Theories of truth without standard models and Yablo's sequences

Studia Logica 96 (3):375-391 (2010)
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
Keywords Truth  Yablo's Paradox  omega-inconsistency
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    References found in this work BETA
    Solomon Feferman (1991). Reflecting on Incompleteness. Journal of Symbolic Logic 56 (1):1-49.
    Volker Halbach, Axiomatic Theories of Truth. Stanford Encyclopedia of Philosophy.

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    Volker Halbach, Axiomatic Theories of Truth. Stanford Encyclopedia of Philosophy.
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