Studia Logica

, Volume 96, Issue 3, pp 375–391

Theories of Truth without Standard Models and Yablo’s Sequences

Article

DOI: 10.1007/s11225-010-9289-8

Cite this article as:
Barrio, E.A. Stud Logica (2010) 96: 375. doi:10.1007/s11225-010-9289-8

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

Yablo’s Paradox non-standard models ω-inconsistency theories of truth 

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Universidad de Buenos AiresBuenos AiresArgentina

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