for us. §7
Elucidation
This subsection proceeds from the immediately preceding topic, the transcendental ideality and empirical reality of time (TIER), to considerations touching not only on time but space as well. Kant begins by attending to an objection which proceeds as if it were uttered by someone who believes him to have said something such as "time is not real." Change, alteration, it will be said, is undoubtedly real and it is impossible unless time elapses. Hence time must be real. Of course, replies Kant, I grant the whole argument, and goes o n to reaffirm the position just developed of the empirical reality of time. He adds that it is only "absolute reality", reality as pertaining to a substratum or thing itself, that cannot be accorded to time (kann ihr nicht zugestanden werden). In the latter phrase, Kemp Smith's "has to be denied" exceeds what Kant says: it is one thing to deny reality to time, another to be unable to attribute reality to it. Defenders of this "objection" will propound it specifically regarding time but not space, says Kant, because while inner experience will appear to entail the reality of time, nothing will so convincingly entail the reality of space: we are thought to be intuitively certain of and to immediately confront the self, whereas the external world is thought to be "problematic." Kant of course boldly sweeps all of this aside. The "self" is just as problematic as the outer world, and also just as little. What we are dealing with are representations, the psychological 65
phenomena of the inner and the physical phenomena of the outer world, that is, the world of appearance. The forms of appearance, time and space, do "really and necessarily" belong to this world. After a glance back at the ideas of the transcendental expositions Kant turns to the defense of TIKR. He sketches out where he stands in reference to the supporters of absolute space and time and relational space and time, typified respectively by the mathematische Naturforscher and the metaphysische Naturlehrer. In neither instance is it the actual content of physical science that is brought into question, since Kant was a Newtonian, but rather the metaphysical interpretation given to space and time. In other words, as far as physics itself was concerned Kant's adherence to the doctrine of fixed coordinates for space and for time was in no degree weakened by his interpretation of them as a priori intuitions: the Aesthetic was not proposing a revision of physics. What he now says is that the first of the above two views renders the synthetic a priori character of geometric propositions inexplicable since it presents space as only transcendentally real. The second view cannot account for the necessity of the propositions since on that view space is not a priori but derivative from experience. Kant argues that his own view disposes effectively of both difficulties. Finally, there are no other forms of pure intuition than these two, Kant states. All other physical notions, for example, motion and alteration, involve something empirical. Space and time are the only pure elements in experience and in its extension in science other than those that are pure concepts, that is, the categories. §8
General Observations on the Transcendental Aesthetic
I. The concluding division of the Aesthetic, particularly I, offers a rather lucid account and some further defense of the whole position that has been arrived at. It states in general the case for the a priori nature of space and time and assures us that this is now established beyond doubt. Alternative standpoints, particularly those of Leibniz and Wolff and less specifically Locke, are declared again to be untenable. In a word, the position defended is that 66
of TIER, which has been affirmed in § 3 and § 6 for both space and time and the doctrine of the Aesthetic that space and time are the a priori forms of intuition, of outer and inner sense. The distinction of appearance and things themselves must be maintained absolutely: Kant says toto coelo. One of the worst of errors, he says, would be to weaken this by supposing that a more assiduous scrutiny of appearances might at last reveal thingsthemselves. It is just possible to offer such an interpretation of Locke's view of physical inquiry into substance. The study of matter was progressing in his lifetime and was already foreseen to be likely to progress further almost without limit. It is difficult to discern a perfect distinction between Locke's idea of body or matter, over which the senses range, and what he called the philosophical idea of substance. But certainly at times Locke speaks as if the empirical advance of physical science in the former will diminish our ignorance of the latter, the "real constitution" of substances. This is what Kant disputes. He seeks to leave us in no doubt about the range of difference of appearances and things themselves. (Of course Kant's own use of the term 'substance' must not be set in place of Locke's or identified with that of 'things themselves': its reference is wholly to appearances.) Kant's distinction between appearance (comprising matter or substance) and things themselves is wholly philosophical and would remain in force even if in some manner we might plumb the depths of matter to an ultimate level, as in a certain sense science has done since Kant's time. His effort here is again a defense of science, giving it the assurance that no philosophical bounds can conceivably be imposed upon it. The Leibnizian view seems to Kant to have done just that. All notions based upon the senses, upon space and time, are declared essentially confused by the rationalist. Only clear and distinct, conceptual ideas present us with realities. Kant points out that the difference between clear and confused ideas is "merely logical" for by definition the content is the same, now confusedly, now clearly discriminated. For Kant, on the other hand, what is given in and through perception or related to it by confirmed physical laws is real. To locate realities in a realm grasped only by the intellect is to render the world of phenomena and phenomenal processes illusory and to grossly misunderstand the role of the intellect, the understanding, 67
in knowledge and its acquisition. Thus Kant on every ; occasion reaffirms the tenet that science is what is • definitively knowledge (not metaphysics, or mathematics: as Plato and perhaps also Descartes conceived it, or theology, still less, mysticism, poetry or other candidates that had been proposed). The rationalist does justice neither to intuition nor to the understanding, ; neither to the domain of sense nor to that of the in- ' tellect. "The Leibniz-Wolffian philosophy," says Kant, "has given an altogether wrong direction to the investigation of nature and the origin of knowledge," locating reality in a domain that transcends intuition and misconceiving the instruments by which knowledge is acquired. What is identified here as a world of reality is indeed a world, in some manner of speaking, of things themselves. But it is not a world that intuition somehow tries but fails to apprehend or know: it is not known at all in any manner, even by the intellect. The intellect, it is true, can think it, but it cannot know it, having ex hypothesi no support from the side of intuition: this must accompany all non-vacuous cognitive thought. It is of the utmost importance to see that Kant is truly revolutionary in the direction and method of his thought. He is not merely reshuffling the cards as between "rationalism" and "empiricism." The metaphysical period of philosophy has been brought to a definitive end. The roles of philosophy and of science have been interchanged: the paradigm of knowledge is science itself. The task of philosophy is critical. From here, after the divagations of the Hegelians in the nineteenth century, the way leads directly through the Neo-Kantians to the positivisms of the twentieth century. Kant's is the first philosophy of science and the first philosophy for science. He is wholly acclimated to the idea as even Hume was not, that science was henceforth to be the domain of truth. Returning to the Leibnizian distinction, Kant presents what amounts to a defense of sensibility. It is not to be treated as merely confused as against clear cognition, as if it were an obstacle to truth that needed to be removed. It differs not logically or formally from conceptual thought but materially. That is to say, sensibility and thought each contribute independently two necessities of knowledge. Moreover, to treat these as respectively the sources of error and truth (for this is what is being 68
done with the distinction of the confused and the clear) is to ignore the reliable, common sense methods of distinguishing these in the domain of sensibility itself. We know perfectly well, Kant is saying, how to tell what in appearances is valid for all human minds and what appears only incidentally in this mind or that or under certain conditions. Appearance is the domain of sensible knowledge; to identify truth with things-themselves is to remove it beyond our reach. Here Kant makes an important distinction in the use of the term 'appearance1. His own term is of course Erscheinung and can also be translated by •phenomenon'. He warns several times in the Critique that we must not confuse Erscheinung with Schein, that is appearance (phenomenon) with illusion; in English one might say we must not confuse appearance and apparition. In this primary sense, an appearance for Kant is, in the ordinary sense, first of all a genuine occurrence,a reality, a thing or event that is intersubjective, publicly verifiable, there for all to see. An appearance is, as the colloquial phrase goes, something that "puts in an appearance." With this, in the same ordinary sense, we often contrast what we say is a mere appearance. The rainbow, Kant says, may be regarded in this manner in comparing it with rain. Both the rain and the rainbow are, however, part of the world of nature as perceived, the world of appearance in Kant's primary sense (A45/B63). With appearance in this sense Kant now contrasts the world as thing in itself. We must not suppose that the latter is the real world and that the former is illusion. On the contrary, as just noted, the world of appearance is the world to which the term reality applies. Thus we must keep separate the distinction between appearance and reality in the ordinary sense (the rain as against the rainbow) from the distinction between appearance, the world of phenomena in general, and the world as thing-in-itself. The term appearance may therefore mean, occasionally, something which, as Kant says, belongs to intuition only accidentally; more commonly it means for him the world of experience generally as against the world of things themselves. "An appearance (in Particular) is simply an undetermined object of 69
empirical intuition" (A20/B34) . The term 'reality', correlated to the first of the foregoing uses of 'reality' is that which in common sense ways is distinguished from what are deemed illusions. In Kant's sense, these are empirically distinguishable in the world of nature to which the term 'reality' is primarily applicable. Finally, the unique philosophical use of 'reality' to refer to things in themselves as if these and not the world of nature were the world of reality is something which Kant invariably denounces as disastrous metaphysical confusion. Things themselves may be said to be transcendentally ideal. To attribute to them transcendental, or as he also says less felicitously, absolute reality, leads us directly into the errors of the so-called rational sciences. Finally, section I attempts yet another proof of the principal contention of the Aesthetic, that space and time must be regarded as a priori. In effect the transcendental expositions are repeated or reaffirmed: we must account for all synthetic and a priori judgments. We observe of certain judgments concerning time and space that they are necessary and universal truths. We ask whether we arrive at them through concepts or intuitions, and whether they are a priori or a posteriori. It is evident that no merely empirical or a posteriori source suffices. When we then ask whether the a priori source is that of concepts or intuitions we see that it cannot be the former. Appeal to mere concepts is for example, insufficient to convince us that two straight lines cannot enclose a space or that given three straight lines a figure is possible. We are forced to appeal to an intuition. When we ask whether it is an a priori or an a posteriori intuition, we see that it cannot be the latter, for here we are not at all prepared to undertake an empirical investigation. The intuition must be a priori. Since the question of what not just an a priori proposition or judgment is, but what an a priori intuition is, is altogether crucial, we may again ask whether on this occasion Kant has thrown any more light on the matter than he did in the Aesthetic. He asks, if there were no such intuition here, how could you say that that which is necessarily contained in the subjective conditions you are specifying for the construction of a triangle must also characterize the 70
triangle itself? (Wie k'önntet ihr sagen, dass, was in euren subj ektiven Bedingungen einen Triangel zu konstruiren notwendig liegt, auch dem Triangel an sich selbst zukommen müsse?) Or again, if it were not so, you could not a priori affirm anything of a synthetic nature about external objects (so k'önntet ihr a priori ganz und gar nichts über "äussere Objekte synthetisch ausmachen.) This of course reiterates one of the basic premises of the Aesthetic that it is impossible to offer fully consequential proofs of geometrical truths from concepts alone. As Russell observed in his Principles of Mathematics (p. 4) in the early years of the development of modern logic, the Aristotelian logic and its early successors in the nineteenth century were in fact "inadequate to mathematical reasoning... In this fact lay the strength of the Kantian view, which asserted that mathematical reasoning is not strictly formal, but always uses intuitions, i.e., a priori knowledge of space and time." Russell adds that "this part of the Kantian philosophy is now capable of final and irrevocable refutation." This undoubtedly still represents the prevailing view. II. The remaining sections are additions of edition B, and as so often happens in this edition, do not always succeed in improving on A. Kant first produces arguments in further support of the TIER of the appearances presented in outer and inner sense. Appearances, we must remind ourselves, are presentations fully structured by the mind's efforts, and all form, structure, or relation derives from this source. The matter of our knowledge, deriving from empirical intuition, enters into knowledge only in connection with our apprehension of structure, that is, the location of the relata, their change of location, and the laws about forces that determine such changes. Of the being of objects we know only that they are related to a subject. As things themselves they are transcendentally ideal: we know things only as they appear to us, not as they are. Kant argues that we are in a similar situation regarding inner sense. Here we have as little a direct apprehension of the self as we had of the external things themselves: we are not gifted with a direct or "intellectual intuition"1^ of a spontaneous, "self-active" self. It also is a world of appearance and we apprehend the self not as it is but only as it 71
