Richard DeWitt

In this paper, I identify the source of the differences between classical logic and many-valued logics (including fuzzy logics) with respect to the set of valid formulas and the set of inferences sanctioned. In the course of doing so, we find the conditions that are individually necessary and jointly sufficient for any many-valued semantics (again including fuzzy logics) to validate exactly the classically valid formulas, while sanctioning exactly the same set of inferences as classical logic. This in turn shows, contrary to what has sometimes been claimed, that at least one class of infinite-valued semantics is axiomatizable

The past twenty or so years have seen the sorites paradox receive a good deal of philosophical air-time. Yet, in what is surely a sign of a good puzzle, no consensus has emerged. It is perhaps a good time to stop and take stock of the current status of the sorites paradox. My main contention is that the proposals offered to date as ways of blocking the paradox are seriously deficient, and hence there is, at present, no acceptable solution to the sorites. In the final section I argue that, although vagueness is the source of the threat to modus ponens engendered by the sorites, it is also vagueness that protects modus ponens from clear counterexample

In a Sentences Commentary written about 1250 the Franciscan Richard Rufus subjects Anselm’s argument for God’s existence in his Proslogion to the most trenchant criticism since Gaunilon wrote his response on behalf of the “fool.” Anselm’s argument is subtle but sophistical, claims Rufus, because he fails to distinguish between signification and supposition. Rufus therefore offers five reformulations of the Anselmian argument, which we restate in modern formal logic and four of which we claim are valid, the fifth turning on a possible scribal error. Rufus’s final conclusion is that the formulation in Proslogion, chapter 3, is convincing, but not that of chapter 2.