Jump liars and Jourdain's card via the relativized t-scheme

Studia Logica 91 (2):239 - 271 (2009)
Abstract
A relativized version of Tarski’s T-scheme is introduced as a new principle of the truth predicate. Under the relativized T-scheme, the paradoxical objects, such as the Liar sentence and Jourdain’s card sequence, are found to have certain relative contradictoriness. That is, they are contradictory only in some frames in the sense that any valuation admissible for them in these frames will lead to a contradiction. It is proved that for any positive integer n , the n -jump liar sentence is contradictory in and only in those frames containing at least an n -jump odd cycle. In particular, the Liar sentence is contradictory in and only in those frames containing at least an odd cycle. The Liar sentence is also proved to be less contradictory than Jourdain’s card sequence: the latter must be contradictory in those frames where the former is so, but not vice versa . Generally, the relative contradictoriness is the common characteristic of the paradoxical objects, but different paradoxical objects may have different relative contradictoriness.
Keywords graph theory  Jourdain’s card paradox  Liar paradox  relativized T-scheme  revision theory of truth
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References found in this work BETA
Anil Gupta (1982). Truth and Paradox. Journal of Philosophical Logic 11 (1):1-60.
Hans G. Herzberger (1982). Notes on Naive Semantics. Journal of Philosophical Logic 11 (1):61 - 102.

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Citations of this work BETA
Ming Hsiung (2013). Equiparadoxicality of Yablo's Paradox and the Liar. Journal of Logic, Language and Information 22 (1):23-31.
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