appears. We have as little comprehension of a transcendentally real self as of a transcendentally real world of things themselves: our position towards these must be that of transcendental idealism. But if we agree with Kant that the obverse of this coin is the empirical reality of the physical world and of inner experience, it is not we but the defenders of TREI who have contented themselves with a phantom. We may at this point anticipate latter matters by sketching out Kant's threefold view of the self. The "inner world" of immediate consciousness, of introspection, may be called the empirical consciousness in order to distinguish it from what Kant by and by will characterize as the transcendental unity of apperception. The latter could properly be called the epistemic presupposition or epistemic self. The empirical consciousness and the epistemic self may be numerically identical, but in fact we can never know this. To have knowledge of x presupposes that we have appropriate intuitions of x, precisely what we do not have of the epistemic self. It is a necessary presupposition of knowledge not an object of knowledge. But our awareness in empirical consciouness affords the subject matter of empirical psychology, which with physics is one of the twin sciences basic to all others for Kant. One must also distinguish both of these from the soul of which theologians and rational psychologists (as against empirical) claim to be able to speak. Kant challenges their capacity to say anything whatsoever that is cognitively meaningful in the Paralogisms of Pure Reason further on. The theologian's mistake rests upon his neglecting to identify and distinguish the empirical consciousness and the epistemic self, as we shall see. III. The third topic discussed continues the second and simply adds the now familiar caution that while the worlds of inner and outer sense are transcendentally ideal (and of course empirically real) they are not illusions. On the contrary the alternative to this does render them illusory, since it locates reality not in the world of inner and outer sense (which it treats as empirically ideal) but in a world that is either inaccessible or is purported to be accessible only to the intellect but not to the senses. That way, says Kant, lies illusion, the inner and outer worlds both dissolving into nothingness with only the dubious 72
compensations of other worlds promised by Platonists and Leibnizians. We may here remark once again Kant's fundamental and irrevocable hostility to scepticism and to Platonism in most of its tenets, and his equally unshakeable commitment to common sense and to science as the prime locus of truth and knowledge. Not only is he hostile to scepticism he ignores it as a madness that is scarcely worth more than patronizing regard. His entire system is built on the premise that there is knowledge: the problem is to find what it is and "how it is possible." He is a descriptive metaphysician, in Strawson's phrase, leaving the world as he finds it and concerned to analyze or "criticize" our knowledge or purported knowledge of it. To the sceptic he says curtly, "Don't be a fool! Of course there is knowledge. Let us do all that is in our power to understand what it is, what its limits are, and how we must interpret what lies outside it." Kant's splendidly sane gesunder Menschenverstand is a tower of hope and optimism. This subsection shows, however, that Kant might have found allies in the very quarter in which he thought he saw sceptics. The "good Berkeley" is alleged to have denied the reality of bodies when in fact his standpoint in regard to outer sense is essentially identical with Kant's in various respects and compatible in others. Berkeley himself repelled charges that he was a sceptic by effectively turning them against his adversaries. Kant either misread Berkeley or, more likely, had inadequate opportunity to read him and spoke of him only on the basis of indirect report, for he knew little English. IV. The final argument in defense of TIER of space and time is theological and not likely to be of much interest to us since it speaks of nearly unintelligible attributes (intellectual or original intuition) of an unconfirmable being. If, says Kant, contrary to TIER we affirm TREI of time and space, they are then conditions of all things, even of God's existence. Surely this could not hold true of the primordial being, Urwesen. But if space and time cannot be TR they must be thought to be conditions of finite, derivative or sensible intuition, such as our own. A similar kind of intuition may be attributed to all finite beings including those, if any, that may be other than human. This argument concludes 73
the defense of the standpoint enunciated in the Aesthetic. Conclusion of the Transcendental Aesthetic The general task of the transcendental philosophy is to answer the question how synthetic propositions are possible a priori (on this occasion Kant says "propositions," Sätze, instead of "judgments"). In space and time we have two of the indispensable necessities for answering this question. If in a proposition the intention is to go beyond the concept of the subject, these a priori intuitions are precisely what is needed in order to effect a synthesis with the idea of the predicate. But the range of the propositions in which this is possible is the objects of the senses, objects of possible experience.
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TRANSCENDENTAL DOCTRINE OF ELEMENTS Second Part Transcendental Logic Introduction Idea of a Transcendental Logic I.
Logic in General
A fairly prevalent view holds that Kant's preoccupation with logic and especially his use of the formal logic of his day as a model for the organization of the Critique (indeed all three Critiques) are misleading and that they suggest to him and often seem to compel him to take up topics that have nothing much to do with the business at hand. The artificiality of the organization is said also to affect the content. This is not an altogether inappropriate criticism. Yet in the end it must be conceded that all of the topics Kant takes up are in some measure relevant. Even when Kant's reason for taking up a topic, being often dictated by the "architectonic", is not good, what he has to say on it is almost invariably significant. One must avoid constantly offering to rewrite an author's book for him. No philosophical author has had to endure so much advice on this matter as Kant. The short sections introducing the Transcendental Logic are relevant examples. We must frequently ask ourselves what role Kant assigns to logic in the structure of knowledge and in particular what he conceives a priori truth to be. The present sections help to answer such questions, on the whole clearly and much to the point. (The subject is taken up once more in a section preceding the Analytic of Principles, at A150/B189.) Kant's view of logic fortunately antedates the Hegelian and later conceptions of it and accords it a much more significant and proper place than the empiricists did. The developments of logic in our own century are almost wholly compatible with what Kant had to say about analytic a priori propositions. What he called transcendental logic is not, nor was ever 75
intended, to be an alternative or rival to formal logic: it is tied up rather with his philosophy of science. What is important in it is not in any very familiar sense transcendental and in fact most of what Kant speaks of as "transcendental" is expressible also in other more familiar terms. There is no doubt that Kant could accept the essential core of modern logic: question would arise only over such questions as whether he would insist on retaining his view of mathematics as synthetic and a priori or accept the views of those who see it as continuous with logic. He could however, without any offense to logic maintain his view that the basic principles of the metaphysics of science (e.g., the causal principle) are synthetic and a priori and demand a proof such as he thinks has been provided in his Deductions, for those are matters that lie outside of logic. We may be brief with his outline of logic since it presents no particular difficulties. What is archaic in it is essentially harmless and corrigible. Pure logic he tells us, "is a body of demonstrated doctrine and everything in it must be entirely certain a priori.' (A54/B78). It has nothing to do with empirical principles nor does it borrow anything from psychology. It abstracts from all content and is concerned altogether with the form of thought. His division of the subject illuminates the distinction between transcendental logic and what he calls common logic; certain divisions are not particularly well discriminated.
Transcendental Logic
Common Logic
General Special Logic (Rules or organon for a particular science) Applied Logic (A cathartic of the understanding the psychology of thought and persuasion : rhetoric)
76 .
Logic
Pure Logic, Formal Logic (pure doctrine of reason)
It is somewhat obscure, but unimportant, precisely what Kant intends by "special logic." Perhaps he is alluding here simply to the procedures which practitioners of particular sciences, and arts too, employ and inculcate in order to advance knowledge. It is not apparent that these techniques or procedures of investigation are different from what is narrowly a part of logic, but in a provisional way allowance may be made for them. One thing is significantly missing here and if it had occurred to Kant to include it, his whole view of the deduction problem might have been different, namely a logic of induction, probability, or generalization. He might, that is to say, have conceived the problem of the Causal Principle in terms closer to both Hume and John Stuart Mill. They were all certainly speaking of the very same thing. What is unique in Kant is his proposed solution of the basic question of the ground of induction (or the uniformity of nature, or the unique "necessity of natural laws") by resting everything on the "possibility" of a special kind of proposition which is said to be both synthetic and a priori. It is almost superfluous to draw attention to the oft-quoted words of this section regarding the mutual necessity of sense and understanding. Since they require no explication we need merely read them and be prepared to reflect on them almost constantly from here to the end of the Transcendental Logic. "Our nature is such that intuition can never be other than sensate, being the mode in which we are affected by objects. The capacity to think objects of sensate intuition, on the other hand, is understanding. Neither one of these capacities is to be preferred to the other. Without sensibility no object would be given us, without understanding none would be thought. Thoughts without content are empty, intuitions without concepts are blind. Hence it is as necessary to render our concepts sensate (that is, to support them with an object in intuition) as it is to make our intuitions intelligible (that is, to bring them under concepts). The understanding cannot intuit, the senses cannot think anything. Only through their union may knowledge arise." (A51/B75) 77
II.
Concerning Transcendental Logic
What Kant now proceeds to describe as "transcendental logic" is, as noted, in no sense a rival or alternative to formal logic. It is given the task of demonstrating certain truths that are indispensable to the pursuit of empirical knowledge. Formal logic performs a different kind of service, demonstrating the principles that must guide sound argument on any and all subject matters. Of course it would now be said that this is certainly not the only purpose of formal logic. Pure or formal logic, says Kant, considers only the form of judgments without regard to whether their content is empirical or a priori. The inquiry he calls transcendental logic abstracts not from all content whatsoever but only from all empirical content, thus confining itself first of all to a priori representations. But to this limitation another must immediately be added: not all a priori representations are transcendental. Only those considerations are to be called transcendental which are essentially "enabling" in character, making experience of objects and thus empirical knowledge possible. One of Kant's most unshakeable tenets is that experience is not something poured into our heads or our sense organs from the "outside": it is itself the product of conditions other than the functioning of intuition or sensation. This is shown by the fact that we are able to say some things a priori about the (inner or outer) world so experienced, and what we can say is not merely guided by the a priori procedures of logic as it is when we say that a cat being a mammal is a vertebrate. We must investigate this "enabling" power. The issue is in no sense a novelty but Kant has placed it into a comprehensive frame of reference. Hume's Treatise had set itself the problem: for what reason do we "pronounce it necessary, that every thing whose existence has a beginning, shou'd also have a cause." And Leibniz had deemed it necessary to propound a principle of sufficient reason in addition to that of identity to account for knowledge. The indispensable role of this ingredient in the economy of empirical knowledge is what Kant singles out for investigation. But his approach is somewhat closer to Leibniz than to Hume, for he is concerned more with why in general categorial notions are indispensable to knowledge than he is with what in detail they say -- and as we recall, 78
Hume's struggle with this issue is heroic, if anything philosophical can be so characterized. We are then in transcendental logic to examine what conceptual conditions are indispensable to knowledge, as in transcendental aesthetic we pursued comparable intuitional conditions. Such a science, says Kant, must study the "origin, extent, and objective validity" of these concepts. III.
