<pn1> The Transcendental Doctrine of Judgment

[B294] We have now not only travelled all over the territory of pure understanding and carefully explored every part of it, but we have also measured its maximum limits, and determined the place of every thing in it. But this territory is an island, and confined within unalterable boundaries by nature itself. It is the land of truth (charming name!), [B295] surrounded by a wide and stormy ocean, the natural habitat of illusion, where many a fog bank, and many a sheet of ice about to melt away, look deceptively like new territories. Nevertheless, this ocean never stops deceiving with empty hopes the seafarer full of enthusiasm for new discoveries, and embroiling him in adventures which he can never give up, but which he can also never bring to fulfilment.

<pn2> We are about to venture out into this sea, in order to explore it in all directions, and to achieve certainty as to whether there is anything to hope for in it. But before we do so, it will be useful to throw one more glance at the map of the territory we are about to leave, and ask ourselves two questions. The first question is whether we cannot be satisfied with what it contains anyway, or at least whether we are forced to be satisfied, because otherwise there is no ground at all for us to build on. The second question is by what right we possess even this territory, and can keep it safe from all hostile claims. Although I have already answered these questions in depth during the course of the Analytic, a summary review of the solutions to them can strengthen conviction by bringing its different strands together into a single point.

<pn3> We have seen that the sole function of everything which the understanding derives from itself, without borrowing it from experience, is its application to experience. The [B296] axioms of pure understanding are either constitutive apriori (the mathematical ones) or merely regulative (the dynamical ones). In both cases, they contain nothing other than, as it were, the pure schema for possible experience. For experience gets its unity only from the synthetic unity which the understanding gives, originally and from itself, to the synthesis of the imagination in relation to apperception. Appearances must already have an apriori relation to, and conform to this synthetic unity, as data for possible knowledge. These rules of the understanding are not merely true apriori, but they are actually the source of all truth (i.e. the correspondence of our knowledge to objects), since they contain the basis for the possibility of experience (as the sum of all knowledge), which is required for objects to be given to us.

<pn4> However, we are dissatisfied with an account which is confined to what is true, and we want an account of what we desire to know. It might seem that these critical investigations tell us no more than we could have achieved by ourselves, merely through the empirical use of the understanding, and without such subtle research. If so, the advantage we gain from it would not seem to be worth the investment of effort. To this it can certainly be replied, that nothing is more damaging to the extension of our knowledge, than the spirit of enquiry which always wants to know in advance [B297] what the benefit will be, before getting involved in the research, and before we could even form the least conception of this benefit, even if it were staring us in the eyes.

<pn5> But there is another advantage, which can be made both comprehensible and interesting to even the most difficult and unenthusiastic student of transcendental investigation. This is that the understanding can indeed make very good progress by confining itself to its empirical use, and giving no thought to the sources of its own knowledge. However, the one thing it cannot achieve by itself is to determine the limits of its application, and to know what might lie inside or outside its total sphere. This requires just those deep investigations which I have conducted. But if it cannot decide whether or not certain questions fall within its horizon, it is never sure of its claims and possessions. It can only count on all sorts of humiliating rebuffs, when it inevitably and repeatedly oversteps the limits of its territory, and loses its way in delusion and error.

<pn6> My claim is that the only use the understanding can make of all its apriori axioms, and indeed of all its concepts, is empirical, and that it can never make a transcendental use of them. If this proposition can be known with conviction, it points to important consequences. [B298] The transcendental use of a concept in any axiom is when it is applied to things in general and as they are in themselves; and their empirical use is when they are applied merely to appearances, i.e. to objects of a possible experience. I shall now show that there is no scope for anything other than their empirical use.

<pn7> Every concept requires, first, the logical form of a concept (or of a thought) in general, and secondly, the possibility of being given an object to which it applies. Without the latter, it has no meaning, and it is completely empty of content — even though it might still contain the logical function for making a concept out of any sort of data. Now an object cannot be given to a concept except in intuition. In the case of an apriori intuition, even though it is apriori possible before an object, it too can acquire its object, and hence its objective validity, only through empirical intuition, of which it is merely the form. So all concepts, and with them all axioms, however apriori they may be, relate to empirical intuitions, i.e. to data for possible experience. Without this, they have no objective validity at all, but are a mere play of representations, whether those of the imagination or those of the understanding.

