María Inés Corbalán

Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic ‘of nonsense’ introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic $$\textbf{K}_{\textbf{3}}^{\textbf{w}}$$ by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; and (iii) that it is hybrid, insofar as it includes both left and right operational introduction as well as elimination rules.

A standing presumption in the literature is that devil’s advocacy is an inherently beneficial argumentative move; and that those who take on this role in conversation are paradigms of argumentative virtue. Outside academic circles, however, devil’s advocacy has acquired something of a notorious reputation: real-world conversations are rife with self-proclaimed devil’s advocates who are anything but virtuous. Motivated by this observation, in this paper we offer the first in-depth exploration of non-ideal devil’s advocacy. We draw on recent analyses of two better known discursive practices—mansplaining and trolling—to illuminate some of the signature traits of vicious devil’s advocacy. Building on this comparative examination, we show that all three practices trade on a manipulation of illocutionary force; and we evaluate their respective options for securing plausible deniability.