The Division of General Logic into Analytic and Dialectic
The essential contemporaneity of Kant's views on logic is further confirmed in the present section which in three brief pages expounds the distinction between material and logical truth and expatiates on the use, or rather the misuse, of the latter. Here we must repudiate the caricature, of "mere game-playing", as the section has been characterized. The distinction of analytic and dialectic enables Kant to make the momentous distinction between non-empirically derived notions such as those named by the categories and rational cosmological, psychological, and theological notions such as the First Cause, the Immortal Soul, and God. Showing that the first class of notions is absolutely necessary and the second absolutely foreign to the economy of experience, and scientific knowledge occupies almost the rest of the Critique. It is a master stroke of philosophical strategy. Whatever shortcomings Kant's analysis of the categories and the categorial principles has, his specification of the criteria by which these "rational ideas" are to be excluded from the domain of empirical knowledge is still very generally respected. The issues which Kant is now on the verge of broaching are that of the real and the illusory in knowledge, of the meaningful and the meaningless, the verifiable and the unverifiable, although none of these notions is here taken in its whole extent. He will speak of unverifiable "rational ideas" in the compassionate manner of one who seeks to understand how and why they arise, what human significance their place in the history of thought betokens, and not with the obtuse pretensions of latter-day positivists who are satisfied only with a brutal Totschlag. Kant now seeks to show that one cannot do justice to science, morality, or religion without a careful distinction of their function and orientation. 79
The first thing Kant has to say about truth is that there can be no universal criterion (his term) of material truth and indeed that it is absurd (ungereimt) to look for one. What a proposition p claims is that some condition P exists, and P can render p and £u> other proposition true, unless it be some other sentence synonymous with p. To cite "correspondence" as what renders a proposition true is in effect merely to offer a definition or even a synonym but in no sense a material criterion of truth. May we then suppose that there is a formal criterion of truth? The answer is as follows. A monadic sentence may have a predicate which is identical with or "contained in" the subject, or incompatible with it, or neither identical nor incompatible with it. If the first situation prevails, the sentence is logically true; it has no material content and makes no material affirmation about anything. If the second, the sentence fails to make any affirmation at all. These are the situations in which formal considerations are alone decisive. For Kant we need go no farther than the concepts themselves to decide this. The truth of the third type of sentence lies wholly outside this scheme of things; material considerations alone are relevant. We may add, if we wish, that sentences of this sort must not contradict themselves but this is strictly unnecessary. It is merely cautionary, a conditio sine qua non; a necessary, not a sufficient condition; a canon of truth, not an organon • a negative touchstone of truth, Probirstein der Wahrheit. Kant's procedure then is this: (1) inspect the sentence to see if the predicate is formally identical with the subject; if it is, the sentence is true; (2) if the predicate is incompatible, that is, formally identical with the subject in all respects except that it negates the subject, the sentence is false; (3) all other predicates are compatible with their subjects (unless other criteria than logical are invoked: e.g., when we exclude, for example, 'red is rational'), being neither identical (1) nor incompatible (2). In this way, Kant, admittedly with some elaboration on our part of what he is saying, seeks to show that logical truths say nothing of a material nature and that logical criteria for sentences show us only which sentences need or do not need material corroborat ion. 80
Here as elsewhere it is not inappropriate to say of Kant's use of formal logic that its purpose is solely good housekeeping: it keeps the house of reason clean and efficient for its purpose, nothing more. Kant's view of logic while scarcely inspiring to the modern logician is at least acceptable on most essentials. There was no reason whatever to attribute very many virtues to logic as it stood in Kant's day. We may now be content to employ the logical criterion of identity in the manner and for the purposes described. We may, however, lose sight of these conditions and proceed as if we were able on the basis of mere logical considerations alone to determine truths without resorting to the empirical inspection of facts. When we do so, we employ formal logic as an organon and not merely as a canon of truth. We have used it as regards its subject not only for analytical purposes but dialectical as well. We may mention an example drawn from transcendental dialectic though it will also serve the purposes of general or formal dialectic, namely the Ontological Argument. The whole purpose of this argument is to show that solely on the basis of a concept, God, we can demonstrate a material truth, God's existence. The source of this fallacy Kant has definitively exposed in the Ideal of Pure Reason. There are also other examples of the misuse of logic, or indeed, of pure reason, as the very title of the Critique suggests. Kant's reason for adopting the term 'dialectical' in this connection to label a certain misuse of thought goes back to Aristotle. The distinction between demonstrative and dialectical reasoning is made in the Topics (100a25ff). The misuse of reason or at least its use for questionable or nefarious ends is a familiar topic in both Plato (cf. Gorgias) and Aristotle. Whatever the precedent may have been, Kant uses 'dialectic' to mean a logic of illusion, covering both the orator's comparatively trivial misuse of reason to impress an audience with pseudological stratagems or the serious effort, as in the Ontological Argument, to reach material truths solely through logical means. As we shall see, transcendental dialectical illusion is far different from and far more philosophically insidious than mere rhetorical deception.
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IV.
The Division of Transcendental Logic into Transcendental Analytic and Dialectic
The application of the distinction in the previous section can now be made very easily. We must again remember that the designation 'logic1 is not an absolute necessity for this portion of the Critique. It suits it only in the sense that intuitions and concepts may by a traditional distinction be assigned respectively to the area of the aesthetic and the logical, in a primary sense of the terms. 'Transcendental' may be defined as pertaining to that which does not arise from experience and so in a limited sense transcends it but applies to experience and makes it possible. In the Transcendental Logic we isolate "that part of thought which has its origin solely in the understanding" (A62/B87). In the preceding section we saw that we cannot with the help of logic alone or through mere conformity to it hope to establish material truth: conformity to material conditions is as necessary as logical circumspectness. So here we must be careful not to sever the bond Intuitions-Concepts. To suppose that knowledge may yet be possible when we employ the Pure Concepts which are now to be expounded in the Transcendental Analytic without providing a reference to intuitions is to be the victim of dialectical illusion. It is to employ such a body of concepts not merely as a canon but as an organon of knowledge. The results will be the evident transgressions of the metaphysical or "rational" sciences -- rational, that is, because they suppose that they may significantly employ transcendental concepts even without possible reference to empirical intuition to establish truths about God or the soul. With these explications, Kant is in a position to introduce the system of pure concepts, to show their provenance and demonstrate the validity of their application in experience, and to expose the errors of their inevitable misuse.
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Transcendental Logic First Division Transcendental Analytic Kant now launches the momentous program aimed at discovering the contribution of the understanding to our store of a priori knowledge having to his satisfaction exhibited the contribution of intuition to it. In both instances a transcendental justification is needed. In the present division of the Transcendental Logic we must first identify the pure concepts of the understanding and then its principles. In the second division we will observe the dialectical employment of these concepts and principles and thus the genesis of the "logic of illusion" and its cause and cure. The pure concepts are not to be picked up like pebbles: a clue, a Leitfaden, must first be turned up that will lead us to them. Kant is determined that the search be free of haphazardness, of groping here and there. Four guidelines are to be observed. First, the concepts we are seeking must be pure and not empirical. Little can be said now in regard to this since it is not yet fully apparent what the difference in fact is. If we focus attention on the question how synthetic propositions are possible a priori, we must of course begin by asking what concepts are employed in the formulation of such propositions. But it is well to be prepared as early as possible to learn that pure concepts are not somehow simply another species of concepts along with empirical concepts. Second, the concepts must be derived from thought and not intuition. Kant has already decided that certain a priori representations are intuitions, namely space and time. The transcendental logic will seek to identify those concepts that have their source in the understanding alone. Third, the concepts must be basic or elementary and not composite or derivative. In the sequel Kant devotes too little time to this matter. There is a want of rigor which he excuses by saying that instruction on the matter is easily found in the manuals of ontology or that he will devote his remaining energies 83
to setting up the system of pure reason as soon as the critique of pure reason is complete. Only the Metaphysical Foundations of Natural Science in some measure realizes this promise. In general, one wishes Kant had devoted more attention to the analysis and articulation of concepts and less to certain peripheral matters in the first Critique. The fourth requirement of completeness is one that Kant earnestly seeks to meet in the early part of the analytic of concepts, the so-called metaphysical deduction. But the question whether we may not turn up concepts necessary to experience or science that are neither among those on the basic list nor derivative from them probably cannot be answered decisively for a reason that could threaten the enterprise of the Critique itself: how can we know exhaustively what experience is and thus what is needful to it or "makes it possible" if experience is by its nature exploratory in nature? This question should make us reflect on these alternatives: We must know in advance of experience what is necessary to or what will count as experience. (1) We cannot know in advance of experience what experience is. (2) Of these Kant elects the first. In order to do so he must assume that experience is not an empirical concept. The whole Critique is built on the notion that we must in advance of experience (not of course in a temporal sense) be able to make certain generalizations about it, namely the Principles expounded in the Analytic. For example, perception cannot validate itself: it is a presupposition of natural science that perception reveals realities, and this presupposition cannot simply be confirmed by perception. Perception does not show us that we can trust perception. Yet a critic may well ask whether anything but experience could tell us whether we can trust experience. This is the kind of "dialectical problem" that the Critique inevitably stimulates. Here the clue to the categories becomes important. Perhaps there is some way to determine all of the basic concepts and principles on which experience and science rest. In any event, the clue is the only place in which Kant undertakes to show this.
84
In view of Kant's further development of these problems, we need not pause over his treatment of the question of elementarity and completeness. He himself qualifies the elementarity of the categories by saying that the third category in each of the four classes "arises out of the union of the second with the first" (this is said only in B at B110). It is interesting to see what further modifications would have to be made in the table of categories if Kant had been in a position to approach the "table of judgments" from the standpoint of present day notions of the sentential and predicate calculus. We shall consider these when we take up the categories themselves.
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Transcendental Analytic Book I Analytic of Concepts A further introductory paragraph disclaims the intent or need in the present context of analyzing particular concepts. A "logical treatment of concepts" is not what is called for in a transcendental inquiry despite the description of an "analytic of concepts." Although we may reiterate our regret that an analysis of the pure concepts was omitted from the Critique, or its sequels, this is not to say that what Kant intends to do in the analytic is labor lost. The study of these concepts pursued "to their original seeds and dispositions in the human understanding" deserves every support. But it is artificial to separate from one another the explicit analysis of concepts and the study of their origin and function in the economy of knowledge.
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j
Analytic of Concepts Chapter I The Clue to the Discovery of all Pure Concepts of the Understanding
Still another introductory section repeats what has been said several times, that the pure concepts of the understanding are now to be collected and examined, that they have a unity or connection deriving from the understanding itself, and with the proper approach or clue we may be certain that we have considered all of them and thus accomplished the most important task of a critique of pure reason.
