Kant's Theory of Knowledge

by H. A. Prichard

THE METAPHYSICAL DEDUCTION OF THE CATEGORIES

The aim of the Aesthetic is to answer the first question of the Critique propounded in the Introduction, viz. 'How is pure mathematics possible?'[1] The aim of the Analytic is to answer the second question, viz. 'How is pure natural science possible?' It has previously[2] been implied that the two questions are only verbally of the same kind. Since Kant thinks of the judgements of mathematics as self-evident, and therefore as admitting of no reasonable doubt[3], he takes their truth for granted. Hence the question, 'How is pure mathematics possible?' means 'Granted the truth of mathematical judgements, what inference can we draw concerning the nature of the reality to which they relate?'; and the inference is to proceed from the truth of the judgements to the nature of the reality to which they relate. Kant, however, considers that the principles underlying natural science, of which the law of causality is the most prominent, are not self-evident, and consequently need proof.[4] Hence, the question, 'How is pure natural science possible?' means 'What justifies the assertion that the presuppositions of natural science are true?' and the inference is to proceed from the nature of the objects of natural science to the truth of the a priori judgements which relate to them.

Again, as Kant rightly sees, the vindication of the presuppositions of natural science, to be complete, requires the discovery upon a definite principle of all these presuppositions. The clue to this discovery he finds in the view that, just as the perceptions of space and time originate in the sensibility, so the a priori conceptions and laws which underlie natural science originate in the understanding; for, on this view, the discovery of all the conceptions and laws which originate in the understanding will be at the same time the discovery of all the presuppositions of natural science.

Kant therefore in the Analytic has a twofold problem to solve. He has firstly to discover the conceptions and laws which belong to the understanding as such, and secondly to vindicate their application to individual things. Moreover, although it is obvious that the conceptions and the laws of the understanding must be closely related,[5] he reserves them for separate treatment.

The Analytic is accordingly subdivided into the Analytic of Conceptions and the Analytic of Principles. The Analytic of Conceptions, again, is divided into the Metaphysical Deduction of the Categories, the aim of which is to discover the conceptions of the understanding, and the Transcendental Deduction of the Categories, the aim of which is to vindicate their validity, i. e. their applicability to individual things.

It should further be noticed that, according to Kant, it is the connexion of the a priori conceptions and laws underlying natural science with the understanding which constitutes the main difficulty of the vindication of their validity, and renders necessary an answer of a different kind to that which would have been possible, if the validity of mathematical judgements had been in question.

"We have been able above, with little trouble, to make comprehensible how the conceptions of space and time, although a priori knowledge, must necessarily relate to objects and render possible a synthetic knowledge of them independently of all experience. For since an object can appear to us, i. e. be an object of empirical perception, only by means of such pure forms of sensibility, space and time are pure perceptions, which contain a priori the condition of the possibility of objects as phenomena, and the synthesis in space and time has objective validity."

"On the other hand, the categories of the understanding do not represent the conditions under which objects are given in perception; consequently, objects can certainly appear to us without their necessarily being related to functions of the understanding, and therefore without the understanding containing a priori the conditions of these objects. Hence a difficulty appears here, which we did not meet in the field of sensibility, viz. how subjective conditions of thought can have objective validity, i. e. can furnish conditions of the possibility of all knowledge of objects; for phenomena can certainly be given us in perception without the functions of the understanding. Let us take, for example, the conception of cause, which indicates a peculiar kind of synthesis in which on A something entirely different B is placed[6] according to a law. It is not a priori clear why phenomena should contain something of this kind ... and it is consequently doubtful a priori, whether such a conception is not wholly empty, and without any corresponding object among phenomena. For that objects of sensuous perception must conform to the formal conditions of the sensibility which lie a priori in the mind is clear, since otherwise they would not be objects for us; but that they must also conform to the conditions which the understanding requires for the synthetical unity of thought is a conclusion the cogency of which it is not so easy to see. For phenomena might quite well be so constituted that the understanding did not find them in conformity with the conditions of its unity, and everything might lie in such confusion that, e. g. in the succession of phenomena, nothing might present itself which would offer a rule of synthesis, and so correspond to the conception of cause and effect, so that this conception would be quite empty, null, and meaningless. Phenomena would none the less present objects to our perception, for perception does not in any way require the functions of thinking."[7]

