In this passage, the meaning of which it is difficult to state satisfactorily, Kant's thought appears to be as follows: 'The activity of thought studied by Formal Logic relates by way of judgement conceptions previously obtained by an analysis of perceptions. For instance, it relates the conceptions of body and of divisibility, obtained by analysis of perceptions of bodies, in the judgement 'Bodies are divisible'. It effects this, however, merely by analysis of the conception 'body'. Consequently, the resulting knowledge or judgement, though a priori, is only analytic, and the conceptions involved originate not from thought but from the manifold previously analysed. But besides the conceptions obtained by analysis of a given manifold, there are others which belong to thought or the understanding as such, and in virtue of which thought originates synthetic a priori knowledge, this activity of thought being that studied by Transcendental Logic. Two questions therefore arise. Firstly, how do these conceptions obtain a matter to which they can apply and without which they would be without content or empty? And, secondly, how does thought in virtue of these conceptions originate synthetic a priori knowledge? The first question is easily answered, for the manifolds of space and time, i. e. individual spaces and individual times, afford matter of the kind needed to give these conceptions content. As perceptions (i. e. as objects of perception), they are that to which a conception can apply, and as pure or a priori perceptions, they are that to which those conceptions can apply which are pure or a priori, as belonging to the understanding. The second question can be answered by considering the process by which this pure manifold of space and time enters into knowledge. All synthetic knowledge, whether empirical or a priori, requires the realization of three conditions. In the first place, there must be a manifold given in perception. In the second place, this manifold must be 'gone through, taken up, and combined'. In other words, if synthesis be defined as 'the act of joining different representations to one another and of including their multiplicity in one knowledge', the manifold must be subjected to an act of synthesis. This is effected by the imagination. In the third place, this synthesis produced by the imagination must be brought to a conception, i. e. brought under a conception which will constitute the synthesis a unity. This is the work of the understanding. The realization of a priori knowledge, therefore, will require the realization of the three conditions in a manner appropriate to its a priori character. There must be a pure or a priori manifold; this is to be found in individual spaces and individual times. There must be an act of pure synthesis of this manifold; this is effected by the pure imagination. Finally, this pure synthesis must be brought under a conception. This is effected by the pure understanding by means of its pure or a priori conceptions, i. e. the categories. This, then, is the process by which a priori knowledge is originated. The activity of thought or understanding, however, which unites two conceptions in a judgement by analysis of them—this being the act studied by Formal Logic—is the same as that which gives unity to the synthesis of the pure manifold of perception —this being the act studied by Transcendental Logic. Consequently, 'the same understanding, and indeed by the same activities whereby in dealing with conceptions it unifies them in a judgement by an act of analysis, introduces by means of the synthetical unity which it produces in the pure manifold of perception a content into its own conceptions, in consequence of which these conceptions are called pure conceptions of the understanding,'[4] and we are entitled to say a priori that these conceptions apply to objects because they are involved in the process by which we acquire a priori knowledge of objects.'

A discussion of the various difficulties raised by the general drift of this passage, as well as by its details,[5] is unnecessary, and would anticipate discussion of the Transcendental Deduction. But it is necessary to draw attention to three points.

