ABSTRACT
According to the iterative concept, a set is something obtainable from some basic objects by iterated applications of the rich operation 'set of' which permits the collecting together of any multitude of 'given' objects or any part thereof into a set. This process includes transfinite iterations. The iterative concept seems close to Cantor's original idea, and has been, in one form or another, developed and emphasized by Mirimanoff, von Neumann, Zermelo, Bernays, and Godel. The reactions of Frege and Cantor to the paradoxes were sharply different and can be described as the bankruptcy theory versus the misunderstanding theory. The central problems of iterative concept are: the power set operation; ordinal numbers. Both involve an element of unlimited generality which cannot be rendered completely explicit. Set theory has been compared to geometry and to physics. The author's discusses the Cantor's views by reference to his collected works. It is relatively easy to be dissatisfied with Cantor's philosophical speculations on the transfinite.