This passage, if read in connexion with that immediately preceding it,[8] may be paraphrased as follows: 'The argument of the Aesthetic assumes the validity of mathematical judgements, which as such relate to space and time, and thence it deduces the phenomenal character of space and time, and of what is contained therein. At the same time the possibility of questioning the validity of the law of causality, and of similar principles, may lead us to question even the validity of mathematical judgements. In the case of mathematical judgements, however, in consequence of their relation to perception, an answer is readily forthcoming. We need only reverse the original argument and appeal directly to the phenomenal character of space and time and of what is contained in them. Objects in space and time, being appearances, must conform to the laws according to which we have appearances; and since space and time are only ways in which we perceive, or have appearances, mathematical laws, which constitute the general nature of space and time, are the laws according to which we have appearances. Mathematical laws, then, constitute the general structure of appearances, and, as such, enter into the very being of objects in space and time. But the case is otherwise with the conceptions and principles underlying natural science. For the law of causality, for instance, is a law not of our perceiving but of our thinking nature, and consequently it is not presupposed in the presentation to us of objects in space and time. Objects in space and time, being appearances, need conform only to the laws of our perceiving nature. We have therefore to explain the possibility of saying that a law of our thinking nature must be valid for objects which, as conditioned merely by our perceiving nature, are independent of the laws of our thinking; for phenomena might be so constituted as not to correspond to the necessities of our thought.'

No doubt Kant's solution of this problem in the Analytic involves an emphatic denial of the central feature of this statement of it, viz. that phenomena may be given in perception without any help from the activity of the understanding.[9] Hence it may be urged that this passage merely expresses a temporary aberration on Kant's part, and should therefore be ignored. Nevertheless, in spite of this inconsistency, the view that phenomena may be given in perception without help from the activity of the understanding forms the basis of the difference of treatment which Kant thinks necessary for the vindication of the judgements underlying natural science and for that of the judgements of mathematics.

We may now consider how Kant 'discovers' the categories or conceptions which belong to the understanding as such.[10] His method is sound in principle. He begins with an account of the understanding in general. He then determines its essential differentiations. Finally, he argues that each of these differentiations involves a special conception, and that therefore these conceptions taken together constitute an exhaustive list of the conceptions which belong to the understanding.

His account of the understanding is expressed thus: "The understanding was explained above only negatively, as a non-sensuous faculty of knowledge. Now, independently of sensibility, we cannot have any perception; consequently, the understanding is no faculty of perception. But besides perception there is no other kind of knowledge, except through conceptions. Consequently, the knowledge of every understanding, or at least of every human understanding, is a knowledge through conceptions,—not perceptive, but discursive. All perceptions, as sensuous, depend on affections; conceptions, therefore, upon functions. By the word function, I understand the unity of the act of arranging different representations under one common representation. Conceptions, then, are based on the spontaneity of thinking, as sensuous perceptions are on the receptivity of impressions. Now the understanding cannot make any other use of these conceptions than to judge by means of them. Since no representation, except only the perception, refers immediately to the object, a conception is never referred immediately to an object, but to some other representation thereof, be that a perception or itself a conception. A judgement, therefore, is the mediate knowledge of an object, consequently the representation of a representation of it. In every judgement there is a conception which is valid for many representations, and among these also comprehends a given representation, this last being then immediately referred to the object. For example, in the judgement 'All bodies are divisible', our conception of the divisible refers to various other conceptions; among these, however, it is herein particularly referred to the conception of body, and this conception of body is referred to certain phenomena which present themselves to us. These objects, therefore, are mediately represented by the conception of divisibility. Accordingly, all judgements are functions of unity in our representations, since, instead of an immediate, a higher representation, which comprehends this and several others, is used for the knowledge of the object, and thereby many possible items of knowledge are collected into one. But we can reduce all acts of the understanding to judgements, so that the understanding in general can be represented as a faculty of judging."[11]

