ABSTRACT
1. It has been shown that the foundations of arithmetic were obscured by confused metaphysical discussion, and that the theory of classes developed from the confused idealism of Cantor. A similar statement may be made concerning classical mathematical analysis. It may be said that the very mathematicians who sought to remain within the domain of accurate reasoning made no progress and did not attain the desired end. On the other hand those who did not hesitate to trust their vision of reality triumphed decisively.
