I.2.1. Phenomena and Noumena

We have now not merely explored the territory of pure understanding, and carefully surveyed every part of it, but have also measured its extent, and assigned to everything in it its rightful place. This domain is an island, enclosed by nature itself within unalterable limits. It is the land of truth—enchanting name!—surrounded by a wide and stormy ocean, the native home of illusion, where many a fog bank and many a swiftly melting iceberg give the deceptive appearance of farther shores, deluding the adventurous seafarer ever anew with empty hopes, and engaging him in enterprises which he can never abandon and yet is unable to carry to completion. Before we venture on this sea, to explore it in all directions and to obtain assurance whether there be any ground for such hopes, it will be well to begin by casting a glance upon the map of the land which we are about to leave, and to enquire, first, whether we cannot in any case be satisfied with what it contains—are not, indeed, under compulsion to be satisfied, inasmuch as there may be no other territory upon which we can settle; and, secondly, by what title we possess even this domain, and can consider ourselves as secured against all opposing claims. Although we have already given a sufficient answer to these questions in the course of the Analytic, a summary statement of its solutions may nevertheless help to strengthen our conviction, by focussing the various considerations in their bearing on the questions now before us.

We have seen that everything which the understanding derives from itself is, though not borrowed from experience, at the disposal of the understanding solely for use in experience. The principles of pure understanding, whether constitutive a priori, like the mathematical principles, or merely regulative, like the dynamical, contain nothing but what may be called the pure schema of possible experience. For experience obtains its unity only from the synthetic unity which the understanding originally and of itself confers upon the synthesis of imagination in its relation to apperception; and the appearances, as data for a possible knowledge, must already stand a priori in relation to, and in agreement with, that synthetic unity. But although these rules of understanding are not only true a priori, but are indeed the source of all truth (that is, of the agreement of our knowledge with objects), inasmuch as they contain in themselves the ground of the possibility of experience viewed as the sum of all knowledge wherein objects can be given to us, we are not satisfied with the exposition merely of that which is true, but likewise demand that account be taken of that which we desire to know. If, therefore, from this critical enquiry we learn nothing more than what, in the merely empirical employment of understanding, we should in any case have practised without any such subtle enquiry, it would seem as if the advantage derived from it by no means repays the labour expended. The reply may certainly be made that in the endeavour to extend our knowledge a meddlesome curiosity is far less injurious than the habit of always insisting, before entering on any enquiries, upon antecedent proof of the utility of the enquiries—an absurd demand, since prior to completion of the enquiries we are not in a position to form the least conception of this utility, even if it were placed before our eyes. There is, however, one advantage which may be made comprehensible and of interest even to the most refractory and reluctant learner, the advantage, that while the understanding, occupied merely with its empirical employment, and not reflecting upon the sources of its own knowledge, may indeed get along quite satisfactorily, there is yet one task to which it is not equal, that, namely, of determining the limits of its employment, and of knowing what it is that may lie within and what it is that lies without its own proper sphere. This demands just those deep enquiries which we have instituted. If the understanding in its empirical employment cannot distinguish whether certain questions lie within its horizon or not, it can never be assured of its claims or of its possessions, but must be prepared for many a humiliating disillusionment, whenever, as must unavoidably and constantly happen, it oversteps the limits of its own domain, and loses itself in opinions that are baseless and misleading.

