Antinomies and the Foundational Problem of Mathematics(Ⅲ)

Abstract:

      A basic principle closely related to Russell's "vicious circle principle" is the statement that "any set (aggregate) cannot be an element of itself". The principal object of this article is to draw a clear distinction between the two principles just mentioned by classifying the forms of impredicative definition into three different kinds. Detailed exposition has been given in §1. Other parts of the article are devoted to analysis & discussion of Tarski's semantics and Godel's incompleteness theorem in relation to some antinomies. Finally the source problem concerning various antinomies has been briefly discussed.