Theories of Truth without Standard Models and Yablo’s Sequences

Studia Logica 96 (3):375-391 (2010)
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Abstract

The aim of this paper is to show that it’s not a good idea to have a theory of truth that is consistent but ω-inconsistent. In order to bring out this point, it is useful to consider a particular case: Yablo’s Paradox. In theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. Firstly, I exhibit some conceptual problems that follow from so introducing it. Secondly, I show that in second order theories with standard semantics the same procedure yields a theory that doesn’t have models. So, while having an ω- inconsistent theory is a bad thing, having an unsatisfiable theory of truth is actually worse. This casts doubts on whether the predicate in question is, after all, a truthpredicate for that language. Finally, I present some alternatives to prove an inconsistency adding plausible principles to certain theories of truth.

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Author's Profile

Eduardo Alejandro Barrio
Universidad de Buenos Aires (UBA)

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.
Paradox without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251-252.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.

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