<t1> The Analytic of Concepts

When teachers of law discuss entitlements and claims, they distinguish between two kinds of question which arise in a lawsuit: questions of law (‘By what right?’), and questions of fact (‘What are the facts?’). Given that both need to be proved, they call the proof of the first the deduction, and its function is to demonstrate the entitlement or legal claim.

<t2> We use many empirical concepts without anyone objecting, and we consider ourselves justified in giving them a sense and a supposed meaning, even without any deduction of them. This is because we always have experience to hand [B117] to prove their objective reality. However, there are also other, illegitimate concepts, such as those of good luck and fate, which circulate with almost universal indulgence, but which are sometimes called to account by the question: ‘By what right?’ Then people find themselves in no little difficulty over the deduction of the concepts, since they can derive no clear basis for their justification, either from experience or from reason, which would give clear authority for their use.

<t3> Among the many sorts of concepts which make up the very mixed texture of human knowledge, there are a few which are destined even for pure apriori use, in complete independence of all experience, and their authority for this use always requires a deduction. Since proofs drawn from experience are insufficient to establish the legitimacy of such a use, we need to know how these concepts can relate to objects which they do not get from any experience. So I call the explanation of the way in which concepts can relate to objects apriori their transcendental deduction. This is different from an empirical deduction, which shows the way in which a concept is obtained through experience and reflection on it. It is therefore a question, not of the legitimacy of the concept, but of the facts as to how it came to be possessed.

<t4> [B118] We already have two entirely different kinds of concept which have it in common that they both relate to objects completely apriori. These are the concepts of space and time as forms of sensibility, and the categories as concepts of the understanding. It would be a total waste of time to attempt an empirical deduction of them, because what is distinctive about their nature is precisely that they relate to their objects without having borrowed anything from experience for representing them. So if a deduction of them is necessary, it must in any event be a transcendental deduction.

<t5> Nevertheless, as with all knowledge, we can look for the occasional causes of their formation in experience, even if we cannot look for the principle of their possibility in experience. It is here that the impressions of the senses provide the first stimulus, which opens out the whole faculty of knowledge to considering these concepts, and brings experience into being. Experience consists of two very different elements, namely the matter for knowledge, which comes from the senses; and a certain form for organising this matter. The form comes from the inner source of pure intuition and thought, which are first aroused to activity and produce concepts on the occasion of sense impressions.

<t6> Without doubt, it is very useful to trace these first strivings of our faculty of knowledge to advance from particular perceptions to [B119] universal concepts, and we have the famous Locke to thank for first opening up the way to this area of investigation. However, this would never bring about a deduction of the pure apriori concepts, which is most emphatically not to be found down this route. In view of their later use, which is to be entirely independent of experience, they must be able to present a birth certificate which is quite other than descent from experiences.

<t7> This attempted naturalistic derivation of the categories cannot be called a deduction at all, since it is concerned with a question of fact. Instead, I shall call it an explanation of our possession of pure knowledge. It is therefore clear that only a transcendental deduction can be given of our pure knowledge, and in no way an empirical one. As far as pure apriori concepts are concerned, empirical deductions are a complete waste of effort, and they can be undertaken only by people who have totally failed to grasp the essential nature of this kind of knowledge.

<t8> Even if it is accepted that the only possible kind of deduction of pure apriori knowledge is along the transcendental route, this does not yet make it obvious that a deduction is unavoidably necessary. I have already traced the concepts of space and time back to their source by means of a transcendental deduction, and I have explained and determined [B120] their apriori objective validity. However, geometry follows its sure path by means of strictly apriori knowledge, without having to ask philosophy for any certification of the pure and legitimate pedigree of its foundational concept of space. But the application of the concept of space in geometry is limited to the outer world of the senses, and space is the pure form of sensory intuition. So in this world, all geometrical knowledge is directly evident, because it is based on apriori intuition, and its objects are given apriori in intuition through that very knowledge of them (at least as far as their form is concerned).

<t9> The situation is quite different in the case of the pure concepts of the understanding, where the unavoidable need to find a transcendental deduction first arises — a deduction not only of the concepts themselves, but also of space. For since they refer to objects, not through predicates of intuition and sensibility, but through predicates of pure apriori thought, they relate universally to objects, without any restriction to sensibility. Again, since they are not based on experience, they cannot use apriori intuition to display any object which could form the basis of their synthesis prior to all experience. Consequently, they arouse suspicion, not only as to the objective validity and scope of their applicability, but also because they make the concept of space ambiguous, since they tend to use it beyond the [B121] restrictions of sensory intuition. And this is why I have already found it necessary to provide a transcendental deduction of the concept of space.

<t10> The reader must therefore be convinced that such a transcendental deduction is unavoidably necessary before taking a single step into the realm of pure reason. Without it, you will stumble around blindly, and after many wrong turns you will inevitably end up back in the state of ignorance from which you set out. But right from the start, you must also be clearly aware of the inescapable difficulty of the task, so that you do not complain of obscurity where the matter itself is deeply shrouded, or become discouraged too quickly over the removal of obstacles. The long and the short of it is that, either we see this critical investigation through to the end, or we must completely give up any claim that pure reason can have insight into its most cherished realm, namely that which extends beyond the limits of all possible experience.

<t11> Earlier, it was easy for me to explain how the concepts of space and time must necessarily relate to objects, despite being instances of apriori knowledge. I also explained how they made it possible for us to have synthetic knowledge of space and time independently of all experience. For it is only through the mediation of these pure forms of sensibility that an object can appear to us — in other words, that it can be an object of empirical intuition. It follows that space and time are pure intuitions which contain apriori the precondition [B122] of the possibility of objects as appearances, and also that acts of synthesis which are carried out in them have objective validity.

<t12> By contrast, the categories of the understanding in no way represent to us the preconditions for objects to be given in intuition. Therefore objects can certainly appear to us, but without necessarily having to relate to functions of the understanding, and without the understanding having to contain their preconditions apriori. This gives rise to a difficulty which we did not come up against in the realm of sensibility — namely, how can subjective preconditions of thought have objective validity? In other words, how can they provide preconditions for the possibility of all knowledge of objects? For appearances can certainly be given in intuition without functions of the understanding.

