A Unified Theory of Truth and Paradox

Abstract

The sentences employed in semantic paradoxes display a wide range of semantic behaviours. However, the main theories of truth currently available either fail to provide a theory of paradox altogether, or can only account for some paradoxical phenomena by resorting to multiple interpretations of the language, as in (Kripke, 1975). In this article, I explore the wide range of semantic behaviours displayed by paradoxical sentences, and I develop a unified theory oftruth and paradox, that is a theory of truth that also provides a unified account of paradoxical sentences. The theory I propose here yields a threefold classification of paradoxical sentences—liar-like sentences, truth-teller–like sentences, and revenge sentences. Unlike existing treatments of semantic paradox, the theory put forward in this article yields a way of interpreting all three kinds of paradoxical sentences, as well as unparadoxical sentences, within a single model.

Modes of Truth

“…For simplicity, we present a theory in which the paradoxical sentences are exactly the sentences that are in the gap of a suitable minimal Kripkean fixed point (see . See Rossi (2019Rossi ( , 2021 for details on how to extend the theory to languages with richer vocabularies, in which further semantic notions, including revenge-breeding notions, can be formulated. 21.…”

Paradoxicality in Kripke’s theory of truth

“…Gupta (1982)); (iv) the inclosure-based conception (see Priest (1994)); and (v) the graph-theoretic conception (cf. Walicky (2017) and Rossi (2019), for a couple of recent examples). Some of these conceptions intend to cover all sorts of paradoxes.…”

Fixed-point models for paradoxical predicates

“…The framework introduce below, on the other hand, is a more familiar Kripkean-style fixed-point semantics, where models are set-theoretic structures built inductively using a monotone operator on the powerset of ω. In any case, considering the similarity of the motivations for this project and that of[Ros19]'s, I will refer to Rossi's paper elsewhere in this article in order to point out some similarities and differences.20 For an overview on paraconsistent logics, see e.g [Pri02,Rip15]…”

“…Let me mention that in[Ros19]'s canonical evaluation, revenge sentences are assigned a set of equations with no solution in the value space.57 See [Bea07, Sha11, Sch13, MR20] for an overview. 58 This hope is what underlies e.g.…”

“…It may be worth mentioning that in[Ros19], the McGee sentence has the same status as Liars and Curry sentences.Australasian Journal of Logic (18:7) 2021, Article no. 2…”