The classical theory of definitions bans so-called circular definitions, namely, definitions of a unary predicate P, based on stipulations of the form $$Px =_{\mathsf {Df}} \phi,$$where ϕ is a formula of a fixed first-order language and the definiendumP occurs into the definiensϕ. In their seminal book The Revision Theory of Truth, Gupta and Belnap claim that “General theories of definitions are possible within which circular definitions [...] make logical and semantic sense” [p. IX]. In order to sustain their claim, they (...) develop in this book one general theory of definitions based on revision sequences, namely, ordinal-length iterations of the operator which is induced by the definition of the predicate. Gupta-Belnap’s approach to circular definitions has been criticised, among others, by D. Martin and V. McGee. Their criticisms point to the logical complexity of revision sequences, to their relations with ordinary mathematical practice, and to their merits relative to alternative approaches. I will present an alternative general theory of definitions, based on a combination of supervaluation and ω-length revision, which aims to address some criticisms raised against revision sequences, while preserving the philosophical and mathematical core of revision. (shrink)

We argue that distinct conditionals—conditionals that are governed by different logics—are needed to formalize the rules of Truth Introduction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field.

En ocasiones, las paradojas involucran principios constitutivos del significado. Priest sostiene que en todos los casos deberíamos retener los principios y aceptar las contradicciones resultantes, mientras que Eklund sugiere modificar los principios en todos los casos. En este artículo, afirmo que las diferentes respuestas son adecuadas para las distintas paradojas. En particular, para paradojas del tipo del mentiroso, es mejor quedarse con el esquema T, que caracteriza el significado de “verdadero”, y aceptar las conclusiones contradictorias; mientras que para la paradoja (...) sorites, uno debería modificar la premisa problemática de Tolerancia. Finalmente, elaboro una solución para la paradoja sorites, que contiene elementos del supervaluacionismo y de la teoría de la revisión. (shrink)