Rewriting the History of Connexive Logic

Journal of Philosophical Logic 51 (3):525-553 (2022)
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Abstract

The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties only apply to “normal” antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning connexive implication don’t give rise, however, to anything like a non-classical logic.

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References found in this work

Counterfactuals.David Lewis - 1973 - Foundations of Language 13 (1):145-151.
The Development of Logic.William Kneale & Martha Kneale - 1962 - Oxford, England: Clarendon Press. Edited by Martha Kneale.
Counterfactuals.David Lewis - 1973 - Philosophy of Science 42 (3):341-344.
The Evidential Conditional.Vincenzo Crupi & Andrea Iacona - 2022 - Erkenntnis 87 (6):2897-2921.

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