We have now not only traversed the region of the pure understanding and carefully surveyed every part of it, but we have also measured it, and assigned to everything therein its proper place. But this land is an island, and enclosed by nature herself within unchangeable limits. It is the land of truth (an attractive word), surrounded by a wide and stormy ocean, the region of illusion, where many a fog-bank, many an iceberg, seems to the mariner, on his voyage of discovery, a new country, and, while constantly deluding him with vain hopes, engages him in dangerous adventures, from which he never can desist, and which yet he never can bring to a termination. But before venturing upon this sea, in order to explore it in its whole extent, and to arrive at a certainty whether anything is to be discovered there, it will not be without advantage if we cast our eyes upon the chart of the land that we are about to leave, and to ask ourselves, firstly, whether we cannot rest perfectly contented with what it contains, or whether we must not of necessity be contented with it, if we can find nowhere else a solid foundation to build upon; and, secondly, by what title we possess this land itself, and how we hold it secure against all hostile claims? Although, in the course of our analytic, we have already given sufficient answers to these questions, yet a summary recapitulation of these solutions may be useful in strengthening our conviction, by uniting in one point the momenta of the arguments.
We have seen that everything which the understanding draws from itself, without borrowing from experience, it nevertheless possesses only for the behoof and use of experience. The principles of the pure understanding, whether constitutive a priori (as the mathematical principles), or merely regulative (as the dynamical), contain nothing but the pure schema, as it were, of possible experience. For experience possesses its unity from the synthetical unity which the understanding, originally and from itself, imparts to the synthesis of the imagination in relation to apperception, and in a priori relation to and agreement with which phenomena, as data for a possible cognition, must stand. But although these rules of the understanding are not only a priori true, but the very source of all truth, that is, of the accordance of our cognition with objects, and on this ground, that they contain the basis of the possibility of experience, as the ensemble of all cognition, it seems to us not enough to propound what is true- we desire also to be told what we want to know. If, then, we learn nothing more by this critical examination than what we should have practised in the merely empirical use of the understanding, without any such subtle inquiry, the presumption is that the advantage we reap from it is not worth the labour bestowed upon it. It may certainly be answered that no rash curiosity is more prejudicial to the enlargement of our knowledge than that which must know beforehand the utility of this or that piece of information which we seek, before we have entered on the needful investigations, and before one could form the least conception of its utility, even though it were placed before our eyes. But there is one advantage in such transcendental inquiries which can be made comprehensible to the dullest and most reluctant learner- this, namely, that the understanding which is occupied merely with empirical exercise, and does not reflect on the sources of its own cognition, may exercise its functions very well and very successfully, but is quite unable to do one thing, and that of very great importance, to determine, namely, the bounds that limit its employment, and to know what lies within or without its own sphere. This purpose can be obtained only by such profound investigations as we have instituted. But if it cannot distinguish whether certain questions lie within its horizon or not, it can never be sure either as to its claims or possessions, but must lay its account with many humiliating corrections, when it transgresses, as it unavoidably will, the limits of its own territory, and loses itself in fanciful opinions and blinding illusions.
That the understanding, therefore, cannot make of its a priori principles, or even of its conceptions, other than an empirical use, is a proposition which leads to the most important results. A transcendental use is made of a conception in a fundamental proposition or principle, when it is referred to things in general and considered as things in themselves; an empirical use, when it is referred merely to phenomena, that is, to objects of a possible experience. That the latter use of a conception is the only admissible one is evident from the reasons following. For every conception are requisite, firstly, the logical form of a conception (of thought) general; and, secondly, the possibility of presenting to this an object to which it may apply. Failing this latter, it has no sense, and utterly void of content, although it may contain the logical function for constructing a conception from certain data. Now, object cannot be given to a conception otherwise than by intuition, and, even if a pure intuition antecedent to the object is a priori possible, this pure intuition can itself obtain objective validity only from empirical intuition, of which it is itself but the form. All conceptions, therefore, and with them all principles, however high the degree of their a priori possibility, relate to empirical intuitions, that is, to data towards a possible experience. Without this they possess no objective validity, but are mere play of imagination or of understanding with images or notions. Let us take, for example, the conceptions of mathematics, and first in its 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 entirely a priori, they would nevertheless have no significance if we were not always able to exhibit their significance in and by means of phenomena (empirical objects). Hence it is requisite that an abstract conception be made sensuous, that is, that an object corresponding to it in intuition be forthcoming, otherwise the conception remains, as we say, without sense, that is, without meaning. Mathematics fulfils this requirement by the construction of the figure, which is a phenomenon evident to the senses. The same science finds support and significance in number; this in its turn finds it in the fingers, or in counters, or in lines and points. The conception itself is always produced a priori, together with the synthetical principles or formulas from such conceptions; but the proper employment of them, and their application to objects, can exist nowhere but in experience, the possibility of which, as regards its form, they contain a priori.
