ABSTRACT
Those who have objected to infinity have not, as a rule, thought it worth while to exhibit precise contradictions in it. To have done so is one of the great merits of Kant. Of the mathematical antinomies, the second, which is concerned, essentially, with the question whether or not the continuum has elements, was resolved in the preceding chapter, on the supposition that there may be an actual infinite-that is, it was reduced to the question of infinite number. The first antinomy is concerned with the infinite, but in an essentially temporal form; for Arithmetic, therefore, this antinomy is irrelevant, except on the Kantian view that numbers must be schematized in time. This view is supported by the argument that it takes time to count, and therefore without time we could not know the number of anything. By this argument we can prove that battles always happen near telegraph wires, because if they did not we should not hear of them. In fact, we can prove generally that we know what we know. But it remains conceivable that we don’t know what we don’t know; and hence the necessity of time remains unproved.
