Notes on ω-inconsistent theories of truth in second-order languages

Review of Symbolic Logic 6 (4):733-741 (2013)
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Abstract

It is widely accepted that a theory of truth for arithmetic should be consistent, but -consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adopting -inconsistent theories of truth are considered: the revision theory of nearly stable truth T # and the classical theory of symmetric truth FS. Briefly, we present some conceptual problems with ω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.

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Author Profiles

Lavinia Maria Picollo
National University of Singapore
Eduardo Alejandro Barrio
Universidad de Buenos Aires (UBA)

Citations of this work

Truth without standard models: some conceptual problems reloaded.Eduardo Barrio & Bruno Da Ré - 2018 - Journal of Applied Non-Classical Logics 28 (1):122-139.
Classical Determinate Truth I.Kentaro Fujimoto & Volker Halbach - forthcoming - Journal of Symbolic Logic:1-44.

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References found in this work

Truth and paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
Notes on naive semantics.Hans Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
An Axiomatic Approach to Self-Referential Truth.Harvey Friedman & Michael Sheard - 1987 - Annals of Pure and Applied Logic 33 (1):1--21.

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