A Critical Examination of the Historical Origins of Connexive Logic

Autor(en): Lenzen, Wolfgang
Stichwörter: ARISTOTLE; Ethics; History & Philosophy Of Science; Logic; Philosophy; Science & Technology - Other Topics; Social Sciences - Other Topics
Erscheinungsdatum: 2020
Herausgeber: TAYLOR & FRANCIS LTD
Journal: HISTORY AND PHILOSOPHY OF LOGIC
Volumen: 41
Ausgabe: 1
Startseite: 16
Seitenende: 35
Zusammenfassung: 
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 [ horizontal ellipsis ] 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.
ISSN: 01445340
DOI: 10.1080/01445340.2019.1650610

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