ourselves of the non-existence of space, though we may easily enough think that no objects are found in it. It must, therefore, be considered as the condition of the possibility of phenomena, and by no means as a determination dependent on them, and is a representation a priori, which necessarily supplies the basis for external phenomena. 3. Space is no discursive, or as we say, general conception of the relations of things, but a pure intuition. For, in the first place, we can only represent to ourselves one space, and, when we talk of divers spaces, we mean only parts of one and the same space. Moreover, these parts cannot antecede this one all-embracing space, as the component parts from which the aggregate can be made up, but can be cogitated only as existing in it. Space is essentially one, and multiplicity in it, consequently the general notion of spaces, of this or that space, depends solely upon limitations. Hence it follows that an a priori intuition (which is not empirical) lies at the root of all our conceptions of space. Thus, moreover, the principles of geometry--for example, that "in a triangle, two sides 22 together are greater than the third," are never deduced from general conceptions of line and triangle, but from intuition, and this a priori, with apodeictic certainty. 4. Space is represented as an infinite given quantity. Now every conception must indeed be considered as a representation which is contained in an infinite multitude of different possible representations, which, therefore, comprises these under itself; but no conception, as such, can be so conceived, as if it contained within itself an infinite multitude of representations. Nevertheless, space is so conceived of, for all parts of space are equally capable of being produced to infinity. Consequently, the original representation of space is an intuition a priori, and not a conception. SS 3. Transcendental Exposition of the Conception of Space. By a transcendental exposition, I mean the explanation of a conception, as a principle, whence can be discerned the possibility of other synthetical a priori cognitions. For this purpose, it is requisite, firstly, that such cognitions do really flow from the given conception; and, secondly, that the said cognitions are only possible under the presupposition of a given mode of explaining this conception. Geometry is a science which determines the properties of space synthetically, and yet a priori. What, then, must be our representation of space, in order that such a cognition of it may be possible? It must be originally intuition, for from a mere conception, no propositions can be deduced which go out beyond the conception, and yet this happens in geometry. (Introd. V.) But this intuition must be found in the mind a priori, that is, before any perception of objects, consequently must be pure, not empirical, intuition. For geometrical principles are always apodeictic, that is, united with the consciousness of their necessity, as: "Space has only three dimensions." But propositions of this kind cannot be empirical judgements, nor conclusions from them. (Introd. II.) Now, how
can an external intuition anterior to objects themselves, and in which our conception of objects can be determined a priori, exist in the human mind? Obviously not otherwise than in so far as it has its seat in the subject only, as the formal capacity of the subject's being affected by objects, and thereby of obtaining immediate representation, that is, intuition; consequently, only as the form of the external sense in general.
Thus it is only by means of our explanation that the possibility of geometry, as a synthetical science a priori, becomes comprehensible. Every mode of explanation which does not show us this possibility, although in appearance it may be similar to ours, can with the utmost certainty be distinguished from it by these marks.
SS 4. Conclusions from the foregoing Conceptions.
(a) Space does not represent any property of objects as things in themselves, nor does it represent them in their relations to each other; in other words, space does not represent to us any determination of objects such as attaches to the objects themselves, and would remain, even though all subjective conditions of the intuition were abstracted. For neither absolute nor relative determinations of objects can be intuited prior to the existence of the things to which they belong, and therefore not a priori.
(b) Space is nothing else than the form of all phenomena of the external sense, that is, the subjective condition of the sensibility, under which alone external intuition is possible. Now, because the receptivity or capacity of the subject to be affected by objects necessarily antecedes all intuitions of these objects, it is easily understood how the form of all phenomena can be given in the mind previous to all actual perceptions, therefore a priori, and how it, as a pure intuition, in which all objects must be determined, can contain principles of the relations of these objects prior to all experience.
It is therefore from the human point of view only that we can speak of space, extended objects, etc. If we depart from the subjective condition, under which alone we can obtain external intuition, or, in other words, by means of which we are affected by objects, the representation of space has no meaning whatsoever. This predicate is only applicable to things in so far as they appear to us, that is, are objects of sensibility. The constant form of this receptivity, which we call sensibility, is a necessary condition of all relations in which objects can be intuited as existing without us, and when abstraction of these objects is made, is a pure intuition, to which we give the name of space. It is clear that we cannot make the special conditions of sensibility into conditions of the possibility of things, but only of the possibility of their existence as far as they are phenomena. And so we may correctly say that space contains all which can appear to us externally, but not all things considered as things in themselves, be they intuited or not, or by whatsoever subject one will. As to the intuitions of other thinking beings, we cannot judge whether they are or are not bound by the same conditions which limit our own intuition, and which for us are universally valid. If we join the limitation of a judgement to the conception of the subject, then the judgement will possess unconditioned validity. For example, the proposition, "All objects are beside each other in space," is valid only under the limitation that these things are taken as objects of our sensuous intuition. But if I join the condition to the conception and say, "All things, as external phenomena, are beside each other in space," then the rule is valid universally, and without any limitation. Our expositions, consequently, teach the reality (i.e., the objective validity) of space in regard of all 23 which can be presented to us externally as object, and at the same time also the ideality of space in regard to objects when they are considered by means of reason as things in themselves, that is, without reference to the constitution of our sensibility. We maintain, therefore, the empirical reality of space in regard to all possible external experience, although we must admit its transcendental ideality; in other words, that it is nothing, so soon as we withdraw the condition upon which the possibility of all experience depends and look upon space as something that belongs to things in themselves. But, with the exception of space, there is no representation, subjective and referring to something external to us, which could be called objective a priori. For there are no other subjective representations from which we can deduce synthetical propositions a priori, as we can from the intuition of space. (See SS 3.) Therefore, to speak accurately, no ideality whatever belongs to these, although they agree in this respect with the representation of space, that they belong merely to the subjective nature of the mode of sensuous perception; such a mode, for example, as that of sight, of hearing, and of feeling, by means of the sensations of colour, sound, and heat, but which, because they are only sensations and not intuitions, do not of themselves give us the cognition of any object, least of all, an a priori cognition. My purpose, in the above remark, is merely this: to guard any one against illustrating the asserted ideality of space by examples quite insufficient, for example, by colour, taste, etc.; for these must be contemplated not as properties of things, but only as changes in the subject, changes which may be different in different men. For, in such a case, that which is originally a mere phenomenon, a rose, for example, is taken by the empirical understanding for a thing in itself, though to every different eye, in respect of its colour, it may appear different. On the contrary, the transcendental conception of phenomena in space is a critical admonition, that, in general, nothing which is intuited in space is a thing in itself, and that space is not a form which belongs as a property to things; but that objects are quite unknown to us in themselves, and what we call outward objects, are nothing else but mere representations of our sensibility, whose form is space, but whose real correlate, the thing in itself, is not known by means of these representations, nor ever can be, but respecting which, in experience, no inquiry is ever made. SECTION
