Axiom of Infinity and Plato’s Third Man

Abstract

As a contribution to the critical appreciation of a central thesis in Russell’s philosophical logic, I consider the Third Man objection to Platonic realism in the philosophy of mathematics, and argue that the Third Man infinite regress, for those who accept its assumptions, provides a worthy substitute for Whitehead and Russell’s Axiom of Infinity in positing a denumerably infinite set or series onto which other sets, series, and formal operations in the foundations of mathematics can be mapped.