The principle of uniform solution (of the paradoxes of self-reference)

Abstract

Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell's Paradox, Burali-Forti's Paradox, Mirimanoff's Paradox, K6nig's Paradox, Berry's Paradox, Richard's Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell's Schema: there is a property 0 and function 3 such that (1) w = {xIO(x)) exists, and (2) if y is a subset of w, then