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

Journal of Philosophy 117 (1):30-54 (2020)
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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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Lucas Rosenblatt
Universidad de Buenos Aires (UBA)

Citations of this work

Limits of Abductivism About Logic.Ulf Hlobil - 2020 - Philosophy and Phenomenological Research 103 (2):320-340.
Should the Non‐Classical Logician be Embarrassed?Lucas Rosenblatt - 2022 - Philosophy and Phenomenological Research 104 (2):388-407.
Paradoxicality Without Paradox.Lucas Rosenblatt - 2021 - Erkenntnis 88 (3):1347-1366.

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