Contextual-hierarchical reconstructions of the strengthened liar problem

• Autores: Christine Schurz
• Localización: Journal of Philosophical Logic, ISSN-e 1573-0433, Vol. 44, Nº. 5, 2015, págs. 517-550
• Idioma: inglés
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• Resumen

  • In this paper we shall introduce two types of contextual-hierarchical (from now on abbreviated by ‘ch’) approaches to the strengthened liar problem. These approaches, which we call the ‘standard’ and the ‘alternative’ ch-reconstructions of the strengthened liar problem, differ in their philosophical view regarding the nature of truth and the relation between the truth predicates T r n and T r n+1 of different hierarchy-levels. The basic idea of the standard ch-reconstruction is that the T r n+1-schema should hold for all sentences of Ln. In contrast, the alternative ch-reconstruction, for which we shall argue in section four, is motivated by the idea that T r n and T r n+1 are coherent in the sense that the same sentences of Ln should be true according to T r n and T r n+1. We show that instances of the standard ch-reconstruction can be obtained by iterating Kripke’s strong Kleene jump operator. Furthermore, we will demonstrate how instances of the alternative ch-reconstruction can be obtained by a slight modification of the iterated axiom system KF and of the iterated strong Kleene jump operator.