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From Paradox to Truth

An Introduction to Self-reference in Formal Language

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Language, Logic, and Computation (TbiLLC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13206))

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Abstract

We present a short introduction to the logical analysis of truth and related concepts. We examine which assumptions are implicit in the paradoxes of truth and self-reference, and present some of the important formal theories of truth that have arisen out of these considerations.

This paper was presented by the author in three lectures at the Thirteenth International Tbilisi Symposium on Language, Logic and Computation held in Batumi, Georgia in September 2019, and is based on work by the author and Volker Halbach [10]. The author would like to thank the anonymous referee for their comments and improvements. The work was supported by the Knut and Alice Wallenberg Foundation (grant no. 2015.0179) and Swedish Research Council VR (grant no. 2017-05111).

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Notes

  1. 1.

    Throughout this article we assume familiarity with the basic concepts of first-order logic, such as in [6].

  2. 2.

    For the present work we consider a theory \( S \) to be inconsistent if every formula of the language is derivable in \( S \).

  3. 3.

    For a proof of McGee’s theorem in the context of syntax theories, including clarification of additional syntactic assumptions, we refer the reader to [10].

  4. 4.

    As with \( \textit{CT}\), our definition of \( \textit{KF}\) brushes over some important details. We refer the interested reader to [9] for an axiomatisation of \( \textit{KF}\) and other theories of truth; the monograph [7] provides a detailed introduction to axiomatic theories of truth.

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Author information

Authors and Affiliations

  1. Department of Philosophy, Linguistics and Theory of Science, University of Gothenburg, Gothenburg, Sweden

    Graham E. Leigh

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  1. Graham E. Leigh
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Correspondence to Graham E. Leigh .

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Editors and Affiliations

  1. University of Amsterdam, Amsterdam, The Netherlands

    Aybüke Özgün

  2. Heinrich Heine University Düsseldorf, Düsseldorf, Germany

    Yulia Zinova

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Leigh, G.E. (2022). From Paradox to Truth. In: Özgün, A., Zinova, Y. (eds) Language, Logic, and Computation. TbiLLC 2019. Lecture Notes in Computer Science, vol 13206. Springer, Cham. https://doi.org/10.1007/978-3-030-98479-3_17

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  • DOI: https://doi.org/10.1007/978-3-030-98479-3_17

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  • Print ISBN: 978-3-030-98478-6

  • Online ISBN: 978-3-030-98479-3

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