2024/09/06 by Luca Castaldo, Castaldo, Luca, Carlo Nicolai +1
Psychology · #FOS: Mathematics #Logic (math.LO) #Philosophy and Theoretical Science
paper · doi:10.48550/arxiv.2409.04316
openalex publication_date 2024/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
The paper proposes and studies new classical, type-free theories of truth and determinateness with unprecedented features. The theories are fully compositional, strongly classical (namely, their internal and external logics are both classical), and feature a defined determinateness predicate satisfying desirable and widely agreed principles. The theories capture a conception of truth and determinateness according to which the generalizing power associated with the classicality and full compositionality of truth is combined with the identification of a natural class of sentences -- the determinate ones -- for which clear-cut semantic rules are available. Our theories can also be seen as the classical closures of Kripke-Feferman truth: their ω-models, which we precisely pinned down, result from including in the extension of the truth predicate the sentences that are satisfied by a Kripkean closed-off fixed point model. The theories compare to recent theories proposed by Fujimoto and Halbach, featuring a primitive determinateness predicate. In the paper we show that our theories entail all principles of Fujimoto and Halbach's theories, and are proof-theoretically equivalent to Fujimoto and Halbach's \cdplus. We also show establish some negative results on Fujimoto and Halbach's theories: such results show that, unlike what happens in our theories, the primitive determinateness predicate prevents one from establishing clear and unrestricted semantic rules for the language with type-free truth.