Journal of Philosophical Logic 45 (3):237-276 (2016)

Authors
Tore Fjetland Øgaard
University of Bergen
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.
Keywords Contraction  Curry’s paradox  Identity  Leibniz’s law  Naïve truth theory  Naïve set theory  Paraconsistent logic  Relevant logic
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Reprint years 2016
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DOI 10.1007/s10992-015-9374-6
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References found in this work BETA

Saving Truth From Paradox.Hartry H. Field - 2008 - Oxford, England: Oxford University Press.
Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Spandrels of Truth.J. C. Beall - 2009 - Oxford, England: Oxford University Press.

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Citations of this work BETA

Prospects for a Naive Theory of Classes.Hartry Field, Harvey Lederman & Tore Fjetland Øgaard - 2017 - Notre Dame Journal of Formal Logic 58 (4):461-506.
Skolem Functions in Non-Classical Logics.Tore Fjetland Øgaard - 2017 - Australasian Journal of Logic 14 (1):181-225.
Substitution in Relevant Logics.Tore Fjetland Øgaard - 2019 - Review of Symbolic Logic (3):1-26.

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