a pure manifold distinct from the manifold of sense.[408] His belief that mathematical science is based upon pure intuition prevented him from recognising that though space may be a pure form of intuition, it can never by itself constitute a complete intuition. Its sole possible _content_ is the manifold of sense. But even apart from the fact that our apprehension of space is always empirically conditioned, Kant’s view of mathematical propositions as grounded in intuition is, as already observed, not itself tenable. For though intuitions may perhaps be the ultimate subject matter of geometry, concepts are its sole possible instruments. Intuitions yield scientific insight in exact proportion to our powers of restating their complex content in the terms of abstract thought. Until the evidence which they supply has been thus intellectually tested and defined, they cannot be accepted as justifying even the simplest proposition.[409] 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_).”