If the assertion, that the understanding can employ its various principles and its various concepts solely in an empirical and never in a transcendental manner, is a proposition which can be known with certainty, it will yield important consequences. The transcendental employment of a concept in any principle is its application to things in general and in themselves; the empirical employment is its application merely to appearances; that is, to objects of a possible experience. That the latter application of concepts is alone feasible is evident from the following considerations. We demand in every concept, first, the logical form of a concept (of thought) in general, and secondly, the possibility of giving it an object to which it may be applied. In the absence of such object, it has no meaning and is completely lacking in content, though it may still contain the logical function which is required for making a concept out of any data that may be presented. Now the object cannot be given to a concept otherwise than in intuition; for though a pure intuition can indeed precede the object a priori, even this intuition can acquire its object, and therefore objective validity, only through the empirical intuition of which it is the mere form. Therefore all concepts, and with them all principles, even such as are possible a priori, relate to empirical intuitions, that is, to the data for a possible experience. Apart from this relation they have no objective validity, and in respect of their representations are a mere play of imagination or of understanding. Take, for instance, the concepts of mathematics, considering them first of all in their pure intuitions. Space has three dimensions; between two points there can be only one straight line, etc. Although all these principles, and the representation of the object with which this science occupies itself, are generated in the mind completely a priori, they would mean nothing, were we not always able to present their meaning in appearances, that is, in empirical objects. We therefore demand that a bare concept be made sensible, that is, that an object corresponding to it be presented in intuition. Otherwise the concept would, as we say, be without sense, that is, without meaning. The mathematician meets this demand by the construction of a figure, which, although produced a priori, is an appearance present to the senses. In the same science the concept of magnitude seeks its support and sensible meaning in number, and this in turn in the fingers, in the beads of the abacus, or in strokes and points which can be placed before the eyes. The concept itself is always a priori in origin, and so likewise are the synthetic principles or formulas derived from such concepts; but their employment and their relation to their professed objects can in the end be sought nowhere but in experience, of whose possibility they contain the formal conditions.

That this is also the case with all categories and the principles derived from them, appears from the following consideration. We cannot define any one of them in any real fashion, that is, make the possibility of their object understandable, without at once descending to the conditions of sensibility, and so to the form of appearances—to which, as their sole objects, they must consequently be limited. For if this condition be removed, all meaning, that is, relation to the object, falls away; and we cannot through any example make comprehensible to ourselves what sort of a thing is to be meant by such a concept.

The concept of magnitude in general can never be explained except by saying that it is that determination of a thing whereby we are enabled to think how many times unity is posited in it. But this how-many-times is based on successive repetition, and therefore on time and the synthesis of the homogeneous in time. Reality, in contradistinction to negation, can be explained only if we think time (as containing all being) as either filled with being or as empty. If I leave out permanence (which is existence in all time), nothing remains in the concept of substance save only the logical representation of a subject—a representation which I endeavour to realise by representing to myself something which can exist only as subject and never as predicate. But not only am I ignorant of any conditions under which this logical pre-eminence may belong to anything; I can neither put such a concept to any use, nor draw the least inference from it. For under these conditions no object is determined for its employment, and consequently we do not know whether it signifies anything whatsoever If I omit from the concept of cause the time in which something follows upon something else in conformity with a rule, I should find in the pure category nothing further than that it is something from which we can conclude to the existence of something else. In that case not only would we be unable to distinguish cause and effect from one another, but since the power to draw such inferences requires conditions of which I know nothing, the concept would yield no indication how it applies to any object. The so-called principle, that everything accidental has a cause, presents itself indeed somewhat pompously, as self-sufficing in its own high dignity. But if I ask what is understood by accidental, and you reply, “That the not-being of which is possible,” I would gladly know how you can determine this possibility of its not-being, if you do not represent a succession in the series of appearances and in it a being which follows upon not-being (or reversewise), that is, a change. For to say that the not-being of a thing does not contradict itself, is a lame appeal to a logical condition, which, though necessary to the concept, is very far from being sufficient for real possibility. I can remove in thought every existing substance without contradicting myself, but I cannot infer from this their objective contingency in existence, that is, that their non-existence is possible. As regards the concept of community, it is easily seen that inasmuch as the pure categories of substance and causality admit of no explanation determinant of the object, neither is any such explanation possible of reciprocal causality in the relation of substances to one another (commercium). So long as the definition of possibility, existence, and necessity is sought solely in pure understanding, they cannot be explained save through an obvious tautology. For to substitute the logical possibility of the concept (namely, that the concept does not contradict itself) for the transcendental possibility of things (namely, that an object corresponds to the concept) can deceive and leave satisfied only the simple-minded.

From all this it undeniably follows that the pure concepts of understanding can never admit of transcendental but always only of empirical employment, and that the principles of pure understanding can apply only to objects of the senses under the universal conditions of a possible experience, never to things in general without regard to the mode in which we are able to intuit them.

