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KF, PKF and Reinhardt’s Program

Luca Castaldo & Johannes Stern

Review of Symbolic Logic (1):33-58 (2022)

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Implicit commitments of instrumental acceptance: A case study.Luca Castaldo & Maciej Głowacki - forthcoming - Philosophical Quarterly.details When accepting an axiomatic theory S, we are implicitly committed to various statements that are independent of its axioms. Examples of such implicit commitments include consistency statements and reflection principles for S. While foundational acceptance has received considerable attention in this context, the study of implicit commitments triggered by weaker notions remains underdeveloped. This article extends the analysis investigating implicit commitments inherent in instrumental acceptance, comparing them with the implicit commitments involved in foundational acceptance. Concentrating on Reinhardt’s instrumentalism vis-à-vis Kripke–Feferman (...) Download Export citation Bookmark
Saving logic from paradox via nonclassical recapture.Luca Castaldo - 2024 - Philosophical Studies 181 (6):1547-1563.details The Liar paradox arguably shows that a coherent and self-applicable notion of truth is governed by nonclassical logic. It then seems natural to conclude that classical logic is inadequate for defining a truth theory. In this article, we argue that this is not the case. In the spirit of Reinhardt (Math Logic Formal Syst 94:227, 1985; J Philos Logic 15:219–251, 1986), and in analogy with Hilbert’s program for the foundation of classical mathematics, we will articulate an instrumentalist justification for the (...) Download Export citation Bookmark
In defence of PKF.Ian Rumfitt - 2023 - Synthese 201 (2):1-21.details I advance arguments in favour of PKF as an articulation of a central sense of the predicate ‘true’, and show how it illuminates the relationship between that sense and the ‘external’ notion of truth found in such claims as ‘An utterance of the Liar Sentence does not say anything, and so is not true’. Download Export citation Bookmark 2 citations
Notes on Models of (Partial) Kripke–Feferman Truth.Luca Castaldo - 2023 - Studia Logica 111 (1):83-111.details This article investigates models of axiomatizations related to the semantic conception of truth presented by Kripke (J Philos 72(19):690–716, 1975), the so-called _fixed-point semantics_. Among the various proof systems devised as a proof-theoretic characterization of the fixed-point semantics, in recent years two alternatives have received particular attention: _classical systems_ (i.e., systems based on classical logic) and _nonclassical systems_ (i.e., systems based on some nonclassical logic). The present article, building on Halbach and Nicolai (J Philos Log 47(2):227–257, 2018), shows that there (...) Download Export citation Bookmark
Is the HYPE about strength warranted?Martin Fischer - 2022 - Synthese 200 (3):1-25.details In comparing classical and non-classical solutions to the semantic paradoxes arguments relying on strength have been influential. In this paper I argue that non-classical solutions should preserve the proof-theoretic strength of classical solutions. Leitgeb’s logic of HYPE is then presented as an interesting possibility to strengthen FDE with a suitable conditional. It is shown that HYPE allows for a non-classical Kripkean theory of truth, called KFL, that is strong enough for the relevant purposes and has additional attractive properties. Download Export citation Bookmark 1 citation
On the Costs of Classical Logic.Luca Castaldo - 2021 - Erkenntnis 88 (3):1157-1188.details This article compares classical (or -like) and nonclassical (or -like) axiomatisations of the fixed-point semantics developed by Kripke (J Philos 72(19): 690–716, 1975). Following the line of investigation of Halbach and Nicolai (J Philos Logic 47(2): 227–257, 2018), we do not compare and qua theories of truth simpliciter, but rather qua axiomatisations of the Kripkean conception of truth. We strengthen the central results of Halbach and Nicolai (2018) and Nicolai (Stud Log 106(1): 101–130, 2018), showing that, on the one hand, (...) Download Export citation Bookmark 2 citations

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