That this is also the case with all of the categories and the principles based upon them is evident from the fact that we cannot render intelligible the possibility of an object corresponding to them without having recourse to the conditions of sensibility, consequently, to the form of phenomena, to which, as their only proper objects, their use must therefore be confined, inasmuch as, if this condition is removed, all significance, that is, all relation to an object, disappears, and no example can be found to make it comprehensible what sort of things we ought to think under such conceptions.
The conception of quantity cannot be explained except by saying that it is the determination of a thing whereby it can be cogitated how many times one is placed in it. But this "how many times" is based upon successive repetition, consequently upon time and the synthesis of the homogeneous therein. Reality, in contradistinction to negation, can be explained only by cogitating a time which is either filled therewith or is void. If I leave out the notion of permanence (which is existence in all time), there remains in the conception of substance nothing but the logical notion of subject, a notion of which I endeavour to realize by representing to myself something that can exist only as a subject. But not only am I perfectly ignorant of any conditions under which this logical prerogative can belong to a thing, I can make nothing out of the notion, and draw no inference from it, because no object to which to apply the conception is determined, and we consequently do not know whether it has any meaning at all. In like manner, if I leave out the notion of time, in which something follows upon some other thing in conformity with a rule, I can find nothing in the pure category, except that there is a something of such a sort that from it a conclusion may be drawn as to the existence of some other thing. But in this case it would not only be impossible to distinguish between a cause and an effect, but, as this power to draw conclusions requires conditions of which I am quite ignorant, the conception is not determined as to the mode in which it ought to apply to an object. The so-called principle: "Everything that is contingent has a cause," comes with a gravity and self-assumed authority that seems to require no support from without. But, I ask, what is meant by contingent? The answer is that the non-existence of which is possible. But I should like very well to know by what means this possibility of non-existence is to be cognized, if we do not represent to ourselves a succession in the series of phenomena, and in this succession an existence which follows a non-existence, or conversely, consequently, change. For to say, that the non-existence of a thing is not self-contradictory is a lame appeal to a logical condition, which is no doubt a necessary condition of the existence of the conception, but is far from being sufficient for the real objective possibility of non-existence. I can annihilate in thought every existing substance without self-contradiction, but I cannot infer from this their objective contingency in existence, that is to say, the possibility of their non-existence in itself. As regards the category of community, it may easily be inferred that, as the pure categories of substance and causality are incapable of a definition and explanation sufficient to determine their object without the aid of intuition, the category of reciprocal causality in the relation of substances to each other (commercium) is just as little susceptible thereof. Possibility, existence, and necessity nobody has ever yet been able to explain without being guilty of manifest tautology, when the definition has been drawn entirely from the pure understanding. For the substitution of the logical possibility of the conception- the condition of which is that it be not self-contradictory, for the transcendental possibility of things- the condition of which is that there be an object corresponding to the conception, is a trick which can only deceive the inexperienced.*
*In one word, to none of these conceptions belongs a corresponding object, and consequently their real possibility cannot be demonstrated, if we take away sensuous intuition- the only intuition which we possess- and there then remains nothing but the logical possibility, that is, the fact that the conception or thought is possible- which, however, is not the question; what we want to know being, whether it relates to an object and thus possesses any meaning.