Accordingly the Transcendental Analytic leads to this important conclusion, that the most the understanding can achieve a priori is to anticipate the form of a possible experience in general. And since that which is not appearance cannot be an object of experience, the understanding can never transcend those limits of sensibility within which alone objects can be given to us. Its principles are merely rules for the exposition of appearances; and the proud name of an Ontology that presumptuously claims to supply, in systematic doctrinal form, synthetic a priori knowledge of things in general (for instance, the principle of causality) must, therefore, give place to the modest title of a mere Analytic of pure understanding.

Thought is the act which relates given intuition to an object. If the mode of this intuition is not in any way given, the object is merely transcendental, and the concept of understanding has only transcendental employment, namely, as the unity of the thought of a manifold in general. Thus no object is determined through a pure category in which abstraction is made of every condition of sensible intuition—the only kind of intuition possible to us. It then expresses only the thought of an object in general, according to different modes. Now the employment of a concept involves a function of judgment whereby an object is subsumed under the concept, and so involves at least the formal condition under which something can be given in intuition. If this condition of judgment (the schema) is lacking, all subsumption becomes impossible. For in that case nothing is given that could be subsumed under the concept. The merely transcendental employment of the categories is, therefore, really no employment at all, and has no determinate object, not even one that is determinable in its mere form. It therefore follows that the pure category does not suffice for a synthetic a priori principle, that the principles of pure understanding are only of empirical, never of transcendental employment, and that outside the field of possible experience there can be no synthetic a priori principles.

It may be advisable, therefore, to express the situation as follows. The pure categories, apart from formal conditions of sensibility, have only transcendental meaning; nevertheless they may not be employed transcendentally, such employment being in itself impossible, inasmuch as all conditions of any employment in judgments are lacking to them, namely, the formal conditions of the subsumption of any ostensible object under these concepts. Since, then, as pure categories merely, they are not to be employed empirically, and cannot be employed transcendentally, they cannot, when separated from all sensibility, be employed in any manner whatsoever, that is, they cannot be applied to any ostensible object. They are the pure form of the employment of understanding in respect of objects in general, that is, of thought; but since they are merely its form, through them alone no object can be thought or determined.

But we are here subject to an illusion from which it is difficult to escape. The categories are not, as regards their origin, grounded in sensibility, like the forms of intuition, space and time; and they seem, therefore, to allow of an application extending beyond all objects of the senses. As a matter of fact they are nothing but forms of thought which contain the merely logical faculty of uniting a priori in one consciousness the manifold given in intuition; and apart, therefore, from the only intuition that is possible to us, they have even less meaning than the pure sensible forms. Through these forms an object is at least given, whereas a mode of combining the manifold—a mode peculiar to our understanding—by itself, in the absence of that intuition wherein the manifold can alone be given, signifies nothing at all. At the same time, if we entitle certain objects, as appearances, sensible entities (phenomena), then since we thus distinguish the mode in which we intuit them from the nature that belongs to them in themselves, it is implied in this distinction that we place the latter, considered in their own nature, although we do not so intuit them, or that we place other possible things, which are not objects of our senses but are thought as objects merely through the understanding, in opposition to the former, and that in so doing we entitle them intelligible entities (noumena). The question then arises, whether our pure concepts of understanding have meaning in respect of these latter, and so can be a way of knowing them.

At the very outset, however, we come upon an ambiguity which may occasion serious misapprehension. The understanding, when it entitles an object in a [certain] relation mere phenomenon, at the same time forms, apart from that relation, a representation of an object in itself, and so comes to represent itself as also being able to form concepts of such objects. And since the understanding yields no concepts additional to the categories, it also supposes that the object in itself must at least be thought through these pure concepts, and so is misled into treating the entirely indeterminate concept of an intelligible entity, namely, of a something in general outside our sensibility, as being a determinate concept of an entity that allows of being known in a certain [purely intelligible] manner by means of the understanding.

If by ‘noumenon’ we mean a thing so far as it is not an object of our sensible intuition, and so abstract from our mode of intuiting it, this is a noumenon in the negative sense of the term. But if we understand by it an object of a non-sensible intuition, we thereby presuppose a special mode of intuition, namely, the intellectual, which is not that which we possess, and of which we cannot comprehend even the possibility. This would be ‘noumenon’ in the positive sense of the term.

