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  1. On the Costs of Classical Logic.Luca Castaldo - forthcoming - Erkenntnis:1-32.
    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 (...)
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  • Is the HYPE about strength warranted?Martin Fischer - 2022 - Synthese 200 (3):1-25.
    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.
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