The really valid argument adduced by Kant for the a priori character of our apprehension of space is based on the nature of geometrical judgements. The universality of our judgements in geometry is not based upon experience, i. e. upon the observation of individual things in space. The necessity of geometrical relations is apprehended directly in virtue of the mind's own apprehending nature. Unfortunately in the present context Kant ignores this argument and substitutes two others, both of which are invalid.

1. "Space is no empirical conception[14] which has been derived from external[15] experiences. For in order that certain sensations may be related to something external to me (that is, to something in a different part of space from that in which I am), in like manner, in order that I may represent them as external to and next to each other, and consequently as not merely different but as in different places, the representation of space must already exist as a foundation. Consequently, the representation of space cannot be borrowed from the relations of external phenomena through experience; but, on the contrary, this external experience is itself first possible only through the said representation."[16] Here Kant is thinking that in order to apprehend, for example, that A is to the right of B we must first apprehend empty space. He concludes that our apprehension of space is a priori, because we apprehend empty space before we become aware of the spatial relations of individual objects in it.

To this the following reply may be made. (a) The term a priori applied to an apprehension should mean, not that it arises prior to experience, but that its validity is independent of experience. (b) That to which the term a priori should be applied is not the apprehension of empty space, which is individual, but the apprehension of the nature of space in general, which is universal. (c) We do not apprehend empty space before we apprehend individual spatial relations of individual bodies or, indeed, at any time. (d) Though we come to apprehend a priori the nature of space in general, the apprehension is not prior but posterior in time to the apprehension of individual spatial relations. (e) It does not follow from the temporal priority of our apprehension of individual spatial relations that our apprehension of the nature of space in general is 'borrowed from experience', and is therefore not a priori.

2. "We can never represent to ourselves that there is no space, though we can quite well think that no objects are found in it. It must, therefore, be considered as the condition of the possibility of phenomena, and not as a determination dependent upon them, and it is an a priori representation, which necessarily underlies external phenomena."[17]

Here the premise is simply false. If 'represent' or 'think' means 'believe', we can no more represent or think that there are no objects in space than that there is no space. If, on the other hand, 'represent' or 'think' means 'make a mental picture of', the assertion is equally false. Kant is thinking of empty space as a kind of receptacle for objects, and the a priori character of our apprehension of space lies, as before, in the supposed fact that in order to apprehend objects in space we must begin with the apprehension of empty space.

The examination of Kant's arguments for the perceptive character of our apprehension of space is a more complicated matter. By way of preliminary it should be noticed that they presuppose the possibility in general of distinguishing features of objects which belong to the perception of them from others which belong to the conception of them. In particular, Kant holds that our apprehension of a body as a substance, as exercising force and as divisible, is due to our understanding as conceiving it, while our apprehension of it as extended and as having a shape is due to our sensibility as perceiving it.[18] The distinction, however, will be found untenable in principle; and if this be granted, Kant's attempt to distinguish in this way the extension and shape of an object from its other features can be ruled out on general grounds. In any case, it must be conceded that the arguments fail by which he seeks to show that space in particular belongs to perception.

There appears to be no way of distinguishing perception and conception as the apprehension of different realities[19] except as the apprehension of the individual and of the universal respectively. Distinguished in this way, the faculty of perception is that in virtue of which we apprehend the individual, and the faculty of conception is that power of reflection in virtue of which a universal is made the explicit object of thought.[20] If this be granted, the only test for what is perceived is that it is individual, and the only test for what is conceived is that it is universal. These are in fact the tests which Kant uses. But if this be so, it follows that the various characteristics of objects cannot be divided into those which are perceived and those which are conceived. For the distinction between universal and individual is quite general, and applies to all characteristics of objects alike. Thus, in the case of colour, we can distinguish colour in general and the individual colours of individual objects; or, to take a less ambiguous instance, we can distinguish a particular shade of redness and its individual instances. Further, it may be said that perception is of the individual shade of red of the individual object, and that the faculty by which we become explicitly aware of the particular shade of red in general is that of conception. The same distinction can be drawn with respect to hardness, or shape, or any other characteristic of objects. The distinction, then, between perception and conception can be drawn with respect to any characteristic of objects, and does not serve to distinguish one from another.

Kant's arguments to show that our apprehension of space belongs to perception are two in number, and both are directed to show not, as they should, that space is a form of perception, but that it is a perception.[21] The first runs thus: "Space is no discursive, or, as we say, general conception of relations of things in general, but a pure perception. For, in the first place, we can represent to ourselves only one space, and if we speak of many spaces we mean thereby only parts of one and the same unique space. Again, these parts cannot precede the one all-embracing space as the component parts, as it were, out of which it can be composed, but can be thought only in it. Space is essentially one; the manifold in it, and consequently the general conception of spaces in general, rests solely upon limitations."[22]

Here Kant is clearly taking the proper test of perception. Its object, as being an individual, is unique; there is only one of it, whereas any conception has a plurality of instances. But he reaches his conclusion by supposing that we first perceive empty space and then become aware of its parts by dividing it. Parts of space are essentially limitations of the one space; therefore to apprehend them we must first apprehend space. And since space is one, it must be object of perception; in other words, space, in the sense of the one all-embracing space, i. e. the totality of individual spaces, is something perceived.

The argument appears open to two objections. In the first place, we do not perceive space as a whole, and then, by dividing it, come to apprehend individual spaces. We perceive individual spaces, or, rather, individual bodies occupying individual spaces.[23] We then apprehend that these spaces, as spaces, involve an infinity of other spaces. In other words, it is reflection on the general nature of space, the apprehension of which is involved in our apprehension of individual spaces or rather of bodies in space, which gives rise to the apprehension of the totality[24] of spaces, the apprehension being an act, not of perception, but of thought or conception. It is necessary, then, to distinguish (a) individual spaces, which we perceive; (b) the nature of space in general, of which we become aware by reflecting upon the character of perceived individual spaces, and which we conceive; (c) the totality of individual spaces, the thought of which we reach by considering the nature of space in general.