Thibault Rushbrooke: 'Self-Dependence and the Liar Paradox'
Chair: Florent Dumont
Ramsey (1925) influentially criticised Russell’s (1903) view that Russell’s Paradox and the Liar Paradox, among others, are fundamentally the same type of antinomy. Instead, Ramsey argued that these paradoxes should be separated into two distinct categories: those involving only logical or mathematical notions, and those involving semantic notions. He placed Russell’s Paradox in the first category, and the Liar Paradox in the second. Since then, whether Russell’s Paradox and the Liar are the same type of paradox has been a matter of lively debate (e.g. Priest, 1994).
In this talk, I’ll identify a feature which is common to both Russell’s Paradox, and the Liar. Working within the framework of a certain formal theory of propositions, I’ll define a relation of ‘dependence’ between propositions. I’ll then argue that both the Russell sentence and the Liar sentence express a proposition which depends on itself. To my knowledge, this particular mode of self-dependence has not been observed before, especially regarding the Liar. I’ll suggest that this self-dependence at least partially explains why both paradoxes arise, and conclude, pace Ramsey, that they are paradoxes of the same fundamental type.