<t13> Take the concept of cause, for example. This concept denotes a particular kind of synthesis, in which, given A, a quite different B is affirmed in accordance with a rule. But it is not clear apriori why appearances should contain anything like the concept of cause — and experience cannot show why they should, since it cannot establish the objective validity of an apriori concept such as this. So, from an apriori point of view, it is conceivable that a concept like that of cause might perhaps be completely empty, and have no object anywhere among appearances.

<t14> It is clear that objects of sensory intuition must be in accordance with [B123] the formal preconditions of sensibility which lie apriori in the mind, because otherwise they would not be objects for us. It is less easy to see why they must also be in accordance with the preconditions which the understanding requires for the synthetic unity of thought. For it would be perfectly possible for our appearances to be such that our understanding found that they were not at all in accordance with the preconditions of its unity. Everything could be in such a state of confusion, that, for example, there was nothing to be found in the succession of appearances which would provide a rule for synthesising the appearances, and thus correspond to the concept of cause and effect. If so, the concept of cause and effect would be completely empty, invalid, and meaningless. Nevertheless, appearances would still provide our intuition with objects, since intuition in no way requires the functions of thought.

<t15> Someone might think of avoiding the laboriousness of these investigations, by the following line of reasoning: experience unceasingly supplies us with examples of a regularity of appearances which gives us sufficient grounds for abstracting the concept of cause from them, and at the same time for confirming the validity of the concept. If so, they will have failed to notice that it is quite impossible for the concept of cause to come into being this way. It must either be grounded in the understanding completely apriori, or it must be given up altogether as a mere figment of the brain. [B124] For the concept of cause absolutely requires that something A is of such a kind that something else B follows from it necessarily and in accordance with a strictly universal rule.

<t16> Appearances do indeed provide us with particular cases, from which we can construct a rule that something usually happens, but never that the succession is necessary. So the synthesis of cause and effect has a special status, which cannot be described at all in empirical terms, namely that the effect is not merely added to the cause, but that it comes into existence through the cause and follows from it. Besides, strict universality is never a property of empirical rules, since induction can give them nothing other than relative universality — that is, widespread applicability. The use of the pure concepts of the understanding would be completely changed, if they were treated merely as the products of experience.

<t17> §14

There are only two possible cases in which synthetic representation and its objects can come together, have a necessary connection to each other, and, as it were, meet each other:

• either if the object alone makes the representation possible;
• or if the representation [B125] alone makes the object possible.

In the first case, the relationship is merely empirical, and the representation can never be possible apriori. This is the case with an appearance, to the extent that what it contains belongs to sensation.

<t18> Now take the second case. Given that we are not here talking about the causality of the will, representation does not by itself bring its object into existence. On the other hand, it does determine its object apriori, since it is only through representation that it is possible to know something as an object.

<t19> There are two preconditions under which alone knowledge of an object is possible. The first is an intuition, through which an object is given, if only as an appearance. The second is a concept, through which an object corresponding to this intuition is thought.

<t20>From what I have already said, it is clear that the first precondition (namely the necessary precondition for objects to be intuited) lies apriori in the mind as the ground of objects as far as their form is concerned. So all intuitions are necessarily in accordance with this formal precondition of sensibility, because it is only through this precondition that they can appear — in other words, that they can be empirically intuited and given.

<t21> The question now arises whether concepts might not also precede objects apriori. If so, they would not be preconditions for anything to be intuited, but they would be necessary preconditions for anything to be thought as an object in general. If so, all empirical [B126] knowledge of objects would necessarily be in accordance with such concepts, since nothing would be possible as an object of experience without presupposing them.

<t22> Now all experience contains both a sensory intuition through which something is given, and a concept of an object which is given in intuition, or appears. Therefore experiential knowledge presupposes concepts of objects in general as apriori preconditions. Consequently, the objective validity of the categories, as apriori concepts, depends on the fact that it is only through them that experience is possible, as far as the form of thought is concerned. So then they relate to objects of experience necessarily and apriori, since no object of experience at all can be thought except by means of the categories.

<t23> Thus the transcendental deduction of all apriori concepts has a principle, which must govern the whole investigation. This principle is that these apriori concepts must be known as apriori preconditions of the possibility of experience — whether of the intuition which it contains, or of the thought. Concepts which provide the necessary foundation for the possibility of experience are necessary by virtue of that very fact. To trace the development of these concepts in the experience in which they are found is not a deduction of them, but an explanation, since this would make them merely contingent. [B127] All objects of knowledge are met with in experience. So it would be impossible to understand how apriori concepts could relate to any sort of object, without this originative relation to possible experience.

<t24> The famous Locke failed to take account of this consideration. Because he found pure concepts of the understanding in experience, he also derived them from experience. But he proceeded so illogically, that he tried to use experience to discover knowledge which lies far outside the limits of experience.

<t25> David Hume recognised that, in order to go beyond experience, it is necessary for these concepts to have an apriori origin. However, he was quite unable to explain how it could be possible that the understanding must think concepts as necessarily connected in the object, when they are not essentially connected in the understanding. It never occurred to him that, through these concepts, the understanding could itself perhaps be the creator of the experience in which the objects of the understanding are met with. So he was forced to derive the concepts from experience.

<t26> More precisely, he derived them from a subjective necessity arising from repeated association in experience, which necessity is eventually, though wrongly, taken to be an objective one — in other words, he derived them from custom. He then continued very consistently, and declared that it was impossible to use these concepts and the axioms they generate to go beyond the limits of experience. However, the empirical derivation [B128] to which both Locke and Hume were attracted, is inconsistent with the scientific apriori knowledge we actually have, namely that of pure mathematics and of general natural science. So the empirical derivation is refuted by the facts of the case.

<t27> The first of these two famous men opened the floodgates to enthusiasm, since once reason has authority on its side, it no longer allows itself to be kept within limits by vague recommendations of moderation. The second gave himself entirely over to scepticism, once he believed he had discovered that what is generally held to be reason is no more than a delusion of our faculty of knowledge. We are now about to begin an experiment, to see whether we can steer human reason safely between these two rocks, by setting definite limits to it, while at the same time leaving open to it the whole realm of its legitimate activity.

