Nonclassical Truth with Classical Strength. A Proof-Theoretic Analysis of Compositional Truth Over Hype

Review of Symbolic Logic 16 (2):425-448 (2023)
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Abstract

Questions concerning the proof-theoretic strength of classical versus nonclassical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of fixed-point semantics. It is known that nonclassical axiomatizations in four- or three-valued logics are substantially weaker than their classical counterparts. In this paper we consider the addition of a suitable conditional to First-Degree Entailment—a logic recently studied by Hannes Leitgeb under the label HYPE. We show in particular that, by formulating the theory PKF over HYPE, one obtains a theory that is sound with respect to fixed-point models, while being proof-theoretically on a par with its classical counterpart KF. Moreover, we establish that also its schematic extension—in the sense of Feferman—is as strong as the schematic extension of KF, thus matching the strength of predicative analysis.

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Author Profiles

Carlo Nicolai
King's College London
Pablo Dopico
King's College London
Martin Fischer
Ludwig Maximilians Universität, München

Citations of this work

Dream of Recapture.Carlo Nicolai - 2022 - Analysis 82 (3):445-450.
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References found in this work

Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Saving truth from paradox.Hartry Field - 2008 - New York: Oxford University Press.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.
Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - New York: Cambridge University Press. Edited by Jan Von Plato.

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