The doctrine of sensibility is likewise the doctrine of the noumenon in the negative sense, that is, of things which the understanding must think without this reference to our mode of intuition, therefore not merely as appearances but as things in themselves. At the same time the understanding is well aware that in viewing things in this manner, as thus apart from our mode of intuition, it cannot make any use of the categories. For the categories have meaning only in relation to the unity of intuition in space and time; and even this unity they can determine, by means of general a priori connecting concepts, only because of the mere ideality of space and time. In cases where this unity of time is not to be found, and therefore in the case of the noumenon, all employment, and indeed the whole meaning of the categories, entirely vanishes; for we have then no means of determining whether things in harmony with the categories are even possible. On this point I need only refer the reader to what I have said in the opening sentences of the General Note appended to the preceding chapter. The possibility of a thing can never be proved merely from the fact that its concept is not self-contradictory, but only through its being supported by some corresponding intuition. If, therefore, we should attempt to apply the categories to objects which are not viewed as being appearances, we should have to postulate an intuition other than the sensible, and the object would thus be a noumenon in the positive sense. Since, however, such a type of intuition, intellectual intuition, forms no part whatsoever of our faculty of knowledge, it follows that the employment of the categories can never extend further than to the objects of experience. Doubtless, indeed, there are intelligible entities corresponding to the sensible entities; there may also be intelligible entities to which our sensible faculty of intuition has no relation whatsoever; but our concepts of understanding, being mere forms of thought for our sensible intuition, could not in the least apply to them. That, therefore, which we entitle ‘noumenon’ must be understood as being such only in a negative sense.

If I remove from empirical knowledge all thought (through categories), no knowledge of any object remains. For through mere intuition nothing at all is thought, and the fact that this affection of sensibility is in me does not [by itself] amount to a relation of such representation to any object. But if, on the other hand, I leave aside all intuition, the form of thought still remains—that is, the mode of determining an object for the manifold of a possible intuition. The categories accordingly extend further than sensible intuition, since they think objects in general, without regard to the special mode (the sensibility) in which they may be given. But they do not thereby determine a greater sphere of objects. For we cannot assume that such objects can be given, without presupposing the possibility of another kind of intuition than the sensible; and we are by no means justified in so doing.

If the objective reality of a concept cannot be in any way known, while yet the concept contains no contradiction and also at the same time is connected with other modes of knowledge that involve given concepts which it serves to limit, I entitle that concept problematic. The concept of a noumenon—that is, of a thing which is not to be thought as object of the senses but as a thing in itself, solely through a pure understanding—is not in any way contradictory. For we cannot assert of sensibility that it is the sole possible kind of intuition. Further, the concept of a noumenon is necessary, to prevent sensible intuition from being extended to things in themselves, and thus to limit the objective validity of sensible knowledge. The remaining things, to which it does not apply, are entitled noumena, in order to show that this knowledge cannot extend its domain over everything which the understanding thinks. But none the less we are unable to comprehend how such noumena can be possible, and the domain that lies out beyond the sphere of appearances is for us empty. That is to say, we have an understanding which problematically extends further, but we have no intuition, indeed not even the concept of a possible intuition, through which objects outside the field of sensibility can be given, and through which the understanding can be employed assertorically beyond that field. The concept of a noumenon is thus a merely limiting concept, the function of which is to curb the pretensions of sensibility; and it is therefore only of negative employment. At the same time it is no arbitrary invention; it is bound up with the limitation of sensibility, though it cannot affirm anything positive beyond the field of sensibility.

The division of objects into phenomena and noumena, and the world into a world of the senses and a world of the understanding, is therefore quite inadmissible in the positive sense, although the distinction of concepts as sensible and intellectual is certainly legitimate. For no object can be determined for the latter concepts, and consequently they cannot be asserted to be objectively valid. If we abandon the senses, how shall we make it conceivable that our categories, which would be the sole remaining concepts for noumena, should still continue to signify something, since for their relation to any object more must be given than merely the unity of thought—namely, in addition, a possible intuition, to which they may be applied. None the less, if the concept of a noumenon be taken in a merely problematic sense, it is not only admissible, but as setting limits to sensibility is likewise indispensable. But in that case a noumenon is not for our understanding a special [kind of] object, namely, an intelligible object; the [sort of] understanding to which it might belong is itself a problem. For we cannot in the least represent to ourselves the possibility of an understanding which should know its object, not discursively through categories, but intuitively in a non-sensible intuition. What our understanding acquires through this concept of a noumenon, is a negative extension; that is to say, understanding is not limited through sensibility; on the contrary, it itself limits sensibility by applying the term noumena to things in themselves (things not regarded as appearances). But in so doing it at the same time sets limits to itself, recognising that it cannot know these noumena through any of the categories, and that it must therefore think them only under the title of an unknown something.

