Model-theoretic semantics and revenge paradoxes

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 antirevenge 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.

A Unified Theory of Truth and Paradox

“…Liar sentences can be used to show that no classical evaluation satisfies NAÏVETÉ. For suppose that a classical evaluation e satisfies NAÏVETÉ, let λ be the sentence ¬Tr( λ ), Leitgeb, & Welch (2003), Halbach & Horsten (2006), Priest (2006), Cieśliński (2007), Field (2008), Beall (2009), Horsten (2009), Zardini (2011), Cobreros, Égré, Ripley, & van Rooij (2013), Field (2013), Nicolai & Rossi (2018), Murzi & Rossi (2019)). Moreover, the analysis of paradoxes has been instrumental to determine the expressive power of theories of truth (see e.g., Ketland (2003), Beall (2006Beall ( , 2007aBeall ( , 2007b, Cook (2007), Field (2007), Leitgeb (2007), Maudlin (2007), Priest (2007), Restall (2007), Scharp (2007), Simmons (2007), Shapiro (2011), Scharp (2013), Rossi (2019)). Finally, the investigation of semantic paradoxes has revealed connections between theories of truth and questions concerning coding, circularity, self-reference, and nonwell-foundedness (see e.g., Yablo (1985), Gaifman (1988), McCarthy (1988), Visser (1989), Gaifman (1992), Yablo (1993), Priest (1997), Yi (1999), Gaifman (2000), Beall (2001),…”

“…12 See e.g., Priest (2006), Field (2007), Beall (2009). 13 For arguments for the legitimacy of revenge-paradoxical notions, see e.g., Cook (2007), Leitgeb (2007), Scharp (2007Scharp ( , 2013, Rossi (2019), Murzi & Rossi (2019). The indefinite extensibility approach developed by Cook (2007Cook ( , 2009, Cook & Tourville (2016) and Schlenker (2010) does not refrain from interpreting revenge sentences.…”

“…5 Consider the treatment of liar and truth-teller sentences in fixed-point and revision theories: in both approaches, several models have to be considered to differentiate liar sentences, truth-teller sentences, and truths or falsities of the base language. 6 For discussion, see Field (2007), Leitgeb (2007), Rossi (2019). 7 The interest of the study of paradoxes goes well beyond the goal of interpreting the sentences of a language featuring a self-applicable truth predicate.…”

Analytic, Paradoxical, and Synthetic Sentences on ABC and The Hard Way Song Lyrics

“…The word cruel contradicts the word kind in meaning and it is not generally accepted that cruel can produce kind, that goodness can produce cruelty. Those two words do not come from the same concept so that this sentence is a paradoxical sentence that contains contradictive meanings, and they are directed against each other (Rossi, 2019).…”