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The Clue of
the Discovery of
All Pure Concepts of
the
Section The Logical Employment of
Understanding
1 the
Understanding
After what appears an endless round of prelimina r i e s , we come at l a s t to grips with the main issue of the C r i t i q u e , the exposition of the contribution of the understanding to our a p r i o r i knowledge. The turning point i s reached in two pages of unbelievably compact and pregnant thought beginning at A68/B93. They seem possessed of a force scarcely p a r a l l e l e d in a l l of modern philosophy, but also of enormous d i f f i c u l t y , u n t i l a clue here and there enables everything to f a l l into p l a c e . One should refer to these pages in the further reading of the Critique again and again. Since i t i s only a matter of some dozens of l i n e s , t h i s passage must be quoted e n t i r e so t h a t we can have i t constantly before u s . The d i f f i c u l t y l i e s in the thought i t s e l f , not in the phraseology. Kemp Smith's t r a n s l a t i o n i s sound enough for the purposes. (I s h a l l refer where necessary to the l i n e s as numbered.) "The understanding has thus far been explained merely negatively, as a non-sensible faculty of knowledge. Now since without sensibility we cannot have any intuition, understanding cannot be a faculty of intuition. But besides intuition there is no other mode of knowledge except by means of concepts. The knowledge yielded by understanding, or at least by the human understanding, must therefore by means of concepts, and so is not intuitive, but discursive. Whereas all intuitions, as sensible, rest on affections, concepts rest of functions. By 'function' I mean the unity of the act of bringing various representations under one common representation. Concepts a r e based on the spontaneity of thought, sensible intuitions on the receptivity of impressions. Now the only use which the understanding can make of these concepts i s to judge by means of them. Since no representation, save when i t i s an intuition, i s in immediate relation, to an object, no concept i s ever related to an object immediately, but to some other
88
5
10
15 i: '-• • ;., 20 j j
representation of i t , be that other representation an intuition, or itself a concept. Judgment is therefore the mediate knowledge of an object, that i s , the representation of a representation of it. In every judgment there is a concept which holds of many representations, and among them of a given representation that is immediately related to an object. Thus in judgment, 'all bodies are divisible 1 , the concept of the divisible applies to various other concepts, but is here applied in particular to the concept of body, and this concept again to certain appearances that present themselves to u s . These objects, therefore, are mediately represented through the concept of divisibility. Accordingly, all judgments are functions of unity among our representations; instead of an immediate representation, a higher representation, which comprises the immediate representation and various others, is used in knowing the object, and thereby much possible knowledge is collected into one. Now we can reduce all acts of the understanding to judgments, and the understanding may therefore be represented as a faculty of judgment. For, as stated above, the understanding is a faculty of thought. Thought is knowledge by means of concepts. But concepts, as predicates of possible judgments, relate to some representation of a not yet determined object. Thus the concept of body means something, for instance, metal, which can be known by means of that concept. It is therefore a concept solely in virtue of its comprehending other representations, by means of which it can relate to objects. It is therefore the predicate of possible judgment, for instance, 'every metal is a body'. The functions of the understanding can, therefore, be discovered if we can give exhaustive statement of the functions of unity in judgments. That this can quite easily be done will be shown in the next section."
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25
30
35
40
45
50
55
60
65
70
What has been said earlier regarding Kant's "breakthrough" in directing the attention of philosophers to sentences (propositions, judgments) may now be doubly affirmed. It is the first great step away from the material to the formal mode of speech. In effect Kant is here asking what a sentence is and showing us why the answer is all-important. Perhaps we should devote a moment to the second question before considering the first. Sentences are important, all-important, because for Kant what he calls experience (we have earlier designated this phenomenal experience , E2) is through and through conceptualized and, if we may coin the terms, propositionalized or sententialized. To experience is to be able to assert propositions or to make judgments. In every waking moment as we make our way through personal or public space and time we are sotto voce, as it were, uttering an endless series of propositions, identifying, classifying, relating, predicting. There is virtually no such thing as finding ourselves in an "alien" world: it is a world of appearances "constructed" (in some sense: Kant will try to explain it to us) out of bits of intuition that owe their origin to things-themselves and of relations that are "our own" creation: space, time, and concepts, both pure and empirical. Kant takes over the structuralistic epistemology of simple and complex representations bequeathed by Locke and Hume. We are on the one hand receptive (as to the bits or materials that enter into experience) and spontaneous (as to the ordering of this material through concepts and judgments). In this section still another pair of "antonyms" is added to matter and form, receptivity and spontaneity, namely affections and functions. In empirical intuition we are affected by something, passively; but a concept is functional, that is, it is a sign of activity and functioning. ( H ) We can call a concept a functor. The role of such a functor is to relate and synthesize. Concepts are contributions of the mind: orderings, relatings, classifyings, synthesizings are our own work. Among concepts there are no such things as ready-mades. This is a fundamental article of faith in Kant. We shall recur to the term functor when we come to the categories. Kant tells us that the only use the understanding can make of these concepts is to judge by means of 90
them; thus anticipating "the meaning of a word is its use in a sentence" that has impressed itself so deeply on recent thought. (18) One might add that our contemporaries might also benefit by seeing the problems this thesis brings with it, as shown in the Critique. The next step Kant takes is to say that if we can understand what concepts and judgments are, thoroughly 'excogitating what we have manufactured these astonishingly complex instruments for, we shall have gone a long way toward explaining what experience, knowledge, and indeed nature itself are. Only when we see that the structure of sentences is what is decisive, can we throw light on all these matters. This then takes us back to our first question: what is a sentence (judgment, proposition)? This too Kant endeavors to explain in this intense pair of pages. The terms judgment and understanding are sometimes sharply distinct in Kant. When they are, understanding means the employment of the intellect (to use a neutral generic term that is here needful) to develop and state the broadest theoretical formulations of knowledge or science. All theory is thus under the care of the understanding, particularly as it approaches the generality of, let us say, the theory of gravitation or mechanics in general, or in later times than Kant's, theories about biological natural selection or electromagnetic phenomena. Judgment on the other hand is a skill that points in the opposing direction, toward the particular case rather than the general law. Here one appeals to a general law, as being already determined and confirmed by the understanding, in order to explain a particular instance as falling under the law, for the sake of practical application, arbitrament, counsel, discrimination, and the like. The distinction is made more specific at the opening of the Analytic of Principles. It is, however, more necessary at the present juncture to note that whether one is moving in the direction of theory or of specific application, both of these faculties express themselves in sentential form. (Kant's use of the term 'faculty' though liberal is from the standpoint of modern psychological criticism harmless). Kant expresses this by saying that the understanding is a faculty of judgment. ^ 50 ' The focus of the problem is now on judgment: to experience, to know, to understand is to judge. We 91
now ask what judgment is. First of all, it is the irreducible unit, the pound or penny of knowledge, or we might also say, it is the cognitive molecule. In the universe of knowledge there are no free atoms or ions; they are all parts of molecules, or judgments. Again, the only use we "can make of concepts is to judge by means of them" ( 19 )- But we can say what the atoms are, even if they do not occur alone; they are distinguishable though not separable components of judgments. These atoms are concepts. We must now close in upon concepts. What does a concept do? Its function, Kant says, is essentially that of appearing as a predicate in a judgment (38). Taken by itself it is, as Russell was later to say, merely a form of a possible proposition, a propositional function. "Concepts (are) predicates of possible judgments" (54). Thus: "...is white," or "...loves roses," etc. This tells us something formally about concepts. Their principal purpose is to appear as predicates, not but what they may also at a suitable level of abstraction appear as subjects: "Color is a quality," "Cleanliness is next to Godliness," "Time is money," etc. But these are theoretical manipulations quite distinct in Kant's scheme from judging, where a substance appears as the subject and some property is attributed to it in the predicate. (Kant's view of substance still retains an Aristotelian flavor in that it is a part of the nature of substance to appear only as subject, never as predicate. Can we not say more than this of concepts? In addition to their formal use, as predicates, we can also say that concepts are devices of synthesis (this is explained in the Deduction in A ) : a judgment is here called "a function of unity among our representations" (41) . vfe may first look at Kant's account of this and then see whether a simpler alternative to it is possible, preserving the essence of what he says. Kant's account is more complex than it needs to be. Kant supposes that in a judgment such as, all bodies are divisible, we begin with actual bodies: * * *. Then the subject term 'bodies' in some sense represents these bodies. The predicate term relates to, applies to (bezogen) the subject term, and thus, he says, the actual bodies are indirectly represented 92
i
(werden mittelbar vorgestellt) by the predicate. Perhaps thus: 'divisibles -> 'bodies' ->• * * * Asserting the proposition in question (it is a "function of unity") is in some way to bind together and give a unique cohesion to many particulars. '41; •
But this is obviously not very satisfactory and what Kant says in the last part of the paragraph suggests the following, which, thought it adds some logical notions not used by him, is, I think, compatible with his account. Seeing that precisely what a concept is and does will be worked out in the Deduction, we may for the time being content ourselves with saying that a concept (that is, a predicative term) has the function of associating an aggregate of particulars or of classes of them. Thus the concept 'divisible' is here to be thought of as a specification of a number of properties the possession of which entitles something to be called a divisible. The sentence 'All bodies are divisible1 is now taken extensionally as saying that all all of the bodies are numbered among the divisibles. Thus in an old-style Venn diagram, the class of the divisibles comprises the bodies and possibly other divisibles also, and the judgment asserting this has now brought a measure of order (or unity as Kant says) into the situation by detecting a way of connecting bodies with other divisibles in a larger group, the divisibles. (39)
Concepts thus function as synthesizers, "functors" of unity, but only in judgments, and there they operate (in the cases under consideration) as predicates. We now see that the predicate is a class that may include other possible particulars and assimilates the particulars comprised under the subject. All of this is concerned only with the extension of the terms: Kant is talking only about propositions of physics that may be so construed. To judge is to realize or perfect this unification or assimilation. To use the copula 'is', Kant says 93
later on, is to say that we are now distinguishing an objective from a mere subjective (associational) unity of representations (B142). This is an immense advance over Hume who scarcely distinguished assertion from the association of ideas. Kant now offers another example, which however is really not well chosen: ein jedes Metall ist ein Körper.- This has to be interpreted (I do not mean translated) "every piece of metal is a body," or something on this order, for surely it is neither fact nor good grammar, in English or German, to say "gold is a body," "platinum is a body/' etc. Kant would have made his point more effectively had he said, for example, "every animal is a body." (Of course, this is a minor objection.) But now we must come to the fulfillment of what this account of judgment promised. If we can see in general how judging, by means of concepts, brings order or unity into experience, the next step is to study judgment itself in its varied forms. This may reveal to us a variety of devices of unification, depending upon the type of judgment. And since, as we said at the outset, experience is judging we shall hereby be in a position to unpack all the other components of this complex notion. Kant is the first philosopher to assert that the way that philosophers can best help us to understand the world is to hold up to the light the kinds of things we say about it. He was in fact so emphatic about this, we may say that he thought it the only way we would ever understand it. The clue to the problem is language itself. Kant loses not an instant after these two momentous pages to turn to a study of the structure of language. Alas, his study of it is too sketchy and superficial to justify the conclusions he draws from it. One hastens to add that this is largely owing to the moribund state of logic and linguistics in his day. There are also momentous philosophical difficulties. )
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The Clue to the Discovery of all Pure Concepts of the Understanding Section 2 §915 The Logical Function of the Understanding in Judgments Having shown why the proposition or judgment must be regarded as the fundamental unit of experience, Kant now proceeds to examine the form which propositions take. We shall not pause long over the actual classification despite the fact that the shape of things to come in the Critique is determined by it. No part of the Critique is in greater need of revision than this. It is, however, pointless to try to revise it. It is much more important for us to look at our present thought on the subject of the forms of sentences and to ask how matters stand on their "categorial presuppositions," having learned all we could from Kant. In a sense this is constantly being done at the present time. Kant is lost sight of because his thought has entered into the fabric of philosophical practice. We shall make a few suggestions of revision simply to put the categories into a new light. The actual derivation of the Kantian classification has been explored by various scholars. A recent one is that of one of Kant's most hostile critics, Magdalena Aebi (Kant's Begründung der Deutschen Philosophie, Basel, 1947). One may find precedents in Aristotle and in later medieval and early modern logicians, but these are of no great relevance. What Kant has in mind is in this instance perfectly clear. (As a handy way of distinguishing the table of judgments in §9 from the table of categories in §10 we shall call the first "Screed I" and the second "Screed II." Particular forms or categories may then be marked 1-1, II-1, etc.) Screed I suggests, though Kant thinks these details needn't be gone into, that propositions are, as to quantity, either universal, particular, or singular, and, as to quality, either affirmative, negative, or infinite, and as to relation, either categorical, hypothetical, or disjunctive, and, as to modality, either problematic, assertoric, or apodeictic. With some qualifications to be explained later, we may say that each proposition must have one and only one of three characters under each of the four classes. 95
Screed I
Screed
Table of Judgments
II
Table of Categories Quantity
I - 1 Universal I - 2 Particular I - 3 Singular
II - 1 Unity II - 2 Plurality II - 3 Totality Quality
I - 4 Affirmative I - 5 Negative I - 6 Infinity
II - 4 Reality II - 5 Negation II - 6 Limitation Relation
I - 7 Categorical I - 8 Hypothetical I - 9 Disjunctive
II - 7 InherenceSubsistence II - 8 CausalityDependence II - 9 Community Modality
I - 10 Problematic I - 11Assertoric I - 12Apodeictic
II - 10 PossibilityImpossibility
II - 11 ExistenceNon-existence I I T- 12 NecessityContingency
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Turning first to Screed I we can illustrate its classifications with the following examples: 1-1
All S is P.
