Ex Incompatibilitate Sequitur Quodlibet (The Explosiveness of Incompatibility and the Compatibility of Negation)

In this chapter, we explain why Ex contradictione sequitur quodlibet is a confusing expression to denote the statement \(p, \neg p \vdash q\) , and we also explain why this statement is ambiguous. We start by setting out a framework about consequence relation and truth. We proceed by presenting the basic concepts of the theory of opposition and the meaning of contradiction according to this theory. We then introduce the notion of incompatibility, and, on the basis of that, we deal with explosion and introduce the notion of compatible negation. The final part of the paper is about John Corcoran.