<t28> But first I shall provide an explanation of what the categories are. Categories are concepts of an object in general, through which an intuition of an object is considered as determined in respect of one of the logical functions for judging. Thus the function of categorical judgments is that of the relation of subject to predicate — for example, ‘All bodies are divisible.’ As long as we confine ourselves to the purely logical use of the understanding, it remains undetermined [B129] which of the two concepts is to be given the function of subject, and which the function of predicate. For it could equally well be said that ‘Something divisible is a body.’ But if I bring the concept of a body under the category of substance, it becomes determinate that the empirical intuition of a body in experience must always be considered only as a subject, and never as a mere predicate. And the same goes for the other categories.

<t29> The Deduction of the Pure Concepts of the Understanding

The multiplicity of representations can be given in an intuition which is purely sensory — that is, which is nothing other than receptivity. The form of this intuition can lie apriori in our faculty of representation, without being anything other than the way in which the subject is affected. But the unification of a multiplicity in general can never come to us through the senses; nor, therefore, can it already be contained in the pure form of sensory intuition along with the rest. [B130] For unification is a self-generated act of the faculty of representation; and this faculty must be called the understanding, in order to distinguish it from sensibility. So all unification is an act of the understanding:

• whether we are conscious of it or not;
• whether it is a unification of the multiplicity of intuition or of a number of concepts;
• and in the case of intuition, whether it is a unification of sensory or of non-sensory intuition.

I shall apply the general term synthesis to this act of the understanding, in order to make it explicit that we cannot conceive anything as unified in the object, which we have not ourselves already unified.

<t30> Of all representations, unification is the only one which is not given through objects. Since it is an act of the self-activity of the subject, it can be carried out only by the subject itself. Here it is easy to see that this act must have a single origin which is equally valid for all unification. Separation, or analysis, might seem to be its opposite, but it always presupposes unification. For the understanding cannot separate what it has not already unified, since it is only through the understanding that anything can be given to the faculty of representation as unified.

<t31> As well as the concept of multiplicity and its synthesis, the concept of unification also implies the concept of its unity. Unification is the representation of the synthetic unity of the multiple.*

[B131] The representation of this unity cannot arise from the unification. Rather, it is the representation of this unity which first makes possible the concept of unification, through being added to the representation of the multiple.

<t32> Since this unity precedes all concepts of unification apriori, it is not the category of unity specified above in §10. For all the categories are based on the logical functions in judgments; and unification — and hence the unity of the given concepts — is already thought in them. Therefore the category of unity already presupposes unification. So we must look for this unity (as a qualitative unity — see §12) at an even higher level, in that which itself contains the foundation of the unity of different concepts in judgments, and hence of the possibility of the understanding, even in its logical use.

<t33> §16.

It must be possible for the I think to accompany all my representations. If not, something would be represented in me [B132] which could not be thought at all. This is as much as to say that the representation would either be impossible, or at least that it would be nothing for me.

<t34> That representation which can be given before any thought is called intuition. So every multiplicity of intuition has a necessary relation to the I think in the same subject as the multiplicity is found in. But the representation of the I think is an act of self-activity — in other words, it cannot be taken as belonging to sensibility. I call it pure apperception, in order to distinguish it from empirical apperception. I also call it originative apperception, because it is the self-consciousness which cannot be accompanied by any higher-level consciousness. It is itself the source of the representation I think, which must be able to accompany all other representations, and which is one and the same in all consciousness.

<t35> I also call the unity of apperception the transcendental unity of self-consciousness, in order to indicate the possibility of deriving apriori knowledge from it. For the multiple representations which are given in any particular intuition would not as a whole be my representations, unless they belonged as a whole to a single self-consciousness. To put it another way, as my representations (even if I am not conscious of them as such), they must necessarily satisfy the precondition for them to be able to come together under a single over-arching self-consciousness — otherwise they would not belong to me as a systematic whole. [B133] Much follows from this originative unification.

<t36> In particular, this holistic identity of the apperception of a multiplicity given in intuition contains a synthesis of the representations, and it is possible only through the consciousness of this synthesis. For the empirical consciousness which accompanies different representations is essentially scattered among them, and it has no relation to the identity of the subject. So this relation is not brought into being through my accompanying every representation with consciousness. Rather, the relation to the identity of the subject is brought into being through my joining one representation to another, and through my being conscious of their synthesis. Therefore it is only because I can unify a multiplicity of given representations into a single consciousness, that it is possible for me to conceive the very identity of the consciousness in these representations. In other words, the analytic unity of apperception is possible only on the presupposition of some sort of synthetic unity.*

<t38> [B134] So the thought that: ‘These representations given in intuition belong to me as a whole,’ amounts to saying that I unite them in a single consciousness, or at least that I can unite them in a single consciousness. And although it is not yet itself the consciousness of the synthesis of the representations, it still presupposes the possibility of such a synthesis. In other words, I can call these representations as a whole my representations, only because I can embrace their multiplicity in a single consciousness. If I could not do this, I would have a self which was as variegated and fragmentary as the representations I am conscious of.

<t39> So the synthetic unity of the multiplicity of intuitions, as given apriori, is the foundation of the identity of apperception itself, and it precedes all my particular thoughts apriori. Unification does not lie in objects, and it cannot first be taken up into the understanding by being derived from objects through some sort of perception. Rather, unification is [B135] the business of the understanding alone. And the understanding itself is no more than the faculty of unifying priori, and of bringing the multiplicity of given representations under the unity of apperception. This is the supreme axiom of the whole of human knowledge.

<t40> Admittedly, this axiom of the necessary unity of apperception is itself an identical, and hence an analytic proposition. Nevertheless, it does make it explicit that a synthesis of the multiplicity given in an intuition is necessary. Without such a synthesis, it would be impossible to think the holistic identity of self-consciousness. No multiplicity is given in the ‘I’, since it is a simple representation. It is only through intuition, which is distinct from the ‘I’, that multiplicity can be given, and thought through unification in a single consciousness.