<pn8> Take for example the concepts of mathematics, [B299] more precisely starting with its pure intuitions. Space has three dimensions; between two points there can be only one straight line; and so on. All these axioms, and the representation of the object which the science of mathematics deals with, are produced in the mind completely apriori. However, they would mean nothing at all, if we were not always able to display their meaning through appearances (empirical objects). So we are also required to make an abstract concept sensible, that is, to display in intuition the object corresponding to it; otherwise the concept (as we say) would remain without sense, i.e. without meaning.

<pn9> Mathematics fulfils this requirement by constructing a figure which is an appearance present to the senses, even though it is brought into being apriori. In the same science, the concept of quantity looks for its status and sense in number; and number is presented to the eyes by means of the fingers, the beads of an abacus, or written strokes and dots. The concept is still always produced apriori, together with the synthetic axioms or formulae put together from such concepts. However, their applicability and relation to any objects which might be supposed, can ultimately be looked for only in experience, since the concepts contain apriori the possibility of objects, at least as far as their form is concerned.

<pn10> [B300] That this is also the case with all the categories and the axioms they give rise to, is clear from the following. We cannot give a real definition of any single one of them (i.e. make the possibility of their object comprehensible) without at once digging down to the preconditions of sensibility, and hence to the form of appearances. The categories must be limited to these preconditions, since they are their only objects. For if this restriction is removed, all meaning (i.e. relation to an object) goes by the board, and we cannot use any example to make it intelligible, even to ourselves, essentially what sort of a thing is meant by such a concept.

<pn11> The concept of quantity in general can be explained only as the determination of a thing such that we can think how many times a unit is to be found in it. But this how-many-times is based on successive repetition, and hence on time, and on the synthesis of things of the same kind in it.

<pn12> Reality (by contrast with negation) can be explained only if we think of a time as either filled with being, or empty of it. This is because time is the sum of all being. If I leave out permanence (which is something existing throughout all time), then the only thing I am left with as constituting the concept of substance is the logical representation of a subject. I try to make it real by representing to myself something which can exist merely as a subject, without being the predicate of anything. [B301] However, not only do I not know of any preconditions for this supreme logical property to belong to anything of any kind, but there is nothing more to be done with it, and not the least consequence to be drawn from it. This is because no object is determined for this concept to apply to, and so one cannot know whether it means anything at all.

<pn13> Next, the concept of cause. If I leave out the time in which something follows something else in accordance with a rule, then I am left with the pure category. But all this contains is that there is something from which the existence of something else can be concluded. Not only would it be impossible to use it to distinguish between cause and effect, but, because this license to draw conclusions also requires preconditions of which I know nothing, the concept would not determine how it applied to any object.

<pn14> The supposed axiom that everything contingent has a cause, steps forward rather grandly, as if its dignity were self-justifying. But if I ask: "What do you mean by ‘contingent’"?, and you say: "That of which the non-existence is possible," then I would like to know how you can know that this non-existence is possible. What you need is to represent a successiveness in the series of appearances, and in the successiveness you need to represent an existence which follows from the non-existent (or vice versa), and hence you need to represent a change. To appeal to the fact that the non-existence of a thing is not a self-contradiction, is a lame appeal [B302] to a merely logical precondition. It is certainly necessary for the concept, but it is completely inadequate for its real possibility. I can think any existing substance away without contradicting myself; but I cannot conclude from this that it is objectively contingent in its existence, i.e. that its non-existence is possible in itself.

<pn15> As for the concept of community, it is easy to appreciate that, since the pure categories of substance and causality cannot be defined in such a way as to determine an object, the same must be true of reciprocal causality in the interactive relationship of substances to each other.

<pn16> Possibility, existence, and necessity can only be defined through manifest tautologies, as long as their definition is drawn exclusively from pure understanding. And to misrepresent the logical possibility of the concept (in that it is not self-contradictory) as the possibility of the thing (in that an object corresponds to the concept), is a trick which can deceive and satisfy only the novice.*

<pm17> [B303] Now from this it undeniably follows that the pure concepts of understanding can never have any transcendental application, but always only an empirical application; and that the axioms of pure understanding can apply only to objects of the senses under the universal preconditions of any possible experience, and never to things in general, without reference to the way we might intuit them.

