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Studia Logica

, Volume 91, Issue 2, pp 239–271 | Cite as

Jump Liars and Jourdain’s Card via the Relativized T-scheme

  • Ming HsiungEmail author
Article

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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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.School of Mathematics and Computational ScienceSun Yat-Sen UniversityGuangzhouP. R. China
  2. 2.School of Politics and AdministrationSouth China Normal UniversityGuangzhouP. R. China

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