Strong Boethius’ Thesis and Consequential Implication

Authors: Pizzi C.¹; Williamson T.²

Source: Journal of Philosophical Logic, Volume 26, Number 5, October 1997 , pp. 569-588(20)

Publisher: Springer

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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.

Language: English

Document Type: Regular paper

Affiliations: 1: Dipartimento di Filosofia e Scienze Sociali, Università di Siena, via Roma 47-53100 Siena, Italy 2: The University of Edinburgh, Philosophy Department, David Hume Tower, George Square, Edinburgh EH8 9JK, Scotland, U.K.

Publication date: 1997-10-01