Logic and Language

Julien Murzi (Salzburg): Instability and Revenge

Speaker: Julien Murzi (Salzburg)
Title: Instability and Revenge
Time: 16:00 - 17:30
Location: ILLC Seminar Room F1.15

Abstract: It is standardly held that paracomplete theories of truth and related notions are incapable of expressing a nonstratified notion of paradoxicality. In this paper, I show that the noncontractive theory defended by Elia Zardini in a number of recent publications (Zardini, 2011, 2013a,c), which is based on a multiplicative affine logic, suffers from the same limitation. The argument depends on interpreting the claim that a sentence A is paradoxical as follows: adding to a theory T a rule that permits structural contraction on A yields inconsistency, and hence triviality. In short: contraction on f explodes T. The notion of being a sentence such that contraction on it explodes a given theory seems an intelligible one. However, as I show, it cannot be defined in Zardini‚Äôs framework, on pain of inconsistency.