But though persistence of the older, un-Critical opposition between the intellectual and the sensuous was partly responsible for Kant’s readiness to regard as radical the very obvious differences between a category such as that of substance and attribute and the visual or tactual extendedness with which objects are endowed, it can hardly be viewed as the really decisive influence. That would rather seem to be traceable to Kant’s conviction that mathematical knowledge is unique both in fruitfulness and in certainty, and to his further belief that it owes this distinction to the _content_ character of the _a priori_ forms upon which it rests. For though the categories of the physical sciences are likewise _a priori_, they are exclusively _relational_,[447] and serve only to organise a material that is empirically given. To account for the superiority of mathematical knowledge Kant accordingly felt constrained to regard space and time as not merely _forms_ in terms of which we interpret the matter of sense, but as also themselves intuited _objects_, and as therefore possessing a character altogether different from anything which can be ascribed to the pure understanding. The opposition between forms of sense and categories of the understanding, in the strict Kantian mode of envisaging that opposition, is thus inseparably bound up with Kant’s doctrine of space and time as being not only forms of intuition, but as also in their purity and independence themselves intuitions. _Even the sensuous subject matter of pure mathematics_--so Kant would seem to contend--_is_ a priori _in nature_. If this latter view be questioned--and to the modern reader it is indeed a stone of stumbling--much of the teaching of the _Aesthetic_ will have to be modified or at least restated. =Fifth (in second edition, Fourth) Argument.=--This argument is quite differently stated in the two editions of the _Critique_, though the purpose of the argument is again in both cases to prove that space is an intuition, not a general concept. In the first edition this is proved by reference to the fact that space is given as an infinite magnitude. This characteristic of our space representation cannot be accounted for so long as it is regarded as a concept. A general conception of space which would abstract out those properties and relations which are common to all spaces, to a foot as well as to an ell, could not possibly determine anything in regard to magnitude. For since spaces differ in magnitude, any one magnitude cannot be a common quality. Space is, however, given us as determined in magnitude, namely, as being of infinite magnitude; and if a general conception of space relations cannot determine magnitude, still less can it determine infinite magnitude. Such infinity must be derived from limitlessness in the progression of intuition. Our conceptual representations of infinite magnitude must be derivative products, acquired from this intuitive source.