It is not worth while to go into all the difficulties of this confused and artificial passage. Three points are clear upon the surface. In the first place, the account of the understanding now given differs from that given earlier in the Critique[12] in that, instead of merely distinguishing, it separates the sensibility and the understanding, and treats them as contributing, not two inseparable factors involved in all knowledge, but two kinds of knowledge. In the second place, the guise of argument is very thin, and while Kant ostensibly proves, he really only asserts that the understanding is the faculty of judgement. In the third place, in describing judgement Kant is hampered by trying to oppose it as the mediate knowledge of an object to perception as the immediate knowledge of an object. A perception is said to relate immediately to an object; in contrast with this, a conception is said to relate immediately only to another conception or to a perception, and mediately to an object through relation to a perception, either directly or through another conception. Hence a judgement, as being the use of a conception, viz. the predicate of the judgement, is said to be the mediate knowledge of an object. But if this distinction be examined, it will be found that two kinds of immediate relation are involved, and that the account of perception is not really compatible with that of judgement. When a perception is said to relate immediately to an object, the relation in question is that between a sensation or appearance produced by an object acting upon or affecting the sensibility and the object which produces it. But when a conception is said to relate immediately to another conception or to a perception, the relation in question is that of universal and particular, i. e. that of genus and species or of universal and individual. For the conception is said to be 'valid for' (i. e. to 'apply to') and to 'comprehend' the conception or perception to which it is immediately related; and again, when a conception is said to relate mediately to an object, the relation meant is its 'application' to the object, even though in this case the application is indirect. Now if a perception to which a conception is related—either directly or indirectly through another conception—were an appearance produced by an object, the conception could never be related to the object in the sense required, viz. that it applies to it; for an appearance does not apply to but is produced by the object. Consequently, when Kant is considering a conception, and therefore also when he is considering a judgement, which is the use of a conception, he is really thinking of the perception to which it is related as an object of perception, i. e. as a perceived individual, and he has ceased to think of a perception as an appearance produced by an object.[13] Hence in considering Kant's account of a conception and of judgement, we should ignore his account of perception, and therefore also his statement that judgement is the mediate knowledge of an object.

If we do so, we see that Kant's account of judgement simply amounts to this: 'Judgement is the use of a conception or 'universal'; the use of a conception or universal consists in bringing under it corresponding individuals or species. Consequently, judgement is a function producing unity. If, for instance, we judge 'All bodies are divisible', we thereby unify 'bodies' with other kinds of divisible things by bringing them under the conception of divisibility; and if we judge 'This body is divisible' we thereby unify this divisible body with others by bringing it and them under the conception of divisibility.'[14] Again, since 'the understanding in general can be represented as a faculty of judging', it follows that the activity of the understanding consists in introducing unity into our representations, by bringing individuals or species—both these being representations—under the corresponding universal or conception.[15]

Having explained the nature of the understanding, Kant proceeds to take the next step. His aim being to connect the understanding with the categories, and the categories being a plurality, he has to show that the activity of judgement can be differentiated into several kinds, each of which must subsequently be shown to involve a special category. Hence, solely in view of the desired conclusion, and in spite of the fact that he has described the activity of judgement as if it were always of the same kind, he passes in effect from the singular to the plural and asserts that 'all the functions of the understanding can be discovered, when we can completely exhibit the functions of unity in judgements'. After this preliminary transition, he proceeds to assert that, if we abstract in general from all content of a judgement and fix our attention upon the mere form of the understanding, we find that the function of thinking in a judgement can be brought under four heads, each of which contains three subdivisions. These, which are borrowed with slight modifications from Formal Logic, are expressed as follows.[16]

I. Quantity.
Universal
Particular
Singular.
II. Quality.
Affirmative
Negative
Infinite.
III. Relation.
Categorical
Hypothetical
Disjunctive.
IV. Modality.
Problematic
Assertoric
Apodeictic.

