to Kant: the theory which he works out in the Transcendental Aesthetic consists in endowing space with an existence independent of its content, in laying down as de jure separable what each of us separates de facto, and in refusing to regard extensity as an abstraction like the others. In this respect the Kantian conception of space differs less than is usually imagined from the popular belief. Far from shaking our faith in the reality of space, Kant has shown what it actually means and has even justified it.
The empiricists really agree with Kant for extensity can not result from synthesis of unextended sensations without an act of the mind.
Moreover, the solution given by Kant does not seem to have been seriously disputed since his time: indeed, it has forced itself, sometimes without their knowledge, on the majority of those who have approached the problem anew, whether nativists or empiricists. Psychologists agree in assigning a Kantian origin to the nativistic explanation of Johann Müller; but Lotze's hypothesis of local signs, Bain's theory, and the more comprehensive explanation suggested by Wundt, may seem at first quite independent of the Transcendental Aesthetic. The authors of these theories seem indeed to have put aside the problem of the nature of space, in order to investigate simply by what process our sensations come to be situated in space and to be set, so to speak, alongside one another: but this very question shows that they regard sensations as inextensive and make a radical distinction, just as Kant did, between the matter of representation and its form. The conclusion to be drawn from the theories of Lotze and Bain, and from Wundt's attempt to reconcile them, is that the sensations by means of which we come to form the notion of space are themselves unextended and simply qualitative: extensity is supposed to result from their synthesis, as water from the combination of two gases. The empirical or genetic explanations have thus taken up the problem of space at the very point where Kant left it: Kant separated space from its contents: the empiricists ask how these contents, which are taken out of space by our thought, manage to get back again. It is true that they have apparently disregarded the activity of the mind, and that they are obviously inclined to regard the extensive form under which we represent things as produced by a kind of alliance of the sensations with one another: space, without being extracted from the sensations, is supposed to result from their co-existence. But how can we explain such an origination without the active intervention of the mind? The extensive differs by hypothesis from the inextensive: and even if we assume that extension is nothing but a relation between inextensive terms, this relation must still be established by a mind capable of thus associating several terms. It is no use quoting the example of chemical combinations, in which the whole seems to assume, of its own accord, a form and qualities which did not belong to any of the elementary atoms. This form and these qualities owe their origin just to the fact that we gather up the multiplicity of atoms in a single perception: get rid of the mind which carries out this synthesis and you will at once do away with the qualities, that is to say, the aspect under which the synthesis of elementary parts is presented to our consciousness. Thus inextensive sensations will remain what they are, viz., inextensive sensations, if nothing be added to them. For their co-existence to give rise to space, there must be an act of the mind which takes them in all at the same time and sets them in juxtaposition: this unique act is very like what Kant calls an a priori form of sensibility.
This act consists in the intuition of an empty homogeneous medium: perhaps peculiar to man and not shared by animals.
If we now seek to characterize this act, we see that it consists essentially in the intuition, or rather the conception, of an empty homogeneous medium. For it is scarcely possible to give any other definition of space: space is what enables us to distinguish a number of identical and simultaneous sensations from one another; it is thus a principle of differentiation other than that of qualitative differentiation, and consequently it is a reality with no quality. Someone may say, with the believers in the theory of local signs, that simultaneous sensations are never identical, and that, in consequence of the diversity of the organic elements which they affect, there are no two points of a homogeneous surface which make the same impression on the sight or the touch. We are quite ready to grant it, for if these two points affected us in the same way, there would be no reason for placing one of them on the right rather than on the left. But, just because we afterwards interpret this difference of quality in the sense of a difference of situation, it follows that we must have a clear idea of a homogeneous medium, i.e. of a simultaneity of terms which, although identical in quality, are yet distinct from one another. The more you insist on the difference between the impressions made on our retina by two points of a homogeneous surface, the more do you thereby make room for the activity of the mind, which perceives under the form of extensive homogeneity what is given it as qualitative heterogeneity. No doubt, though the representation of a homogeneous space grows out of an effort of the mind, there must be within the qualities themselves which differentiate two sensations some reason why they occupy this or that definite position in space. We must thus distinguish between the perception of extensity and the conception of space: they are no doubt implied in one another, but, the higher we rise in the scale of intelligent beings, the more clearly do we meet with the independent idea of a homogeneous space. It is therefore doubtful whether animals perceive the external world quite as we do, and especially whether they represent externality in the same way as ourselves. Naturalists have pointed out, as a remarkable fact, the surprising ease with which many vertebrates, and even some insects, manage to find their way through space. Animals have been seen to return almost in a straight line to their old home, pursuing a path which was hitherto unknown to them over a distance which may amount to several hundreds of miles. Attempts have been made to explain this feeling of direction by sight or smell, and, more recently, by the perception of magnetic currents which would enable the animal to take its bearings like a living compass. This amounts to saying that space is not so homogeneous for the animal as for us, and that determinations of space, or directions, do not assume for it a purely geometrical form. Each of these directions might appear to it with its own shade, its peculiar quality. We shall understand how a perception of this kind is possible if we remember that we ourselves distinguish our right from our left by a natural feeling, and that these two parts of our own extensity do then appear to us as if they bore a different quality; in fact, this is the very reason why we cannot give a proper definition of right and left. In truth, qualitative differences exist everywhere in nature, and I do not see why two concrete directions should not be as marked in immediate perception as two colours. But the conception of an empty homogeneous medium is something far more extraordinary, being a kind of reaction against that heterogeneity which is the very ground of our experience. Therefore, instead of saying that animals have a special sense of direction, we may as well say that men have a special faculty of perceiving or conceiving a space without quality. This faculty is not the faculty of abstraction: indeed, if we notice that abstraction assumes clean-cut distinctions and a kind of externality of the concepts or their symbols with regard to one another, we shall find that the faculty of abstraction already implies the intuition of a homogeneous medium. What we must say is that we have to do with two different kinds of reality, the one heterogeneous, that of sensible qualities, the other homogeneous, namely space. This latter, clearly conceived by the human intellect, enables us to use clean-cut distinctions, to count, to abstract, and perhaps also to speak.
Time, in so far as it is a homogenious medium, and not concrete duration, is reducible to space.
Now, if space is to be defined as the homogeneous, it seems that inversely every homogeneous and unbounded medium will be space. For, homogeneity here consisting in the absence of every quality, it is hard to see how two forms of the homogeneous could be distinguished from one another. Nevertheless it is generally agreed to regard time as an unbounded medium, different from space but homogeneous like the latter: the homogeneous is thus supposed to take two forms, according as its contents co-exist or follow one another. It is true that, when we make time a homogeneous medium in which conscious states unfold themselves, we take it to be given all at once, which amounts to saying that we abstract it from duration. This simple consideration ought to warn us that we are thus unwittingly falling back upon space, and really giving up time. Moreover, we can understand that material objects, being exterior to one another and to ourselves, derive both exteriorities from the homogeneity of a medium which inserts intervals