It follows incontestably, that the pure conceptions of the understanding are incapable of transcendental, and must always be of empirical use alone, and that the principles of the pure understanding relate only to the general conditions of a possible experience, to objects of the senses, and never to things in general, apart from the mode in which we intuite them.
Transcendental analytic has accordingly this important result, to wit, that the understanding is competent' effect nothing a priori, except the anticipation of the form of a possible experience in general, and that, as that which is not phenomenon cannot be an object of experience, it can never overstep the limits of sensibility, within which alone objects are presented to us. Its principles are merely principles of the exposition of phenomena, and the proud name of an ontology, which professes to present synthetical cognitions a priori of things in general in a systematic doctrine, must give place to the modest title of analytic of the pure understanding.
Thought is the act of referring a given intuition to an object. If the mode of this intuition is unknown to us, the object is merely transcendental, and the conception of the understanding is employed only transcendentally, that is, to produce unity in the thought of a manifold in general. Now a pure category, in which all conditions of sensuous intuition- as the only intuition we possess- are abstracted, does not determine an object, but merely expresses the thought of an object in general, according to different modes. Now, to employ a conception, the function of judgement is required, by which an object is subsumed under the conception, consequently the at least formal condition, under which something can be given in intuition. Failing this condition of judgement (schema), subsumption is impossible; for there is in such a case nothing given, which may be subsumed under the conception. The merely transcendental use of the categories is therefore, in fact, no use at all and has no determined, or even, as regards its form, determinable object. Hence it follows that the pure category is incompetent to establish a synthetical a priori principle, and that the principles of the pure understanding are only of empirical and never of transcendental use, and that beyond the sphere of possible experience no synthetical a priori principles are possible.
It may be advisable, therefore, to express ourselves thus. The pure categories, apart from the formal conditions of sensibility, have a merely transcendental meaning, but are nevertheless not of transcendental use, because this is in itself impossible, inasmuch as all the conditions of any employment or use of them (in judgements) are absent, to wit, the formal conditions of the subsumption of an object under these conceptions. As, therefore, in the character of pure categories, they must be employed empirically, and cannot be employed transcendentally, they are of no use at all, when separated from sensibility, that is, they cannot be applied to an object. They are merely the pure form of the employment of the understanding in respect of objects in general and of thought, without its being at the same time possible to think or to determine any object by their means.
But there lurks at the foundation of this subject an illusion which it is very difficult to avoid. The categories are not based, as regards their origin, upon sensibility, like the forms of intuition, space, and time; they seem, therefore, to be capable of an application beyond the sphere of sensuous objects. But this is not the case. They are nothing but mere forms of thought, which contain only the logical faculty of uniting a priori in consciousness the manifold given in intuition. Apart, then, from the only intuition possible for us, they have still less meaning than the pure sensuous forms, space and time, for through them an object is at least given, while a mode of connection of the manifold, when the intuition which alone gives the manifold is wanting, has no meaning at all. At the same time, when we designate certain objects as phenomena or sensuous existences, thus distinguishing our mode of intuiting them from their own nature as things in themselves, it is evident that by this very distinction we as it were place the latter, considered in this their own nature, although we do not so intuite them, in opposition to the former, or, on the other hand, we do so place other possible things, which are not objects of our senses, but are cogitated by the understanding alone, and call them intelligible existences (noumena). Now the question arises whether the pure conceptions of our understanding do possess significance in respect of these latter, and may possibly be a mode of cognizing them.
But we are met at the very commencement with an ambiguity, which may easily occasion great misapprehension. The understanding, when it terms an object in a certain relation phenomenon, at the same time forms out of this relation a representation or notion of an object in itself, and hence believes that it can form also conceptions of such objects. Now as the understanding possesses no other fundamental conceptions besides the categories, it takes for granted that an object considered as a thing in itself must be capable of being thought by means of these pure conceptions, and is thereby led to hold the perfectly undetermined conception of an intelligible existence, a something out of the sphere of our sensibility, for a determinate conception of an existence which we can cognize in some way or other by means of the understanding.