In the first place, as has been said, Kant here introduces—and introduces without warning—a totally new account of knowledge. It has its origin in his theory of perception, according to which knowledge begins with the production of sensations in us by things in themselves. Since the spatial world which we come to know consists in a multiplicity of related elements, it is clear that the isolated data of sensation have somehow to be combined and unified, if we are to have this world before us or, in other words, to know it. Moreover, since these empirical data are subject to space and time as the forms of perception, individual spaces and individual times, to which the empirical data will be related, have also to be combined and unified. On this view, the process of knowledge consists in combining certain data into an individual whole and in unifying them through a principle of combination.[6] If the data are empirical, the resulting knowledge will be empirical; if the data are a priori, i. e. individual spaces and individual times, the resulting knowledge will be a priori.[7] This account of knowledge is new, because, although it treats knowledge as a process or act of unifying a manifold, it describes a different act of unification. As Kant first described the faculty of judgement,[8] it unifies a group of particulars through relation to the corresponding universal. As Formal Logic, according to Kant, treats the faculty of judgement, it unifies two conceptions or two prior judgements into a judgement. As Kant now describes the faculty of judgement or thought, it unifies an empirical or an a priori manifold of perception combined into an individual whole, through a conception which constitutes a principle of unity. The difference between this last account and the others is also shown by the fact that while the first two kinds of unification are held to be due to mere analysis of the material given to thought, the third kind of unification is held to be superinduced by thought, and to be in no way capable of being extracted from the material by analysis. Further, this new account of knowledge does not replace the others, but is placed side by side with them. For, according to Kant, there exist both the activity of thought which relates two conceptions in a judgement,[9] and the activity by which it introduces a unity of its own into a manifold of perception. Nevertheless, this new account of knowledge, or rather this account of a new kind of knowledge, must be the important one; for it is only the process now described for the first time which produces synthetic as opposed to analytic knowledge.

In the second place, the passage incidentally explains why, according to Kant, the forms of judgement distinguished by Formal Logic do not involve the categories.[10] For its doctrine is that while thought, if exercised under the conditions under which it is studied by Formal Logic, can only analyse the manifold given to it, and so has, as it were, to borrow from the manifold the unity through which it relates the manifold,[11] yet if an a priori manifold be given to it, it can by means of a conception introduce into the manifold a unity of its own which could not be discovered by analysis of the manifold. Thus thought as studied by Formal Logic merely analyses and consequently does not and cannot make use of conceptions of its own; it can use conceptions of its own only when an a priori manifold is given to it to deal with.

In the third place, there is great difficulty in following the part in knowledge assigned to the understanding. The synthesis of the manifold of perception is assigned to the imagination, a faculty which, like the new kind of knowledge, is introduced without notice. The business of the understanding is to 'bring this synthesis to conceptions' and thereby to 'give unity to the synthesis'. Now the question arises whether 'the activity of giving unity to the synthesis' really means what it says, i. e. an activity which unifies or introduces a unity into the synthesis, or whether it only means an activity which recognizes a unity already given to the synthesis by the imagination. Prima facie Kant is maintaining that the understanding really unifies, or introduces the principle of unity. For the twice-repeated phrase 'give unity to the synthesis' seems unmistakable in meaning, and the important rôle in knowledge is plainly meant to be assigned to the understanding. Kant's language, however, is not decisive; for he speaks of the synthesis of the manifold as that which 'first produces a knowledge which indeed at first may be crude and confused and therefore needs analysis[12]', and he says of the conceptions which give unity to the synthesis that 'they consist solely in the representation[13] of this necessary synthetical unity'.[14] Again, 'to bring the synthesis to a conception' may well be understood to mean 'to recognize the synthesis as an instance of the conception'; and, since Kant is speaking of knowledge, 'to give unity to the synthesis' may only mean 'to give unity to the synthesis for us', i. e. 'to make us aware of its unity'. Moreover, consideration of what thought can possibly achieve with respect to a synthesis presented to it by the imagination renders it necessary to hold that the understanding only recognizes the unity of the synthesis. For if a synthesis has been effected, it must have been effected in accordance with a principle of construction or synthesis, and therefore it would seem that the only work left for the understanding is to discover the principle latent in the procedure of the imagination. At any rate, if the synthesis does not involve a principle of synthesis, it is impossible to see how thought can subsequently introduce a principle. The imagination, then, must be considered to have already introduced the principle of unity into the manifold by combining it in accordance with a conception or principle of combination, and the work of the understanding must be considered to consist in recognizing that the manifold has been thereby combined and unified through the conception. We are therefore obliged to accept one of two alternatives. Either the understanding merely renders the mind conscious of the procedure of a faculty different from itself, viz. the imagination, in which case the important rôle in knowledge, viz. the effecting of the synthesis according to a principle, is played by a faculty different from the understanding; or the imagination is the understanding working unreflectively, and the subsequent process of bringing the synthesis to a conception is merely a process by which the understanding becomes conscious of its own procedure. Moreover, it is the latter alternative which we must accept as more in accordance with the general tenor of Kant's thought. For the synthesis of the imagination is essentially the outcome of activity or spontaneity, and, as such, it belongs to the understanding rather than to the sensibility; in fact we find Kant in one place actually saying that 'it is one and the same spontaneity which at one time under the name of imagination, at another time under that of understanding, introduces connexion into the manifold of perception'.[15] Further, it should be noted that since the imagination must be the understanding working unreflectively, and since it must be that which introduces unity into the manifold, there is some justification for his use of language which implies that the understanding is the source of the unity, though it will not be so in the sense in which the passage under discussion might at first sight lead us to suppose.