<t41> If there were an understanding such that the whole multiplicity was given to it at one and the same time through self-consciousness, it would be an intuitive understanding. But our understanding can only think, and it must look for intuition in the senses. So I am conscious of the identity of my self by reference to the multiplicity of representations which are given to me in an intuition, because I call them as a whole my representations, constituting a single intuition. This amounts to saying that I am conscious of a necessary apriori synthesis of my representations, which is called the originative synthetic unity of apperception. All representations which are given to me must be subject to this unity, but they can be brought under it only through a synthesis.

<t42> [B136] §17

As I said in the Transcendental Aesthetic, the supreme axiom of the possibility of all intuition as far as sensibility is concerned, is that every multiplicity of intuition comes under the formal preconditions of space and time. The supreme axiom of the possibility of all intuition as far as the understanding is concerned, is that every multiplicity of intuition comes under the preconditions of the originative-synthetic unity of apperception.*

<t44> All multiple representations of intuition come under the first axiom in so far as they are given to us, and under the second axiom in so far as it must be possible for them to be unified in a single consciousness. [B137] Without such unification, nothing could be thought or known, because the representations given would not have the act of apperception ‘I think’ in common. Consequently they could not be blended together in a single consciousness.

<t45> Generally speaking, the understanding is the faculty of knowledge. Knowledge consists in the particular relation of given representations to an object. The concept of an object is that in which the multiplicity of a given intuition is united. But all uniting of representations requires unity of consciousness in their synthesis. Consequently, the unity of consciousness is that which alone brings about the relation of representations to an object, and hence their objective validity, and therefore makes them instances of knowledge. Consequently, the very possibility of the understanding depends on the unity of consciousness.

<t46> The primary pure knowledge of the understanding is the axiom of the originative synthetic unity of apperception. All other use of the understanding is based on it, and it is also completely independent of any preconditions of sensory intuition. Thus space, which is merely the form of outer sensory intuition, is not yet knowledge at all. All it provides is the multiplicity of apriori intuition for possible knowledge. In order to know something in space, for example a line, I must pull it out, and thus [B138] synthetically bring into being a particular unification of the given multiplicity. The unity of this action is at the same time the unity of consciousness (in the concept of a line), and through this unity of consciousness an object is first known (as a particular space). So the synthetic unity of consciousness is an objective precondition of all knowledge. It is not merely that I myself need it in order to know an object, but that every intuition must be subject to it in order to become an object for me. If it happened in any other way, and without this synthesis, the multiplicity would not be united in a single consciousness.

<t47> As I have already said, this proposition is itself analytic, even though it makes synthetic unity the precondition of all thought. It says no more than that all my representations in any given intuition must be subject to the necessary precondition for me to be able to ascribe them to one and the same self as my representations, and so to embrace them as synthetically connected together in a single apperception through the universal expression: ‘I think’.

<t48> However, this axiom is not a principle which applies to absolutely every possible understanding, but only to an understanding such that no multiplicity at all is given through its pure apperception in the representation ‘I am’. Let us suppose that there is an understanding such that the multiplicity of intuition is given to it simultaneously with its self-consciousness [B139] — in other words, an understanding such that the objects of its representation exist simultaneously with its representation. Such an understanding would not require an additional act of synthesis of the multiplicity for the unity of its consciousness. By contrast, human understanding does require this act of synthesis, since it merely thinks, and does not intuit. It is so inescapably the primary axiom for human understanding, that human understanding cannot even form the least conception of a different kind of possible understanding — whether of one which itself intuits, or of one which has sensory intuition, but of a very different kind from intuition based on space and time.

<t49> §18

The transcendental unity of apperception is that through which every multiplicity given in an intuition is united in a concept of the object. This is why it is called objective, and must be distinguished from the subjective unity of consciousness. The subjective unity of consciousness is a determination of the inner sense, through which that multiplicity of intuition is empirically given for such a unification.

<t50> Whether I can be empirically conscious of the multiplicity as co-existent or as successive depends on circumstances or empirical conditions. Therefore the empirical [B140] unity of consciousness, which arises from the association of representations, concerns only an appearance, and is completely contingent. By contrast, the pure form of intuition in time is subject to the originative unity of consciousness. This is because time is nothing other than the universal intuition which contains any given multiplicity. And it is subject to the unity of consciousness through the necessary relation of the multiplicity of intuition to the single ‘I think’, and hence through the pure synthesis of the understanding, which is the apriori basis of empirical synthesis.

<t51> Only the transcendental unity of apperception is objectively valid. The empirical unity of apperception (which I am not dealing with here) has only subjective validity, since it is derived from the pure synthesis merely under particular given conditions. One person connects the representation corresponding to a particular word with one thing, and another person with a different thing. Similarly, in an empirical context, the unity of consciousness is not necessarily and universally valid of what is given.

<t52> §19

I have never been satisfied with the definition logicians give of a judgment in general. They say it is the representation of a relation between two concepts. [B141] Here I am not going to quibble with them over the defects of this definition:

• that it applies only to categorical, and not to hypothetical or disjunctive judgments;
• that hypothetical and disjunctive judgments contain a relation, not between concepts, but between judgments themselves.

This is despite the fact that many harmful consequences have arisen from this oversight on the part of logic.*

<t54> All I want to say here is that the logicians’ definition fails to determine what this relation consists in.

<t55> Looking more closely at the relation between the items of knowledge in every judgment, I distinguish between this relation, which belongs to the understanding, from any relationship arising from the laws of the reproductive imagination, which has only subjective validity. I then find that a judgment is nothing other than the way we make given items of knowledge subject to the objective unity of apperception.

<t56> This is the function of the connective ‘is’ in [B142] a judgment, which distinguishes the objective unity from the subjective unity of the representations that are given. The word ‘is’ indicates the relation of the representations to the originative apperception, and to the necessary unity of apperception.

<t57> The above holds even when the judgment itself is empirical, and hence contingent — for example, the judgment ‘Bodies are heavy.’ Here, I certainly do not mean to say that these representations necessarily belong to each other in empirical intuition. Rather, they belong to each other by virtue of the necessary unity of apperception in the synthesis of intuitions. In other words, they belong to each other in accordance with principles of the objective determination of all representations, in so far as they can yield knowledge. And all these principles are derived from the axiom of the transcendental unity of apperception.

