A Critical Examination of the Historical Origins of Connexive Logic. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Lenzen, Wolfgang
• Is Part Of: History and philosophy of logic. Volume 41:Issue 1(2020)
• Page Start: 16
• Page End: 35
• Publication Date: 2020-01-02
• Subjects: Logic -- Periodicals; 160.905
• DOI: 10.1080/01445340.2019.1650610
• Languages: English
• ISSNs: 0144-5340

Abstract

Abstract : 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.