Journal of Philosophical Logic

, Volume 26, Issue 5, pp 569–588

Strong Boethius’ Thesis and Consequential Implication


  • Claudio Pizzi
    • Dipartimento di Filosofia e Scienze SocialiUniversità di Siena
  • Timothy Williamson
    • Philosophy DepartmentThe University of Edinburgh

DOI: 10.1023/A:1004230028063

Cite this article as:
Pizzi, C. & Williamson, T. Journal of Philosophical Logic (1997) 26: 569. doi:10.1023/A:1004230028063


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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© Kluwer Academic Publishers 1997