<pn18> The Transcendental Analytic therefore results in the following important conclusion. The most the understanding can achieve apriori is to anticipate the form of any possible experience in general. Since anything which is not an appearance cannot be an object of experience, the understanding can never overstep the limits of sensibility, within which alone objects are given to us. Its axioms are merely principles for displaying appearances; and the boastful name of an ontology, which presumes to provide synthetic apriori knowledge of things in general (e.g. the axiom of causality) as a systematic doctrine, must give way to the humble name of merely an analytic of pure understanding.

<pn19> [B304] Thought is the action of relating a given intuition to an object. If it is in no way given what kind of intuition this is, then the object is merely transcendental, and the concept of understanding has only a transcendental application, namely as the unity of the thought of a multiplicity in general. No object is determined through a pure category, since it takes no account of any of the preconditions of sensory intuition, which is the only kind of intuition possible for us. All it contains is the thought of an object in general, expressed in one of a number of different modes.

<pn20> Now the application of a concept involves a different function of judgment, through which an object is subsumed under the concept, and hence at least the formal precondition for it to be possible for something to be given in intuition. If this precondition for judgment (the schema) is lacking, then nothing can be subsumed under the concept, since nothing is given which could be subsumed under it. Thus the merely transcendental application of the categories is in fact no application at all, and it has no determinate object, nor even an object which is determinable only as to its form. From this it follows that a pure category is insufficient even for any synthetic apriori axiom, and that the axioms of pure understanding have only an empirical application, and never a transcendental one. Beyond [B305] the field of possible experience, there can be no synthetic apriori axioms at all.

<pn21> It might be a good idea to put it the following way. Without formal preconditions of sensibility, the pure categories have transcendental meaning, but no transcendental application. This is because a transcendental application is intrinsically impossible, since it lacks all the preconditions of any application (in judgments), namely the formal preconditions for subsuming under these concepts any object which might be given. Merely as pure categories, they should have no empirical application, and can have no transcendental application. So if they are divorced from all sensibility, they have no application at all — that is, they cannot be brought to bear on any object which might be given. Instead, they are simply the pure form of the application of the understanding with respect to objects in general and to thought, without it being possible for any object to be thought or determined through them alone.

<pn22> Nevertheless, there is here a deep-seated illusion which it is difficult to avoid. In their origin, the categories are not based on sensibility (by contrast with the forms of intuition, namely space and time); so they seem to allow their application to be extended beyond all objects of the senses. But just as space and time are forms of intuition, the categories are nothing other than forms of thought, which contain merely the logical capacity of uniting the multiplicity given [B306] in intuition into a single consciousness apriori. So if we take away sensory intuition (which is the only kind possible for us), they can have even less significance than the pure sensory forms. The sensory forms do at least provide an object, whereas the way of combining the multiplicity which is peculiar to our understanding signifies nothing at all, in the absence of the intuition through which alone the multiplicity can be given.

<pn23> We call certain objects phenomena, because they are appearances, or sensory beings. However, we distinguish between the way we intuit them and their intrinsic nature. So it is already contained in our concept, either that we, as it were, contrast phenomena with their nature, even though we do not intuit their nature in them, or that we contrast phenomena with other possible things, which are not objects of our senses at all. Since these objects are merely thought through our understanding, we call them intellectual beings or noumena. The question now arises as to whether our concepts of pure understanding might not have significance in respect of noumena, and so be a means of knowing them.

<pn24> Right from the start, there emerges an ambiguity which can give rise to a serious misunderstanding. When the understanding calls an object in a certain relationship a mere phenomenon, as well as this relationship, it also forms a representation of an object in itself. So it comes to represent itself as [B307] also being able to make itself concepts of such objects. Since the understanding supplies no concepts other than the categories, it supposes that it must at least be possible for the object to be thought through these pure concepts of understanding. But this misleads it into treating the completely indeterminate concept of an intellectual being, namely a something-in-general beyond our sensibility, as a determinate concept of a being which we can somehow know through the understanding.

<pn25> If by ‘noumenon’ we mean a thing in so far as it is not an object of our sensory intuition, by leaving out of account our way of intuiting it, then this is a noumenon in the negative sense. But if we mean by it an object of a non-sensory intuition, then we presuppose a special kind of intuition, namely intellectual intuition; and this would be a noumenon in the positive sense. However, we do not have this kind of intuition, and we cannot even have any insight into how it might be possible.

