Between Saying and Doing: Towards an Analytic Pragmatism

Pragmatic definitions of material incompatibility and two kinds of consequence: • Incompatibility of p and q: If S is committed to p, then S is not entitled to q. • Committive consequence: If S is committed to p, then S is committed to q. • Permissive consequence: If S is committed and entitled to p, then S is (prima facie) entitled to q. " And those who introduce the notion of connexion say that a conditional is sound when the contradictory of its consequent is incompatible with its antecedent. " (Sextus Empiricus) Definition of a third kind of consequence: p incompatibility-entails q just in case everything incompatible with q is incompatible with p. Semantic suggestion: Represent the propositional content expressed by a sentence by the set of sentences that express propositions incompatible with it. More generally, associate with each set of sentences, as its semantic interpretant, the set of sets of sentences that are incompatible with it. The semantically primitive incompatibility relations are standard if and only if they satisfy: 1. Symmetry: If S is incompatible with S', then S' is incompatible with S. 2. Persistence: If one set of claims is incompatible with another, so is any larger set containing it. That is, one cannot remove or repair an incompatibility by throwing in some further claims. Incompatibility semantics is directly modal. That is, it does not proceed by defining (non-modal) truth at an index, and then generalizing over indices.