History and Philosophy of Logic 41 (1):16-35 (2019)

It is often assumed that Aristotle, Boethius, Chrysippus, and other ancient logicians advocated a connexive conception of implication according to which no proposition entails, or is entailed by, its own negation. Thus Aristotle claimed that the proposition ‘if B is not great, B itself is great […] is impossible’. Similarly, Boethius maintained that two implications of the type ‘If p then r’ and ‘If p then not-r’ are incompatible. Furthermore, Chrysippus proclaimed a conditional to be ‘sound when the contradictory of its consequent is incompatible with its antecedent’, a view which, in the opinion of S. McCall, entails the aforementioned theses of Aristotle and Boethius. Now a critical examination of the historical sources shows that the ancient logicians most likely meant their theses as applicable only to ‘normal’ conditionals with antecedents which are not self-contradictory. The corresponding restrictions of Aristotle’s and Boethius’ theses to such self-consistent antecedents, 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,
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DOI 10.1080/01445340.2019.1650610
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References found in this work BETA

The Development of Logic.William Calvert Kneale & Martha Kneale - 1962 - Oxford, England: Clarendon Press.
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Citations of this work BETA

Connexive Logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
Kilwardby's 55th Lesson.Wolfgang Lenzen - forthcoming - Logic and Logical Philosophy:1.

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