Noisy vs. merely equivocal logics

Patrick Allo

pp. 57-79

in: Koji Tanaka, Francesco Berto, Edwin D. Mares, Francesco Paoli (eds), Paraconsistency, Berlin, Springer, 2013

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. First, I argue that substructural logicians should care about these connectives; next, I describe a consequence relation between a set of ambiguous premises and an ambiguous conclusion, and review the logical properties of ambiguous connectives; finally, I highlight how ambiguous connectives might explain our intuitions about logical rivalry.