Self-Reference and the Problem of Antinomies

Abstract

In this paper, I try to give an account of situations in which self-reference is likely to occur. Generally, self-reference or circularity is relation in which something refers to itself (directly or via another, intermediate, objects). Self-referential objects sometimes lead to antinomies (inconsistencies) and sometimes do not. We can distinguish between vicious and innocuous self-referential objects. There is controversy whether all antinomies essentially involve some form of self-reference (S. Yablo has given an ingenious liar-style antinomy that, he claims, avoids self-reference). I suggest that self-reference is necessarily involved in finite antinomies, but not in infinity ones.