Erkenntnis:1-32 (forthcoming)

Authors
Luca Castaldo
University of Warsaw
Abstract
This article compares classical and nonclassical axiomatisations of the fixed-point semantics developed by Kripke : 690–716, 1975). Following the line of investigation of Halbach and Nicolai : 227–257, 2018), we do not compare KF and PKF qua theories of truth simpliciter, but rather qua axiomatisations of the Kripkean conception of truth. We strengthen the central results of Halbach and Nicolai and Nicolai : 101–130, 2018), showing that, on the one hand, there is a stronger sense in which some variants of KF and some variants of PKF can be taken to be, truth-theoretically, equivalent. On the other hand, we show that this truth-theoretical equivalence is not preserved by some other variants of KF and PKF, arguing that the PKF variants are more adequate axiomatisations of the fixed-point semantics than the corresponding KF variants.
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DOI 10.1007/s10670-021-00397-7
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References found in this work BETA

Saving Truth From Paradox.Hartry Field - 2008 - Oxford, England: Oxford University Press.
Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.
Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.

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