1-7
All S is P, or simply, S is P. If S is P, T is Q Either S is P, or T is
1-2 1-3
Some S is P. a is P.
1-8 1-9
1-4 1-5
All S is P.
1-10 S may be P. 1-11 S is P, in fact. 1-12 Necessarily, S is P.
Q.
1-6
No S is P. All S is non-P.
But it is obvious that this is little more than a sketch of some of the possibilities. 1-1, for example, specifies only that a proposition be affirmative, but if so, then it may also be Some S is P, Some S may be P, S is necessarily P, and so on. With leisure one could explore a good many other possibilities, but perhaps not very profitably. When we come to Screed II we may then expect that the categories which organize experience and which are, as it were, being invoked in particular experiences or Erkenntnisse, are, depending upon what has been asserted, similarly determined. Thus a proposition negatively but universally generalizing some causal fact but only as a possibility, will normally have been expressed by a proposition formally classifiable under 1-1, 1-5, 1-8, 1-10. ("Unity" in II-1 may loosely be read "Universality" for the moment.) No doubt there are other ways of interpreting the organization of the screeds, but this- one seems the most intelligible from the present standpoint. It is evident that Kant's program of tracking down the a priori concepts in experience by observing the forms of language makes many assumptions. Consider the following. If the forms are truly empty, they can scarcely even be read. If we read 1-8 as "If p, then q", we are already offering an application or interpretation of the form, saying at least that some assertion depends in some way upon some other assertion; but this already places a limit upon the form, so that it is not a truly uninterpreted form. On the other hand, if we cannot even read the forms we do not know what possible relevance they can have as clues to the pure concepts. The latter is a serious or even fatal issue for Kant, for he proposes to learn something about experience and scientific thought from inspecting the forms. But if he cannot even read the 97
the
forms . . . ?
•'
Kant certainly does not wish to say that every if-then proposition is about a causal event, where we may be saying that the if-event preceded the thenevent, etc. He knows that we also use this form when we want to cite a reason for something: "If A took the money, A was desperate": taking the money is not necessarily the cause of A's desperation. Or again, take, "Necessarily, P." Theologians have said, "Necessarily, God exists," or physicists, "Necessarily, no velocity exceeds c," perhaps in the same sense, perhaps not. In Screed II Kant is concerned with assertions having the unique kind of necessity ascribable to natural laws. (See his discussion of the third Postulate of Empirical Thought -the name is carefully chosen — for the interpretation of "Necessarily, P," as it appears in science, at A226/B279 ff.) But he knows also that, "Necessarily, Barbara," a law of logic, has an exemplification in 1-12 though not in 11-12. Thus he cannot wish to say that every instance of 1-12 is an instance of 11-12, inferring the nature of scientific thought from language, that is, from this form alone. Our only hope or understanding the derivations is to take the whole thing in a much looser manner than Kant desires. It may prove to be much less than the deduction he describes the derivation of Screed II from Screed I to be (that is, a "metaphysical deduction", see §26 below). How can it be a deduction, we may ask, when from mere uninterpreted forms of judgment nothing follows about empirical thought: if anything can be learned, must we not attend to more than mere forms? Rather than pursuing a deduction, the question should be, to what uses do we put the various forms of judgment, taking these to be something much less formal than what we would mean by 'uninterpreted forms.' It is too much to say that from Kant's point of view he ought to have begun with Screed II instead of trying to arrive at it through I for then he would really not have needed I at all. I think there is something valuable to be learned from Kant's approach although it needs to be modified drastically. It is really a question of resorting to a different but still altogether Kantian approach: instead of the method of atomistic synthesis, one should adopt a method of reductive or diremptive analysis, of "unpacking." 98
The approach of the Prolegomena is often dismissed as a failure. To the contrary, I believe it offers a real solution. Kant begins with a proposition or judgment of experience, as he calls it, and in full cognizance of what it says, thinks out, ex-cogitates in a very particular way, not merely what it means (this is in a familiar way obvious), but rather asks himself what sources of thought and experience must be drawn upon to interpret it and establish its cognitive value (be it truth-falsity, or some other). "In the first place we must state that, while all judgments of experience are empirical (that is, have their ground in immediate sense-perception), all empirical judgments are not judgments of experience; but, besides the empirical, and in general besides what is given to the sensuous intuition, special concepts must yet be superaddedconcepts which have their origin wholly a priori in the pure understanding, and under which every perception must be first of all subsumed and then by their means changed into experience. "Empirical judgments, so far as they have objective validity, are judgments of experience, but those which are only subjectively valid I name mere judgments of perception. The latter require no pure concept of the understanding, but only the logical connection of perception in a thinking subject. But the former always require, besides the representation of the sensuous intuition, special concepts originally begotten in the understanding, which make possible the objective validity of the judgment of experience... "As an example, we may take the following: 'When the sun shines on the stone, it grows warm.' This judgment, however often I and others may have perceived it, is a mere judgment of perception and contains no necessity; perceptions are only usually conjoined in this manner. But if I say, 'The sun warms the stone', I add to the perception a concept of the understanding; namely, that of cause, which necessarily connects with the concept of sunshine that of hear, and the synthetical judgment becomes of necessity universally valid, namely, objective, and is converted from a perception into experience." (Prolegomena,§ 18,§ 20.)
99
Here we see Kant's diremptive method at work. In a proposition such as "air is elastic" (that is, it expands), the method uncovers the facts that certain judgments of perception are relevant to this (for example, in a toy balloon I observe the distention of the bag itself, its tautness, the pressure on my hand when I remove the cap, and so o n ) , that I am speaking of something occupying space and very likely a stretch of time, that a certain passing state is at hand, that that which the state qualifies may qualify several states successively, and so on. I also observe that the subject and the predicate of the sentence in question are employed in a certain manner to express all of this. This method only lays bare the components of the fact (one must beware of the mechanical metaphor here), but of course that is its sole purpose. The task which Kant undertakes in the Transcendental Deduction is yet to be done, tracing each of the "components" to its source or origin, the rules of its application, and so on. In the example "when the sun shines on the stone, it grows warm," we have two subjects (or substances) qualified by states, an implied duration, a relation between them identified as causal, and so on. We learn none of this by simply scrutinizing "S is P 1 , or "if S is P, T is Q 1 , ever more sharply but only by close study of what a fact is and what a sentence is and of the purpose that each serves. The problem with the diremptive method is that there is no way one can readily see to terminate the task, how one can be certain that all such ingredient notions as space, time, substance-state, cause-effect, possibility, and so on have been tallied up. If that is so, it only means that one cannot speak in full a priori confidence about the world -- a situation we ought accept with what grace we can command. Here the method of the Critique, the so-called Metaphysical Deduction, seeks to offer an alternative. It hopes to cut short the endless way toward identifying the contribution of the understanding to experience and to science. In the Prolegomena there is the suspicion that the trail must be blazed step by step. The Metaphysical Deduction by contrast hopes to 1 00
I
accomplish it all at once. The difficulty is that mere forms like Screed I tell us so little. Are "air is elastic" and "iron is malleable" the same kind of fact or not? Are the same categories involved in both and is it because they have the same "form of judgment?" Is "all nitrates are soluble in water" or "cinnabar is red" different from these or not? Are we not well advised to explore a range of facts before we say what enters into the act of asserting them? The forms of judgment explored, expounded, and systematized by formal logic are in Kant's opinion the best guide to the kinds of fact there are and to the kind of stance we take toward factual content. For example, we may formulate the following for him. (One would prefer Kant's having done so.) 1.
Universal propositions have the purpose of uniting many different representations under a class designated by a predicative term.
3.
Singular propositions have the purpose of relating an individual to a class designated by a predicative term.
5.
Negative propositions have the purpose of saying that a designated stretch of space and of time is occupied by nothing of a specified description.
7.
Categorical propositions have the purpose of affirming that some continuant in time has a certain property or is in a certain state at a given time.
8.
Hypothetical propositions have the purpose of affirming a relation of dependence of some continuant, or some state or property of some continuant, upon some other.
12.
Some substance, event, or process is entirely determined in terms of empirical laws.