These distinctions, since they concern only the form of judgements, belong, according to Kant, to the activity of judgement as such, and in fact constitute its essential differentiations.

Now, before we consider whether this is really the case, we should ask what answer Kant's account of judgement would lead us to expect to the question 'What are all the functions of unity in judgement?' The question must mean 'What are the kinds of unity produced by judgement?' To this question three alternative answers are prima facie possible. (1) There is only one kind of unity, that of a group of particulars unified through relation to the corresponding universal. The special unity produced will differ for different judgements, since it will depend upon the special universal involved. The kind or form of unity, however, will always be the same, viz. that of particulars related through the corresponding universal. For instance, 'plants' and 'trees' are unified respectively by the judgements 'This body is a plant' and 'This body is a tree'; for 'this body' is in the one case related to other 'plants' and in the other case to other 'trees'. And though the unity produced is different in each case, the kind of unity is the same; for plants and trees are, as members of a kind, unities of a special kind distinct from unities of another kind, such as the parts of a spatial or numerical whole. (2) There are as many kinds of unity as there are universals. Every group of particulars forms a unity of a special kind through relation to the corresponding universal. (3) There are as many kinds of unity as there are highest universals or summa genera. These summa genera are the most general sources of unity through which individuals are related in groups, directly or indirectly. The kinds of unity are therefore in principle the Aristotelian categories, i. e. the highest forms of being under which all individuals fall.

Nevertheless, it is easy to see that the second and third answers should be rejected in favour of the first. For though, according to Kant, a judgement unifies particulars by bringing them under a universal, the special universal involved in a given judgement belongs not to the judgement as such, but to the particulars unified. What belongs to the judgement as such is simply the fact that the particulars are brought under a universal. In other words, the judgement as such determines the kind of unity but not the particular unity. The judgements 'Gold is a metal' and 'Trees are green', considered merely as judgements and not as the particular judgements which they are, involve the same kind of unity, viz. that of particulars as particulars of a universal; for the distinction between 'metal' and 'green' is a distinction not of kinds of unity but of unities. Moreover, to anticipate the discussion of Kant's final conclusion, the moral is that Kant's account of judgement should have led him to recognize that judgement involves the reality, not of any special universals or—in Kant's language—conceptions, but of universality or conception as such. In other words, on his view of judgement the activity of the understanding implies simply that there are universals or conceptions; it does not imply the existence of special conceptions which essentially belong to the understanding, e. g. that of 'cause' or 'plurality'.[17]

If we now turn to the list of the activities of thought in judgement, borrowed from Formal Logic, we shall see that it is not in any way connected with Kant's account of judgement.[18] For if the kinds of judgement distinguished by Formal Logic are to be regarded as different ways of unifying, the plurality unified must be allowed to be not a special kind of group of particulars, but the two conceptions which constitute the terms of the judgement[19]; and the unity produced must be allowed to be in no case a special form of the unity of particulars related through the corresponding universal. Thus the particular judgement 'Some coroners are doctors' must be said to unify the conceptions of 'coroner' and of 'doctor', and presumably by means of the conception of 'plurality'. Again, the hypothetical judgement 'If it rains, the ground will be wet' must be said to unify the judgements 'It rains' and 'The ground will be wet', and presumably by means of the conception of 'reason and consequence'. In neither case can the act of unification be considered a special form of the act of recognizing particulars as particulars of the corresponding universal. The fact is that the distinctions drawn by Formal Logic are based on a view of judgement which is different from, and even incompatible with, Kant's, and they arise from the attempt to solve a different problem. The problem before Kant in describing judgement is to distinguish the understanding from the sensibility, i. e. thought from perception. Hence he regards judgement as the act of unifying a manifold given in perception, directly, or indirectly by means of a conception. But this is not the problem with which Formal Logic is occupied. Formal Logic assumes judgement to be an act which relates material given to it in the shape of 'conceptions' or 'judgements' by analysis of this material, and seeks to discover the various modes of relation thereby effected. The work of judgement, however, cannot consist both in relating particulars through a conception and in relating two conceptions or judgements.

