Maximal Non-trivial Sets of Instances of Your Least Favorite Logical Principle

Journal of Philosophy 117 (1):30-54 (2020)

Abstract

The paper generalizes Van McGee's well-known result that there are many maximal consistent sets of instances of Tarski's schema to a number of non-classical theories of truth. It is shown that if a non-classical theory rejects some classically valid principle in order to avoid the truth-theoretic paradoxes, then there will be many maximal non-trivial sets of instances of that principle that the non-classical theorist could in principle endorse. On the basis of this it is argued that the idea of classical recapture, which plays such an important role for non-classical logicians, can only be pushed so far.

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2020-01-25

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Lucas Rosenblatt
University of Buenos Aires

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Citations of this work

Limits of Abductivism About Logic.Ulf Hlobil - 2021 - Philosophy and Phenomenological Research 103 (2):320-340.
Classical Recapture and Maximality.Lucas Rosenblatt - 2021 - Philosophical Studies 178 (6):1951-1970.
Non-reflexivity and Revenge.Julien Murzi & Lorenzo Rossi - 2022 - Journal of Philosophical Logic 51 (1):201-218.
Paradoxicality Without Paradox.Lucas Rosenblatt - forthcoming - Erkenntnis:1-20.

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