Supposition: No Problem for Bilateralism

Abstract

In a recent paper, Nils Kürbis argues that bilateral natural deduction systems in which assertions and denials figure as hypothetical assumptions are unintelligible. In this paper, I respond to this claim on two counts. First, I argue that, if we think of bilateralism as a tool for articulating discursive norms, then supposition of assertions and denials in the context of bilateral natural deduction systems is perfectly intelligible. Second, I show that, by transposing such systems into sequent notation, one can make perfect sense of them without talking about supposition at all, just talking in terms of relations of committive consequence. I conclude by providing some motivation for adopting this normative interpretation of bilateralism on which this response to Kürbis’s argument is based.