It may be urged that this criticism only affects Kant's argument, but not his conclusion. Possibly, it may be said, the list of types of judgement borrowed from Formal Logic really expresses the essential differentiations of judgement, and, in that case, Kant's only mistake is that he bases them upon a false or at least inappropriate account of judgement.[20] Moreover, since this list furnishes Kant with the 'clue' to the categories, provided that it expresses the essential differentiations of judgement, the particular account of judgement upon which it is based is a matter of indifference.

This contention leads us to consider the last stage of Kant's argument, in which he deduces the categories in detail from his list of the forms of judgement. For it is clear that unless the forms of judgement severally involve the categories, it will not matter whether these forms are or are not the essential differentiations of judgement.

Kant's mode of connecting the categories in detail with the forms of judgement discovered by Formal Logic is at least as surprising as his mode of connecting the latter with the nature of judgement in general. Since the twelve distinctions within the form of judgement are to serve as a clue to the conceptions which belong to the understanding, we naturally expect that each distinction will be found directly to involve a special conception or category, and that therefore, to discover the categories, we need only look for the special conception involved in each form of judgement.[21] Again, since the plurality unified in a judgement of each form is the two conceptions or judgements which form the matter of the judgement, we should expect the conception involved in each form of judgement to be merely the type of relationship established between these conceptions or judgements. This expectation is confirmed by a cursory glance at the table of categories.[22]

I. Of Quantity.
Unity
Plurality
Totality.
II. Of Quality.
Reality
Negation
Limitation.
III. Of Relation.
Inherence and Subsistence (Substantia et Accidens)
Causality and Dependence (Cause and Effect)
Community (Reciprocity between the agent and patient.)
IV. Of Modality.
Possibility—Impossibility
Existence—Non-existence
Necessity—Contingence.

If we compare the first division of these categories with the first division of judgements we naturally think that Kant conceived singular, particular, and universal judgements to unify their terms by means of the conceptions of 'one', of 'some', and of 'all' respectively; and we form corresponding, though less confident, expectations in the case of the other divisions.

Kant, however, makes no attempt to show that each form of judgement distinguished by Formal Logic involves a special conception. In fact, his view is that the activities of thought studied by Formal Logic do not originate or use any special conceptions at all. For his actual deduction of the categories[23] is occupied in showing that although thought, when exercised under the conditions under which it is studied by Formal Logic, does not originate and use conceptions of its own, it is able under certain other conditions to originate and use such conceptions, i. e. categories.[24] Hence if we attend only to the professed procedure of the deduction, we are compelled to admit that the deduction not only excludes any use of the 'clue' to the categories, supposed to be furnished by Formal Logic, but even fails to deduce them at all. For it does not even nominally attempt to discover the categories in detail, but reverts to the prior task of showing merely that there are categories. Doubtless Kant thinks that the forms of judgement formulated by Formal Logic in some way suggest the conceptions which become operative in thought under these other conditions. Nevertheless, it is impossible to see how these forms of judgement can suggest these conceptions, unless they actually presuppose them.

It is clear, however, that the professed link[25] between the forms of judgement and the categories does not represent the actual process by which Kant reached his list of categories; for he could never have reached any list of categories by an argument which was merely directed to show that there are categories. Moreover, an inspection of the list shows that he actually reached it partly by noticing the conceptions which the forms of judgement seemed to presuppose, and partly by bearing in mind the general conceptions underlying physics which it was his ultimate aim to vindicate. Since this is the case, and since the categories can only be connected with the forms of judgement by showing that they are presupposed in them, the proper question to be considered from the point of view of the metaphysical deduction is simply whether the forms of judgement really presuppose the categories.[26]

If, however, we examine the forms of judgement distinguished by Formal Logic, we find that they do not presuppose the categories. To see this, it is only necessary to examine the four main divisions of judgement seriatim.

