Strong Boethius' thesis and consequential implication

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 q does not imply not q) is identified.The full-text of this article is not currently available in ORA, but the original publication is available at springerlink.com (which you may be able to access via the publisher copy link on this record page). N.B. Timothy Williamson is now based at the Philosophy Faculty, University of Oxford