Abstract

This paper is concerned with a general account of logicism as developed within Russell’s philosophy of mathematics. At first Russell’s approach in metaphysic was idealistic and he relied on this point of view for extending his platonic atomism. To expound this account it will be demonstrated that after developing platonic atomism, Russell attempted to present his logicism in The Principles of Mathematics as a view opposed to an idealistic account of mathematics. However, a number of paradoxes arose had their roots deep in Russell’s metaphysical views. At this point he was forced to moderate his realistic extreme approach. Afterward it is shown that to evade these paradoxes, Russell adopts a view that allows for ontological distinctions and then introduces a full-fledged theory of types in Principia Mathematica. Nevertheless, the new framework yields problems of its own that pose a threat to Russell’s object-centered metaphysics but also deprives him of handling truths of unrestricted generality. Then to present a final version of his logicism, Russell’s way out of these issues will be set forth which comes in form of axioms of reducibility and infinity. Although these axioms represent a solution to remove paradoxes, actually those are too complicated to use.