<pn26> The thesis that all our knowledge depends on sensibility implies that noumena must be taken in the negative sense. In other words, they are things which the understanding must think independently of our way of intuiting them, and hence as things in themselves, rather than as mere appearances. But at the same time, the understanding is well aware that, because it has separated things in themselves from our way of intuiting them, it cannot apply its categories to things in themselves as if they were objects of intuition. [B308] This is because the categories have meaning only in relation to the unity of intuitions in space and time. And it is only because of the mere ideality of space and time that the categories can determine apriori even this unity, by means of universal concepts which combine things together. Where this unity of time is not to be found, and hence in the noumenon, the categories completely lose all their applicability, and even all their meaning, since we can have no insight into the very possibility of the things which are supposed to correspond to the categories. On this, I would merely refer to what I said near the beginning of the general note to the previous chapter.

<pn27> The possibility of a thing can never be proved simply from the non-contradictory nature of its concept. It can be verified only through an intuition which corresponds to it. So if we wanted to apply the categories to objects which are not considered to be appearances, we would have to base this on a kind of intuition which was non-sensory — but then the object would be a noumenon in the positive sense. Now since an intellectual intuition lies completely outside our faculty of knowledge, it is equally impossible for the categories to have any application beyond the boundaries of the objects of experience. I readily accept that there are intellectual beings corresponding to sensory beings, [B309] and that there may also be intellectual beings which have no relation at all to our faculty of sensory intuition. However, they are completely out of the reach of our concepts of understanding, which are mere forms of thought for our sensory intuition. Therefore what we call a ‘noumenon’ must be understood as being such only in the negative sense.

<pn28>If I take all thought (through the categories) away from empirical knowledge, there remains no knowledge at all of any object. For nothing whatever is thought through mere intuition, and the fact that this affection of sensibility is in me does not establish any relation of this representation to any object. But if I leave out all intuition, the form of thought still remains — that is, the way of determining an object for the multiplicity of a possible intuition. Hence the categories have a wider reach than sensory intuition, in so far as they think objects in general, without regard to the specific mode of intuition (in our case sensibility) in which objects might be given. However, this does not mean that they determine a larger sphere of objects. For we cannot assume that such objects can be given, without presupposing the possibility of a non-sensory mode of intuition — but we have no justification at all for such a presupposition.

<pn29> [B310] I call a concept ‘problematic’, if it has the following characteristics:

• it is not self-contradictory;
• it is connected with other types of knowledge by limiting concepts given in them;
• its objective reality can in no way be known.

The concept of a noumenon is the concept of a thing which is to be thought, not as an object of the senses, but as a thing in itself, and only through a pure understanding. It is certainly not self-contradictory, since we cannot stipulate that sensibility is the only possible mode of intuition.

<pn30> Further, this concept is necessary, in order to prevent sensory intuition from extending to things in themselves, and so to limit the objective validity of sensory knowledge. Everything else, which sensory knowledge does not reach, is called ‘noumena’, precisely so as to indicate that sensory knowledge cannot extend its territory over everything which the understanding can think.

<pn31> However, we ultimately have no insight at all into how such noumena are possible, and the circumference which lies outside the sphere of appearances is empty (for us, at least). That is, we have an understanding which extends itself beyond this sphere problematically. On the other hand, we do not have any intuition, or even the concept of a possible intuition, which could give us objects outside the field of sensibility, and enable the understanding to be used assertorically outside this field. Thus the concept of a noumenon is merely a limiting concept [B311] to curb the pretensions of sensibility, and it is therefore only of negative use. However, it is not arbitrarily thought up. It is intimately bound up with the limitation of sensibility, though without being able to establish anything positive outside the circumference of the sphere of sensibility.

<pn32> It is therefore completely illegitimate to divide objects into phenomena and noumena, and the world into a sensory world and an intellectual world, in the positive sense. However, it is perfectly admissible to divide concepts into those that are sensible and those that are intellectual, since we cannot determine any object for intellectual concepts, and hence pass them off as objectively valid. If we leave the senses out, how will we make it comprehensible that our categories (which would be the only remaining concepts for noumena) still mean anything at all? In order for them to relate to any object, something more must be given than mere unity of thought, namely a possible intuition to which they can be applied.

<pn33> Nevertheless, the concept of a noumenon, provided it is taken in the merely problematic sense, remains not only permissible, but actually indispensable, as a concept which sets limits to sensibility. But in this case, a noumenon is not a special intelligible object for our understanding. Rather, the problem is the nature of an understanding to which it could belong. For it would have to know its object, not discursively through categories, [B312] but intuitively through a non-sensory intuition — and we cannot form the least representation of how this is possible.

