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Journal of Philosophical Logic

, Volume 44, Issue 5, pp 517–550 | Cite as

Contextual-Hierarchical Reconstructions of the Strengthened Liar Problem

  • Christine Schurz
Article
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Abstract

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 \(\mathcal {L}^{n}\). 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 \(\mathcal {L}^{n}\) 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.

Keywords

Truth Liar paradox Context Hierarchy 

Notes

Acknowledgments

Preparatory material of this paper can be found in my PhD-thesis (cf. Christine Schurz [14]). This paper is however a substantial extension of what has been done there. I would like to thank Hans Czermak, Alexander Hieke, Reinhard Kleinknecht and Hannes Leitgeb for their help and support, as well as two anonymous referees for their valuable comments.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.WalsAustria

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