We can now turn to the argument of the Transcendental Deduction itself. Kant introduces it in effect by raising the question, 'How is it that, beginning with the isolated data of sense, we come to acquire knowledge?' His aim is to show (1) that knowledge requires the performance of certain operations by the mind upon the manifold of sense; (2) that this process is a condition not merely of knowledge, but also of self-consciousness; and (3) that, since the manifold is capable of entering into knowledge, and since we are capable of being self-conscious, the categories, whose validity is implied by this process, are valid.

Kant begins by pointing out[16] that all knowledge, a priori as well as empirical, requires the manifold, produced successively in the mind, to be subjected to three operations.

1. Since the elements of the manifold are as given mere isolated units, and since knowledge is the apprehension of a unity of connected elements, the mind must first run through the multiplicity of sense and then grasp it together into a whole, i. e. into an image.[17] This act is an act of synthesis; it is called 'the synthesis of apprehension' and is ascribed to the imagination. It must be carried out as much in respect of the pure or a priori elements of space and time as in respect of the manifold of sensation, for individual spaces and times contain a multiplicity which, to be apprehended, must be combined.[18] The necessity of this act of synthesis is emphasized in the second edition. "We cannot represent anything as combined in the object without having previously combined it ourselves. Of all representations, combination is the only one which cannot be given through objects,[19] but can be originated only by the subject itself because it is an act of its own activity."[20]

2. Since the data of perception are momentary, and pass away with perception, the act of grasping them together requires that the mind shall reproduce the past data in order to combine them with the present datum. "It is plain that if I draw a line in thought, or wish to think of the time from one midday to another, or even to represent to myself a certain number, I must first necessarily grasp in thought these manifold representations one after another. But if I were continually to lose from my thoughts the preceding representations (the first parts of the line, the preceding parts of time or the units successively represented), and were not to reproduce them, while I proceeded to the succeeding parts, there could never arise a complete representation, nor any of the thoughts just named, not even the first and purest fundamental representations of space and time."[21] This act of reproduction is called 'the synthesis of reproduction in the imagination'.[22]

Further, the necessity of reproduction brings to light a characteristic of the synthesis of apprehension. "It is indeed only an empirical law, according to which representations which have often followed or accompanied one another in the end become associated, and so form a connexion, according to which, even in the absence of the object, one of these representations produces a transition of the mind to another by a fixed rule. But this law of reproduction presupposes that phenomena themselves are actually subject to such a rule, and that in the manifold of their representations there is a concomitance or sequence, according to a fixed rule; for, without this, our empirical imagination would never find anything to do suited to its capacity, and would consequently remain hidden within the depths of the mind as a dead faculty, unknown to ourselves. If cinnabar were now red, now black, now light, now heavy, if a man were changed now into this, now into that animal shape, if our fields were covered on the longest day, now with fruit, now with ice and snow, then my empirical faculty of imagination could not even get an opportunity of thinking of the heavy cinnabar when there occurred the representation of red colour; or if a certain name were given now to one thing, now to another, or if the same thing were called now by one and now by another name, without the control of some rule, to which the phenomena themselves are already subject, no empirical synthesis of reproduction could take place."