The Fallacy in Russell’s Schema

Abstract

An analysis of the paradoxes of self-reference, which Bertrand Russell initiated, exposes the common fallacy in them, and has consequences for some of Graham Priest’s work. Notably it undermines his defence of the Domain Principle, and his consequent belief that there are true contradictions. Use of Hilbert’s epsilon calculus shows, instead, that we must allow for indeterminacy of sense in connection with paradoxes of self-reference.