In the writings of modern philosophers I find the expressions mundus sensibilis and intelligibilis used with a meaning altogether different from that of the ancients—a meaning which is easily understood, but which results merely in an empty play upon words. According to this usage, some have thought good to entitle the sum of appearances, in so far as they are intuited, the world of the senses, and in so far as their connection is thought in conformity with laws of understanding, the world of the understanding. Observational astronomy, which teaches merely the observation of the starry heavens, would give an account of the former; theoretical astronomy, on the other hand, as taught according to the Copernican system, or according to Newton’s laws of gravitation, would give an account of the second, namely, of an intelligible world. But such a twisting of words is a merely sophistical subterfuge; it seeks to avoid a troublesome question by changing its meaning to suit our own convenience. Understanding and reason are, indeed, employed in dealing with appearances; but the question to be answered is whether they have also yet another employment, when the object is not a phenomenon (that is, is a noumenon); and it is in this latter sense that the object is taken, when it is thought as merely intelligible, that is to say, as being given to the understanding alone, and not to the senses. The question, therefore, is whether in addition to the empirical employment of the understanding—to its employment even in the Newtonian account of the structure of the universe—there is likewise possible a transcendental employment, which has to do with the noumenon as an object. This question we have answered in the negative.

When, therefore, we say that the senses represent objects as they appear, and the understanding objects as they are, the latter statement is to be taken, not in the transcendental, but in the merely empirical meaning of the terms, namely as meaning that the objects must be represented as objects of experience, that is, as appearances in thoroughgoing interconnection with one another, and not as they may be apart from their relation to possible experience (and consequently to any senses), as objects of the pure understanding. Such objects of pure understanding will always remain unknown to us; we can never even know whether such a transcendental or exceptional knowledge is possible under any conditions—at least not if it is to be the same kind of knowledge as that which stands under our ordinary categories. Understanding and sensibility, with us, can determine objects only when they are employed in conjunction. When we separate them, we have intuitions without concepts, or concepts without intuitions—in both cases, representations which we are not in a position to apply to any determinate object.

If, after all these explanations, any one still hesitates to abandon the merely transcendental employment of the categories, let him attempt to obtain from them a synthetic proposition. An analytic proposition carries the understanding no further; for since it is concerned only with what is already thought in the concept, it leaves undecided whether this concept has in itself any relation to objects, or merely signifies the unity of thought in general—complete abstraction being made from the mode in which an object may be given. The understanding [in its analytic employment] is concerned only to know what lies in the concept; it is indifferent as to the object to which the concept may apply. The attempt must therefore be made with a synthetic and professedly transcendental principle, as, for instance, ‘Everything that exists, exists as substance, or as a determination inherent in it’, or ‘Everything contingent exists as an effect of some other thing, namely, of its cause’. Now whence, I ask, can the understanding obtain these synthetic propositions, when the concepts are to be applied, not in their relation to possible experience, but to things in themselves (noumena)? Where is here that third something, which is always required for a synthetic proposition, in order that, by its mediation, the concepts which have no logical (analytic) affinity may be brought into connection with one another? The proposition can never be established, nay, more, even the possibility of any such pure assertion cannot be shown, without appealing to the empirical employment of the understanding, and thereby departing completely from the pure and non-sensible judgment. Thus the concept of pure and merely intelligible objects is completely lacking in all principles that might make possible its application. For we cannot think of any way in which such intelligible objects might be given. The problematic thought which leaves open a place for them serves only, like an empty space, for the limitation of empirical principles, without itself containing or revealing any other object of knowledge beyond the sphere of those principles.