<t58> This is the only way the relation can give rise to a judgment, that is, a relation which is objectively valid, and sufficiently distinguished from a merely subjectively valid relation between exactly the same representations — for example, one that arises from the laws of association. If it arises from the laws of association, all I can say is ‘If I lift a body, I feel a burden of heaviness.’ What I cannot say is ‘It, the body, is heavy,’ since this amounts to saying that both these representations are in the object. In other words, it amounts to saying that, irrespective of the state of the subject, being bodily and being heavy are united together in the object, and not merely in perception, however often the same perception might be repeated.

<t59> [B143] §20

The multiple given in a sensory intuition is necessarily subject to the originative synthetic unity of apperception, because it is only through this that the unity of the intuition is possible (see §17). But the act of the understanding through which the multiplicity of given representations is brought under a single apperception in general, is the logical function of judgment (see §19). This is the case whether the representations are intuitions or concepts. So every multiplicity given in a single empirical intuition is determined in respect of one of the logical functions of judgment; and this is how it is brought into a consciousness in general. But the categories are nothing other than just these functions of judgment, in so far as the multiplicity of a given intuition is determined in respect of them (see §10). So it follows that the multiplicity in any given intuition is also necessarily subject to the categories.

<t60> [B144] §21

A multiplicity contained in an intuition which I call mine, will be represented as belonging to the necessary unity of self-consciousness through the synthesis which the understanding carries out by means of a category.*

So this need for a category shows that the empirical consciousness of the multiplicity given in a single intuition is subject to pure apriori self-consciousness, just as empirical intuition is subject to a pure sensory intuition, which is equally apriori.

<t61> The above proposition marks the beginning of a deduction of the pure concepts of the understanding. The categories arise from the understanding alone, without any dependence on sensibility. So I must leave out of account the way in which the multiplicity for an empirical intuition is given, in order to concentrate on the unity which the understanding gives to the intuition by means of the categories. Later (in §26 below), I shall show from the way empirical intuition is given in sensibility, [B145] that the unity of empirical intuition is nothing other than the unity which the categories prescribe to the multiplicity of a given intuition in general (as I said in §20 above). Thus the goal of the deduction will not be fully attained until the apriori validity of the categories with respect to all objects of our senses has been explained.

<t62> However, there is one point in the above proof which I could not leave out of account. This is that the multiplicity for intuition must be given, before the synthesis of the understanding, and independently of it. But how this can be so remains undecided here. I can imagine an understanding which itself has intuitions — for example a divine understanding, which would not conceive objects given to it, but through whose conception the objects themselves would be given or created. However, the categories would have absolutely no meaning with respect to knowledge of this sort.

<t63> The categories are merely rules for an understanding whose powers are limited to thought — that is, to the act of bringing the synthesis of the multiplicity to the unity of apperception; and this multiplicity is given in intuition from some other source. Such an understanding knows nothing at all by itself, but merely unifies and organises the material for knowledge (intuition), which must be given to it through the object. It is impossible to provide any deeper reason for the peculiarity of our understanding, that it can bring about the apriori unity of apperception only by means of the categories, and [B146] only of this particular kind and number. The same goes for why we have precisely these and no other functions of judgment, or why time and space are the only possible forms of our intuition.

<t64> §22

To think an object and to know an object are not the same thing. Knowledge has two components:

1. a concept through which an object is thought in general (the category);
2. an intuition through which the object is given.

If no intuition at all could be given corresponding to the concept, the concept would be a thought as far as its form was concerned; but without any object, it could not possibly provide any knowledge of any kind of thing. This is because, as far as I knew, nothing was given, or even could be given, to which my thought could be directed.

<t65> As I showed in the Aesthetic, the only kind of intuition possible for us is sensory intuition. So, for us, the thought of an object in general, thought through a pure concept of the understanding, can become knowledge only if this concept is related to objects of the senses. Sensory [B147] intuition is either pure intuition (space and time), or empirical intuition of what is directly represented through sensation as actual in space or time.

<t66> Determination of pure intuition enables us to obtain apriori knowledge of objects (in mathematics); but such knowledge consists of appearances only in respect of their form. It still remains undecided whether there could actually be things which must be intuited in this form. It follows that no mathematical concepts constitute knowledge by themselves, unless it is assumed that there actually are things which can be presented to us only in accordance with the pure form of sensory intuition. But things in space and time are given only in so far as they are perceptions (representations accompanied by sensation), and hence through empirical representation. It follows that the pure concepts of the understanding, even when they are applied to pure apriori intuitions (as in mathematics), provide knowledge only in so far as these apriori intuitions can be applied to empirical intuitions. Thus the concepts themselves can also be applied to empirical intuitions through the mediation of the apriori intuitions.

<t67> Consequently, the categories do not supply any knowledge of things by means of pure intuition, but only through their possible application to empirical intuition — in other words, they serve only for the possibility of empirical knowledge, which is called experience. Therefore the categories have a use for the knowledge of things only [B148] in so far as things are taken as objects of possible experience.

<t68> §23

The above proposition is of the utmost importance. It sets limits to the application of the pure concepts of the understanding to objects, just as the Transcendental Aesthetic set limits to the application of the pure form of our sensory intuition. As restrictions on the way in which it is possible for objects to be given to us, space and time have no validity beyond objects of the senses, and hence they are valid only of experience. Beyond these limits, they represent nothing, since they exist only in the senses, and have no actuality outside them.

<t69> The pure concepts of the understanding are free from this restriction, and they extend to objects of any kind of intuition, whether it is like ours or not, provided only that it is sensory and not intellectual. However, this wider scope of concepts beyond our particular kind of sensory intuition is of no use to us. For then they are empty concepts, since they do not provide us with any means at all for judging whether their objects are even possible or not — they are merely forms of thought, without any objective reality. The synthetic unity of apperception presupposes an intuition. But in this case we do not have available an intuition to which the synthetic unity of apperception can be applied, and so we cannot determine any object. [B149] Only our sensory and empirical intuition can provide the pure concepts of the understanding with sense and meaning.