These show us the uses to which propositions are put when they are employed to talk about events and processes in space and time. But the point must be made that we know none of this from the bare forms (truly bare), and that if we take account of the content of the propositions, then we must be open to instruction by the facts. In other words, we have not in fact learned nor can we learn thing-and -property, causation, 1 01
possibility and the rest of these notions from the forms alone. Therefore Screed I can at most hint at what we have in Screed II and then only because we have independently reflected upon facts. It should be pointed out that Kant's programmatic reliance upon formal logic as an architectonic model makes a serious error in not distinguishing between the apodeictic certainty of the formulae of logic, of analytic a priori truths, and the much less certain character of the dodecuple division of propositional types. The formulae are no less true now than they were in the previous Aristotelian framework. The dodecuple division has disappeared, but one need only reflect on the revisions that have been made in modern logic to see that many if not all of the notions Kant mentions in his division find a new place or different interpretations as a result the theory of quantification, of classes, relations, identity, descriptions, of modal logic and so on. What one can learn from Kant in this is that questions analogous to those which he raised using the classical logic as the model of language may be just as appropriate if not imperative for a logic of quite a different order. One might well call this kind of inquiry metaphysical in the same sense in which Kant's Analytic is. A single very particular example of the consequences of a revision in logical categories may be cited for the forms I - 7,8,9. Kant hangs a number of for him momentous issues on the division into categorical, hypothetical, and disjunctive forms. It is not just II-7, 8, 9 that depend upon it but also, for example, the three divisions of the Transcendental Dialectic, the transcendentally pseudological arguments in the Paralogisms, the Antinomies, and the Ideal of Pure Reason. Kant recognizes properly that there is an important difference between 1-7 and 1-8, 1-9 in that the first (assuming it to be a monadic sentence) is a relation between two concepts (subject and predicate), while of the latter the first is a relation between two propositions and the second a relation among two or more propositions. Leaving aside 1-7, we may ask whether 1-8 and 1-9 have the ultimacy or irreducibility Kant attributes to them and can serve for the excogitation of II-8 and II-9. Of course, we are not taxing Kant with failure to uncover the truth-function but merely seeking to show that an alternative scheme to 1 02
h i s j u d g m e n t s of r e l a t i o n t h a t m o d e r n l o g i c h a s e s tablished necessarily puts categories I I - 8 , 9 ( c a u s a l i t y and c o m m u n i t y ) i n t o an a l t o g e t h e r d i f f e r e n t light. F o r e x a m p l e , R u s s e l l and W h i t e h e a d , u s i n g the n o t i o n s of p r o p o s i t i o n , n e g a t i o n , and d i s j u n c t i o n as b a s i c d e r i v e the e n t i r e s e n t e n t i a l c a l c u l u s from i t . If K a n t had had t h i s l o g i c a l s c h e m e at h a n d h i s c h o i c e of c a t e g o r i e s w o u l d p r e s u m a b l y h a v e r e f l e c t e d it and a v e r y d i f f e r e n t k i n d of C r i t i q u e w o u l d be the r e s u l t . W h e n o n e c o n s i d e r s n e x t the s i m p l i f i c a t i o n i n t r o d u c e d by S h e f f e r ' s s t r o k e - f u n c t i o n for the l o g i c a l n o t i o n of i n c o m p a t i b i l i t y , r e p l a c i n g n e g a t i o n and d i s j u n c t i o n , s t i l l a n o t h e r r e v i s i o n of c a t e g o r i e s w o u l d a p p e a r to be in o r d e r . M o r e o v e r , one can a l s o go in the o p p o s i t e d i r e c tion. T h e r e are s i x t e e n d i s t i n c t t r u t h - f u n c t i o n a l c o m b i n a t i o n s of two v a r i a b l e s w h i c h a K a n t i a n p h i l o s o p h e r m i g h t h a v e set up and u s e d as the b a s i s for categories. The o n e s t h a t are r e a d i l y r e n d e r e d by f a m i l i a r t e r m s in E n g l i s h are t h e s e : 1.
2. 3. 4. 5. 6.
Con]unction: Implication: Strong Disjunction : Weak D i s junction : Joint Denial : Equivalence:
p and q if p , t h e n
q
e i t h e r p or q, b u t n o t
both
p and/or q neither p nor q if and o n l y if p
q
then
T h e s e and the ten o t h e r r a t h e r m o r e n a m e l e s s p o s s i b i l i t i e s a r e e a s i l y r e n d e r e d in t e r m s of R u s s e l l and W h i t e h e a d ' s p r o p o s i t i o n , n e g a t i o n , and d i s j u n c t i o n . B u t if some f i c t i o n a l p h i l o s o p h e r , P s e u d o - K a n t , had k n o w n n o t h i n g of t h e s e r e d u c t i o n s , he m i g h t h a v e r e g a r d e d all of t h e m as u l t i m a t e and b a s e d some s i x t e e n r e l a t i o n a l c a t e g o r i e s on the lot of t h e m . (One m a y r e a d i l y i d e n t i f y t h e m in W i t t g e n s t e i n ' s T r a c t a t u s , 5.101). ~ It is u n n e c e s s a r y c h o i c e of " f o r m s " h e r e for K a n t . But a l s o , a jured up for l o g i c and
to l a b o r the p o i n t t h a t the is a l l — i m p o r t a n t . It w a s so s i m i l a r p r o b l e m can be c o n l a n g u a g e in its p r e s e n t s t a t e .
1 03
Kant appends comments on each of the four classes of judgments. We may be brief with these since as already remarked drastic revisions would in any event have to be made in the table to square it with current thought. ad 1. Kant remarks on the fact that in the traditional logic the singular judgment (e.g. "Socrates is a man") functions in some essential respects like the universal proposition. Thus the subject term is treated as "distributed." On the other hand, says Kant, one must distinguish the two, since the individual is to the universal as unity to infinity. Certainly Kant's distinction is endorsed in modern logic, but the role of proper names and definite descriptions is much more complex than the old syllogistic provides for. Kant's general philosophical point concerns the derivation of a category from 1-3. Here the result is baffling because II-3 is totality, which has no apparent kinship with 1-3. Nothing further is heard in the Critique about totality or, in this sense, about singular judgment. The Schematism (A137/B176 ff.) which attempts to define in intuitional terms or at least to establish a link between the doctrine of the categories and the Aesthetic mentions all the categories except this one. The question of progressing from 1-3 to II-3 is in this instance abandoned. The Axioms of Intuition make no mention of totality although nominally they are based upon II-1, 2, 3, and thus 1-1, 2, 3. That there is more to this question than first meets the eye is readily apparent when we look at Kant's other works. Recently Michael Frede and Lorenz Kruger have reviewed the question of the coordination of the two screeds in "Über die Zuordnung der Quantitäten des Urteils und der Kategorien der Grosse bei Kant," Kant-Studien, 61-1, 1970, pp. 28-49. The fact is that two different coordinations are possible and are in fact both mentioned by Kant. B .. A 1-1 Universal II-1 Unity I -1 II-3 1-2 Particular II-2 Plurality I -2 II-2 1-3 Singular I -3 II-l II-3 Totality B is the coordination of the first and second editions of the Critique and of the text of the Prolegomena. A is the coordination of the footnote to § 20 in the 1 04
.i
Prolegomena and of several of Kant's lecture manuscripts. Prof. Frede and his colleague show why A should be regarded as corresponding to Kant's real intentions in this matter, that is, the category of unity to the singular, not the universal, judgment, and totality to the universal, not the singular judgment. This interpretation brings Kant more closely into line with modern logic. ad. 2 The assimilation of the infinite predicate (e.g. "The soul is non-mortal") to the affirmative judgment is acceptable so far as syllogistic form is concerned. But no further development appears beyond II-6 (Limitation)which is in effect explained here rather than in II. No further mention appears of the infinite judgment in the Schematism or in the Anticipations of Perception (A166/B207) which are ostensibly based upon II-4, 5, 6. ad. 3 The division of the relation of judgments into the categorical, hypothetical, and disjunctive has already been gone into at some length. It is interesting to note that Kant sees disjunction as creating a logical sum or union of elements distinct in themselves. But the derivation of II-9, community, from 1-9 is not convincing. Would not the notion of conjunction, the logical product, have been more appropriate as a source for the idea of community? The world would then be the conjunction of facts, "everything that is the case." Kant seems to have grasped the notion of logical sum or union correctly but what he needs to derive community is more nearly the logical product. No hint is here given of the use of the hypothetical proposition in formulating causal facts nor of the categorical in making assertions about substances and their properties. In this instance the metaphysical "deduction" fails to point the way to the categories. ad. 4 Virtually everything Kant says must puzzle us in 4. We are now told that unlike quantity, quality, and relation, modalities contribute nothing to the content of judgments. But from the first we have been treating only the form of judgment, jJLg_tracting from all content (B96) . Either Kant has incredibly forgotten this program or 'content' must nave a somewhat different or much looser meaning at point.
L
1 05
Second, Kant fails to concentrate on the nature of these functions of judgment themselves. To explain what the three modal characters of propositions are, Kant says, nothing more than that in assertoric propositions, the affirmation or negation (as the case may be) is set forth as being true; in the problematic it is called optional (beliebig), scarcely an apt characterization since the question of truth is not left to our option but is rather put in abeyance; in the apodeictic it is said to be necessary. But instead of explicating optional . true , and necessary , and showing how these qualifiers may affect any proposition, universal, particular, singular, affirmative, negative, infinite, categorical, hypothetical, and disjunctive, he limits the application to the last three in a very particular manner. Thus in the hypothetical judgment he believes the apodosis is problematically asserted, the protasis assertorically. This ignores the fact that the proposition is asserted as a whole. It should more nearly be said that the protasis is not asserted at all and that the apodosis is problematically asserted only on the condition of the protasis. We must be able to consider the proposition as a whole to be true or false and as necessarily or only problematically so. Instead, Kant assimilates the hypothetical and disjunctive judgment to the problematic, or perhaps better, problematic character pertains only to hypothetical and disjunctive judgments. But if it were simply a trait of these types there would scarcely be any need to have separate classifications for them under Relation and Modality. What might have been a better alternative than this? Kant might have simply singled out three modal operators, "Possibly (p) " , "Necessarily (p) " , "Assertedly (p)", and then gone on to ask what a priori modes of thought are presupposed when p is some judgment of experience or proposition of, let us say, physics. This would then lead him directly to the categories, if anything would, and the forms would be true clues to their discovery. Aristotle's treatment of modal operators had already provided a clear precedent, which Kant might more profitably have followed (De Interp. 21 a 35 ff). It is hard to resist the charge of mere gameplaying regarding the last dozen or more lines of 4 which try to link the three modalities with the three propositions of the hypothetical syllogism, where major, minor, and conclusion are assimilated 1 06
respectively to the problematic, assertoric and apodeictic modes. (Further development of this sort of "analogizing" is found in the introductory sections A and B to the Dialectic, A299/B355 ff.)
