Provably True Sentences Across Axiomatizations of Kripke’s Theory of Truth

Studia Logica 106 (1):101-130 (2018)
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Abstract

We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘\-like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules are all valid in fixed-point models; the second by ‘\-like’ theories first introduced by Solomon Feferman, that lose this property but reflect the classicality of the metatheory in which Kripke’s construction is carried out. We show that to any natural system in one cluster—corresponding to natural variations on induction schemata—there is a corresponding system in the other proving the same sentences true, addressing a problem left open by Halbach and Horsten and accomplishing a suitably modified version of the project sketched by Reinhardt aiming at an instrumental reading of classical theories of self-applicable truth.

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Carlo Nicolai
King's College London

Citations of this work

The power of naive truth.Hartry Field - 2022 - Review of Symbolic Logic 15 (1):225-258.
On the Costs of Nonclassical Logic.Volker Halbach & Carlo Nicolai - 2018 - Journal of Philosophical Logic 47 (2):227-257.
KF, PKF and Reinhardt’s Program.Luca Castaldo & Johannes Stern - 2022 - Review of Symbolic Logic (1):33-58.

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References found in this work

Saving truth from paradox.Hartry H. Field - 2008 - New York: Oxford University Press.
Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.
A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Reflecting on incompleteness.Solomon Feferman - 1991 - Journal of Symbolic Logic 56 (1):1-49.

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