Strong Boethius’ Thesis and Consequential Implication
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- Pizzi, C. & Williamson, T. Journal of Philosophical Logic (1997) 26: 569. doi:10.1023/A:1004230028063
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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.