107
The Clue to the Discovery of all Pure Concepts of the Understanding Section 3 §10 The Pure Concepts of the Understanding or Categories
j,j; »!':
One may well prepare himself by turning back to Section 1 at A68/B93 since the present section in a : sense continues the analysis begun there. ^The purpose of the present section is to show what is involved in synthesis, both as process and and as product. In Section 1 synthesis was found to be the inherent purpose of judgement, of the capacity ot express our experience sententially. It involves first, a multiplicity or manifold of elements, of data in a basic framework of space and time; second, the elements must be "gone through, taken up, and connected" with the aid of imagination, that is, what is absent (either past or elsewhere) must be made present; ana third, a unity must be lent to these data. A multiplicity of representations must be put together and , held together in one act of knowledge. Kant believes that in some original sense or on some original level representations are separately and distinctly presented and a process of connecting simple ideas into complex ideas transpires (A 99). As a result of the synthesizing process we arrive at the ordinary objects particularly of vision., Only when we arrive at this result can we begin to speak of experience, of knowledge. The question is, through what instruments, what functors of synthesis do we arrive at the end or result? ' ience, for that is what it is, but one must remember '\ what Kant is trying to do. His main purpose is not :| to give a comprehensive account of the self. Nor is what he is saying a rejection or correction of Hume's ; account of how in principle the idea of the (empirical) self is constructed. Kant can in principle accept Hume's account of the development of the empirical self. What he cannot accept is Hume's failure to allow for the second view of the self, his failure to explain how there can be knowledge if the continuity of the physical world is only one of association, but an association that is not done or witnessed by any one agent. As we have seen in the previous deduction and also in the Aesthetic, Kant is careful to provide both for the empirical facts of the matter in hand and what we may call the cognitive requirements. Under the empirical facts, he allows fully for our inner experience, introspection, the development of empirical self-awareness and continuity, 172
association, and so on. The concept of the self, as much as space, time, or the regularity of events, deserves what he called an explanation of possession, how we come by such a concept (A85/B117). But it is equally necessary to answer questions about all of these notions that go far beyond the empirical explanation of their presence, to allow, in other words, for the cognitive requirements or the claims that they make. And in order to provide for them we must resort to another mode of confirmation because the claims are not empirically confirmable, nor are they analytically true, nor highly probable generalizations. But since they are absolutely indispensable for knowledge, and since it is absurd to suppose that we never have knowledge, we are entitled to affirm or confirm these claims. This is what he means by a transcendental procedure. The continuant self is thus what may be called a transcendental entity. It is, as already explained, one, or a unity, and its characteristic function is the review or apperception of what we are at particular passing moments conscious of. It is not derived or derivative from experience, nor dependent upon it: precisely the reverse is true. Hence it is original, and in a similar vein, Kant speaks of it as a priori. When we sum up all these properties we see the different functions performed by such a self: original, synthesizing, unifying, apperceiving, transcendental, a priori. The name for this self is as accurate as it is awkward: the transcendental unity of apperception. It also appears under slightly varying titles, emphasizing other functions. Tnere remains a troublesome question which may be raised but scarcely answered, and it touches not only this but all the other key parts of the Critique. The question is how we are to construe the key terms in the characterization of the transcendental unity. 'Transcendental' is no problem, of course, since it refers only to the mode of deriving the notion. But how shall we understand 'unity', or 'continuity', and 'apperception'? This is like asking about the use of 'cause' in connection with things themselves. If we think of the terms as analogical or metaphorical we will have difficulty in assimilating the construction and the decoding of the analogy or metaphor to more familiar cases of these. We must at all costs avoid giving the appearance of solving a problem merely by offering a new name for it. The problem is not only Kant's, but is already vigorously evident in Neo-Platonism and medieval "negative theology" with 173
their effort to characterize a being that is in principle beyond observation. Moreover, Kant must heed his self-imposed restriction that nothing more than 'I think' can be attributed to the self. In the Paralogisms he remarks that in Rational Psychology we have an alleged "science built solely on one proposition, 'I think1." Of course his point is phrased as a warning to theologians, but he emphatically does regard this as all we can attribute to the self. The question is of course, whether even this is too much to attribute to it and whether the other predicates 'unity', 'continuity' and so on are not in fact much too much as well. I shall not undertake to answer this question so long as we keep it in mind as we go. We must ponder carefully Kant's own way of dealing with the matter -I do not at all wish to suggest that he was unaware of the problem or that he avoided it. We must consider j; such remarks as that the proposition ('I think1) "is I of course not an experience but only the form of i apperception" (A 354) ; "it is only the formal condition,! the logical unity of every thought" (A 398); the 'I' in "I think' is not "an empirical representation ... it is purely intellectual" (B 423 n . ) . Adickes thinks there is no way of avoiding the charge that there is simply an irremediable contradiction at hand in this situation: Kant is "attributing existence to the self, and thus applying the category of existence to it, whereas his whole system, consistently carried through,forbids it" (Adickes1 edition, p. 332 n . ) . This problem has turned up before: the use (or misuse) of categorial terms in application to transcendental entities. I think we will not falsify Kant's meaning if we present the relationship between the empirical (Em) and the epistemological self (Ep) in the following terms. The order of acquaintance (or discovery) is from Em to Ep, that is, what I am first acquainted with is a "bundle of perceptions" (to be brief about it) which I find to be resembling, connected, and regard as all mine. (This is the order Kant recognizes in what he spoke of earlier as the "empirical deduction" or "explanation of possession" (A85/B117 ff.). I cannot of course infer Ep_ from Em, although that is what the theological approach to the matter seems to sanction, but I am undoubtedly "induced to believe" (again Hume's phraseology is apt) in E£. because of the way I find E_m. Kant's point is that 174
proceeding in this direction is invalid if it is brought forward as explanation. We must, he argues, proceed contrariwise. Only on condition of E_p_ can I explain how all my experiences are intuitively my own. The order of explanation is what is decisive. In it we proceed from Ej3 to Ein and this is what the Critique means to offer us here. We are not of course directly aware of Eja as we are of .Em. I am, Kant says, "aware of an identical self in view of (in reference to, by virtue of, jji ansehung des) the multiplicity of representations given in an intuition, because I call them all nry_ representations that collectively make up one intuition." He then adds the explanation that this is to say that I am conscious a priori of a necessary synthesis, dass ich mir einer notwendigen Synthesis a. priori bewusst bin. I take this to say that the ground of the unification of elements is an a priori condition: nothing of this sort is ever to be found in empirical consciousness. "Being conscious a priori of" is perhaps easy to misinterpret: there is not another consciousness that lurks in the background while the empirical occupies the foreground; rather, there is and must be a ground of the latter. To proceed to establish the reality of anything in this way is what Kant means by the "transcendental" method.
§17 The Fundamental Principle of the Synthetic Unity of Apperception is the Supreme Principle of all Employment of the Understanding The cogito which has been established by reference to subjective intuitive continuity of experience is now to be shown as the condition not only of inner experience but of objects. What is an object? "An object is that in whose concept the multiplicity of a given intuition is united." An object or an objective process is discrete and continuous. Moreover, it is "a something", which is to say that it falls under some concept or concepts. To say that it is something, K, for example, is to say that it has all the traits anything must have to be named by 'K'. To find a K in experience then means we have found something which affords us all the intuitions covered by the defining traits of K. But concepts do not lie about like pebbles on the beach; the selection of traits they represent is an artfully constructed mosaic. The 175
world and what is in it are not pre-structured, according to Kant, but factured. Since being an object, having the continuity and stability of an object (no matter how momentary), is not just "being there", being a thing itself, and since its order or structure is acquired from some source other than itself, we must now ask after this source. An object is an assemblage (Vereinigung) of representations and such a synthesis can only be produced by a unitary conscious-, ness. This consciousness, which is Ep, the synthetic | unity of apperception, is the source of all synthesis. \ This brings us to one of the cornerstones of the I deduction, the principle that the unity of objects and ; thus the possibility of objectivity in knowledge, is • one and the same as the unity of consciousness. Since what we mean by knowledge is by its very nature objective, this consciousness proves to be responsible : for objective knowledge. Kant adds that the foregoing act of synthesis must be presupposed only for beings like ourselves, or in particular, for beings whose intuitions are ordered in space and time. In such beings two sources are active in the generation of knowledge, intuition and understanding, and one of these cannot do the work or produce the result of the other. The concepts of the understanding, we recall, are empty without reference to intuitions, and intuitions are blind without concepts. But in beings in whom knowledge did not depend upon sense organs, divine beings no doubt, beings whose very understandings or intellects were intuitive, the work that is distinct in us would be accomplished without distinct tasks being carried on by understanding and by intuition. Kant frequently touches on this theme because he wishes his theory to be of completely general scope, so that once intellect and intuition are treated of in a truly generic manner specific applications may then be made to beings of certain particular sorts. Man's intellect is thus not treated of as that of man as such but of a being of a certain general description. § 18 What Objective Unity of Self-Consciousness Is The present sub-section introduces nothing new but repeats and emphasizes succinctly the points that have been made in the two previous sections. Kant again 176
contrasts what he has variously referred to as subjective unity or empirical unity of consciousness or empirical apperception with the transcendental or objective unity, or transcendental apperception. The latter, the 'I think1, is what is fundamental, accomplishing essentially the same result in every person. The former differs from person to person. Whereas all those who speak the same language will for that reason use the same criteria in the application of concepts, they will nevertheless have differing, perhaps idiosyncratic mental associations and imagery in turning them over in their minds. Kant repeats that subjective unity depends upon objective unity, that it is the ground of it and even derived from it (abgeleitet). This holds also of the framework of objective time: subjective time may lag for me but not for you, whereas we all have a conception of objective time with a steady and equal flow. In this as in former presentations of the same matter Kant offers nothing that helps us to understand better the crucial terms and turnings of the argument. Among these one must certainly be concerned about the meaning to be given to the way in which the objective unity can serve as the ground of the subjective or permit it to be derived, or what one is to conceive the nature of the former to be when all we can say of it is that it is the 'I think', and even this may be saying too much. Taken strictly the present subsection does not answer the question it addresses itself to, what is the objective unity of self-consciousness? but only declares it to be the ground of the subjective, the source from which the latter derives. §19 The Logical Form of all Judgments Consists in the Objective Unity of the Apperception of the Concepts Contained Therein I take this somewhat baffling title to mean that judging, being a process of synthesis, as Kant has said earlier, is possible only because it is the effort of an apperceiving being. What then is the nature of the relating in judgment? Kant begins by a kind of warning that we must not suppose this is a merely logical matter for in fact logicians have either neglected to ask what precisely 177
the relation is that is being expressed in judgment or confined it to the relation of a subject to a predicate which obtains in the categorical but not in hypothetical or disjunctive judgments. As he reminds us in a footnote, these are quite distinct; the latter two cannot be reduced to the first. (One may well review what he has said in §9, to which he refers us, but also to the all-important brief subsection on judgment which immediately precedes §9.) The section shows the development of Kant's views on the nature of judgment and of the nature and need of a deduction of the categories as he saw these matters when he wrote the Prolegomena (published in 1783, two years after A ) . The essential point Kant makes there is to point out the distinction between judgments of perception (JJL) and judgments of experience (Jj2) , a distinction that is essentially the same as that of twentieth century philosophy of perception between sense-datum or basic propositions (Protokollsätze ) and physical object propositions. Kant is aware that jJP's are not truly judgments like the JE's. The same fact is re-discovered in the later investigation since the JP_ or protocol must simply inform us of conjunction of sense data, without any real !••? attribution. In Kant, the JP uses the form of judg- .'';, ment ("when I lift a body, I feel the pressure of its | weight") , though at most one seems almost forced to !( utter jerky phrases such as, "here, now a body-feel; * there, now a heavy-feel," or something on this order unless one believes one can venture something closer to a standard sentence, perhaps beginning, "I feel ..." or "It appears to me that ..." In some such manner Kant wants to inform us that there is a difference between the full, objective synthesis that is evidenced in jJ_E and the mere subjective association of impressions that we may try to record in Jj?. In the Prolegomena we learn that the difference between a JJ3 such as, "The body is heavy" or "The sun warms the stone," and the corresponding JP_ is precisely that the JE involves the additional functors of the categories. When I say that the stone is warm or the sun is hot I am not merely associating two impressions, but saying there is a continuant, perduring substance that for a time, or even a moment, has some property or is in some state or condition. And when I say the sun warms the stone I am also saying that there is a causal relation between one substance, or an event in one substance, and another.
