Professor Kitaro Nishida advocated his theory of "the contradictory self identity" (矛盾的自己同一) and "the active intuition" (行為的直観) in the problem of continuity of real number. His theories were influenced deeply by Buddhism. But Buddhism is religious teleology, and I have a doubt that Prof. Nishida built up his theories without criticism to the religious teleology of Buddhism. In this essay I have studied the propriety of his theories about the continuity of real number. My conclusion is that there is a contradiction between the concept of a point as a limitation of continuum and the concept of the continuity on the point itself. That is to say, the continuum has its original continuity, and its limitation by a point has no continuity. In spite of that, we intend to call up the original continuity on a point as limitation. This contradiction is not a mathematical problem but a philosophical one. So that the proofs on the continuity in mathematical arguments by R. Dedekind and G. Cantor are not sufficient. The mathematical theory that the infinitesimal is equal to zero is the theory with the intention of the solution of this contradiction. The intentional theory is subjective. This suggests that the theories of Prof. Nishida are also an intentional and subjective theories.