<t70> If I suppose an object of a non-sensory intuition as given, I can certainly represent it through all the predicates involved in the assumption that it contains nothing belonging to sensory intuition:

• it is not extended, or in space;
• its persistence is not over a period of time;
• it does not undergo any alteration (succession of determinations in time) — and so on.

But this is not knowledge as such, if I merely indicate what the intuition of the object is not, without being able to say what the intuition contains. I have in no way represented the possibility of an object for my pure concept of the understanding, because I have not been able to supply an intuition which corresponds to it. All I have been able to say is that our intuition is not valid for it.

<t71> Here, the most important point is that no category at all could ever be applied to such a ‘something’. For example, the concept of a substance is the concept of that which can exist as a subject, but never as a mere predicate. However, I could not know whether anything could be given which corresponded to this particular form of thought, unless empirical intuition provided me with the occasion for applying it. More of this later.

<t72> [B150] §24

The pure concepts of the understanding relate to objects of intuition in general through the understanding alone. This is the case whether the understanding is ours, or some other kind of understanding, provided it is a sensory one. But for this reason, the pure concepts are mere forms of thought, through which no determinate object is yet known. The synthesis or unification of the multiplicity in these concepts relates merely to the unity of apperception. This makes it the basis for the possibility of apriori knowledge in so far as it depends on the understanding. Consequently, the synthesis is not merely transcendental, but it is also nothing but purely intellectual.

<t73> However, we have deep within ourselves a particular kind of apriori form of sensory intuition, and this form depends on the receptivity of our faculty of representation (our sensibility). So, since the understanding is self-active, it can determine inner sense through the multiplicity of given representations in accordance with the synthetic unity of apperception. Thus it can think the synthetic unity of the apperception of the multiplicity of sensory intuition apriori. It thinks it as the precondition which all objects of our (human) intuition must necessarily be subject to. For this is how the categories, despite being mere forms of thought, attain objective reality — that is, application to objects [B151] which can be given to us in intuition. However, these objects are merely appearances, since it is only of appearances that we can have apriori intuition.

<t74> Since this synthesis of the multiplicity of sensory intuition is apriori possible and necessary, it can be called figurative synthesis, to distinguish it from the intellectual synthesis, which is thought with respect to the multiplicity of an intuition in general through the categories alone. Both are transcendental, not simply because they take place apriori, but also because they are the basis for the possibility of further apriori knowledge.

<t75> However, figurative synthesis can concern merely the originative-synthetic unity of apperception, that is, the transcendental unity which is thought in the categories. So in order to distinguish it from purely intellectual unification, it must be called the transcendental synthesis of the imagination.

<t76> Imagination is the faculty of representing an object in intuition, even without its actual presence. But since all our intuition is sensory, the imagination belongs to sensibility. This is because of the subjective precondition under which alone the imagination can supply the concepts of the understanding with a corresponding intuition. But the synthesis of the imagination can also be an exercise of self-activity. If so, unlike sense, [B152] which is merely passively determinable, it is actively determining, and hence it can determine the form of sense apriori, in accordance with the unity of apperception. To this extent, the imagination is a faculty for determining sensibility apriori, and its synthesis of intuitions in accordance with the categories must be the transcendental synthesis of the imagination. This transcendental synthesis is an operation of the understanding on sensibility, and it is the first application of the understanding to objects of the kind of intuition that is possible for us. At the same time, it is the basis for all other applications of the understanding to objects.

<t77> As figurative, this synthesis is distinct from intellectual synthesis, which is performed without any contribution from the imagination, and by the understanding alone. In so far as the imagination is self-active, I sometimes call it the productive imagination. By this means I distinguish it from the reproductive imagination, whose synthesis is subject to purely empirical laws, namely the laws of association. The reproductive imagination makes no contribution to explaining the possibility of apriori knowledge, and it therefore belongs to psychology rather than to transcendental philosophy.

<t78> This is the right place to explain a paradox, which must have occurred to everyone in my exposition of the form of inner sense (§6). The paradox is that inner sense presents even our selves to our consciousness, not as we are in ourselves, but only as we appear to ourselves, [B153] because we intuit ourselves only as we are inwardly affected. It seems to be a contradiction, because we must relate actively to our selves as passive. This is why psychology textbooks usually treat inner sense and the faculty of apperception as one and the same thing, whereas I carefully keep them distinct.

<t79> What determines inner sense is the understanding, and its originative faculty for unifying the multiplicity of intuition — that is, its faculty for bringing the multiplicity under a single apperception. Indeed, the very possibility of the understanding itself depends on this faculty. But in us humans, the understanding is a faculty which essentially has nothing to do with intuitions. So even when intuitions are given through sensibility, the understanding cannot take them up into itself, in order, as it were, to unify the multiplicity of its own intuition. Therefore the synthesis of the understanding, considered in isolation, is nothing other than the unity of the action through which it is able to determine sensibility. Since this is its own action, the understanding is conscious of it as such, even without any sensibility. But through this action, the understanding can itself determine the form in which the multiplicity of intuition can be given to inner sense. So the expression transcendental synthesis of the imagination enables us to say that the understanding carries out this action on a passive subject, even though the understanding is a faculty of that subject; and we can correctly say that inner sense [B154] is affected by the action.

<t80> Apperception and its synthetic unity are utterly different from inner sense. As the source of all unification, apperception applies to the multiplicity of intuitions in general. Through the authority of the categories, it applies to objects in general, before any sensory intuition. By contrast, inner sense contains merely the form of intuition, without any unification of the multiplicity within intuition. Consequently, it does not yet contain any determinate intuition. This is possible only through consciousness of the determination of the multiplicity through the transcendental action of the imagination (the synthetic influence of the understanding on inner sense), which I have called figurative synthesis.

<t81> We also always perceive this in ourselves. We cannot think a line without drawing it out in thought; we cannot think a circle without drawing it round its centre; we cannot represent the three dimensions of space without placing three lines at right-angles to each other from the same point. We cannot even represent time without drawing a straight line, which is the only possible external way of representing time figuratively. In drawing the line, we focus our attention on the act of synthesising the multiplicity. It is through this act that we determine inner sense successively, and focus on the successiveness of this determination in inner sense.

