What is it about?
Aristotle, Chrysippus and Boethius are often thought to have defended a connexive conception of implication according to which no proposition entails, or is entailed by, its own negation. This sounds intuitively o.k., but - at least in its unrestricted form, it leads to rather unwelcome results. In particular it follows that a self-inconsistent proposition does not entail its own negation, although the latter is a tautology and hence cannot fail to be true.
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Why is it important?
The critical examination of the historical sources shows that the ancient logicians most likely meant their theses as applicable only to »normal« propositions which are neither logically false nor logically true. The corresponding restrictions of Aristotle’s and Boethius’ theses to contingent propositions, however, turn out to be theorems of ordinary modal logic and thus don’t give rise to any non-classical system of genuinely connexive logic.
Perspectives
My paper was meant to show that the highly debated field of connexive logic is based on a gross misunderstanding of the views of the ancient logicians. Maybe only Chrysippus makes an exception. His ideas about implication shall be examined in a separate paper.
Wolfgang Lenzen
University of Osnabrueck, Germany
Read the Original
This page is a summary of: A Critical Examination of the Historical Origins of Connexive Logic, History and Philosophy of Logic, August 2019, Taylor & Francis,
DOI: 10.1080/01445340.2019.1650610.
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