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Strong Boethius’ Thesis and Consequential Implication

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Abstract

The paper studies the relation between systems of modal logic and systems of consequential implication, a non-material form of implication satisfying “Aristotle's Thesis” (p does not imply not p ) and “Weak Boethius' Thesis” (if p implies q, then p does not imply not q ). Definitions are given of consequential implication in terms of modal operators and of modal operators in terms of consequential implication. The modal equivalent of “Strong Boethius' Thesis” (that p implies q implies that p does not imply not q) is identified.

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Authors and Affiliations

  1. Dipartimento di Filosofia e Scienze Sociali, Università di Siena, via Roma, 47-53100, Siena, Italy

    Claudio Pizzi

  2. Philosophy Department, The University of Edinburgh, David Hume Tower, George Square, Edinburgh, EH8 9JK, Scotland, U.K

    Timothy Williamson

Authors
  1. Claudio Pizzi
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  2. Timothy Williamson
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Pizzi, C., Williamson, T. Strong Boethius’ Thesis and Consequential Implication. Journal of Philosophical Logic 26, 569–588 (1997). https://doi.org/10.1023/A:1004230028063

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  • DOI: https://doi.org/10.1023/A:1004230028063

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