<t82> Suppose we consider motion as an action of the subject, and not as a determination [B155] of an object.*

If we leave out of account the multiplicity in space, and focus simply on the act of synthesising it, through which we determine the form of inner sense, then motion is the first thing that generates the concept of succession. So the understanding does not find such a unification of the multiplicity ready-made in inner sense, but it produces it by affecting inner sense.

<t83> So the I which I think is distinct from the I which intuits itself — even though I can at least conceive the possibility of a different kind of intuition. But, given that they are distinct, how can the two be one and the same subject? So how can I say the following? — ‘I, as intelligence and thinking subject, know myself as the object which is thought, in that I am given to myself as something over and above what is contained in intuition; and yet, like other phenomena, I am given to myself, not as something given to the understanding, but as I appear to myself.’ But these questions are no more or less difficult than the question of how I can be an object to myself at all, and in particular an object of intuition [B156] and inner perceptions.

<t84> However, it can be clearly shown that this must actually be the case, by the following considerations. It has to be accepted that space is nothing other than the form of appearances of outer sense. Now since time is not an object of outer intuition, the only way we can make it conceivable to ourselves is by means of the image of a line, in so far as we draw it out. If we did not represent it in this way, we would be quite unable to know that it had only one dimension. Similarly, in the case of all our inner perceptions, we must always derive the determination of periods of time, and also points in time, from changes presented to us by outer things. So, given that the determinations of inner sense are appearances in time, they must be ordered in exactly the same way as we order the appearances of outer sense in space. Therefore, if we accept that outer appearances give us knowledge of objects only in so far as we are outwardly affected, then we must also admit that inner sense gives us intuitions of our selves only as we are inwardly affected by our selves. In other words, as far as inner intuition is concerned, we know our own subject only as an appearance, and not as it is in itself.*

<t86> [B157] §25

On the other hand, in the transcendental synthesis of the multiplicity of representations in general, and hence in the synthetic originative unity of apperception, I am conscious of my self, not as I appear to myself, still less as I am in myself, but only that I exist. This representation is a thought, not an intuition. In order to know ourselves, it is not enough for there to be the activity of thought which brings the multiplicity of any possible intuition under the unity of apperception — we also require a particular kind of intuition, through which this multiplicity is given. So my own existence is not an appearance, and still less is it a mere illusion. However, the determination of my existence* [B158] can take place only in accordance with the form of inner sense, in the particular way in which the multiplicity which I unify is given in inner intuition. Hence I have no knowledge of myself as I am, but merely as I appear to myself.

<t88> So consciousness of the self is far from being knowledge of the self, since it leaves out all the categories, which make up the thought of an object in general by unifying the multiplicity in a single apperception. In the case of my knowledge of an object distinct from myself, I require not only the thought of an object in general (which is thought through the categories), but also an intuition to make this general concept determinate. Similarly, in order to have knowledge of my self, I require not only consciousness (or my thinking my self), but also an intuition of the multiplicity in me, to make this thought determinate. I exist as an intelligence which is conscious only of its power of unification. But [B159] with respect to the multiplicity which it is to unify, it is subject to a limiting condition, which is called inner sense. That is, this unification can be intuited only in accordance with time-relations, which lie completely outside the concepts of the understanding as such. Consequently, this intelligence can know itself only as it seems to itself by reference to an intuition; and the intuition cannot be an intellectual one provided by the understanding itself. The intelligence cannot know itself as it would if its intuition were intellectual.

<t89> §26

In the Metaphysical Deduction, I proved the apriori origin of the categories in general, through their complete correspondence with the universal logical functions of thought. In the Transcendental Deduction, I have established their possibility as apriori knowledge of objects of intuition in general (§§20–21). Now I must explain how we can know apriori, through the categories, any objects whatever that could come before our senses. Indeed, I shall explain how we can know, not just the form of their intuition, but the laws of their interconnection, so that we can, as it were, lay down the law to nature, and even make nature possible. [B160] If the categories could not fulfil this function, it would be impossible to explain how everything that could ever come before our senses must be subject to laws which have their origin apriori in the understanding alone.

<t90> First of all, I should note that by the synthesis of apprehension, I mean putting together the multiplicity in a single empirical intuition. Without this, there could be no perception, or empirical consciousness of the intuition as an appearance.

<t91> We have apriori forms of both outer and inner sensory intuition in the representations of space and time. The synthesis of the apprehension of the multiplicity of appearance must always conform to these, because synthesis itself can take place only in accordance with this form. But space and time are represented apriori, not merely as forms of sensory intuition, but as intuitions themselves, also containing a multiplicity. So they are represented together with the determination of the unity of this multiplicity which they contain (see the Transcendental Aesthetic).*

<t93> Thus [B161] the unity of the synthesis of the multiplicity (whether outer or inner) is itself already given apriori as the precondition for the synthesis of any apprehension, along with (but not in) these intuitions of space and time. The same is therefore also true of a unification, to which everything that is to be represented as determined in space and time must conform. However, this synthetic unity cannot be anything other than the unity of the unification of the multiplicity of a given intuition in general in an originative consciousness. The unification is carried out in accordance with the categories, and it applies only to our sensory intuition. It follows that all synthesis is subject to the categories. But perception itself is possible only through synthesis, and since experience is knowledge through interconnected perceptions, the categories are preconditions for the possibility of experience, and are therefore also valid apriori of all objects of experience.

