No more definite statement could be desired of the fact that though in arithmetical science as in other fields of study our processes of apprehension are subject to time, the quantitative relations determined by the science are independent of time and are intellectually apprehended. But if the above psychological interpretation of Kant’s teaching is untenable, how is his position to be defined? We must bear in mind the doctrine which Kant had already developed in his pre-Critical period, that mathematical differs from philosophical knowledge in that its concepts can have concrete individual form.[520] In the _Critique_ this difference is expressed in the statement that the mathematical sciences alone are able to _construct_ their concepts. And as they are _pure_ mathematical sciences, this construction is supposed to take place by means of the _a priori_ manifold of space and of time. Now though Kant had a fairly definite notion of what he meant by the construction of geometrical figures in space, his various utterances seem to show that in regard to the nature of arithmetical and algebraic construction he had never really attempted to arrive at any precision of view. To judge by the passage already quoted[521] from the _Dissertation_, Kant regarded space as no less necessary than time to the construction or intuition of number. ”[The intellectual concept of number] demands for its concrete actualisation the auxiliary notions of time _and space_ (in the successive addition and in the _juxtaposition of a plurality_)” A similar view appears in the _Critique_ in A 140 = B 179 and in B 15. In conformity, however, with the general requirements of his doctrine of _Schematism_, Kant defines the schema of number in exclusive reference to time; and, as we have noted, it is to this definition that Schulze appeals in support of his view of arithmetic as the science of counting and therefore of time. It at least shows that Kant perceived _some_ form of connection to exist between arithmetic and time. But in this matter Kant’s position was probably simply a corollary from his general view of the nature of mathematical science, and in particular of his view of geometry, the “exemplar”[522] of all the others. Mathematical science, as such, is based on intuition;[523] therefore arithmetic, which is one of its departments, must be so likewise. No attempt, however, is made to define the nature of the intuitions in which it has its source. Sympathetically interpreted, his statements may be taken as suggesting that arithmetic is the study of _series_ which find concrete expression in the order of sequent times. The following estimate, given by Cassirer,[524] does ample justice both to the true and to the false elements in Kant’s doctrine.