Vol. 31 Nro. 1 (2011)
Articles

Teorías de la verdad sin modelos estándar: Un nuevo argumento para adoptar jerarquías

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  • Eduardo A. Barrio
Eduardo A. Barrio
Universidad de Buenos Aires / CONICET / GAF
DOI: https://doi.org/10.36446/af.2011.120

Published 2011-05-01

Keywords

  • Truth,
  • Omega-Inconsistency,
  • Non-Standard Models
  • Verdad,
  • Omega-inconsistencia,
  • Modelos no-estándar
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Abstract

In this paper, I have two different purposes. Firstly, I want to show that it's not a good idea to have a theory of truth that is consistent but omega-inconsistent. In order to bring out this point, it is useful to consider a particular case: FS (Friedman-Sheard). I argue that in First-order languages omega-inconsistency implies that a theory of truth has not standard model. Then, there is no model whose domain is the set of natural numbers in which this theory of truth could acquire a consistent interpretation. So, in theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. I add that in Higher-order languages the situation is even worst. In second order theories with standard semantic the same introduction produces a theory that doesn't have a model. So, if an omega-inconsistent theory of truth is bad, an unsatisfiable theory is really bad. Secondly, I propose to give up the union principle of theories FSn and accept an indefinite extensibility of theories FS0, FS1, FS2, FS3, ... According to my view, the sequence of theories has the same virtues of FS without its disgusting consequences.

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