<pn34> Now through the concept of a noumenon, our understanding acquires a negative extension. In other words, our understanding is not limited by sensibility, but instead it limits sensibility by giving the name ‘noumena’ to things as they are in themselves, and not considered as appearances. But in doing so it also sets limits to itself, since it cannot know noumena through the categories, and so it can think them only by calling them an ‘unknown something’.

<pn35> In the writings of modern philosophers, I find a use of the expressions ‘sensible world’ and ‘intelligible world’* which departs radically from their meanings in antiquity.

<pn36> I admit that the modern usage does not cause any difficulty; but it consists of nothing other than mere empty playing with words. What it amounts to is that some philosophers have taken to calling the sum of appearances the ‘sensible world’ in so far as it is intuited, and the ‘intelligible world’ in so far as its interconnectedness is thought through general laws of understanding.

<pn37> [B313] On this account, practical astronomy would give us a representation of the sensible world, in that it merely reports observations of the starry heavens; whereas theoretical astronomy would give us a representation of the intelligible world, by explaining these observations in terms of the Copernican system, or Newton’s laws of gravitation. But twisting words in this way is merely a sophistical let-out. It is an attempt to worm one’s way out of a difficult question by distorting the meaning of the question so as to makes things easier for oneself.

<pn38> There is no question that understanding and reason are applicable to appearances. But the point at issue is whether or not they are also applicable when their object is not an appearance, but a noumenon. And their object is taken as being a noumenon when it is thought as being intrinsically nothing other than intelligible —in other words, it is thought as being given to the understanding alone, and not to the senses at all. So the point at issue is whether, in addition to the empirical use of the understanding (and Newton’s representation of the structure of the universe is still empirical), there could not also be a transcendental use of the understanding, which has the noumenon as its object. I have given a negative answer to this question.

<pn39> So when I say that the senses represent objects to us as they appear, and the understanding represents them to us as they are, the second half of this statement is to be taken merely in an empirical, and not in a transcendental sense. In other words, objects must be represented to us as objects of experience through the holistic interconnection of appearances, [B314] and not as they might be without their relation to possible experience, and hence to sense in general, and hence as objects of pure understanding. Objects divorced from experience will always remain unknown to us. It will even remain unknown to us whether such a transcendental or miraculous knowledge is possible at all, at least as a kind of knowledge which comes under the categories we are subject to.

<pn40> As far as we are concerned, understanding and sensibility can determine objects only in connection with each other. If we separate them, we have intuitions without concepts, or concepts without intuitions. In both cases, these are representations which we cannot relate to any determinate object.

<pn41> If, despite all these explanations, you still have reservations about renouncing the purely transcendental use of the categories, you should test them through any synthetic proposition. For an analytic proposition does not take the understanding any further. Since the understanding deals only with what it has already thought in the concept, it leaves it undecided whether the concept has an intrinsic relation to objects, or whether it merely signifies the unity of thought in general — which takes absolutely no account of the way an object might be given. In its analytic use, it is enough for the understanding to know what is contained in the concept before it, and it is irrelevant what the concept itself might apply to.

<pn42> So the test must be conducted with [B315] any axiom which is both synthetic, and supposedly transcendental. To give just a couple of examples:

• everything that exists, exists either as a substance, or as a determination inhering in a substance; or
• everything contingent exists as the effect of another thing, namely its cause.

Now the question I ask is this: where will you get this synthetic axiom from, since the concepts are to be valid of things in themselves (noumena), and not just in relation to possible experience? Where is the third thing, which a synthetic proposition always requires, in order to join together the concepts it contains, given that they have no logical (analytic) affinity? You will never be able to prove your proposition, and what is more, you will never even be able to justify the possibility of a pure assertion like this, without appealing to the empirical use of the understanding, and thus completely renouncing your claim that the judgment is pure and independent of the senses.

<pn43> So the concept of pure and merely intelligible objects is completely devoid of any axioms for its application, since we cannot think of any way in which such objects might be given to us. The mere thought of their existence, taken in the problematic sense, does indeed keep a place open for them. However, like an empty space, its only function is to limit the empirical axioms. It does not contain or reveal any object of knowledge outside the sphere of these axioms.

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