Model-theoretic semantics and revenge paradoxes

Lorenzo Rossi

doi:10.1007/s11098-018-1041-7

Abstract

Revenge arguments purport to show that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate. In this paper, I focus on revenge arguments that employ the model-theoretic semantics of a target theory and I argue, contra the current revenge-theoretic wisdom, that they can constitute genuine expressive limitations. I consider the anti-revenge strategy elaborated by Field (J Philos Log 32:139–177, 2003; Revenge of the Liar, Oxford University Press, Oxford, pp 53–144, 2007; Saving truth from paradox, Oxford University Press, Oxford, 2008, §§21–23) and argue that it does not offer a way out of the revenge problem. More generally, I argue that the difference between ‘standard’ and ‘revenge’ paradoxes is ill-conceived and should be abandoned. This will contribute to show that the theories that provide a uniform account of truth and other semantic notions are the ones best equipped to avoid the paradoxes altogether—‘standard’ and ‘revenge’ alike.

Highlights

Prima facie, revenge paradoxes can be characterized as arguments to the effect that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate
Revenge arguments are typically used to conclude that revenge-prone theories do not solve the semantic paradoxes in general: even though they avoid the ‘standard’ semantic paradoxes, they suffer from new, structurally similar antinomies, that can only be avoided at the cost of significant expressive limitations
The growing attention which truth theorists devote to revenge paradoxes witnesses that they are considered to be worthy of attack

Summary

Introduction

Revenge paradoxes can be characterized as arguments to the effect that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate Such paradoxes often make use of notions employed in the theories they are directed against, and are argued to be similar to. I will argue that the difference between ‘standard’ and ‘revenge’ paradoxes is ill-conceived and should be abandoned. 5 I discuss a possible rejoinder, namely the idea that the MTsemantics is a mere tool to prove non-triviality results and, as such, it does not characterize genuine semantic notions; I argue that this reply fails to neutralize MT-revenge arguments.

Paradoxes and revenge

Field on MT-revenge

Intelligibility and extensions

Model-theoretic instrumentalism

Concluding remarks