[13] B. 49-50 (b) and (c), M. 30 (b) and (c).
To establish the first conclusion, Kant argues that time has nothing to do with shape or position, but, on the contrary, determines the relation of representations in our internal state. His meaning is that we have a succession of perceptions or representations of bodies in s.p.a.ce,[14] and that while the bodies perceived are not related temporally, our perceptions or representations of them are so related. Here "representations" refers to our apprehension, and is distinguished from what is represented, viz. bodies in s.p.a.ce.
[14] Kant here refers to bodies by the term "phenomena", but their character as phenomena is not relevant to his argument.
How, then, does Kant reach the second result? He remembers that bodies in s.p.a.ce are "phenomena", i. e. representations. He is, therefore, able to point out that all representations belong, as determinations of the mind, to our internal state, whether they have external things, i. e. bodies in s.p.a.ce, for their objects or not, and that, consequently, they are subject to time. Hence time is concluded to be the form of all phenomena. In this second argument, however, it is clear that Kant has pa.s.sed from his previous treatment of bodies in s.p.a.ce as something represented or perceived to the treatment of them as themselves representations or perceptions.[15]
[15] It may be noted that Kant"s a.s.sertion (B. 50, M. 31) that time is the immediate condition of internal phenomena, and thereby also mediately the condition of external phenomena, does not help to reconcile the two positions.
In conclusion, we may point out an insoluble difficulty in Kant"s account of time. His treatment of s.p.a.ce and time as the forms of outer and inner sense respectively implies that, while spatial relations apply to the realities which we perceive, temporal relations apply solely to our perceptions of them. Unfortunately, however, as Kant in certain contexts is clearly aware, time also belongs to the realities perceived. The moon, for instance, moves round the earth. Thus there are what may be called real successions as well as successions in our perception. Further, not only are we aware of this distinction in general, but in particular cases we succeed in distinguishing a succession of the one kind from a succession of the other. Yet from Kant"s standpoint it would be impossible to distinguish them in particular cases, and even to be aware of the distinction in general.
For the distinction is possible only so long as a distinction is allowed between our perceptions and the realities perceived. But for Kant this distinction has disappeared, for in the end the realities perceived are merely our perceptions; and time, if it be a characteristic of anything, must be a characteristic only of our perceptions.
CHAPTER VII
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 _a.n.a.lytic_ 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 a.s.sertion 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.
[1] B. 20, M. 13.
[2] pp. 23-5.
[3] Cf. p. 24, note 1.
[4] Cf. p. 24, notes 2 and 3.
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 s.p.a.ce 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 _a.n.a.lytic_ 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.
[5] E. g. the conception of "cause and effect", and the law that "all changes take place according to the law of the connexion between cause and effect".
The _a.n.a.lytic_ is accordingly subdivided into the _a.n.a.lytic of Conceptions_ and the _a.n.a.lytic of Principles_. The _a.n.a.lytic 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 const.i.tutes 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 s.p.a.ce 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, s.p.a.ce and time are pure perceptions, which contain _a priori_ the condition of the possibility of objects as phenomena, and the synthesis in s.p.a.ce 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 const.i.tuted 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]
[6] _Gesetzt._
[7] B. 121-3, M. 75-6.
This pa.s.sage, if read in connexion with that immediately preceding it,[8] may be paraphrased as follows: "The argument of the _Aesthetic_ a.s.sumes the validity of mathematical judgements, which as such relate to s.p.a.ce and time, and thence it deduces the phenomenal character of s.p.a.ce 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 s.p.a.ce and time and of what is contained in them. Objects in s.p.a.ce and time, being appearances, must conform to the laws according to which we have appearances; and since s.p.a.ce and time are only ways in which we perceive, or have appearances, mathematical laws, which const.i.tute the general nature of s.p.a.ce and time, are the laws according to which we have appearances. Mathematical laws, then, const.i.tute the general structure of appearances, and, as such, enter into the very being of objects in s.p.a.ce 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 s.p.a.ce and time. Objects in s.p.a.ce 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 const.i.tuted as not to correspond to the necessities of our thought."
[8] B. 120-1, M. 73-4.
No doubt Kant"s _solution_ of this problem in the _a.n.a.lytic_ 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 pa.s.sage 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.
[9] Cf. B. 137-8, M. 85, and B. 160 note, M. 98 note.
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 const.i.tute an exhaustive list of the conceptions which belong to the understanding.
[10] B. 91-105, M. 56-63.
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]
[11] B. 92-4, M. 56-7.
It is not worth while to go into all the difficulties of this confused and artificial pa.s.sage. 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 _a.s.serts_ 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.
[12] B. 74-6, M. 45-6.
[13] Kant, in _ill.u.s.trating_ the nature of a judgement, evades the difficulty occasioned by his account of perception, by ill.u.s.trating a "perception" by the "conception of body", and "objects" by "certain phenomena". He thereby covertly subst.i.tutes the relation of universal and individual for the relation of an appearance and the object which causes it.
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]
[14] It is not Kant"s general account of judgement given in this pa.s.sage, but the account of perception incompatible with it, which leads him to confine his ill.u.s.trations to universal judgements.
[15] We may note three minor points. (1) Kant"s definition of function as "the unity of the act of arranging [i. e. the act which produces unity by arranging] different representations under a common representation" has no justification in its immediate context, and is occasioned solely by the forthcoming description of judgement. (2) Kant has no right to distinguish the activity which _originates_ conceptions, or upon which they depend, from the activity which _uses_ conceptions, viz. judgement. For the act of arranging diverse representations under a common representation which originates conceptions is the act of judgement as Kant describes it. (3) It is wholly artificial to speak of judgement as "the representation of a representation of an object".
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 pa.s.ses in effect from the singular to the plural and a.s.serts 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 a.s.sert 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. _Quant.i.ty._ Universal Particular Singular.
II. _Quality._ Affirmative Negative Infinite.
III. _Relation._ Categorical Hypothetical Disjunctive.
IV. _Modality._ Problematic a.s.sertoric 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 const.i.tute its essential differentiations.
[16] B. 95, M. 58.
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"