1 Conjunction and Contradiction

The Law of Non-Contradiction (LNC) says that no contradiction can be true. But what is a contradiction? And what would it take for a contradiction to be true? As Patrick Grim [5] has pointed out, a quick look at the literature will re-veal a large menagerie of different interpretations of the basic terms and, conse-quently, of LNC. Grim actually identifies as many as 240 different options (on a conservative count), and I don’t think there is any need to dwell further on the conceptual combinatorics that hides behind this familiar piece of logical no-menclature. I do, however, want to focus on one of the main ambiguities enu-merated by Grim, one that seems to me to lie at the heart of the matter. And I want to offer an argument to the effect that on one way of resolving the ambi-guity LNC is non-negotiable, but on another way it is perfectly plausible to suppose that LNC may, in some rather special and perhaps undesirable circum-stances, fail to hold. 1. Two Notions of Contradiction The ambiguity I have in mind is that which stems from the opposition betwee