Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.580721
Title: Non-classical propositional calculi
Author: McCall, Storrs
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 1964
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Abstract:
There exist well-known varieties of implication, such as strict, intuitionist, three-valued and rigorous, which are non-classical in the sense of being more restrictive than material implication. But there exists also a type of implication, intuitively plausible, which is nonclassical not only in being more restrictive, but in satisfying certain theses which are classically false. These theses are exceedingly venerable, dating back to Aristotle and Boethius, but, despite their plausibility, have been generally rejected by logicians since. It has not been noticed, however, that in Sextus Empiricus reference is made to a species of Stoic implication which fits them perfectly. In this work formal recognition is given to this species of implication, known as connexive implication. It is shown that none of the well-known systems of prepositional logic is connexive, and a new system is accordingly constructed. A proof of consistency is given, and a number of problems posed for further investigation.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.580721  DOI: Not available
Keywords: Propositional calculus
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