If, by the term noumenon, we understand a thing so far as it is not an object of our sensuous intuition, thus making abstraction of our mode of intuiting it, this is a noumenon in the negative sense of the word. But if we understand by it an object of a non-sensuous intuition, we in this case assume a peculiar mode of intuition, an intellectual intuition, to wit, which does not, however, belong to us, of the very possibility of which we have no notion- and this is a noumenon in the positive sense.
The doctrine of sensibility is also the doctrine of noumena in the negative sense, that is, of things which the understanding is obliged to cogitate apart from any relation to our mode of intuition, consequently not as mere phenomena, but as things in themselves. But the understanding at the same time comprehends that it cannot employ its categories for the consideration of things in themselves, because these possess significance only in relation to the unity of intuitions in space and time, and that they are competent to determine this unity by means of general a priori connecting conceptions only on account of the pure ideality of space and time. Where this unity of time is not to be met with, as is the case with noumena, the whole use, indeed the whole meaning of the categories is entirely lost, for even the possibility of things to correspond to the categories is in this case incomprehensible. On this point, I need only refer the reader to what I have said at the commencement of the General Remark appended to the foregoing chapter. Now, the possibility of a thing can never be proved from the fact that the conception of it is not self-contradictory, but only by means of an intuition corresponding to the conception. If, therefore, we wish to apply the categories to objects which cannot be regarded as phenomena, we must have an intuition different from the sensuous, and in this case the objects would be a noumena in the positive sense of the word. Now, as such an intuition, that is, an intellectual intuition, is no part of our faculty of cognition, it is absolutely impossible for the categories to possess any application beyond the limits of experience. It may be true that there are intelligible existences to which our faculty of sensuous intuition has no relation, and cannot be applied, but our conceptions of the understanding, as mere forms of thought for our sensuous intuition, do not extend to these. What, therefore, we call noumenon must be understood by us as such in a negative sense.
If I take away from an empirial intuition all thought (by means of the categories), there remains no cognition of any object; for by means of mere intuition nothing is cogitated, and, from the existence of such or such an affection of sensibility in me, it does not follow that this affection or representation has any relation to an object without me. But if I take away all intuition, there still remains the form of thought, that is, the mode of determining an object for the manifold of a possible intuition. Thus the categories do in some measure really extend further than sensuous intuition, inasmuch as they think objects in general, without regard to the mode (of sensibility) in which these objects are given. But they do not for this reason apply to and determine a wider sphere of objects, because we cannot assume that such can be given, without presupposing the possibility of another than the sensuous mode of intuition, a supposition we are not justified in making.
I call a conception problematical which contains in itself no contradiction, and which is connected with other cognitions as a limitation of given conceptions, but whose objective reality cannot be cognized in any manner. The conception of a noumenon, that is, of a thing which must be cogitated not as an object of sense, but as a thing in itself (solely through the pure understanding), is not self-contradictory, for we are not entitled to maintain that sensibility is the only possible mode of intuition. Nay, further, this conception is necessary to restrain sensuous intuition within the bounds of phenomena, and thus to limit the objective validity of sensuous cognition; for things in themselves, which lie beyond its province, are called noumena for the very purpose of indicating that this cognition does not extend its application to all that the understanding thinks. But, after all, the possibility of such noumena is quite incomprehensible, and beyond the sphere of phenomena, all is for us a mere void; that is to say, we possess an understanding whose province does problematically extend beyond this sphere, but we do not possess an intuition, indeed, not even the conception of a possible intuition, by means of which objects beyond the region of sensibility could be given us, and in reference to which the understanding might be employed assertorically. The conception of a noumenon is therefore merely a limitative conception and therefore only of negative use. But it is not an arbitrary or fictitious notion, but is connected with the limitation of sensibility, without, however, being capable of presenting us with any positive datum beyond this sphere.