<t94> [B162] So, for example, if I turn the empirical intuition of a house into a perception by apprehending its multiplicity, my apprehension is grounded in the necessary unity of space, and of outer sensory intuition in general. I so to speak draw the shape of the house in accordance with this synthetic unity of the multiplicity in space. But if I leave the form of space out of account, exactly the same synthetic unity has its place in the understanding. It is the category of the synthesis of the homogeneous in an intuition in general — in other words, the category of quantity. So the synthesis of apprehension (perception, that is) must be completely in accordance with this category.*

<t96> To give another example: if I perceive the freezing of water, I apprehend two states (fluidity and solidity) as standing in a temporal relation to one another. But this appearance is grounded in time, in so far as the appearance is an inner intuition. [B163] So I necessarily represent the synthetic unity of the multiplicity in time; and without this unity, the temporal relation could not be given in an intuition as determined in respect of succession in time. But this synthetic unity is the apriori precondition for me to be able to unify the multiplicity of an intuition in general. So if I leave out of account the permanent form of my inner intuition, namely time, I am left with the category of cause. When I apply the category of cause to my sensibility, I use it to determine everything that happens in time in general in respect of its relation. Therefore the apprehension of such an event, and hence the event itself considered as a possible perception, is subject to the concept of the relation of effects and causes. The same goes for all other cases.

<t97> Categories are concepts which prescribe apriori laws to appearances, and hence to nature as the sum total of all appearances (or nature considered in its material aspect). But this means that these laws are not derived from nature, nor do they accommodate themselves to nature as their pattern, otherwise they would be merely empirical. So the question then arises: How are we to make sense of the fact that nature must accommodate itself to apriori laws? In other words, how can these laws determine the interconnection of the multiplicity of nature apriori, and not be derived from nature? Here is the solution to this puzzle.

<t98> [B164] It may seem strange that the laws of appearances in nature must agree with the understanding and its apriori form, namely its power to unify the multiple in general. But it is no stranger than the fact that the appearances themselves must agree with the apriori form of sensory intuition. For laws do not exist in appearances, but only relative to the subject in which the appearances inhere, provided that the subject has an understanding — just as appearances do not exist in themselves, but only relative to the same being, provided that it has senses.

<t99> Things in themselves will necessarily obey their own laws, independently of whether or not they are known by an understanding. But appearances are only representations of things, and it is unknown what these things might be in themselves. As mere representations, the only law of interconnection they are subject to is that which is prescribed by the faculty which connects them. The faculty which connects the multiplicity of sensory intuition is the imagination; and the imagination depends on the understanding for the unity of its intellectual synthesis, and on sensibility for the multiplicity of its apprehension. Now all possible perception depends on the synthesis of apprehension, and the synthesis of apprehension, which is an empirical synthesis, depends in turn on the transcendental synthesis, and hence on the categories. So it follows that all possible perceptions are subject to the categories for their unification, and hence the same is true of absolutely anything that can ever attain empirical consciousness — in other words, [B165] all appearances of nature.

<t100> Nature, considered merely as nature in general, depends on the categories as the originative basis for its necessary conformity to laws (nature considered in its formal aspect). However, the pure faculty of understanding cannot, through the categories alone, prescribe to appearances apriori laws which go beyond what is essential for a nature in general to be a system of law-governed appearances in space and time. Since particular laws concern appearances which are empirically determined, they cannot be derived in all their detail from the categories, even though they are all subject to them. Experience must be added for us actually to come to know them. But only the apriori laws tell us about experience in general, and about what can be known as an object of experience.

<t101> §27

We cannot think any object, except through categories; and we cannot know any object we have thought, except through intuitions corresponding to those concepts. Since all our intuition is sensory, this knowledge is empirical, in so far as the object of knowledge is given. But empirical knowledge [B166] is experience. So it follows that the only apriori knowledge possible for us is knowledge of objects of possible experience.*

<t103> But although this knowledge is confined to objects of experience, it is not on that account all derived from experience. The pure intuitions and the pure concepts together make up the elements of knowledge, and they are found apriori within us.

<t104> There are only two ways in which it is possible to think a necessary agreement of experience with the concepts of its objects:

• either experience makes these concepts possible;
• or these concepts make experience possible.

[B167] The first alterative is ruled out in the case of the categories (as also in the case of pure sensory intuition), since they are apriori concepts, and hence independent of experience. To claim that they had an empirical origin would be a sort of spontaneous generation.

<t105> So only the second alternative remains. It is, as it were, a system of the epigenesis of pure reason — in other words, the understanding supplies the categories, which contain the foundation of the possibility of all experience in general. In the next chapter (on the transcendental use of the faculty of judgment), I shall say more about how the categories make experience possible, and what axioms of the possibility of experience they supply in their application to appearances.

<t106> Someone might wish to propose a compromise between the two ways I have mentioned above as the only possible ones. It might be claimed that the categories are neither self-thought apriori first principles of our knowledge, nor derived from experience, but that they are subjective. In other words, they are natural dispositions to thought which are planted in us at the very moment of our coming into existence. Our creator has set them up in such a way that their application corresponds exactly to the laws of nature which experience obeys. This would be a kind of preformation system of pure reason.

<t107> An immediate objection is that, on this hypothesis, there is no limit to the number of predetermined dispositions which must be presupposed in order to cater for future judgments. But the decisive objection against this proposed [B168] middle way is that, if it were true, then the categories would lack the necessity which belongs essentially to the concept of them.

<t108> For example, the concept of cause expresses the necessity of a consequence on the assumption of a certain precondition. But it would be false if it depended merely on a subjective necessity, arbitrarily planted in us, of connecting particular empirical representations in accordance with such a rule of causal relation. I would not be able to say: ‘The effect is connected with the cause in the object,’ (that is, necessarily connected), but only: ‘I am so constituted that I cannot think this representation as connected in any other way.’

<t109> This is precisely what the sceptic wants most. It turns all our insight depending on the supposed objective validity of our judgements into nothing other than sheer illusion. Furthermore, there would be no lack of people who would refuse to admit even this subjective necessity as applying to themselves, since it has to be felt. At the very least, there is no scope for arguing with anyone about something which depends merely on the way they are constituted as a subject.

<t110> Brief Summary of this Deduction

This deduction is the exposition of:

• the pure concepts of the understanding (together with all theoretical apriori knowledge) as principles of the possibility of experience;
• experience as the determination of appearances in space and time in general;
• this determination (which has its source in the principle of the originative synthetic unity of apperception) as the form of the understanding in relation to space and time (which are the originative forms of sensibility).

<t111> I have considered division into numbered sections necessary up to this point, because I was dealing with the fundamental concepts. Now that I am going to explain their application, I can dispense with numbered sections, and continue my exposition without such breaks.

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