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The present exposition, as compared with that of the Prologomena. does not yet mention categories either in general or in particular: it merely affirms that there is a difference between the synthesis recorded, or asserted, in full judgment and in mere subjective association. Kant's point then is that what the logicians neglected to mention is precisely the subject matter of the deduction. They failed to explain what a judgment really was, offering only, according to Kant, the suggestion that it was "the representation of a relation between concepts." It is the categories that must be recognized as making true judgment, JE. something more than a verbal sign for an association of impressions, or however we choose to understand JT. Accordingly, Kant is now ready to present the categories, and this is done in the following sub-section and the remaining discussion of Section 2. The actual theoretical content of §19 is by now familiar. We distinguish between the reproductive and the productive imagination, between the understanding itself, the subjective unity of representations and the objective, between empirical and original (a priori) apperception, between connection through association and objectively valid relations. The examples discussed are meant to help us understand that there must be differences between these pairs. We now ask what they are. §20 All Sensate Intuitions are Subject to the Categories as Conditions under which alone they in their Multiplicity can enter into a Single Consciousness This section presents in five sentences an extraordinarily condensed version of the Transcendental Deduction itself. As such, every phrase is significant. Actually everything that appears here has appeared before except that the place of the categories in the general scheme of the deduction in B has not yet been made clear up to this point. Kant is, I think, much more certain of himself in this third deduction of the- categories (counting the Prolegomena) and he is accordingly briefer and less repetitious, and he knows better where each part of the argument fits. I shall attempt merely a paraphrase of §20: but of course nothing is really better than simply 179
concentrating on the original especially brief.
since it is
Unity of apperception is the necessary condition for the connectedness of the multiplicity among our representations. That mechanism that the mind, or in particular, the understanding, employs to effect connection under such apperception is judgment. Whatever is judged is expressed by one or another of the forms of judgment and subject to one or another of the logical functions of the understanding. The categories are nothing but these functions which present the content of the judgment under thing or substance and property or state, cause and effect, determining and determined members of a systematic whole, and so on. Hence everything in experience is subject to the categories. Presented in slightly amplified form we may put the present version of the deduction as follows: (1)
(2)
(3)
Only when we presuppose a unitary apperception have we a ground supporting the apparent connectedness of the subject's experience. I This apperceptive capacity effects its opera- I tions through the synthesizing device of ?. concepts whose only use is to appear as predicates of judgments. Since the whole of experience is subject to judging, it is necessarily subject to the logical functions of judgments.
;
(4)
These functions are the categories, which confer a determining order on our intuitions.
(5)
accordingly, since all experience is subject to original apperception, it is subject to the categories.
The whole purpose of the deduction is to justify the claim to the objectivity (necessity, in Kant's terms) of the results arrived at in science, or in experience generally, to justify the claim to knowledge, in other words. If there is knowledge (and Kant believes there" i s ) , we must in advance grant certain propositions which are neither analytically true, nor empirically confirmable, nor capable of being established in any other manner. But to put the matter thus as one of 180
granting propositions, rather than acknowledging that certain concepts or functors (the categories) are in effect or in operation in knowledge, is to get ahead of the story, going beyong the analytic of concepts (categories) to the analytic of principles. One of the difficult, and perhaps unresolvable problems of the Critique that lies ahead of us is to try to see why both these regimens must be gone through. §21 Supplementary Remark The content of this section is somewhat puzzling in both form and substance. It surprises us by saying that what has gone before has now made a beginning of the deduction of the categories, while in fact all the essentials of it are now before us. The first paragraph is difficult in phraseology. It draws a comparison between the synthesis in empirical intuition as a whole and the synthesis within a given intuition that has just been explained. Categories are the instruments of synthesis of the understanding by means of which the multiplicity in a given intuition has been shown to belong to one self-consciousness. The point is now generalized to show that categories perform in the same manner in respect to all objects. In this way, says Kant, the fully general intent of the deduction will be revealed. The application of the categories is restricted to empirical intuition. What is excluded is of course intellectual intuition which minds such as ours do not command. Kant adds that the ultimate reason why this restriction should hold admits of no further explanation. Whether it does or not is perhaps not as interesting as the comparison he makes between this situation and the parallel inexplicability why there are just so many functions of judgment, from which we derive the categories, or just so many forms of intuition, namely, space and time, and no others. With this Kant underscores his particular choice of categories as set forth in the Metaphysical Deduction. But it also permits what one might in our times call a "Kantian revisionist" position: namely if, as is apparent, the list of functions of judgment must be drastically revised in accordance with modern logic, the list of categories must itself be revised. We have, of course, reviewed aspects of this at length 181
earlier in presenting the metaphysical deduction.
§2 2 The Only Use of the Category as Contributing to Knowledge of Things is its Application to Objects of Experience Sections §22- §24 (first part) reiterate the familiar stipulation that intuitions are an indispensable component in knowledge and that categories unsupported by corresponding intuitions (the term is Kant's own, korrespondieren) cannot yield knowledge. If we emphasize the negative aspect of this, the consequences of the absence of intuitions, the Dialectic is in some measure anticipated. Of course, displaying the limits of the proper use of the categories is actually a proper part of the exposition of the categories themselves. The first section ( §22) develops the familiar theme that there must be empirical intuitions if there is to be empirical knowledge; categories without intuitional reference cannot afford knowledge. The second says that non-sensible intuitions will not meet the demand for intuitional reference. The third opens a discussion, further developed in the Schematism, of the manner in which the imagination serves to relate the understanding and sensibility. First, concepts and intuitions are necessary for ., knowledge (Erkenntnis). Failing the intuitions, we || may often find it needful to think out the logical f( ! possibility of something, but this can furnish no S knowledge of it or about it. Knowledge involves pure ;, and empirical intuitions and pure and empirical con' cepts, and none of the four components may be missing. The familiar demand for empirical intuitions is now extended also to mathematics. Relying on pure intuition one may have a species of mathematical knowledge of the mere form of objects. But this is not knowledge in the full sense of the term unless also empirical representations are at hand. Of course mathematical knowledge in this sense is severely restricted to applied mathematics or it is being equated with a kind of mathematical physics. This is only momentarily surprising. Pure mathematics is provided for but the main point of the argument is to drive home the point that there can be "knowledge of things (Kant's italics) 182
:
only insofar as these can be taken to be objects of possible experience." Here experience is emphatically intuitional experience, E-| .
§2 3 This section has no formal title but is a continuation of the preceding line of thought. The categories have reference only to objects of intuition. This excludes reference to things themselves but it also raises the question as to the scope of the term 1 intuition. ' The requisite intuition, says Kant with emphasis, must be "our sensate and empirical intuition," for this alone can lend the concepts of the understanding sense and significance (Sinn und B e d e u t u n g ) . The notion of non-sensible intuition now reappears as on several previous occasions. The difficulty with this, says Kant, is that one cannot affirm anything positive of it: one can only define or characterize it by staying that it is not extended in space and that its duration is not temporal, that rio. change is to be encountered in it> and so on. And even if one could identify such a species of intuition how could any category apply to it? For as we shall see in the Schematism and later, the categories are not to be defined or analyzed without reference to our way of experiencing time. One query should be raised as something to be kept in mind in the study of the present sections and of the Schematism. In each of the sections ( §22-§24) Kant uses the term 'corresponding' (korrespondieren) in speaking of the relation between intuition and concept. What precisely does he intend with this term? Hume would say that impressions and ideas can resemble one another closely, but this way is obviously not open to Kant, considering the distance he has placed between intuitions and concepts. We must ask whether Kant has adequately explained himself when he takes up the question of the link between them in the Schematism. In the immediately following section he considers the role of imagination as an intermediary in this situation.
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§2 4 The Application of the Categories to Objects of Sense in General The title of this subsection refers principally to the first three paragraphs after which a pause is indicated in the text and Kant takes up a discussion of inner sense. No doubt from the very beginning Kant has had in mind the question of the interrelation of the aesthetic and logical elements of knowledge, intuitions and concepts, since he regards both of them as absolutely necessary to knowledge. How can categories, which are in and of themselves mere abstract and intellectual forms of thought, relate to intuitions and thus objects of appearance, objects of experience? In one sense, the question is as old as Plato's thoughts on participation ( vie9e£ia ) , although Kant does not concern himself with that view of the problem. The problem is of course a characteristically Platonic, and Neo-Platonic, problem and recurs in the Incarnation question in Christian theology: how can the Logos "become flesh and dwell among us?" Something must "humanize" it. So also something must enable us to see the category as relating itself to or organizing a manifold of sensible intuition. Kant's terms for the "third thing," the 'schema', that effects this is not employed in the present sub- ~ section; the schema is the product of the imagination, and this is presented as mediating between intellect and sense: imagination represents its object in an intuitive, auschauend, fashion, but what it represents is not itself present. One may well say that a very large part of intelligence is nothing but imagination and capacity to imagine. How then in thinking with and through abstract categories do we reach the ground of sense? What is needed is a capacity for schematic, figurative thought, a synthesis speciosa, as Kant says, that is, thought in "well-appearing", "presentable" form. The Aesthetic has in fact already expounded what is essential here. "The understanding, being spontaneous, can determine inner sense because there is in us a certain form of sensate intuition a priori" (B150). The a priori forms of intuition of course are space and time: it is time that is decisive here, the more pervasive of the forms, for as we saw in the 184
Aesthetic, "time is simply the form of inner sense" and "the formal condition a priori of all appearance whatsoever" (A33/B49 ff.) Thus the pure understanding, or the transcendental unity of apperception, does not organize mere "raw" intuitions, which are in themselves, as we know, blind and, we might add, intractable: it is the fact that they can appear in the framework of time and its modi that enables them to be related to the categories, which are the instruments of the understanding. This is gone into in detail later (A138/B177 ff.). As we have implied earlier, Kant here attributes the synthesis speciosa, or figurative synthesis, to I the imagination. In fact, he has here allowed the 1 lines among his "faculties" to fade. For the figura••> tive synthesis is also associated with a priori 5 intuition, and being synthesis, with understanding. ; The latter association is underlined by the reappearance of the notion of productive imagination, ] which was discussed twice in the first deduction. ; The present section cannot I think, be regarded as an effective exposition of its topic. The Schematism, difficult as it is, will improve upon it.
Appended to the foregoing section is a discussion of inner sense which was taken up for the first time in B in §6 and in the General Remarks appended to the Aesthetic. The discussion is relevant to the distinction which we find Kant to have followed throughout the Deduction between the self as a presupposition of knowledge, the transcendental unity of apperception, and the self as the object of study of introspective psychology. The former is the active source of unity but is in no way an object of awareness: there are no intuitions of it and of course, without intuitions there can be no object of knowledge. The consequences of the error of presuming that we know the self as if we had intuitions of it are expounded in the Paralogisms of Pure Reason. The "self itself" is a kind of thing in itself of which we know nothing. What we know of ourselves is confined to inner sense in which intuitions are ordered only in time but not as objects or substances. Being subject to inner sense means only that a manifold is subject to inner awareness. The connection of the parts of the manifold is altogether owing to the understanding and the 185
imagination . Kant now draws a parallel between the ontological character of things we think of as organized and ordered in space and those which as mental are not located in space but in consciousness. First, as the former have been shown to be appearances, that is, multiple elements synthesized under the form of space, so also is mental content known but not as evidence of anything in itself. The object of introspection is what we think of as "ourselves" or perhaps as "our selves." It is not a thing in itself but may bear the same relation to this as a ground ,as physical substances and processes do to things in themselves. Kant formulates this as a distinction between the I that thinks and the I that intuits itself, or also the I as an intelligence and thinking subject and I as an object thought. The very form of words here is difficult. Kant speaks of "the I that thinks", das Ich, der ich denke, which if it is his actual intent may be seeking to say something such as in English might be put as "that I which is he that thinks." I believe this is actually more plausible than Vaihinger's emendation das Ich, das denkt, which is our first phrase above, "the I that thinks." Kant was well aware that conventional language was an obstacle to what he was trying to say: it must be respected but not reverenced. What he appears to be saying here is that if we admit that we know objects only insofar as we are externally affected, we must also admit of inner sense that through it we intuit ourselves only insofar as we are inwardly affected by ourselves: that is, so far as concerns inner intuition, we know our own subject only as appearance but not as what it is in itself. The ultimate subject is as plausible . ,: or as problematic an existent as objects in themselves