The Philosophical Basis of Connexive Logic

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This project will investigate the philosophical basis of connexive logic, in the sense that it carefully examines the intuitions that make connexivity plausible and then develops the best formal treatment of these intuitions. ||Connexive logics are characterized by the following principles: ||ARISTOTLE¬(A → ¬A) and ¬(¬A → A) are valid.
 ||BOETHIUS
(A → B) → ¬(A → ¬B) and (A → ¬B) → ¬(A → B) are valid. ||Connexive logic is a very interesting field in non-classical logic that has been around for a long time. Most of that time, it has to be admitted, it has spent on the side-lines of general interest. This, however, has been changing over the last years in which much more attention has been paid to connexivity, attention that I believe is wholly deserved: This project proposal is based on the conviction that connexivity is based on very strong natural language intuitions that should not be ignored by logicians and philosophers of language alike. ||That said, in earlier work I have developed an original and somewhat revisionist view on the nature of connexive logic, which I am convinced is an improvement over the earlier picture as well as one which is much harder to dismiss for non-connexive logicians. My re-framing of the connexive enterprise has been published in two papers entitled “Strong Connexivity” and “Humble Connexivity”, which both contain modifications of the connexive principles, ARISTOTLE and BOETHIUS. Moreover, in unpublished work I have argued that natural language pragmatics might have a role in explaining parts of the connexive intuitions (all works are appended to this proposal).|| The aim of this project is to develop further arguments for that revisionistic view primarily by applying it in two distinct logical environments: Conditonal logics (a.k.a. logics with variably strict conditionals, best known as analyses for counterfactuals in the style of D. Lewis and R. Stalnaker) and constructive logics suitable for handling the inferential aspects of a theory of meaning in the style of M. Dummett. ||Drawing on the lessons of these two applications, I hope to further consolidate my views on the philosophical basis of connexive logic into a coherent and convincing picture, which I will aim to publish in further papers and an encompassing monograph.