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Page 1 of 5

  • 1 - Aims and Ends

  • Volker Halbach, University of Oxford, Graham E. Leigh, University of Gothenburg, Sweden
  • Book:
    The Road to Paradox
    Published online:
    17 October 2024
    Print publication:
    31 October 2024, pp 5-12
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  • Summary

    This chapter provides an introduction to and an overview of the themes and content of the monograph.

  • 6 - The Paradoxes

  • Volker Halbach, University of Oxford, Graham E. Leigh, University of Gothenburg, Sweden
  • Book:
    The Road to Paradox
    Published online:
    17 October 2024
    Print publication:
    31 October 2024, pp 75-118

  • Summary

    Some simple applications of the diagonal lemma are given. Many of the well-known paradoxes (liar, Montague’s, Yablo’s, Curry’s paradoxes, Tarski’s theorem) are presented.

The Road to Paradox
  • A Guide to Syntax, Truth and Modality
  • Volker Halbach, Graham E. Leigh
  • Published online:
    17 October 2024
    Print publication:
    31 October 2024
  • Truth, provability, necessity, and other concepts are fundamental to many branches of philosophy, mathematics, computer science, and linguistics. Their study has led to some of the most celebrated achievements in logic, such as Gödel's incompleteness theorems, Tarski's theorem on the undefinability of truth, and numerous accounts of the paradoxes associated with these concepts. This book provides a clear and direct introduction to the theory of paradoxes and the Gödel incompleteness theorems. It offers new analyses of the ideas of self-reference, circularity, and the semantic paradoxes, and helps readers to see both how paradoxes arise and what their common features are. It will be valuable for students and researchers with a minimal background in logic and will equip them to understand and discuss a wide variety of topics in philosophical logic.

  • CLASSICAL DETERMINATE TRUTH I

  • Part of
  • KENTARO FUJIMOTO, VOLKER HALBACH
  • Journal:
    The Journal of Symbolic Logic / Volume 89 / Issue 1 / March 2024
    Published online by Cambridge University Press:
    05 July 2023, pp. 218-261
    Print publication:
    March 2024
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  • We introduce and analyze a new axiomatic theory $\mathsf {CD}$ of truth. The primitive truth predicate can be applied to sentences containing the truth predicate. The theory is thoroughly classical in the sense that $\mathsf {CD}$ is not only formulated in classical logic, but that the axiomatized notion of truth itself is classical: The truth predicate commutes with all quantifiers and connectives, and thus the theory proves that there are no truth value gaps or gluts. To avoid inconsistency, the instances of the T-schema are restricted to determinate sentences. Determinateness is introduced as a further primitive predicate and axiomatized. The semantics and proof theory of $\mathsf {CD}$ are analyzed.

Page 1 of 5