The complicated ambiguities of Kant’s treatment of space may be illustrated and further clarified by discussion of another difficulty. Is space a totum analyticum or a totum syntheticum? Does the whole precondition the parts, or does it arise through combination of the parts? Or to ask another but connected question, do we intuit infinitude, or is it conceptually apprehended only as the presupposition of our limited intuitions? To these questions diametrically opposite answers can be cited from the Critique. As we have above noted, Kant teaches in the Aesthetic that space is given as a whole, and that the parts arise only by limitation of it. But in A 162 = B 203 we find him also teaching that a magnitude is to be entitled extensive
“...when the representation of the parts makes possible, and therefore necessarily precedes, the representation of the whole. I cannot represent to myself a line, however small, without drawing it in thought, i.e. generating from a point all its parts one after another, and thus for the first time recording this intuition.”[410]
He adds in the second edition[411] that extensive magnitude cannot be apprehended save through a “synthesis of the manifold,” a “combination of the homogeneous.”
The note which Kant appends to B 136 is a very strange combination of both views. It first of all reaffirms the doctrine of the Aesthetic that space and time are not concepts, but intuitions within which as in a unity a multitude of representations are contained; and then proceeds to argue that space and time, as thus composite, must presuppose an antecedent synthesis. In A 505 = B 533 we find a similar attempt to combine both assertions.
“The parts of a given appearance are first given through and in the regress of decomposing synthesis (decomponirenden Synthesis).”
The clash of conflicting tenets which Kant is striving to reconcile could hardly find more fitting expression than in this assertion of an analytic synthesis. The same conflict appears, though in a less violent form, in A 438 = B 466.
“Space should properly be called not compositum but totum, since its parts are possible only in the whole, not the whole through the parts. It might, indeed, be said to be a compositum that is ideale, but not reale. That, however, is a mere subtlety.”[412]
The arguments by which Kant proves space to be an a priori intuition rest upon the view that space is given as infinite, and that its parts arise through limitation of this prior-existent whole. But a principle absolutely fundamental to the entire Critique is the counter principle, that all analysis rests upon and presupposes a previously exercised synthesis. Synthesis or totality as such can never be given. Only in so far as a whole is synthetically constructed can it be apprehended by the mind. Representation of the parts precedes and renders possible representation of the whole.
The solution of the dilemma arising out of these diverse views demands the drawing of two distinctions. First, between a synthesised totality and a principle of synthesis; the former may involve a prior synthesis; the latter does not depend upon synthesis, but expresses the predetermined nature of some special form of synthesis. Secondly, it demands a distinction between the a priori manifolds of space and time and the empirical manifold which is apprehended in and through them. This, as we have already noted, is a distinction difficult to take quite seriously, and is entirely unsupported by psychological evidence. But it would seem to be insisted upon by Kant, and to have been a determining factor in the formulation of several of his main doctrines.
In terms of the first distinction we are compelled to recognise that the view of space which underlies the Aesthetic is out of harmony with the teaching of the Analytic. In the Aesthetic Kant interprets space not merely as a form of intuition but also as a formal intuition, which is given complete in its totality, and which is capable of being apprehended independently of its empirical contents, and even prior to them. That would seem to be the view of space which is presupposed in Kant’s explanation of pure mathematical science. The passages from the Analytic, quoted above, are, however, its express recantation. Space, as the intuition of a manifold, is a totum syntheticum, not a totum analyticum. It is constructed, not given. The divergence of views between the Aesthetic and the Analytic springs out of the difficulty of meeting at once the logical demands of a world which Kant conceives objectively, and the psychological demands which arise when this same world is conceived as subjectively conditioned. In principle, the whole precedes the parts; in the process of being brought into existence as an intuition, the parts precede the whole. The principle which determines our apprehension of any space, however small or however large, is that it exists in and through universal space. This is the principle which underlies both the synthetic construction of space and also its apprehension once it is constructed. In principle, therefore, i.e. in the order of logical thought, the whole precedes the parts.[413] The process, however, which this principle governs and directs, cannot start with space as a whole, but must advance to it through synthesis of smaller parts.