Paper based on Paraconsistency and the Logic of Ambiguous Connectives
Published in Paraconsistency: Logic and Applications (Logic, Epistemology and the Unity of Science) edited by Koji Tanaka, Francesco Berto, Edwin Mares and Francesco Paoli, 2012: 57–79.
Abstract. Substructural pluralism about the meaning of logical connectives is best understood as the view that natural language connectives have all (and only) the properties conferred by classical logic, but that particular occurrences of these connectives cannot simultaneously exhibit all these properties. This is just a more sophisticated way of saying that while natural language connectives are ambiguous, they are not so in the way classical logic intends them to be. Since this view is usually framed as a means to resolve paradoxes, little attention is paid to the logical properties of the ambiguous connectives themselves. The present paper sets out to fill this gap by arguing that substructural logicians should care about these connectives, by describing a consequence relation between a set of ambiguous premises and an ambiguous conclusion, and finally by exhaustively characterising the logical properties of ambiguous connectives.
