Aristotle’s dilemma

Abstract The contra-classicality of connexive logics presents a challenge to classical logic that is interestingly different from other non-classical logics, and discussions of that difference have been a main feature of the literature around connexive logic. Seldom, if ever, however, is the following question addressed: is this challenge more severe or less severe than the one presented by sub-classical logics (i.e. almost all other non-classical projects)? This paper will aim to show that, in fact, the connexive project, suitably unpacked, contains a charge that is not only different, but qualitatively more weighty than other non-classical logics. In order to make that argument, I introduce a new principle I call Aristotle’s Dilemma that is, I argue, closely related to the connexive axioms, and that gives an answer to this question. It also suggests an answer to a second question, namely why connective logics are not better known in philosophical logical circles, or, to the extent that they are, why it has taken so long. In part, I suggest, this is down to the unusual formal guise in which the connexive cause is normally voiced. Aristotle’s Dilemma offers a remedy to this.