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  1. Paths to Triviality.Tore Fjetland Øgaard - 2016 - Journal of Philosophical Logic 45 (3):237-276.
    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 (...)
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  • Reply to Bjørdal.Zach Weber - 2011 - Review of Symbolic Logic 4 (1):109-113.
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  • Transfinite Numbers in Paraconsistent Set Theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
    This paper begins an axiomatic development of naive set theoryin a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead (...)
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  • Relevantism, Material Detachment, and the Disjunctive Syllogism Argument.R. Routley - 1984 - Canadian Journal of Philosophy 14 (2):167 - 188.