The first division of judgements is said to be a division in respect of quantity into singular, particular, and universal. So stated, the division is numerical. It is a division of judgements according as they make an assertion about one, more than one, or all the members of a kind. Each species may be said to presuppose (1) the conception of quantity, and (2) a conception peculiar to itself: the first presupposing the conception of one member of a kind, the second that of more than one but less than all members of a kind, the third that of all members of a kind. Moreover, a judgement of each kind may perhaps be said to relate the predicate conception to the subject conception by means of one of these three conceptions.

The fundamental division, however, into which universal and singular judgements enter is not numerical at all, and ignores particular judgements altogether. It is that between such judgements as 'Three-sided figures, as such, are three-angled' and 'This man is tall'. The essential distinction is that in the universal judgement the predicate term is apprehended to belong to the subject through our insight that it is necessitated by the nature of the subject term, while in the singular judgement our apprehension that the predicate term belongs to the subject is based upon the perception or experience of the coexistence of predicate and subject terms in a common subject. In other words, it is the distinction between an a priori judgement and a judgement of perception.[27] The merely numerically universal judgement, and the merely numerically particular judgement[28] are simply aggregates of singular judgements, and therefore are indistinguishable in principle from the singular judgement. If then we ask what conceptions are really presupposed by the kinds of judgement which Kant seeks to distinguish in the first division, we can only reply that the universal judgement presupposes the conception of a connected or systematic whole of attributes, and that the singular judgement presupposes the conception of the coexistence of two attributes in a common subject. Neither kind of judgement presupposes the conception of quantity or the conceptions of unity, plurality, and totality.

The second division of judgements is said to be a division in respect of quality into affirmative, negative, and infinite, i. e. into species which may be illustrated by the judgements, 'A college is a place of education,' 'A college is not a hotel,' and 'A college is a not-hotel'. The conceptions involved are said to be those of reality, of negation, and of limitation respectively. The conception of limitation may be ignored, since the infinite judgement said to presuppose it is a fiction. On the other hand, the conceptions of reality and negation, even if their existence be conceded, cannot be allowed to be the conceptions presupposed. For when we affirm or deny, we affirm or deny of something not mere being, but being of a particular kind. The conceptions presupposed are rather those of identity and difference. It is only because differences fall within an identity that we can affirm, and it is only because within an identity there are differences that we can deny.

The third division of judgements is said to be in respect of relation into categorical, hypothetical, and disjunctive judgements. Here, again, the conclusion which Kant desires is clearly impossible. The categorical judgement may be said to presuppose the conception of subject and attribute, but not that of substance and accident. The hypothetical judgement may be conceded to presuppose the conception of reason and consequence, but it certainly does not presuppose the conception of cause and effect.[29] Lastly, while the disjunctive judgement may be said to presuppose the conception of mutually exclusive species of a genus, it certainly does not presuppose the conception of reciprocal action between physical things.

The fourth division of judgement is said to be in respect of modality into assertoric, problematic, and apodeictic, the conceptions involved being respectively those of possibility and impossibility, of actuality and non-actuality, and of necessity and contingence. Now, from the point of view of Kant's argument, these conceptions, like those which he holds to be involved in the other divisions of judgement, must be considered to relate to reality and not to our attitude towards it. Considered in this way, they resolve themselves into the conceptions of—

(1) the impossible (impossibility);

(2) the possible but not actual (possibility, nonexistence);

(3) the actual but not necessary (existence, contingence);

(4) the necessary (necessity).

But since it must, in the end, be conceded that all fact is necessary, it is impossible to admit the reality of the conception of the possible but not actual, and of the actual but not necessary. There remain, therefore, only the conceptions of the necessary and of the impossible. In fact, however, the distinctions between the assertoric, the problematic, and the apodeictical judgement relate to our attitude to reality and not to reality, and therefore involve no different conceptions relating to reality. It must, therefore, be admitted that the 'metaphysical' deduction of the categories breaks down doubly. Judgement, as Kant describes it, does not involve the forms of judgement borrowed from Formal Logic as its essential differentiations; and these forms of judgement do not involve the categories.