Abstract

BARRIO, Eduardo Alejandro. Teorías de la verdad sin modelos estándar: Un nuevo argumento para adoptar jerarquías. Anal. filos. [online]. 2011, vol.31, n.1, pp.7-32. ISSN 1851-9636.

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.

Keywords : Truth; Omega-Inconsistency; Non-Standard Models.

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