Document Type : Research Paper

Authors

• Masoomeh Ali Hassanzadeh Asl ¹
• Masoud Omid ²

¹ MA of Philosophy, University of Tabriz

² Associate Professor of Philosophy Department, University of Tabriz

Abstract

This dissertation is concerned with a general account of Logicism as developed within Russell’s philosophy of mathematics. 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 that had their roots deep in Russell’s metaphysical views. 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. He 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.

Keywords

• Mathematics Philosophy
• Russell
• Logicism
• Set Theory
• On Denoting