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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Author's Profile

Tore Fjetland Øgaard
University of Bergen (PhD)

Citations of this work

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.
Structural Weakening and Paradoxes.Bruno Da Ré - 2021 - Notre Dame Journal of Formal Logic 62 (2):369-398.

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References found in this work

Saving truth from paradox.Hartry H. Field - 2008 - New York: Oxford University Press.
Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
Spandrels of truth.J. C. Beall - 2009 - New York: Oxford University Press.

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