The division of objects into phenomena and noumena, and of the world into a mundus sensibilis and intelligibilis is therefore quite inadmissible in a positive sense, although conceptions do certainly admit of such a division; for the class of noumena have no determinate object corresponding to them, and cannot therefore possess objective validity. If we abandon the senses, how can it be made conceivable that the categories (which are the only conceptions that could serve as conceptions for noumena) have any sense or meaning at all, inasmuch as something more than the mere unity of thought, namely, a possible intuition, is requisite for their application to an object? The conception of a noumenon, considered as merely problematical, is, however, not only admissible, but, as a limitative conception of sensibility, absolutely necessary. But, in this case, a noumenon is not a particular intelligible object for our understanding; on the contrary, the kind of understanding to which it could belong is itself a problem, for we cannot form the most distant conception of the possibility of an understanding which should cognize an object, not discursively by means of categories, but intuitively in a non-sensuous intuition. Our understanding attains in this way a sort of negative extension. That is to say, it is not limited by, but rather limits, sensibility, by giving the name of noumena to things, not considered as phenomena, but as things in themselves. But it at the same time prescribes limits to itself, for it confesses itself unable to cognize these by means of the categories, and hence is compelled to cogitate them merely as an unknown something.
I find, however, in the writings of modern authors, an entirely different use of the expressions, mundus sensibilis and intelligibilis, which quite departs from the meaning of the ancients- an acceptation in which, indeed, there is to be found no difficulty, but which at the same time depends on mere verbal quibbling. According to this meaning, some have chosen to call the complex of phenomena, in so far as it is intuited, mundus sensibilis, but in so far as the connection thereof is cogitated according to general laws of thought, mundus intelligibilis. Astronomy, in so far as we mean by the word the mere observation of the starry heaven, may represent the former; a system of astronomy, such as the Copernican or Newtonian, the latter. But such twisting of words is a mere sophistical subterfuge, to avoid a difficult question, by modifying its meaning to suit our own convenience. To be sure, understanding and reason are employed in the cognition of phenomena; but the question is, whether these can be applied when the object is not a phenomenon and in this sense we regard it if it is cogitated as given to the understanding alone, and not to the senses. The question therefore is whether, over and above the empirical use of the understanding, a transcendental use is possible, which applies to the noumenon as an object. This question we have answered in the negative.
When therefore we say, the senses represent objects as they appear, the understanding as they are, the latter statement must not be understood in a transcendental, but only in an empirical signification, that is, as they must be represented in the complete connection of phenomena, and not according to what they may be, apart from their relation to possible experience, consequently not as objects of the pure understanding. For this must ever remain unknown to us. Nay, it is also quite unknown to us whether any such transcendental or extraordinary cognition is possible under any circumstances, at least, whether it is possible by means of our categories. Understanding and sensibility, with us, can determine objects only in conjunction. If we separate them, we have intuitions without conceptions, or conceptions without intuitions; in both cases, representations, which we cannot apply to any determinate object.
If, after all our inquiries and explanations, any one still hesitates to abandon the mere transcendental use of the categories, let him attempt to construct with them a synthetical proposition. It would, of course, be unnecessary for this purpose to construct an analytical proposition, for that does not extend the sphere of the understanding, but, being concerned only about what is cogitated in the conception itself, it leaves it quite undecided whether the conception has any relation to objects, or merely indicates the unity of thought- complete abstraction being made of the modi in which an object may be given: in such a proposition, it is sufficient for the understanding to know what lies in the conception- to what it applies is to it indifferent. The attempt must therefore be made with a synthetical and so-called transcendental principle, for example: "Everything that exists, exists as substance," or, "Everything that is contingent exists as an effect of some other thing, viz., of its cause." Now I ask, whence can the understanding draw these synthetical propositions, when the conceptions contained therein do not relate to possible experience but to things in themselves (noumena)? Where is to be found the third term, which is always requisite PURE site in a synthetical proposition, which may connect in the same proposition conceptions which have no logical (analytical) connection with each other? The proposition never will be demonstrated, nay, more, the possibility of any such pure assertion never can be shown, without making reference to the empirical use of the understanding, and thus, ipso facto, completely renouncing pure and non-sensuous judgement. Thus the conception of pure and merely intelligible objects is completely void of all principles of its application, because we cannot imagine any mode in which they might be given, and the problematical thought which leaves a place open for them serves only, like a void space, to limit the use of empirical principles, without containing at the same time any other object of cognition beyond their sphere.