The term ‘hyperconnexive logic’ (or ‘hyperconnexivity’ in general) in relation to a certain logical system was coined by Sylvan to indicate that not only do Boethius’ theses hold in such a system, but also their converses. The plausibility of the latter was questioned by some connexive logicians. Without going into the discussion regarding the plausibility of hyperconnexivity and the converses of Boethius’ theses, this paper proposes a quite simple way to escape the hyperconnexivity within the semantic framework of Wansing-style constructive (...) connexive logics. In particular, we present a working method for escaping hyperconnexivity of constructive connexive logic $${{\textbf{C}}}$$, discuss the problem that creates an obstacle to using the same method in the case of logic $${{\textbf{C3}}}$$ and provide a possible solution to this problem that allows us to construct a logical theory which is similar to $${{\textbf{C3}}}$$ and free from hyperconnexivity. All new logics introduced in this paper are equipped with sound and complete Hilbert-style calculi, and their relationships with other well-known connexive logics are discussed. (shrink)

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. (shrink)