Paths to Triviality

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. The final version of this research has been published in the Journal of Philosophical Logic. © 2015 Springer Verlag