Online research in philosophy

Discussions of higher-order vagueness rarely define what it is for a term to have nth-order vagueness for n>2. This paper provides a rigorous definition in a framework analogous to possible worlds semantics; it is neutral between epistemic and supervaluationist accounts of vagueness. The definition is shown to have various desirable properties. But under natural assumptions it is also shown that 2nd-order vagueness implies vagueness of all orders, and that a conjunction can have 2nd-order vagueness even if its conjuncts do not. Relations between the definition and other proposals are explored; reasons are given for preferring the present proposal.

Though he’s perhaps best known for his work on vagueness, Timothy Williamson also produced a series of outstanding papers in epistemology in the late 1980's and the 1990's. Knowledge and its Limits brings this work together. The result is, in my opinion, the best book in epistemology to come out since 1975.

Several philosophers offer explanations of linguistic vagueness by appealing to the referential context-dependence of vague terms. Timothy Williamson argues pre-emptively that any such approach must fail, on the grounds that context-dependence is neither necessary nor sufficient for vagueness. He supports this claim, in turn, by example. This paper argues that his examples fail to show that context-dependence is either unnecessary or insufficient for vagueness, and hence that he has failed by his own lights to show that it cannot explain vagueness.

Vagueness provides the first comprehensive examination of a topic of increasing importance in metaphysics and the philosophy of logic and language. Timothy Williamson traces the history of this philosophical problem from discussions of the heap paradox in classical Greece to modern formal approaches such as fuzzy logic. He illustrates the problems with views which have taken the position that standard logic and formal semantics do not apply to vague language, and defends the controversial realistic view that vagueness is a kind of ignorance--that there really is a grain of sand whose removal turns a heap into a non-heap, but we cannot know which one it is.