This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic (...) logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

Philosophy has four forms: wonder, faith, doubt and scepticism. These are not separate categories, but separate ideal possibilities. Modern academic philosophy has fallen, for several centuries, into an error: which is the error of supposing that philosophy is only what I call doubt. Philosophy may be doubt: indeed, it is part of my argument that this is undeniably one element of, or one possibility in, philosophy; but doubt is only one of four points of the compass. In this essay I (...) indicate the nature of each point of the compass as it has been found in the history of philosophy. (shrink)

Common-sense morality divides acts into those that are right and those that are wrong, but it thinks some wrong acts are more seriously wrong than others, for example murder than breaking a promise. If an act is more seriously wrong, you should feel more guilt about it and, other things equal, are more blameworthy for it and can deserve more punishment; more serious wrongs are also more to be avoided given empirical or moral uncertainty. This paper examines a number of (...) different views about what makes for more serious wrongness and considers the possibility that this may be different for acts that violate deontological vs. consequentialist duties. It also asks whether there’s a parallel concept that admits of degrees on the side of rightness, one of being, as we can say, more importantly right. (shrink)