Paths to Triviality

Journal of Philosophical Logic 45 (3):237-276 (2016)
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Abstract
This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann constant. An overview over various ways to formulate Leibniz’s law in non-classical logics and two new triviality proofs for naïve set theory are also provided.
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Archival date: 2019-06-28
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