On Classical Determinate Truth
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866918286868873216 |
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| author | Castaldo, Luca Nicolai, Carlo |
| author_facet | Castaldo, Luca Nicolai, Carlo |
| contents | 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 \emph{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 \emph{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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04316 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Classical Determinate Truth Castaldo, Luca Nicolai, Carlo Logic 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 \emph{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 \emph{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. |
| title | On Classical Determinate Truth |
| topic | Logic |
| url | https://arxiv.org/abs/2409.04316 |